Research ArticleDifferential Diagnostic ReasoningMethod for Benign ParoxysmalPositional Vertigo Based on Dynamic Uncertain Causality Graph

Chunling Dong 12 Yanjun Wang 3 Jing Zhou1 Qin Zhang2 and Ningyu Wang3

1School of Computer Science and Cybersecurity Communication University of China Chaoyang District Beijing 100024 China2Department of Computer Science and Technology Tsinghua University Haidian District Beijing 100084 China3Department of Otorhinolaryngology Head and Neck Surgery Beijing Chaoyang Hospital Captical Medical UniversityBeijing 100020 China

Correspondence should be addressed to Chunling Dong dongcl15tsinghuaorgcn and Yanjun Wang docwyjn163com

Received 24 June 2019 Revised 8 September 2019 Accepted 11 November 2019 Published 24 January 2020

Academic Editor Luca Faes

Copyright copy 2020 Chunling Dong et al 0is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

0e accurate differentiation of the subtypes of benign paroxysmal positional vertigo (BPPV) can significantly improve the efficacy ofrepositioning maneuver in its treatment and thus reduce unnecessary clinical tests and inappropriate medications In this studyattempts have beenmade towards developing approaches of causality modeling and diagnostic reasoning about the uncertainties thatcan arise frommedical information A dynamic uncertain causality graph-based differential diagnosis model for BPPV including 354variables and 885 causality arcs is constructed New algorithms are also proposed for differential diagnosis through logical andprobabilistic inference with an emphasis on solving the problems of intricate and confounding disease factors incomplete clinicalobservations and insufficient sample data 0is study further uses vertigo cases to test the performance of the proposed method inclinical practice0e results point to high accuracy a satisfactory discriminatory ability for BPPV and favorable robustness regardingincomplete medical information 0e underlying pathological mechanisms and causality semantics are verified using compactgraphical representation and reasoning process which enhance the interpretability of the diagnosis conclusions

1 Introduction

Benign paroxysmal positional vertigo (BPPV) is a majorcause of vertigo and accounts for approximately 17ndash42 ofthe cases It has a lifetime prevalence of 24 in the generalpopulation [1] BPPV is caused by displaced otoconia in thesemicircular canal and its clinical characteristics include abrief episodic and position-provoked vertigo BPPV typi-cally causes balance disturbance which considerably in-creases the risk of falls in patients Furthermore it causesmalignant secondary damage especially for elderly people[2] 0e commonly used therapy for BPPV is the particlerepositioning maneuver (PRM) also known as the canalithrepositioning procedure 0eoretically almost all patientscan be readily treated with accurate diagnosis and patho-genesis [3 4] However the average resolution rate with onePRM treatment for posterior semicircular canal BPPV inmany trials was revealed to be only 86 Notably there arevarious treatment options therefore the effectiveness of

PRM (such as the Epley and Semont maneuvers) depends onthe accurate classification of BPPV 0e classification pro-cess would include determining the underlying pathogenylocating the calcium carbonate debris and identifyingwhether the material is free-floating or adherent to thecupula among others BPPV can be classified into manysubtypes in clinical practice such as the idiopathic BPPVand secondary BPPV or the typical BPPV and atypicalBPPV However distinguishing among several causes ofvertiginous disorders with similar symptoms is quitecomplex 0erefore clinical subtype differentiation of BPPVis important for effective repositioning maneuvers intreatment to reduce inappropriate vestibular suppressantmedications and minimize unnecessary ancillary tests

In recent years some automatic multiaxial positioningdevices electronystagmograms and videonystagmographyhave been applied in the management of BPPV [5] 0eseapplications have digitized and standardized laying a foun-dation for computer-aided intelligent diagnosis and clinical

HindawiComputational and Mathematical Methods in MedicineVolume 2020 Article ID 1541989 13 pageshttpsdoiorg10115520201541989

decision-making Medical data typically contain hidden andcomplicated patterns and causality semantics thus appro-priate encoding and interpretation of medical data result inbetter diagnosis medicine and treatment [6 7] Numerousresearch has been done on this for instance in the man-agement of vertigo there is a wide spectrum of potentialailments and intricate confounding factors which complicatesthe accuracy of identifying the different types of vertiginousdisorders Based on this several otoneurological expert sys-tems including VERTIGO [8] Carnisel [9] and otoneuro-logical expert system (ONE) [10 11] were developed NotablyONE is a mature system that has been validated in practiceand its inference approach resembles methods of weightedk-nearest neighbor (k-NN) genetic algorithm (GA) fuzzylogic and decision tree

Previous attempts have been made at exploring methodsfor automatic differential diagnosis of diseases A method fordifferentiating pancreatic serous from mucinous cys-tadenomas based on morphological features extraction wasproposed in [12] this approach utilized classifiers such asBayesian k-NN support vector machine (SVM) and artificialneural network (ANN) Furthermore a method for inte-grating Hopfield networks retrieval networks and k-NN tomine the medical data for differential diagnosis was proposedin [6] Moreover Lopes et al developed a decision-supportsystem based on the fuzzy cognitive map to discriminate thediagnoses of alterations in urinary elimination [13] A su-pervised machine learning algorithm based on the combi-nation of principal components analysis and SVM for thedifferential diagnosis of Parkinsonian syndrome (PS) wasproposed in [14] Mudali et al [15] studied the classification ofPS using decision trees based on the scaled subprofile modeland principal component analysis methods Ota et al [16]proposed a differential diagnosis tool for PS by applying thediscriminant techniques derived by stepwise methods 0eSVM and logistic regression-based models were developed in[17] for the classification and prediction of PS A methodbased on the Bayesian network (BN) was proposed in [18] toperform classification of early glaucoma and cluster data intodifferent stages of the disease Moreover multidimensionalBN classifiers are proposed to assist the treatment of multiplesclerosis [19] A BN-based method was used for classificationof EEG-based multiclass motor imagery BCI [20] Further-more a method was proposed in [21] for individualizedcharacterization and diagnosis of cognitive impairmentsMelin et al [22] described a method of competitive neuralnetworks and the learning vector quantization algorithm forclassification of electrocardiogram signals Finally an expertsystem was provided in [23] for the differential diagnosis ofstrabismus based on the architecture of ANN and the Lev-enbergndashMarquardt back propagation method

0ere are several challenges in this field of research Firstit is difficult to faithfully model the pathogenesis andpathophysiology characterized by individual differences anduncertain factors including intricate and confounding dis-ease factors and insufficient sample data among others Toaddress this problem we believe that medical knowledge andexperience could play an important role 0e knowledgederived from clinical data and that specified by the domain

experts should be integrated to provide a basis for practicaldecision-making [24 25] 0e introduction of expertknowledge has been further recognized as an effective so-lution for reducing the inherent uncertainty of the modelsbased on automatic learning methods [26]

Second many diagnosis approaches are mostly deficientin handling incomplete examinations and tests in clinicalpractice 0e dependence of the models on the completenessof medical data limits some methodsrsquo functions in caseswhere the information is incomplete or imperfect Someapproaches have been proposed to deal with cases of missingdata in the diagnosis of chronic obstructive pulmonarydisease these include evaluating the similarity of attributeswith unknown values or filling the gaps statistically withplausible values [27] Although there has been research onthe plugging missing values by identifying the regularities inthe occurrence model very few studies have been devoted toeffectively improving the diagnostic reasoning method incases where there is incomplete information Notably indisease diagnosis using incomplete information to accu-rately diagnose a disease reduces the need for unnecessarymedical examinations

0ird although the probability is known to be capable ofproviding a sound and flexible procedure for interpretinguncertain evidence with which the clinical practice is con-fronted it is difficult to make a conclusion readily compre-hensible to the users It is important to determine theunderlying etiology and pathology for disease occurrencesthe process of systematic diagnosis and a means of con-firming that the right conclusion has been reached0ereforean explicable diagnostic reasoning model that matches themethod for drawing conclusions is essential Furthermoreundesirable interpretability or explicability is a commonhinderance for the practical application of most methods

In summary it is well known that distinguishing thewide range of vertigo causes is a complicated endeavor evenfor experienced physicians Even though BPPV is suggestedin the diagnostic reasoning outcome the subtype cannot beeasily discriminated In our opinion an in-depth under-standing and appropriate representation of the pathogenesisand pathophysiology characterized by individual differencescontribute to the diagnostic accuracy 0is study thereforeseeks to develop an efficient and easy-to-implement dif-ferential diagnosis method for BPPV based on the dynamicuncertain causality graph (DUCG) 0e main focus of theproposed method is solving the three aforementionedproblems of the knowledge-based modeling incompletenessof the medical data and interpretability of the method

0e knowledge representation and inference methods ofDUCG are introduced in [28ndash31] In recent years DUCG hasbeen applied in several medical diagnostic systems involvingmultiple diseases such as jaundice syncope and sellar regiondisease among others Our earlier work in [30] presented amodeling and reasoning methodology for vertigo diagnosisand developed a decision-support system which covered 22common vertigo diseases However the methods are notcompletely applicable to the differential diagnosis problems0erefore this paper proposes new algorithms for reasoningabout BPPV subtype differentiation

2 Computational and Mathematical Methods in Medicine

0e structure of this article is as follows Section 2 de-scribes the proposed method based on DUCG including theuncertain causality representation the BPPVmodel and thedifferential diagnostic reasoning algorithms In Section 3 aseries of verification experiments using clinical cases arepresented followed by a comparative analysis and an ap-plication analysis Finally Section 4 contains theconclusions

2 Methods

21 DUCG Causality Representation and DiagnosticReasoning Method

211 Uncertain Causality Representation Scheme 0eDUCG graphically and compactly represents the events andcausalities among events Figure 1 shows an example ofDUCG An X-type variable (oval-shaped node) representsan observable effect event which can include medical in-formation such as symptoms signs and examinationfindings A B-type variable (square-shaped node) denotes aroot cause event or a disease origin A G-type (logic gatenode) variable represents the combinational logic relationsbetween its inputs and outputs (eg G12 in Figure 1(a) withits state expression specified in Table 1) A D-type variable(pentagon node) represents the default or unspecified causeof an X-type variable A certain state j of variable Vi (V canbe a B- X- G- or D-type) referred to as Vij represents anevent state number j 0 indicates a normal state and jne 0indicates an abnormal state

0e arc Vij⟶ Xnk represents a virtual functionalevent Fnkij equiv (rnirn)Ankij that describes the causalitybetween a child event Xnk and a parent event Vij Ankij

denotes the independent causality function that Vij causesXnk 0e intensity of causal relationship between Xn and Vi

is defined as rni and rni ge 0 rn equiv 1113936irni As a weightingfactor of Ani the coefficient (rnirn) balances these inde-pendent causality functions for all parent events on a samechild event For AFa-type variables the variable subscriptsare in the format of ldquochild parentrdquo and the variableidentifiers in lower case letters denote the probability pa-rameters of the variables in corresponding upper case lettersfor example ankij Pr Ankij1113966 1113967 and bij Pr Bij1113966 1113967

0e causality representation mechanism of DUCG is aweighted logic event expansion which is denoted below

Xnk 1113944i

FnkiVi 1113944i

rni

rn

1113944j

AnkijVij (1)

A child event Xnk can be logically expanded into aweighted sum of independent causality functions from all itsparent events Vik 0us the multivalued causalities betweenchild-parent events in each pair are independently repre-sented rather than using joint probability distribution as inthe other models such as BN 0e use of a compact causalityrepresentation accords the intuitive cognition of people tothe real world and is more explicable For DUCG it isconvenient to represent the causalities and parameters basedon findings of medical research and clinical knowledge orstatistical learning from clinical sample data

212 DUCG-Based Diagnostic Reasoning Method 0ediagnostic inference method includes three steps (1) sim-plifying the original causality graph based on observedevidence (2) weighted logic event expansion and logicalreasoning for evidential events and (3) probabilistic rea-soning If Hkj represents a candidate hypothesis ie apossible root cause (disease origin) of evidence E then thestate probability of Hkj conditioned on E and denoted byhs

kj is calculated as

hskj Pr Hkj | E1113966 1113967

Pr HkjE1113966 1113967

Pr E (2)

where E is defined by E 1113937nXnk Every evidence event Xnk

is independently expanded into logic expressions accordingto (1) by tracing their upstream causality chains back to-wards the root cause event(s) respectively Such an in-ference process is called chaining inference Meanwhilesome basic logic operations including OR AND NOTXOR absorption exclusion (events are mutually incom-patible) and complementation are performed 0us thecandidate hypothesis space SH Hkj1113966 1113967 can be obtainedFinally the posterior probabilities of the hypothesis eventHkj can be calculated In case of more than one candidatehypotheses in SH the state probability of Hkj is modified bythe weight coefficient defined on the prior probability ofevidence (referred to as ζk ζk equiv Pr E ) in the causalitycontext of each hypothesis Hkj

hskj h

skj

ζk

1113936kζk

(3)

0e probabilistic normalization of weighted logic eventexpanding expressions ie 1113936kPr Xnk1113966 1113967 1113936k1113936i(rnirn)

1113936jankijvij 1 holds automatically because 1113936i(rnirn) 11113936kankij 1 and 1113936jvij 1 By virtue of such an automaticnormalization feature the chaining inference can be provenas self-reliant such that Pr Xnk1113966 1113967 is calculated without the useof Pr Xnkprime1113966 1113967(kprime ne k) and the irrelevant parameters (egankprimeij) can be absent without affecting the inference ac-curacy Moreover the variation of parameter values in thenumerator of (2) corresponds to the variation in the pa-rameter values in the denominator It is thus the ratio of theparameter values in the event expanding expressions ofPr HkjE1113966 1113967 to that of Pr E that has an actual effect on thefinal result Based on the aforementioned features the exactinference can be used in case of incomplete and inaccurateparameters and clinical data

0e causality graph in Figure 1 can be used as a cal-culation case to clarify the details of the diagnostic inferencealgorithm Let us suppose that the parameter matrices aregiven as follows (for the sake of simplicity the weightingfactors rni are all set to 1) For a matrix element ankij (ega3171 a5122 and a6281) k and j correspond to the rownumber and column number of the matrix respectively 0esymbol ldquominus rdquo indicates unknown unavailable or irrelevantparameters

Computational and Mathematical Methods in Medicine 3

b1 minus

0021113888 1113889

b2

minus

002004

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

a37 minus minus minus

minus 0 051113888 1113889

a48 minus minus

minus 061113888 1113889

a52 minus minus minus

minus 02 01113888 1113889

a54 minus minus

minus 081113888 1113889

a68

minus minus

minus 06minus 0

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

a78

minus minus

minus 0minus 09

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

a81 minus minus

minus 091113888 1113889

a82 minus minus minus

minus 06 01113888 1113889

a96 minus minus minus

minus 06 01113888 1113889

a1010D

minus

0208

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

a1112

minus minus

minus 0minus 09

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

(4)

Besides the normal or unknown variables suppose thatthe evidence for the DUCG example in Figure 1(a) isobtained as E 1113937iEi

prime X31X51X72X81X91X102X112 Byapplying the simplification rules of DUCG [28 30] all theirrelevant incorrect and meaningless causalities andevents can be eliminated from the graph based on themedical evidence 0us the simplified graph is obtained asshown in Figure 1(b) DUCG uses different colored nodesto distinguish the X-type variablesrsquo states green indicates anormal state indexed by 0 sky blue and blue indicate state1 and state 3 respectively yellow and brown indicate state2 and state 4 respectively and colorless indicates anunknown state implying an unconfirmedunidentifiablepathological feature or an unexamined item

Based on (1) and Figure 1(b) the expanding expressionsof evidence X31 X51 and X112 in the causality context ofB21 respectively are shown below

E1prime X31 A3172A7281A8121B21

E2prime X51 12

1113874 1113875A5121B21 +12

1113874 1113875A5141A4181A8121B21

E7prime X112 A112121A10210DA9161A6181A8121B21

(5)

Likewise other abnormal evidence is expanded and theexpanding expression for E is obtained as

B13

B14

B15

B16

X17

X9

X6

X3X7

B2

B1

X4

X5

X10X8

G12 X11

D10

Other variablesGroup 2

Other variablesGroup 1

X18

(a)

X6X4

B1

B2

G12

D10

X112

X102

X72

X81

X51

X91

X31

(b)

Figure 1 Example of DUCG diagnostic causality graph (a) original causality graph and (b) simplified causality graph

Table 1 Logic gate specification of G12

Logic gate State State expression

G120 Remnant state1 X91X102 +X101

4 Computational and Mathematical Methods in Medicine

E A3172A7281A112121A10210DA9161A6181A8121B21

middot12

1113874 1113875A5121B21 +12

1113874 1113875A5141A4181A8121B211113874 1113875

12

1113874 1113875A3172A7281A112121A10210DA9161A6181A8121

middot A5121B21 +12

1113874 1113875A3172A7281A112121A10210DA9161

middot A6181A5141A4181A8121B21

(6)

Similarly the expanding expression of E in the causalitycontext of B11 is

E A3172A7281A112121A10210DA9161A6181A5141

middot A4181A8111B11

(7)

Finally hypothesis space SH under evidence E is ob-tained as follows SH H11 H211113966 1113967 where H11 equiv B11 andH21 equiv B21 0erefore the two hypotheses are determined asthe probable causes of the observed evidence as both canindependently interpret all the symptoms 0e probabilisticcalculation results are hs

11 0679 and hs21 0321 0e

inference results can be explained using the graphicalcausality semantics as shown in Figure 1(b) Based on thesesemantics users can not only deduce the results but alsounderstand their logic

Based on the self-reliant chaining inference the missingparameters such as a3172 a7281 a112121 a10210D a9161and a6181 do not have an impact on the reasoning resultMoreover the most probable hypotheses could be typicallydetermined uniquely just within the logical reasoningprocess (before the probabilistic reasoning is performed)0us the causality structure that accurately represents thedisease pathogenesis is what really matters It is evident thatDUCG does not impose stringent requirements for com-pleteness of the parameters and clinical examination data0us it can be used to facilitate modeling through medicalknowledge and experience

22 Construction of Differential Diagnosis Model for BPPV

221 BPPV Characteristics

(1) Pathophysiology of BPPV0e vestibular receptor consistsof two otolith organs (the utricle and saccule) which overseelinear acceleration and gravity as well as three semicircularcanals (SCCs) that sense angular acceleration 0e SCCsinclude anterior SCCs (ASCCs) posterior SCCs (PSCCs)and lateral SCCs (LSCCs) 0e afferent nerves from otolithorgans and SCCs project symmetrical activities to the centralvestibular system to maintain the balance and spatial ori-entation BPPV results from misplaced calcium carbonatecrystals (otoconia) that are detached from utricle macula andcollected within the SCCs due to trauma infection or even

aging 0ese crystals either remain free-floating in the SCCsor become attached to the cupula Normally as the motionsensor of SCCs that are filled with endolymph cupula is agelatinous mass with the same density as endolymph Sincethe calcium particles are denser than the endolymph andcupula the SCCs become pathologically sensitive to linearacceleration and gravity the afferent nerves from SCCs thusfire asymmetrically leading to vertigo and nystagmusWhenmoving into the SCC the calcium carbonate crystal debrismay cause endolymph movement which consequentlystimulates the cupula of the affected canal during headmovement or while stationary (this is called canalithiasis)Similarly if adherent to the cupula the particles may alsoactivate it (this is called cupulolithiasis) [32]

(2) Clinical Characteristics of BPPV BPPV is characterizedby brief attacks of vertigo after lying down in bed looking upor bending down among others 0e vertigo attacks in mostcases last less than 1sim2 minutes and mostly occur at night orupon awakening [1] 0e diagnosis rests on the observationof characteristic nystagmus accompanying symptoms ofvertigo when a patientrsquos head is moved into a specific ori-entation with respect to gravity 0is is due to shred calciumcrystals from macula which may cause age-related changesin the protein and gelatinous matrix of the otolithicmembrane Although most of BPPV cases are idiopathic asignificant proportion can be associated with precedingtraumatic events including head trauma dental treatmentand ear surgery Other conditions such as viral vestibularneuritis otitis media Menierersquos disease idiopathic suddensensorineural hearing loss posterior circulation ischemiaand migraine can also trigger cases of BPPV

BPPV may affect each of the three SCCs Alternatively itcan affect more than one canal simultaneously resulting invarying nystagmus patterns [33] Notably due to its gravity-dependent position the most commonly affected semicir-cular canal is the posterior canal 0e positional and posi-tioning tests (eg DixndashHallpike diagnostic maneuver andsupine roll test) can provide an accurate diagnosis for thiscondition Furthermore the features of nystagmus in-cluding latency direction duration reversal and fatiga-bility are significant during diagnosis

(3) Subtype Differentiation of BPPV Based on the epide-miology causes of disease pathophysiology anatomy pa-thology clinical features and treatment outcomes a BPPVdisease may be classified into distinct categories along fourdimensions (1) depending on the localization of the par-ticles and the involved semicircular canals there are foursubtypes (PSCC ASCC LSCC and multiple-SCC (MSCC))(2) BPPV is subdivided into idiopathic BPPV and secondaryBPPV as it may occur as a primary disease or secondary toother otology disorders or systemic conditions [4] (3) BPPVcan be divided into canalithiasis and cupulolithiasisdepending on the nystagmus provoked characteristics fromthe positioning test based on the pathophysiology mecha-nism [32] and (4) based on the clinical features andtreatment outcomes BPPV falls into two categories typicaland atypical 0e atypical BPPV can be further identified as

Computational and Mathematical Methods in Medicine 5

subjective BPPV persistent BPPV and recurrent BPPVSubjective BPPV refers to the cases associated with a positivehistory of BPPV and DixndashHallpike or supine roll tests whichare positive for vertigo but negative for nystagmus [34] Apersistent BPPV refers to cases lasting for more than twoweeks while a recurrent BPPV indicates recurrence of BPPVin the same canal after a symptom-free interval of at leasttwo weeks from a previously successful treatment [35]

222 Constructed Model for Differential Diagnosis of BPPVAs a causality representation to the aforementioned path-ogenesis and pathophysiology of BPPV a new DUCG-basedcausality graph was constructed based on the vertigo modelpresented in [30] 0e BPPV differential diagnosis model isshown in Figure 2 it includes 125 variables (X-type 85 D-type 8 G-type 21 and B-type 11) and 286 arcs

(1) Modularized Modeling Scheme A modularized modelingscheme is applied in the construction of the causality graphshown in Figure 2 All BPPV subtypes are handled as in-dividual sub-DUCGs For example the three sub-DUCGsrepresenting the idiopathic PSCC LSCC and cupuloli-thiasis BPPV are demonstrated in Figures 3ndash5 respectivelyWhen the sub-DUCGs are merged solutions are proposedfor addressing the ambiguous contradictory and incom-plete information to ensure global coherence [30] Such amodularized modeling scheme reduces the difficulty inmodel construction using a divide-and-conquer approach

(2) Definition of Variables Based on the characteristics ofBPPV and the international diagnostic criteria [36] themedical information of patients including symptoms signsfindings of examinations medical histories etiology andpathogenesis pathophysiology and socio-psychological andenvironmental factors is incorporated into the model Table 2lists some of the variables of the model shown in Figure 2

(3) Representation of Causal Relationships In this repre-sentation arcs are established to represent and quantifycausal correlations among related symptoms and diseaseorigins complex causalities are denoted by a combination ofcausal functions via logic gates All causalities and param-eters in Figure 2 are determined by otoneurologists based ontheir knowledge experience epidemiology statistics andresearch achievements As stated before both the incom-pleteness of knowledge and imprecision of parameters havelittle impact on the reasoning accuracy thus DUCG is moreflexible for the model construction

23 e Algorithm of Differential Diagnostic ReasoningDifferential diagnosis aims at narrowing down the diseases tothe most probable one from a list of candidate diseases thatshow similar symptoms 0e differential diagnostic reasoningalgorithm is presented as Algorithm 1 which implements ahypothesis-driven process 0e posterior probability of thehypothesis event Hkj is used to quantify Hkjrsquos ability tointerpret the medical evidence E Notably a rare disease doesnot necessarily respond to a weak causality If a rare disease

(with a low prior probability) better explains a patientrsquossymptoms and medical evidence then the strength of thecausality functions can be high thus the disease will get ahigher ranked probability as a hypothesis event

231 New Causality Simplification Mechanisms Based onthe collected medical evidence E for a patient the process ofcausality simplifications is performed to the BPPV causalitygraph Causality simplification aims to eliminate the irrel-evant meaningless and impossible events and relationsfrom a causality graph 0erefore the model scale andcomplexity are both significantly decreased and the diseasehypothesis space converges0e root cause event can even bepreliminarily determined based on the simplified causalitygraph

As a complement to the original simplification rules ofDUCG [28 30] several new causality simplificationmechanisms including a pruning strategy and causalitytracking process are presented

Definition 1 (Pruning Strategy) 0e meaningless diseasehypothesis and its corresponding causalities are identifiedand pruned from the causality graph using a scheme ofcausality tracking for all the abnormal evidences

Definition 2 (Causality Tracking Process) 0e causalitytracking process starts from an observed event and traces itsupstream causality chains and ancestors back towards the B-type event(s) For any Bi only if all the abnormal evidence isreachable to it via a causality tracking process can it beidentified as a candidate hypothesis otherwise Bi should beeliminated from the hypothesis space and its correspondingcausalities should be pruned from the graph

232 Weighted Logic Inference Rules of Differential Diag-nosis for BPPV Based on the simplified causality graph andmedical evidence the process of logical inference is per-formed to obtain the hypothesis space according to (1)sim(3)Our earlier study showed that by applying event expandingand logical operations the logical inference can effectivelydecrease the complexity of probabilistic reasoning [28]However in response to BPPV differential diagnosis theweighted logic inference algorithm requires majormodifications

Some BPPV subtypes can be present in a patient si-multaneously For instance a diagnosis can be termed as anASCC-idiopathic-canalithiasis BPPV Such a case is knownas concurrency of subtypes Meanwhile the subtypes be-longing to the same category are mutually exclusive when adiagnostic conclusion is drawn Some examples of this arePSCC-BPPV (B231) LSCC-BPPV (B241) ASCC-BPPV(B251) and MSCC-BPPV (B261) 0erefore to deal withthese cases new weighted logic inference rules for exclusionand concurrency among others are developed as shownbelow

Rule 1 Suppose that the basic events (namely root causeevents) in a BPPV differential diagnosis model are

6 Computational and Mathematical Methods in Medicine

represented in terms of category sets as C1 B231 B241B251 B261 C2 B271 B281 C3 B291 B301 andC4 B311 B321 B331 State 1 of a B-type event indicatesthat the root cause event has occurred on the contrary state0 of a B-type event indicates that the root cause event has notoccurred 0e mutual exclusion rules for basic events inBPPV differential diagnosis can thus be defined asBi1Biprime 1 0 where Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 )

Proof From the definition the category sets C1 C2 and C3indicate different classification perspectives of BPPV0erefore all basic events within the same category set areexclusive and exhaustive Specifically there is B231B241 0

B231B251 0 B231B261 0 B241B251 0 B241B261 0B251B261 0 B271B281 0 and B291B301 0

Rule 2 Bi1Biprime 1 ne 0 for Bi Biprime isin C4 (ine iprime) and Bi1Biprime 1 ne 0 forBi1 isin Cm Biprime1 isin Cn(ine iprime mne n)

Proof 0e events in C4 describe the respective differenttypes of atypical BPPV in an overlapping manner Namelyall the basic events in B311 B321 B331 are likely to beconcurrent 0is sets the basis for Rule 2

Definition 3 (Maximizing Concurrent Basic Event SetStrategy) To obtain an ultimate disease hypothesis Hkj ifthe events that constitute Hkj are concurrent and consistentwith each other the maximum number of basic eventswithin the hypothesis space SH should be incorporated

It is essential to explore every possible outcome beforeruling out any basic event For example as SH B241 B281B301 is obtained for a case we should get only the correcthypothesis H11 B241B281B301 ne 0 in which the threeevents together interpret the observed symptoms ratherthan B241B281 B281B301 or so on

Rule 3 Given V isin B X G D jne jprime and integer yge 2then (Vij)

y Vij and VijVij 0

Figure 2 0e DUCG-based differential diagnostic causality graph for BPPV

Figure 3 Sub-DUCG for LSCC-idiopathic-recurrent BPPV

Figure 4 Sub-DUCG for PSCC-idiopathic-recurrent BPPV

Figure 5 0e sub-DUCG for cupulolithiasis BPPV

Computational and Mathematical Methods in Medicine 7

Rule 4 Given integer yge 2 kne kprime and jne jprime then(Fnkij)

y (rnirn)yAnkij FnkijFnkprimeij 0 FnkijFnkijprime 0 andFnkijFnkprimeijprime 0 if Bi1Biprime 1 0 is given Bi1 Biprime 1 isin Cm

ine iprime m isin 1 2 3 then it follows that Fnkiprime1Bi1 0 Fnki1Biprime1 0 and Fnki1Fnkiprime1 0

Proof 0e latter part of Rule 4 is based on Rule 1 and theother part has been proven in [28] From Rule 1 Bi1Biprime 1 0which implies that the basic events Bi1 and Biprime1 cannot beconcurrent and consequently brings about the mutual ex-clusions among the function events related to Bi1 and Biprime10erefore Anki1Ankiprime1 0 and Fnki1Fnkiprime1 0 as Anki1cannot be present in combination with Ankirsquo1 similarlythen Fnkiprime1Bi1 0 and Fnki1Biprime1 0 Notably Fnki1Fnkiprime0ne 0 is true because Anki1 and Ankiprime0 are independent ofeach other (since they are given independently)

Rule 5 1113936Mm11113937iisinSm

FnkijiViji

(1113936Mm11113937iisinSm

(rnirn))1113937

iisinS1AnkijiViji

where Sm denotes the set of variable number ina product item m isin 12 M and S1 sube S2 sube middot middot middot sube SM

Rule 6 Suppose that no mutually exclusive basic eventscoexist in the candidate hypothesis space thenFnkijVij(1113936iprimeFnkiprimej

iprimeViprimej

iprime) FnkijVij if j ji is given

Proof To complement the ordinary conditions of Rule 14discussed in [28] consider a situation related to mutuallyexclusive basic events Vij Bi1 and VijprimeBiprime1Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 ) as proposed in Rule 10eproposition of Rule 6 can thus be represented as

FnkijVij 1113944

iprime

FnkiprimejiprimeViprimej

iprime⎛⎝ ⎞⎠ FnkijVij middot FnkijVij

+ FnkijVij middot 1113944

iprime ne i

FnkiprimejiprimeViprimej

iprime

rnirn1113872 11138732AnkijVij

neFnkijVij

(8)

0e inclusion of mutually exclusive events leads to theaforementioned outcomes (ie the inconsistence betweenRule 1 and Rule 6) and the autonormalization feature nolonger holds 0erefore a solution for BPPV subtype dif-ferentiation known as a scheme of dummy basic variable(DBV) is proposed

233 Scheme of Dummy Basic Variable

Definition 4 (DBV) If mutually exclusive candidate hy-potheses coexist in the candidate hypothesis space ieBi1Biprime 1 0 Bi1 Biprime1 isin Cm(ine iprime m isin 1 2 3 ) Bi1 andBiprime1are converted into different states of a DBV each state of theDBV elicits an individual pathogenesis causality graphaccording to the hypothesis related to that state the specificcausalities of different diseases can be distinguished by theA-parameter values of DBV which can either be zero or not0e exclusive rules among basic events are thus transformedinto an inherent exclusive law among the states of an event

Table 2 Definition of variables for differential diagnosis of BPPV

Variables Descriptions

X1ndash3201ndash206

210ndash217

Pathophysiology of BPPV the lesion of theotolithic membrane of utricle macula thedegenerated otolith broken off from utriclemacula misplaced calcium carbonate crystalsdebris calcium free-floating particles enteringthe SCCs calcium particles adherent to the

cupula of SCC the endolymph movement withfree-floating particles that pathologicallystimulates the ampulla of canal and the

sensitivity to linear acceleration and gravityinduced by the abnormal deflection of cupula

X48ndash11

0e description of vertigo an illusion ofmovement the sensation that objects in the

environment is moving when the eyes are openand the sensation that a patient feels as if he or

she is moving when the eyes are closed

X1142454682

0e main accompanying symptomsspontaneous nystagmus and autonomic nerve

symptoms

X20-25

0e detailed description of the features ofvertigo attacks attack characteristics the onsetand duration of an attack causes of disease

frequency and severity

X26ndash28209

Changes in head position relative to gravityrotation of the head relative to the body while in

an upright position

X83ndash871300e feature of spontaneous nystagmus and the

Romberg test for vestibular function

X5249161163238

Other accompanying symptoms cochlearsymptoms hearing loss tinnitus the symptoms

of central nervous system and themanifestations of the primary and underlying

disordersX184185 Patientrsquos gender and age

X186189198234

0e typical and characteristic medical history amigraine hypertension head trauma and inner

ear pathology

X207ndash208

More than one semicircular canal is affectedsimultaneously (obtained statistically duringthe pretreatment process of medical data)

X218ndash221227228Positioning test vertigo and nystagmus when

the head is moving or rotating

X222ndash226

DixndashHallpike test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)

X229ndash233

Supine roll test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)X236 0e outcomes of the maneuver treatment

B23ndash33

PSCC-BPPV (B23) LSCC-BPPV (B24) ASCC-BPPV (B25) MSCC-BPPV (B26) secondary

BPPV (B27) idiopathic BPPV (B28)canalithiasis BPPV (B29) cupulolithiasis BPPV(B30) subjective BPPV (B31) persistent BPPV

(B32) and recurrent BPPV (B33)

8 Computational and Mathematical Methods in Medicine

0e problem of disobeying the autonormalization fea-ture can thus be addressed 0is method is illustrated via anexample in Figure 6(a) Suppose that B11 and B21 aremutually exclusive events 0ey are then combined into aDBV-Bv during the reasoning process corresponding to Bv1and Bv2 respectively From the definition of DBVa31v1 equiv a3111 a41v2 equiv a4121 a51v2 equiv a5121 and rnv equiv rniwhere i isin 1 2 and n isin 3 4 5 Figure 6(b) shows an ex-ample where an event (eg X3) is connected to more thanone basic event In this case rnv is defined as rnv equiv 1113936irni ifFnine 00us r3v r31 + r32 for the case in Figure 6(b) whichpoints out to a combination of basic events

In the context of differential diagnosis and upon thecompletion of causality simplifications the obtained can-didate hypotheses of C1 B231 B241 B251 B261 (there aremore than one basic event in the set) should be combinedinto a DBV-Bm with Bmk denoting Bi1 where k 1 2 3 4and i 23 24 25 26 PrBmk refers to the prior probabilityof Bi1 and Pr Bm01113966 1113967 1 minus 1113936kne0Pr Bmk1113966 1113967

Definition 5 (Ranked Independent Probability) 0e rankedindependent probability represents a new metric proposedfor quantifying the degree of confidence in whether a BPPVsubtype (eg Bi1 as a part of the hypothesis Hkj) can in-dependently interpret all the medical evidence in com-parison with the other subtypes coexisting in Hkj 0eranked independent probability of Bi1 is calculated as fol-lows (1) get hs

i1 of Bi1 according to (2) and (3) in which ζi isbased on the individual causality tracking graph of Bi1 and(2) for all the Bi1 within the set of Hkj hs

i1 is ranked byhs

i11113936ihsi1

24 eoretical Analysis of the Reasoning Complexity 0einference algorithm for the proposed method reduces thereasoning complexity in two ways First the causality graphsimplification and pruning strategy significantly decreases themodel scale 0e variables that are irrelevant or inconsistentwith the medical evidence are excluded from the reasoning

calculation 0is significantly reduces the computationalcomplexity Moreover the diagnostic reasoning conclusioncan even be accurately drawn solely via the causality sim-plification Second prior to probabilistic reasoning weightedlogic inference is performed based on the simplified causalitygraph 0us the multiple connected causalities can bedecomposed independently leading the chaining inference toexhibit high efficiency Furthermore the proposed logicalinference rules and logical operations can decrease thecomplexity and scale of logical event expressions

0e actual efficiency tests for the DUCG inference al-gorithm have been performed using online fault diagnosisdata from several large-scale industrial systems (eg nuclearpower plants) in which thousands of variables and causalityarcs are involved [28 31] 0e diagnostic reasoning cantypically be finished within 05ndash1 s (on a personal computer)Moreover the inference efficiency has been verified from ourpast clinical diagnosis applications that involved dozens ofdiseases such as jaundice and sellar region disease

3 Experiments and Analyses

31 Clinical Validation of the BPPV Differential DiagnosisMethod

311 Differential Diagnosis for BPPVmdashCase 1 Suppose thatthe medical evidence of a patient was observed in part asX41 X212 X243 X1844 X1852 X2094 X2292 X2302 X2070X2080 X2360 in Figure 2 and other X-type variables arenormal or unknown (incomplete medical information) 0emedical information in this experiment is from a 65-year-oldfemale patient who suffered from brief episodes of vertigowhen rolling over in bed for two weeks and was suspected tobe a BPPV case according to the supine roll test

Based on the evidence in this case Figure 2 can besimplified into the graph shown in Figure 7 by applying thecausality simplification rules and pruning strategy Manymeaningless relationships and events under current situa-tion are eliminated accordingly with SH B241 B281 B301

BeginFor a BPPV patientCollect medical evidence E including symptoms signs examination findings laboratory tests and medical historiesPerform causality simplification to the BPPV causality graph based on the evidence EApply the causality simplification mechanisms including the pruning strategy and causality tracking processObtain the simplified diagnostic causality graph

Perform the algorithms of weighted logic inference based on the simplified causality graphPerform the weighted logic event expansion to the evidence according to (1)Perform logic inference according to (2)

Apply the weighted logic inference rules 1sim6 of differential diagnosis for BPPVApply the scheme of dummy basic variablePerform the basic logic operations

Obtain the hypothesis event space SH Hkj1113966 1113967

Perform the probabilistic reasonings to obtain the posterior probability of Hkj conditioned on E hskj

Calculate the ranked independent probability of a BPPV subtypeEnd

ALGORITHM 1 Differential diagnostic reasoning method for BPPV

Computational and Mathematical Methods in Medicine 9

being inferred as the possible root causes 0e resultinghypothesis space SH is concise with all unlikely hypothesesbeing excluded from concern Moreover the individualcausality tracking graphs for the three root cause events B24B28 and B30 in Figure 7 are shown in Figure 8 whereby eachsubgraph independently covers all evidence0e graphs thusintuitively and faithfully represent the causalities underlyingthe pathogenesis of Case 1

By applying the algorithm of differential diagnosticreasoning for Case 1 the state probability ofH11 B241B281B301 can be obtained as hs

11

Pr H11 | E1113966 1113967 1 0e obtained ldquoranked independent prob-abilitiesrdquo of B241 B281 and B301 are listed in Table 3 0eLSCC-idiopathic-cupulolithiasis BPPV is therefore deter-mined as the diagnostic result of Case 1 this result isconsistent with the clinical conclusions confirmed byotoneurologists

312 Differential Diagnosis for BPPVmdashCase 2 A 72-year-old female patient complained about paroxysmal positionalvertigo for a month the attacks of vertigo were brief lastingfor one minute the vertigo frequently occurred whilelooking up or down0us the medical evidence for this caseis X41 X212 X243 X1844 X1852 X2070 X2080 X2093 X2223X2231 X2241 X2251 X2261 X2360 the other X-type variablesare normal or unknown (incomplete medical information)

By applying the algorithm of differential diagnosticreasoning the hypothesis event H11 B231B281B291B321 isuniquely determined as the origin of the disease whichindicates a PSCC-idiopathic-cupulolithiasis-persistentBPPV 0e diagnostic causality graph is shown in Figure 9which is based on the causality simplification of Figure 20e resulting ranked independent probabilities of B231B281 B291 and B321 are listed in Table 4 By explicitlyrepresenting the disease causes symptoms pathogenesisand the latent correlations among medical informationFigure 9 offers intuitive insights into the underlying path-ological mechanisms

313 Other Validated BPPV Subtype Cases A verificationexperiment on some other clinical cases was performed toevaluate the effectiveness of the proposed method 0ecorrectness was based on the otoneurologistsrsquo judgement onthe diagnostic outcomes in contrast to the practical con-clusions In the clinical center for vertigo in BeijingChaoyang Hospital BPPV cases are common howeverthere are multiple repetitions in the meaningful informationfor the BPPV patients on their medical histories and physicalexaminations regarding subtype differentiation Based on

this 75 typical BPPV cases were selected from the thousandsof cases containing medical records interviews and physicalassessments in the verification experiments 0e BPPVsubtypes involved are outlined in Table 5 0e selectionprinciple of BPPV cases was based on the internationaldiagnostic criteria for BPPV [36] and the typicality andrepresentativeness of BPPV subtype diseases Notably sincethe nystagmus cannot be observed for a subjective BPPVcase it is difficult to classify the case either as canalithiasisBPPV or cupulolithiasis BPPV

0e diagnostic outcomes of the DUCG-based modelagreed with the otoneurologistsrsquo conclusions with a cor-rectness index of 100 Based on the available publishedliterature no other research has reported a model-basedautomatic subtype differentiation of BPPV in the past

32 Comparative Analysis of DUCG and BN 0e maindifference between DUCG and BN in terms of the theoreticalframework is that the model structure and parameters ofDUCG are decoupled By virtue of such a feature the in-dependent causality representation by the weighted causalityfunction event Ankij in DUCG makes it possible to simplifythe original causality graph based on the collected medicalevidence 0e irrelevant and meaningless events and rela-tions are thus eliminated from the model Taking the sim-plified causality graph as the basis of diagnostic reasoningreduces the computational scale and complexity to a largeextent In contrast BN cannot be easily simplified owing tothe structural coupling feature among the variables thecausalities among the child-parent events in BN are typicallyrepresented through a joint probability distribution (eg aconditional probabilistic table CPT) in case any variablesand relations are removed from a BN the remaining pa-rameters in the CPTs may need major adjustments more-over the number of parameters specified in a CPTfor a BN isexponential to the number of the parent variables and statesinvolved while the parameters needed in the DUCG are lessthan the parameters in a BN

Others

B1X3

X4

X5

Others

X3

X4

X5

B2

BV

(a)

Others

X3

X4

Others

X3

X4

BV

B1

B2

(b)

Figure 6 Example of DBV (a) Example 1 (b) Example 2

Figure 7 Diagnostic causality graph for Case 1

10 Computational and Mathematical Methods in Medicine

Furthermore by the independence representation andautomatic normalization feature for the weighted logic eventexpansion the ldquoself-reliantrdquo chaining inference and logicoperations can be performed in DUCG 0e parameters andinformation that are eliminated during the causality simpli-fication and those that are not involved in the chaining in-ference can all be missing (or some parameters which are notof concern are thus not provided) during this reasoningprocess and do not affect the diagnostic accuracy 0e diag-nostic inference method under incomplete information in-dicates that some unnecessary clinical tests and inappropriatemedications can be omitted thereby decreasing the patientsrsquo

medical costs For a BN the reasoning accuracy depends onthe completeness of the parameters in the CPTs

33 Application Analysis 0e proposed method can be de-veloped as an automatic diagnostic system for clinicians Basedon the compact independent and graphical causality repre-sentation using DUCG the model construction and diagnosis

(a) (b)

(c)

Figure 8 Individual causality tracking graphs of the hypotheses for Case 1 (a) LSCC-BPPV (B24) (b) Idiopathic BPPV (B28) (c)Cupulolithiasis BPPV (B30)

Table 3 Diagnostic reasoning results of Case 1

BPPVsubtype Description Ranked independent

probabilityB241 LSCC-BPPV 00388B281 Idiopathic BPPV 09542

B301Cupulolithiasis

BPPV 0007

H11 B241B281B301 1

Figure 9 Diagnostic causality graph for Case 2

Table 4 Diagnostic reasoning results of Case 2

BPPVsubtype Description Ranked independent

probabilityB231 PSCC-BPPV 01435B281 Idiopathic BPPV 07653

B291Canalithiasis

BPPV 00091

B321 Persistent BPPV 00821H11 B231B281B291B321 1

Table 5 BPPV subtypes involved in the validated cases

BPPV subtype No of casesPSCC 53ASCC 1LSCC 16MSCC 5Idiopathic 55Secondary 16Canalithiasis 61Cupulolithiasis 8Subjective 4Persistent 4Recurrent 8Typical 59

Computational and Mathematical Methods in Medicine 11

application are both easy to implement For a patient theclinical data through can be obtained through inquiry physicalexamination and auxiliary examination among others Nextthe clinical data including symptoms signs examination andtest data are input into the diagnostic reasoning interface ofthe system and the diagnosis results can be obtained throughreasoning calculation 0e clinical application of this methodis thus very convenient 0rough incorporation into the au-tomatic medical devices this method could improve the ef-ficiency of BPPV diagnosis and therapy especially for generalpractitioners in primary health care institutions In additionthe system can also be used inmobile and Internet terminals asa secondary tool for telemedicine finally it can serve as ateaching tool for doctor training in related disciplines

4 Summary

0is study proposes a DUCG method for differential di-agnosis of BPPV To distinguish among various causes ofvertiginous disorders with similar symptoms the proposedmethod involves a graphical and compact representation inaddition to logical reasoning algorithms for pathologicalmechanisms and related uncertain causalities New algo-rithms of differential diagnostic reasoning are proposed byintegrating a pruning strategy in the causality simplificationprocess a maximizing concurrent basic event set strategy inthe formulation of hypothesis space and the weighted logicinference rules for subtype differentiation of BPPV Fur-thermore a scheme of dummy basic variable is introduced tosettle the problems related to mutually exclusive root causeevents 0e model manifests higher correctness favorablerobustness to incomplete evidence and satisfactory dis-criminatory power for BPPV subtypes Furthermore usingthe diagnostic reasoning method and graphical represen-tation mechanism not only provides a diagnostic result butalso explains the rationale for suggesting the diseases whichjustifies the probability results

In light of these encouraging preliminary results moreclinical studies will be performed Furthermore a newmethod of probabilistic prediction for the vestibular dys-function-induced fall risk will be the subject of our futureresearch endeavors

Data Availability

0e data used to support the findings of this study are se-lected from the clinical cases of Department of Otorhino-laryngology Head and Neck Surgery Beijing Chaoyanghospital Requests for access to these data should be made toYanjun Wang (docwyjn163com Beijing Chaoyanghospital)

Disclosure

Chunling Dong and Yanjun Wang are cofirst authors

Conflicts of Interest

0e authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

0is work was supported in part by the National NaturalScience Foundation of China under Grant no 71671103 andin part by the Fundamental Research Funds for the CentralUniversities under Grant nos CUC2019B023CUC19ZD008 and CUC19ZD007

References

[1] N Bhattacharyya R F Baugh L Orvidas et al ldquoClinicalpractice guideline benign paroxysmal positional vertigordquoOtolaryngologymdashHead and Neck Surgery vol 139 no 5_suppl pp S47ndashS81 2008

[2] J S Oghalai S Manolidis J L Barth M G Stewart andH A Jenkins ldquoUnrecognized benign paroxysmal positionalvertigo in elderly patientsrdquo OtolaryngologymdashHead and NeckSurgery vol 122 no 5 pp 630ndash634 2000

[3] M P Prim-Espada J I De Diego-Sastre and E Perez-Fernandez ldquoEstudio metaanalıtico de la eficacia de la man-iobra de Epley en el vertigo posicional paroxıstico benignordquoNeurologıa vol 25 no 5 pp 295ndash299 2010

[4] L S Parnes S K Agrawal and J Atlas ldquoDiagnosis andmanagement of benign paroxysmal positional vertigo(BPPV)rdquo Canadian Medical Association Journal vol 169no 7 pp 681ndash693 2003

[5] J C Li and J Epley ldquo0e 360-degree maneuver for treatmentof benign positional vertigordquo Otology amp Neurotology vol 27no 1 pp 71ndash77 2006

[6] R Isola R Carvalho and A K Tripathy ldquoKnowledge dis-covery in medical systems using differential diagnosisLAMSTAR and $k$-NNrdquo IEEE Transactions on InformationTechnology in Biomedicine vol 16 no 6 pp 1287ndash1295 2012

[7] A L Barabasi N Gulbahce and J Loscalzo ldquoNetworkmedicine a network-based approach to human diseaserdquoNature Reviews Genetics vol 12 no 1 pp 56ndash68 2011

[8] E Mira A Buizza G Magenes M Manfrin and R SchmidldquoExpert systems as a diagnostic aid in otoneurologyrdquo Journalfor Oto-Rhino-Laryngology and Its Related Specialties (ORL)vol 52 no 2 pp 96ndash103 1990

[9] C E S Gavilan J E Gallego and J Gavilan ldquoCarnisel anexpert system for vestibular diagnosisrdquo Acta Oto-Lar-yngologica vol 110 no 3-4 pp 161ndash167 1990

[10] E Kentala I Pyykko Y Auramo J Laurikkala andM Juhola ldquoOtoneurological expert system for vertigordquo ActaOto-Laryngologica vol 119 no 5 pp 517ndash521 1999

[11] E Kentala K Viikki I Pyykko andM Juhola ldquoProduction ofdiagnostic rules from a neurotologic database with decisiontreesrdquo Annals of Otology Rhinology and Laryngology vol 109no 2 pp 170ndash176 2000

[12] J W Song J H Lee J H Choi and S J Chun ldquoAutomaticdifferential diagnosis of pancreatic serous and mucinouscystadenomas based on morphological featuresrdquo Computersin Biology and Medicine vol 43 no 1 pp 1ndash15 2013

[13] M H Lopes N R Ortega P S Silveira E Massad R Higaand F Marin Hde ldquoFuzzy cognitive map in differential di-agnosis of alterations in urinary elimination a nursing ap-proachrdquo International Journal of Medical Informatics vol 82no 3 pp 201ndash208 2013

[14] C Salvatore A Cerasa I Castiglioni et al ldquoMachine learningon brain MRI data for differential diagnosis of Parkinsonrsquosdisease and Progressive Supranuclear Palsyrdquo Journal ofNeuroscience Methods vol 222 pp 230ndash237 2014

12 Computational and Mathematical Methods in Medicine

0e structure of this article is as follows Section 2 de-scribes the proposed method based on DUCG including theuncertain causality representation the BPPVmodel and thedifferential diagnostic reasoning algorithms In Section 3 aseries of verification experiments using clinical cases arepresented followed by a comparative analysis and an ap-plication analysis Finally Section 4 contains theconclusions

2 Methods

21 DUCG Causality Representation and DiagnosticReasoning Method

211 Uncertain Causality Representation Scheme 0eDUCG graphically and compactly represents the events andcausalities among events Figure 1 shows an example ofDUCG An X-type variable (oval-shaped node) representsan observable effect event which can include medical in-formation such as symptoms signs and examinationfindings A B-type variable (square-shaped node) denotes aroot cause event or a disease origin A G-type (logic gatenode) variable represents the combinational logic relationsbetween its inputs and outputs (eg G12 in Figure 1(a) withits state expression specified in Table 1) A D-type variable(pentagon node) represents the default or unspecified causeof an X-type variable A certain state j of variable Vi (V canbe a B- X- G- or D-type) referred to as Vij represents anevent state number j 0 indicates a normal state and jne 0indicates an abnormal state

0e arc Vij⟶ Xnk represents a virtual functionalevent Fnkij equiv (rnirn)Ankij that describes the causalitybetween a child event Xnk and a parent event Vij Ankij

denotes the independent causality function that Vij causesXnk 0e intensity of causal relationship between Xn and Vi

is defined as rni and rni ge 0 rn equiv 1113936irni As a weightingfactor of Ani the coefficient (rnirn) balances these inde-pendent causality functions for all parent events on a samechild event For AFa-type variables the variable subscriptsare in the format of ldquochild parentrdquo and the variableidentifiers in lower case letters denote the probability pa-rameters of the variables in corresponding upper case lettersfor example ankij Pr Ankij1113966 1113967 and bij Pr Bij1113966 1113967

0e causality representation mechanism of DUCG is aweighted logic event expansion which is denoted below

Xnk 1113944i

FnkiVi 1113944i

rni

rn

1113944j

AnkijVij (1)

A child event Xnk can be logically expanded into aweighted sum of independent causality functions from all itsparent events Vik 0us the multivalued causalities betweenchild-parent events in each pair are independently repre-sented rather than using joint probability distribution as inthe other models such as BN 0e use of a compact causalityrepresentation accords the intuitive cognition of people tothe real world and is more explicable For DUCG it isconvenient to represent the causalities and parameters basedon findings of medical research and clinical knowledge orstatistical learning from clinical sample data

212 DUCG-Based Diagnostic Reasoning Method 0ediagnostic inference method includes three steps (1) sim-plifying the original causality graph based on observedevidence (2) weighted logic event expansion and logicalreasoning for evidential events and (3) probabilistic rea-soning If Hkj represents a candidate hypothesis ie apossible root cause (disease origin) of evidence E then thestate probability of Hkj conditioned on E and denoted byhs

kj is calculated as

hskj Pr Hkj | E1113966 1113967

Pr HkjE1113966 1113967

Pr E (2)

where E is defined by E 1113937nXnk Every evidence event Xnk

is independently expanded into logic expressions accordingto (1) by tracing their upstream causality chains back to-wards the root cause event(s) respectively Such an in-ference process is called chaining inference Meanwhilesome basic logic operations including OR AND NOTXOR absorption exclusion (events are mutually incom-patible) and complementation are performed 0us thecandidate hypothesis space SH Hkj1113966 1113967 can be obtainedFinally the posterior probabilities of the hypothesis eventHkj can be calculated In case of more than one candidatehypotheses in SH the state probability of Hkj is modified bythe weight coefficient defined on the prior probability ofevidence (referred to as ζk ζk equiv Pr E ) in the causalitycontext of each hypothesis Hkj

hskj h

skj

ζk

1113936kζk

(3)

0e probabilistic normalization of weighted logic eventexpanding expressions ie 1113936kPr Xnk1113966 1113967 1113936k1113936i(rnirn)

1113936jankijvij 1 holds automatically because 1113936i(rnirn) 11113936kankij 1 and 1113936jvij 1 By virtue of such an automaticnormalization feature the chaining inference can be provenas self-reliant such that Pr Xnk1113966 1113967 is calculated without the useof Pr Xnkprime1113966 1113967(kprime ne k) and the irrelevant parameters (egankprimeij) can be absent without affecting the inference ac-curacy Moreover the variation of parameter values in thenumerator of (2) corresponds to the variation in the pa-rameter values in the denominator It is thus the ratio of theparameter values in the event expanding expressions ofPr HkjE1113966 1113967 to that of Pr E that has an actual effect on thefinal result Based on the aforementioned features the exactinference can be used in case of incomplete and inaccurateparameters and clinical data

0e causality graph in Figure 1 can be used as a cal-culation case to clarify the details of the diagnostic inferencealgorithm Let us suppose that the parameter matrices aregiven as follows (for the sake of simplicity the weightingfactors rni are all set to 1) For a matrix element ankij (ega3171 a5122 and a6281) k and j correspond to the rownumber and column number of the matrix respectively 0esymbol ldquominus rdquo indicates unknown unavailable or irrelevantparameters

Computational and Mathematical Methods in Medicine 3

b1 minus

0021113888 1113889

b2

minus

002004

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

a37 minus minus minus

minus 0 051113888 1113889

a48 minus minus

minus 061113888 1113889

a52 minus minus minus

minus 02 01113888 1113889

a54 minus minus

minus 081113888 1113889

a68

minus minus

minus 06minus 0

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

a78

minus minus

minus 0minus 09

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

a81 minus minus

minus 091113888 1113889

a82 minus minus minus

minus 06 01113888 1113889

a96 minus minus minus

minus 06 01113888 1113889

a1010D

minus

0208

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

a1112

minus minus

minus 0minus 09

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

(4)

Besides the normal or unknown variables suppose thatthe evidence for the DUCG example in Figure 1(a) isobtained as E 1113937iEi

prime X31X51X72X81X91X102X112 Byapplying the simplification rules of DUCG [28 30] all theirrelevant incorrect and meaningless causalities andevents can be eliminated from the graph based on themedical evidence 0us the simplified graph is obtained asshown in Figure 1(b) DUCG uses different colored nodesto distinguish the X-type variablesrsquo states green indicates anormal state indexed by 0 sky blue and blue indicate state1 and state 3 respectively yellow and brown indicate state2 and state 4 respectively and colorless indicates anunknown state implying an unconfirmedunidentifiablepathological feature or an unexamined item

Based on (1) and Figure 1(b) the expanding expressionsof evidence X31 X51 and X112 in the causality context ofB21 respectively are shown below

E1prime X31 A3172A7281A8121B21

E2prime X51 12

1113874 1113875A5121B21 +12

1113874 1113875A5141A4181A8121B21

E7prime X112 A112121A10210DA9161A6181A8121B21

(5)

Likewise other abnormal evidence is expanded and theexpanding expression for E is obtained as

B13

B14

B15

B16

X17

X9

X6

X3X7

B2

B1

X4

X5

X10X8

G12 X11

D10

Other variablesGroup 2

Other variablesGroup 1

X18

(a)

X6X4

B1

B2

G12

D10

X112

X102

X72

X81

X51

X91

X31

(b)

Figure 1 Example of DUCG diagnostic causality graph (a) original causality graph and (b) simplified causality graph

Table 1 Logic gate specification of G12

Logic gate State State expression

G120 Remnant state1 X91X102 +X101

4 Computational and Mathematical Methods in Medicine

E A3172A7281A112121A10210DA9161A6181A8121B21

middot12

1113874 1113875A5121B21 +12

1113874 1113875A5141A4181A8121B211113874 1113875

12

1113874 1113875A3172A7281A112121A10210DA9161A6181A8121

middot A5121B21 +12

1113874 1113875A3172A7281A112121A10210DA9161

middot A6181A5141A4181A8121B21

(6)

Similarly the expanding expression of E in the causalitycontext of B11 is

E A3172A7281A112121A10210DA9161A6181A5141

middot A4181A8111B11

(7)

Finally hypothesis space SH under evidence E is ob-tained as follows SH H11 H211113966 1113967 where H11 equiv B11 andH21 equiv B21 0erefore the two hypotheses are determined asthe probable causes of the observed evidence as both canindependently interpret all the symptoms 0e probabilisticcalculation results are hs

11 0679 and hs21 0321 0e

inference results can be explained using the graphicalcausality semantics as shown in Figure 1(b) Based on thesesemantics users can not only deduce the results but alsounderstand their logic

Based on the self-reliant chaining inference the missingparameters such as a3172 a7281 a112121 a10210D a9161and a6181 do not have an impact on the reasoning resultMoreover the most probable hypotheses could be typicallydetermined uniquely just within the logical reasoningprocess (before the probabilistic reasoning is performed)0us the causality structure that accurately represents thedisease pathogenesis is what really matters It is evident thatDUCG does not impose stringent requirements for com-pleteness of the parameters and clinical examination data0us it can be used to facilitate modeling through medicalknowledge and experience

22 Construction of Differential Diagnosis Model for BPPV

221 BPPV Characteristics

(1) Pathophysiology of BPPV0e vestibular receptor consistsof two otolith organs (the utricle and saccule) which overseelinear acceleration and gravity as well as three semicircularcanals (SCCs) that sense angular acceleration 0e SCCsinclude anterior SCCs (ASCCs) posterior SCCs (PSCCs)and lateral SCCs (LSCCs) 0e afferent nerves from otolithorgans and SCCs project symmetrical activities to the centralvestibular system to maintain the balance and spatial ori-entation BPPV results from misplaced calcium carbonatecrystals (otoconia) that are detached from utricle macula andcollected within the SCCs due to trauma infection or even

aging 0ese crystals either remain free-floating in the SCCsor become attached to the cupula Normally as the motionsensor of SCCs that are filled with endolymph cupula is agelatinous mass with the same density as endolymph Sincethe calcium particles are denser than the endolymph andcupula the SCCs become pathologically sensitive to linearacceleration and gravity the afferent nerves from SCCs thusfire asymmetrically leading to vertigo and nystagmusWhenmoving into the SCC the calcium carbonate crystal debrismay cause endolymph movement which consequentlystimulates the cupula of the affected canal during headmovement or while stationary (this is called canalithiasis)Similarly if adherent to the cupula the particles may alsoactivate it (this is called cupulolithiasis) [32]

(2) Clinical Characteristics of BPPV BPPV is characterizedby brief attacks of vertigo after lying down in bed looking upor bending down among others 0e vertigo attacks in mostcases last less than 1sim2 minutes and mostly occur at night orupon awakening [1] 0e diagnosis rests on the observationof characteristic nystagmus accompanying symptoms ofvertigo when a patientrsquos head is moved into a specific ori-entation with respect to gravity 0is is due to shred calciumcrystals from macula which may cause age-related changesin the protein and gelatinous matrix of the otolithicmembrane Although most of BPPV cases are idiopathic asignificant proportion can be associated with precedingtraumatic events including head trauma dental treatmentand ear surgery Other conditions such as viral vestibularneuritis otitis media Menierersquos disease idiopathic suddensensorineural hearing loss posterior circulation ischemiaand migraine can also trigger cases of BPPV

BPPV may affect each of the three SCCs Alternatively itcan affect more than one canal simultaneously resulting invarying nystagmus patterns [33] Notably due to its gravity-dependent position the most commonly affected semicir-cular canal is the posterior canal 0e positional and posi-tioning tests (eg DixndashHallpike diagnostic maneuver andsupine roll test) can provide an accurate diagnosis for thiscondition Furthermore the features of nystagmus in-cluding latency direction duration reversal and fatiga-bility are significant during diagnosis

(3) Subtype Differentiation of BPPV Based on the epide-miology causes of disease pathophysiology anatomy pa-thology clinical features and treatment outcomes a BPPVdisease may be classified into distinct categories along fourdimensions (1) depending on the localization of the par-ticles and the involved semicircular canals there are foursubtypes (PSCC ASCC LSCC and multiple-SCC (MSCC))(2) BPPV is subdivided into idiopathic BPPV and secondaryBPPV as it may occur as a primary disease or secondary toother otology disorders or systemic conditions [4] (3) BPPVcan be divided into canalithiasis and cupulolithiasisdepending on the nystagmus provoked characteristics fromthe positioning test based on the pathophysiology mecha-nism [32] and (4) based on the clinical features andtreatment outcomes BPPV falls into two categories typicaland atypical 0e atypical BPPV can be further identified as

Computational and Mathematical Methods in Medicine 5

subjective BPPV persistent BPPV and recurrent BPPVSubjective BPPV refers to the cases associated with a positivehistory of BPPV and DixndashHallpike or supine roll tests whichare positive for vertigo but negative for nystagmus [34] Apersistent BPPV refers to cases lasting for more than twoweeks while a recurrent BPPV indicates recurrence of BPPVin the same canal after a symptom-free interval of at leasttwo weeks from a previously successful treatment [35]

222 Constructed Model for Differential Diagnosis of BPPVAs a causality representation to the aforementioned path-ogenesis and pathophysiology of BPPV a new DUCG-basedcausality graph was constructed based on the vertigo modelpresented in [30] 0e BPPV differential diagnosis model isshown in Figure 2 it includes 125 variables (X-type 85 D-type 8 G-type 21 and B-type 11) and 286 arcs

(1) Modularized Modeling Scheme A modularized modelingscheme is applied in the construction of the causality graphshown in Figure 2 All BPPV subtypes are handled as in-dividual sub-DUCGs For example the three sub-DUCGsrepresenting the idiopathic PSCC LSCC and cupuloli-thiasis BPPV are demonstrated in Figures 3ndash5 respectivelyWhen the sub-DUCGs are merged solutions are proposedfor addressing the ambiguous contradictory and incom-plete information to ensure global coherence [30] Such amodularized modeling scheme reduces the difficulty inmodel construction using a divide-and-conquer approach

(2) Definition of Variables Based on the characteristics ofBPPV and the international diagnostic criteria [36] themedical information of patients including symptoms signsfindings of examinations medical histories etiology andpathogenesis pathophysiology and socio-psychological andenvironmental factors is incorporated into the model Table 2lists some of the variables of the model shown in Figure 2

(3) Representation of Causal Relationships In this repre-sentation arcs are established to represent and quantifycausal correlations among related symptoms and diseaseorigins complex causalities are denoted by a combination ofcausal functions via logic gates All causalities and param-eters in Figure 2 are determined by otoneurologists based ontheir knowledge experience epidemiology statistics andresearch achievements As stated before both the incom-pleteness of knowledge and imprecision of parameters havelittle impact on the reasoning accuracy thus DUCG is moreflexible for the model construction

23 e Algorithm of Differential Diagnostic ReasoningDifferential diagnosis aims at narrowing down the diseases tothe most probable one from a list of candidate diseases thatshow similar symptoms 0e differential diagnostic reasoningalgorithm is presented as Algorithm 1 which implements ahypothesis-driven process 0e posterior probability of thehypothesis event Hkj is used to quantify Hkjrsquos ability tointerpret the medical evidence E Notably a rare disease doesnot necessarily respond to a weak causality If a rare disease

(with a low prior probability) better explains a patientrsquossymptoms and medical evidence then the strength of thecausality functions can be high thus the disease will get ahigher ranked probability as a hypothesis event

231 New Causality Simplification Mechanisms Based onthe collected medical evidence E for a patient the process ofcausality simplifications is performed to the BPPV causalitygraph Causality simplification aims to eliminate the irrel-evant meaningless and impossible events and relationsfrom a causality graph 0erefore the model scale andcomplexity are both significantly decreased and the diseasehypothesis space converges0e root cause event can even bepreliminarily determined based on the simplified causalitygraph

As a complement to the original simplification rules ofDUCG [28 30] several new causality simplificationmechanisms including a pruning strategy and causalitytracking process are presented

Definition 1 (Pruning Strategy) 0e meaningless diseasehypothesis and its corresponding causalities are identifiedand pruned from the causality graph using a scheme ofcausality tracking for all the abnormal evidences

Definition 2 (Causality Tracking Process) 0e causalitytracking process starts from an observed event and traces itsupstream causality chains and ancestors back towards the B-type event(s) For any Bi only if all the abnormal evidence isreachable to it via a causality tracking process can it beidentified as a candidate hypothesis otherwise Bi should beeliminated from the hypothesis space and its correspondingcausalities should be pruned from the graph

232 Weighted Logic Inference Rules of Differential Diag-nosis for BPPV Based on the simplified causality graph andmedical evidence the process of logical inference is per-formed to obtain the hypothesis space according to (1)sim(3)Our earlier study showed that by applying event expandingand logical operations the logical inference can effectivelydecrease the complexity of probabilistic reasoning [28]However in response to BPPV differential diagnosis theweighted logic inference algorithm requires majormodifications

Some BPPV subtypes can be present in a patient si-multaneously For instance a diagnosis can be termed as anASCC-idiopathic-canalithiasis BPPV Such a case is knownas concurrency of subtypes Meanwhile the subtypes be-longing to the same category are mutually exclusive when adiagnostic conclusion is drawn Some examples of this arePSCC-BPPV (B231) LSCC-BPPV (B241) ASCC-BPPV(B251) and MSCC-BPPV (B261) 0erefore to deal withthese cases new weighted logic inference rules for exclusionand concurrency among others are developed as shownbelow

Rule 1 Suppose that the basic events (namely root causeevents) in a BPPV differential diagnosis model are

6 Computational and Mathematical Methods in Medicine

represented in terms of category sets as C1 B231 B241B251 B261 C2 B271 B281 C3 B291 B301 andC4 B311 B321 B331 State 1 of a B-type event indicatesthat the root cause event has occurred on the contrary state0 of a B-type event indicates that the root cause event has notoccurred 0e mutual exclusion rules for basic events inBPPV differential diagnosis can thus be defined asBi1Biprime 1 0 where Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 )

Proof From the definition the category sets C1 C2 and C3indicate different classification perspectives of BPPV0erefore all basic events within the same category set areexclusive and exhaustive Specifically there is B231B241 0

B231B251 0 B231B261 0 B241B251 0 B241B261 0B251B261 0 B271B281 0 and B291B301 0

Rule 2 Bi1Biprime 1 ne 0 for Bi Biprime isin C4 (ine iprime) and Bi1Biprime 1 ne 0 forBi1 isin Cm Biprime1 isin Cn(ine iprime mne n)

Proof 0e events in C4 describe the respective differenttypes of atypical BPPV in an overlapping manner Namelyall the basic events in B311 B321 B331 are likely to beconcurrent 0is sets the basis for Rule 2

Definition 3 (Maximizing Concurrent Basic Event SetStrategy) To obtain an ultimate disease hypothesis Hkj ifthe events that constitute Hkj are concurrent and consistentwith each other the maximum number of basic eventswithin the hypothesis space SH should be incorporated

It is essential to explore every possible outcome beforeruling out any basic event For example as SH B241 B281B301 is obtained for a case we should get only the correcthypothesis H11 B241B281B301 ne 0 in which the threeevents together interpret the observed symptoms ratherthan B241B281 B281B301 or so on

Rule 3 Given V isin B X G D jne jprime and integer yge 2then (Vij)

y Vij and VijVij 0

Figure 2 0e DUCG-based differential diagnostic causality graph for BPPV

Figure 3 Sub-DUCG for LSCC-idiopathic-recurrent BPPV

Figure 4 Sub-DUCG for PSCC-idiopathic-recurrent BPPV

Figure 5 0e sub-DUCG for cupulolithiasis BPPV

Computational and Mathematical Methods in Medicine 7

Rule 4 Given integer yge 2 kne kprime and jne jprime then(Fnkij)

y (rnirn)yAnkij FnkijFnkprimeij 0 FnkijFnkijprime 0 andFnkijFnkprimeijprime 0 if Bi1Biprime 1 0 is given Bi1 Biprime 1 isin Cm

ine iprime m isin 1 2 3 then it follows that Fnkiprime1Bi1 0 Fnki1Biprime1 0 and Fnki1Fnkiprime1 0

Proof 0e latter part of Rule 4 is based on Rule 1 and theother part has been proven in [28] From Rule 1 Bi1Biprime 1 0which implies that the basic events Bi1 and Biprime1 cannot beconcurrent and consequently brings about the mutual ex-clusions among the function events related to Bi1 and Biprime10erefore Anki1Ankiprime1 0 and Fnki1Fnkiprime1 0 as Anki1cannot be present in combination with Ankirsquo1 similarlythen Fnkiprime1Bi1 0 and Fnki1Biprime1 0 Notably Fnki1Fnkiprime0ne 0 is true because Anki1 and Ankiprime0 are independent ofeach other (since they are given independently)

Rule 5 1113936Mm11113937iisinSm

FnkijiViji

(1113936Mm11113937iisinSm

(rnirn))1113937

iisinS1AnkijiViji

where Sm denotes the set of variable number ina product item m isin 12 M and S1 sube S2 sube middot middot middot sube SM

Rule 6 Suppose that no mutually exclusive basic eventscoexist in the candidate hypothesis space thenFnkijVij(1113936iprimeFnkiprimej

iprimeViprimej

iprime) FnkijVij if j ji is given

Proof To complement the ordinary conditions of Rule 14discussed in [28] consider a situation related to mutuallyexclusive basic events Vij Bi1 and VijprimeBiprime1Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 ) as proposed in Rule 10eproposition of Rule 6 can thus be represented as

FnkijVij 1113944

iprime

FnkiprimejiprimeViprimej

iprime⎛⎝ ⎞⎠ FnkijVij middot FnkijVij

+ FnkijVij middot 1113944

iprime ne i

FnkiprimejiprimeViprimej

iprime

rnirn1113872 11138732AnkijVij

neFnkijVij

(8)

0e inclusion of mutually exclusive events leads to theaforementioned outcomes (ie the inconsistence betweenRule 1 and Rule 6) and the autonormalization feature nolonger holds 0erefore a solution for BPPV subtype dif-ferentiation known as a scheme of dummy basic variable(DBV) is proposed

233 Scheme of Dummy Basic Variable

Definition 4 (DBV) If mutually exclusive candidate hy-potheses coexist in the candidate hypothesis space ieBi1Biprime 1 0 Bi1 Biprime1 isin Cm(ine iprime m isin 1 2 3 ) Bi1 andBiprime1are converted into different states of a DBV each state of theDBV elicits an individual pathogenesis causality graphaccording to the hypothesis related to that state the specificcausalities of different diseases can be distinguished by theA-parameter values of DBV which can either be zero or not0e exclusive rules among basic events are thus transformedinto an inherent exclusive law among the states of an event

Table 2 Definition of variables for differential diagnosis of BPPV

Variables Descriptions

X1ndash3201ndash206

210ndash217

Pathophysiology of BPPV the lesion of theotolithic membrane of utricle macula thedegenerated otolith broken off from utriclemacula misplaced calcium carbonate crystalsdebris calcium free-floating particles enteringthe SCCs calcium particles adherent to the

cupula of SCC the endolymph movement withfree-floating particles that pathologicallystimulates the ampulla of canal and the

sensitivity to linear acceleration and gravityinduced by the abnormal deflection of cupula

X48ndash11

0e description of vertigo an illusion ofmovement the sensation that objects in the

environment is moving when the eyes are openand the sensation that a patient feels as if he or

she is moving when the eyes are closed

X1142454682

0e main accompanying symptomsspontaneous nystagmus and autonomic nerve

symptoms

X20-25

0e detailed description of the features ofvertigo attacks attack characteristics the onsetand duration of an attack causes of disease

frequency and severity

X26ndash28209

Changes in head position relative to gravityrotation of the head relative to the body while in

an upright position

X83ndash871300e feature of spontaneous nystagmus and the

Romberg test for vestibular function

X5249161163238

Other accompanying symptoms cochlearsymptoms hearing loss tinnitus the symptoms

of central nervous system and themanifestations of the primary and underlying

disordersX184185 Patientrsquos gender and age

X186189198234

0e typical and characteristic medical history amigraine hypertension head trauma and inner

ear pathology

X207ndash208

More than one semicircular canal is affectedsimultaneously (obtained statistically duringthe pretreatment process of medical data)

X218ndash221227228Positioning test vertigo and nystagmus when

the head is moving or rotating

X222ndash226

DixndashHallpike test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)

X229ndash233

Supine roll test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)X236 0e outcomes of the maneuver treatment

B23ndash33

PSCC-BPPV (B23) LSCC-BPPV (B24) ASCC-BPPV (B25) MSCC-BPPV (B26) secondary

BPPV (B27) idiopathic BPPV (B28)canalithiasis BPPV (B29) cupulolithiasis BPPV(B30) subjective BPPV (B31) persistent BPPV

(B32) and recurrent BPPV (B33)

8 Computational and Mathematical Methods in Medicine

0e problem of disobeying the autonormalization fea-ture can thus be addressed 0is method is illustrated via anexample in Figure 6(a) Suppose that B11 and B21 aremutually exclusive events 0ey are then combined into aDBV-Bv during the reasoning process corresponding to Bv1and Bv2 respectively From the definition of DBVa31v1 equiv a3111 a41v2 equiv a4121 a51v2 equiv a5121 and rnv equiv rniwhere i isin 1 2 and n isin 3 4 5 Figure 6(b) shows an ex-ample where an event (eg X3) is connected to more thanone basic event In this case rnv is defined as rnv equiv 1113936irni ifFnine 00us r3v r31 + r32 for the case in Figure 6(b) whichpoints out to a combination of basic events

In the context of differential diagnosis and upon thecompletion of causality simplifications the obtained can-didate hypotheses of C1 B231 B241 B251 B261 (there aremore than one basic event in the set) should be combinedinto a DBV-Bm with Bmk denoting Bi1 where k 1 2 3 4and i 23 24 25 26 PrBmk refers to the prior probabilityof Bi1 and Pr Bm01113966 1113967 1 minus 1113936kne0Pr Bmk1113966 1113967

Definition 5 (Ranked Independent Probability) 0e rankedindependent probability represents a new metric proposedfor quantifying the degree of confidence in whether a BPPVsubtype (eg Bi1 as a part of the hypothesis Hkj) can in-dependently interpret all the medical evidence in com-parison with the other subtypes coexisting in Hkj 0eranked independent probability of Bi1 is calculated as fol-lows (1) get hs

i1 of Bi1 according to (2) and (3) in which ζi isbased on the individual causality tracking graph of Bi1 and(2) for all the Bi1 within the set of Hkj hs

i1 is ranked byhs

i11113936ihsi1

24 eoretical Analysis of the Reasoning Complexity 0einference algorithm for the proposed method reduces thereasoning complexity in two ways First the causality graphsimplification and pruning strategy significantly decreases themodel scale 0e variables that are irrelevant or inconsistentwith the medical evidence are excluded from the reasoning

calculation 0is significantly reduces the computationalcomplexity Moreover the diagnostic reasoning conclusioncan even be accurately drawn solely via the causality sim-plification Second prior to probabilistic reasoning weightedlogic inference is performed based on the simplified causalitygraph 0us the multiple connected causalities can bedecomposed independently leading the chaining inference toexhibit high efficiency Furthermore the proposed logicalinference rules and logical operations can decrease thecomplexity and scale of logical event expressions

0e actual efficiency tests for the DUCG inference al-gorithm have been performed using online fault diagnosisdata from several large-scale industrial systems (eg nuclearpower plants) in which thousands of variables and causalityarcs are involved [28 31] 0e diagnostic reasoning cantypically be finished within 05ndash1 s (on a personal computer)Moreover the inference efficiency has been verified from ourpast clinical diagnosis applications that involved dozens ofdiseases such as jaundice and sellar region disease

3 Experiments and Analyses

31 Clinical Validation of the BPPV Differential DiagnosisMethod

311 Differential Diagnosis for BPPVmdashCase 1 Suppose thatthe medical evidence of a patient was observed in part asX41 X212 X243 X1844 X1852 X2094 X2292 X2302 X2070X2080 X2360 in Figure 2 and other X-type variables arenormal or unknown (incomplete medical information) 0emedical information in this experiment is from a 65-year-oldfemale patient who suffered from brief episodes of vertigowhen rolling over in bed for two weeks and was suspected tobe a BPPV case according to the supine roll test

Based on the evidence in this case Figure 2 can besimplified into the graph shown in Figure 7 by applying thecausality simplification rules and pruning strategy Manymeaningless relationships and events under current situa-tion are eliminated accordingly with SH B241 B281 B301

BeginFor a BPPV patientCollect medical evidence E including symptoms signs examination findings laboratory tests and medical historiesPerform causality simplification to the BPPV causality graph based on the evidence EApply the causality simplification mechanisms including the pruning strategy and causality tracking processObtain the simplified diagnostic causality graph

Perform the algorithms of weighted logic inference based on the simplified causality graphPerform the weighted logic event expansion to the evidence according to (1)Perform logic inference according to (2)

Apply the weighted logic inference rules 1sim6 of differential diagnosis for BPPVApply the scheme of dummy basic variablePerform the basic logic operations

Obtain the hypothesis event space SH Hkj1113966 1113967

Perform the probabilistic reasonings to obtain the posterior probability of Hkj conditioned on E hskj

Calculate the ranked independent probability of a BPPV subtypeEnd

ALGORITHM 1 Differential diagnostic reasoning method for BPPV

Computational and Mathematical Methods in Medicine 9

being inferred as the possible root causes 0e resultinghypothesis space SH is concise with all unlikely hypothesesbeing excluded from concern Moreover the individualcausality tracking graphs for the three root cause events B24B28 and B30 in Figure 7 are shown in Figure 8 whereby eachsubgraph independently covers all evidence0e graphs thusintuitively and faithfully represent the causalities underlyingthe pathogenesis of Case 1

By applying the algorithm of differential diagnosticreasoning for Case 1 the state probability ofH11 B241B281B301 can be obtained as hs

11

Pr H11 | E1113966 1113967 1 0e obtained ldquoranked independent prob-abilitiesrdquo of B241 B281 and B301 are listed in Table 3 0eLSCC-idiopathic-cupulolithiasis BPPV is therefore deter-mined as the diagnostic result of Case 1 this result isconsistent with the clinical conclusions confirmed byotoneurologists

312 Differential Diagnosis for BPPVmdashCase 2 A 72-year-old female patient complained about paroxysmal positionalvertigo for a month the attacks of vertigo were brief lastingfor one minute the vertigo frequently occurred whilelooking up or down0us the medical evidence for this caseis X41 X212 X243 X1844 X1852 X2070 X2080 X2093 X2223X2231 X2241 X2251 X2261 X2360 the other X-type variablesare normal or unknown (incomplete medical information)

By applying the algorithm of differential diagnosticreasoning the hypothesis event H11 B231B281B291B321 isuniquely determined as the origin of the disease whichindicates a PSCC-idiopathic-cupulolithiasis-persistentBPPV 0e diagnostic causality graph is shown in Figure 9which is based on the causality simplification of Figure 20e resulting ranked independent probabilities of B231B281 B291 and B321 are listed in Table 4 By explicitlyrepresenting the disease causes symptoms pathogenesisand the latent correlations among medical informationFigure 9 offers intuitive insights into the underlying path-ological mechanisms

313 Other Validated BPPV Subtype Cases A verificationexperiment on some other clinical cases was performed toevaluate the effectiveness of the proposed method 0ecorrectness was based on the otoneurologistsrsquo judgement onthe diagnostic outcomes in contrast to the practical con-clusions In the clinical center for vertigo in BeijingChaoyang Hospital BPPV cases are common howeverthere are multiple repetitions in the meaningful informationfor the BPPV patients on their medical histories and physicalexaminations regarding subtype differentiation Based on

this 75 typical BPPV cases were selected from the thousandsof cases containing medical records interviews and physicalassessments in the verification experiments 0e BPPVsubtypes involved are outlined in Table 5 0e selectionprinciple of BPPV cases was based on the internationaldiagnostic criteria for BPPV [36] and the typicality andrepresentativeness of BPPV subtype diseases Notably sincethe nystagmus cannot be observed for a subjective BPPVcase it is difficult to classify the case either as canalithiasisBPPV or cupulolithiasis BPPV

0e diagnostic outcomes of the DUCG-based modelagreed with the otoneurologistsrsquo conclusions with a cor-rectness index of 100 Based on the available publishedliterature no other research has reported a model-basedautomatic subtype differentiation of BPPV in the past

32 Comparative Analysis of DUCG and BN 0e maindifference between DUCG and BN in terms of the theoreticalframework is that the model structure and parameters ofDUCG are decoupled By virtue of such a feature the in-dependent causality representation by the weighted causalityfunction event Ankij in DUCG makes it possible to simplifythe original causality graph based on the collected medicalevidence 0e irrelevant and meaningless events and rela-tions are thus eliminated from the model Taking the sim-plified causality graph as the basis of diagnostic reasoningreduces the computational scale and complexity to a largeextent In contrast BN cannot be easily simplified owing tothe structural coupling feature among the variables thecausalities among the child-parent events in BN are typicallyrepresented through a joint probability distribution (eg aconditional probabilistic table CPT) in case any variablesand relations are removed from a BN the remaining pa-rameters in the CPTs may need major adjustments more-over the number of parameters specified in a CPTfor a BN isexponential to the number of the parent variables and statesinvolved while the parameters needed in the DUCG are lessthan the parameters in a BN

Others

B1X3

X4

X5

Others

X3

X4

X5

B2

BV

(a)

Others

X3

X4

Others

X3

X4

BV

B1

B2

(b)

Figure 6 Example of DBV (a) Example 1 (b) Example 2

Figure 7 Diagnostic causality graph for Case 1

10 Computational and Mathematical Methods in Medicine

Furthermore by the independence representation andautomatic normalization feature for the weighted logic eventexpansion the ldquoself-reliantrdquo chaining inference and logicoperations can be performed in DUCG 0e parameters andinformation that are eliminated during the causality simpli-fication and those that are not involved in the chaining in-ference can all be missing (or some parameters which are notof concern are thus not provided) during this reasoningprocess and do not affect the diagnostic accuracy 0e diag-nostic inference method under incomplete information in-dicates that some unnecessary clinical tests and inappropriatemedications can be omitted thereby decreasing the patientsrsquo

medical costs For a BN the reasoning accuracy depends onthe completeness of the parameters in the CPTs

33 Application Analysis 0e proposed method can be de-veloped as an automatic diagnostic system for clinicians Basedon the compact independent and graphical causality repre-sentation using DUCG the model construction and diagnosis

(a) (b)

(c)

Figure 8 Individual causality tracking graphs of the hypotheses for Case 1 (a) LSCC-BPPV (B24) (b) Idiopathic BPPV (B28) (c)Cupulolithiasis BPPV (B30)

Table 3 Diagnostic reasoning results of Case 1

BPPVsubtype Description Ranked independent

probabilityB241 LSCC-BPPV 00388B281 Idiopathic BPPV 09542

B301Cupulolithiasis

BPPV 0007

H11 B241B281B301 1

Figure 9 Diagnostic causality graph for Case 2

Table 4 Diagnostic reasoning results of Case 2

BPPVsubtype Description Ranked independent

probabilityB231 PSCC-BPPV 01435B281 Idiopathic BPPV 07653

B291Canalithiasis

BPPV 00091

B321 Persistent BPPV 00821H11 B231B281B291B321 1

Table 5 BPPV subtypes involved in the validated cases

BPPV subtype No of casesPSCC 53ASCC 1LSCC 16MSCC 5Idiopathic 55Secondary 16Canalithiasis 61Cupulolithiasis 8Subjective 4Persistent 4Recurrent 8Typical 59

Computational and Mathematical Methods in Medicine 11

application are both easy to implement For a patient theclinical data through can be obtained through inquiry physicalexamination and auxiliary examination among others Nextthe clinical data including symptoms signs examination andtest data are input into the diagnostic reasoning interface ofthe system and the diagnosis results can be obtained throughreasoning calculation 0e clinical application of this methodis thus very convenient 0rough incorporation into the au-tomatic medical devices this method could improve the ef-ficiency of BPPV diagnosis and therapy especially for generalpractitioners in primary health care institutions In additionthe system can also be used inmobile and Internet terminals asa secondary tool for telemedicine finally it can serve as ateaching tool for doctor training in related disciplines

4 Summary

0is study proposes a DUCG method for differential di-agnosis of BPPV To distinguish among various causes ofvertiginous disorders with similar symptoms the proposedmethod involves a graphical and compact representation inaddition to logical reasoning algorithms for pathologicalmechanisms and related uncertain causalities New algo-rithms of differential diagnostic reasoning are proposed byintegrating a pruning strategy in the causality simplificationprocess a maximizing concurrent basic event set strategy inthe formulation of hypothesis space and the weighted logicinference rules for subtype differentiation of BPPV Fur-thermore a scheme of dummy basic variable is introduced tosettle the problems related to mutually exclusive root causeevents 0e model manifests higher correctness favorablerobustness to incomplete evidence and satisfactory dis-criminatory power for BPPV subtypes Furthermore usingthe diagnostic reasoning method and graphical represen-tation mechanism not only provides a diagnostic result butalso explains the rationale for suggesting the diseases whichjustifies the probability results

In light of these encouraging preliminary results moreclinical studies will be performed Furthermore a newmethod of probabilistic prediction for the vestibular dys-function-induced fall risk will be the subject of our futureresearch endeavors

Data Availability

0e data used to support the findings of this study are se-lected from the clinical cases of Department of Otorhino-laryngology Head and Neck Surgery Beijing Chaoyanghospital Requests for access to these data should be made toYanjun Wang (docwyjn163com Beijing Chaoyanghospital)

Disclosure

Chunling Dong and Yanjun Wang are cofirst authors

Conflicts of Interest

0e authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

0is work was supported in part by the National NaturalScience Foundation of China under Grant no 71671103 andin part by the Fundamental Research Funds for the CentralUniversities under Grant nos CUC2019B023CUC19ZD008 and CUC19ZD007

References

[1] N Bhattacharyya R F Baugh L Orvidas et al ldquoClinicalpractice guideline benign paroxysmal positional vertigordquoOtolaryngologymdashHead and Neck Surgery vol 139 no 5_suppl pp S47ndashS81 2008

[2] J S Oghalai S Manolidis J L Barth M G Stewart andH A Jenkins ldquoUnrecognized benign paroxysmal positionalvertigo in elderly patientsrdquo OtolaryngologymdashHead and NeckSurgery vol 122 no 5 pp 630ndash634 2000

[3] M P Prim-Espada J I De Diego-Sastre and E Perez-Fernandez ldquoEstudio metaanalıtico de la eficacia de la man-iobra de Epley en el vertigo posicional paroxıstico benignordquoNeurologıa vol 25 no 5 pp 295ndash299 2010

[4] L S Parnes S K Agrawal and J Atlas ldquoDiagnosis andmanagement of benign paroxysmal positional vertigo(BPPV)rdquo Canadian Medical Association Journal vol 169no 7 pp 681ndash693 2003

[5] J C Li and J Epley ldquo0e 360-degree maneuver for treatmentof benign positional vertigordquo Otology amp Neurotology vol 27no 1 pp 71ndash77 2006

[6] R Isola R Carvalho and A K Tripathy ldquoKnowledge dis-covery in medical systems using differential diagnosisLAMSTAR and $k$-NNrdquo IEEE Transactions on InformationTechnology in Biomedicine vol 16 no 6 pp 1287ndash1295 2012

[7] A L Barabasi N Gulbahce and J Loscalzo ldquoNetworkmedicine a network-based approach to human diseaserdquoNature Reviews Genetics vol 12 no 1 pp 56ndash68 2011

[8] E Mira A Buizza G Magenes M Manfrin and R SchmidldquoExpert systems as a diagnostic aid in otoneurologyrdquo Journalfor Oto-Rhino-Laryngology and Its Related Specialties (ORL)vol 52 no 2 pp 96ndash103 1990

[9] C E S Gavilan J E Gallego and J Gavilan ldquoCarnisel anexpert system for vestibular diagnosisrdquo Acta Oto-Lar-yngologica vol 110 no 3-4 pp 161ndash167 1990

[10] E Kentala I Pyykko Y Auramo J Laurikkala andM Juhola ldquoOtoneurological expert system for vertigordquo ActaOto-Laryngologica vol 119 no 5 pp 517ndash521 1999

[11] E Kentala K Viikki I Pyykko andM Juhola ldquoProduction ofdiagnostic rules from a neurotologic database with decisiontreesrdquo Annals of Otology Rhinology and Laryngology vol 109no 2 pp 170ndash176 2000

[12] J W Song J H Lee J H Choi and S J Chun ldquoAutomaticdifferential diagnosis of pancreatic serous and mucinouscystadenomas based on morphological featuresrdquo Computersin Biology and Medicine vol 43 no 1 pp 1ndash15 2013

[13] M H Lopes N R Ortega P S Silveira E Massad R Higaand F Marin Hde ldquoFuzzy cognitive map in differential di-agnosis of alterations in urinary elimination a nursing ap-proachrdquo International Journal of Medical Informatics vol 82no 3 pp 201ndash208 2013

[14] C Salvatore A Cerasa I Castiglioni et al ldquoMachine learningon brain MRI data for differential diagnosis of Parkinsonrsquosdisease and Progressive Supranuclear Palsyrdquo Journal ofNeuroscience Methods vol 222 pp 230ndash237 2014

12 Computational and Mathematical Methods in Medicine

b1 minus

0021113888 1113889

b2

minus

002004

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

a37 minus minus minus

minus 0 051113888 1113889

a48 minus minus

minus 061113888 1113889

a52 minus minus minus

minus 02 01113888 1113889

a54 minus minus

minus 081113888 1113889

a68

minus minus

minus 06minus 0

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

a78

minus minus

minus 0minus 09

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

a81 minus minus

minus 091113888 1113889

a82 minus minus minus

minus 06 01113888 1113889

a96 minus minus minus

minus 06 01113888 1113889

a1010D

minus

0208

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

a1112

minus minus

minus 0minus 09

⎛⎜⎜⎜⎜⎝ ⎞⎟⎟⎟⎟⎠

(4)

Besides the normal or unknown variables suppose thatthe evidence for the DUCG example in Figure 1(a) isobtained as E 1113937iEi

prime X31X51X72X81X91X102X112 Byapplying the simplification rules of DUCG [28 30] all theirrelevant incorrect and meaningless causalities andevents can be eliminated from the graph based on themedical evidence 0us the simplified graph is obtained asshown in Figure 1(b) DUCG uses different colored nodesto distinguish the X-type variablesrsquo states green indicates anormal state indexed by 0 sky blue and blue indicate state1 and state 3 respectively yellow and brown indicate state2 and state 4 respectively and colorless indicates anunknown state implying an unconfirmedunidentifiablepathological feature or an unexamined item

Based on (1) and Figure 1(b) the expanding expressionsof evidence X31 X51 and X112 in the causality context ofB21 respectively are shown below

E1prime X31 A3172A7281A8121B21

E2prime X51 12

1113874 1113875A5121B21 +12

1113874 1113875A5141A4181A8121B21

E7prime X112 A112121A10210DA9161A6181A8121B21

(5)

Likewise other abnormal evidence is expanded and theexpanding expression for E is obtained as

B13

B14

B15

B16

X17

X9

X6

X3X7

B2

B1

X4

X5

X10X8

G12 X11

D10

Other variablesGroup 2

Other variablesGroup 1

X18

(a)

X6X4

B1

B2

G12

D10

X112

X102

X72

X81

X51

X91

X31

(b)

Figure 1 Example of DUCG diagnostic causality graph (a) original causality graph and (b) simplified causality graph

Table 1 Logic gate specification of G12

Logic gate State State expression

G120 Remnant state1 X91X102 +X101

4 Computational and Mathematical Methods in Medicine

E A3172A7281A112121A10210DA9161A6181A8121B21

middot12

1113874 1113875A5121B21 +12

1113874 1113875A5141A4181A8121B211113874 1113875

12

1113874 1113875A3172A7281A112121A10210DA9161A6181A8121

middot A5121B21 +12

1113874 1113875A3172A7281A112121A10210DA9161

middot A6181A5141A4181A8121B21

(6)

Similarly the expanding expression of E in the causalitycontext of B11 is

E A3172A7281A112121A10210DA9161A6181A5141

middot A4181A8111B11

(7)

Finally hypothesis space SH under evidence E is ob-tained as follows SH H11 H211113966 1113967 where H11 equiv B11 andH21 equiv B21 0erefore the two hypotheses are determined asthe probable causes of the observed evidence as both canindependently interpret all the symptoms 0e probabilisticcalculation results are hs

11 0679 and hs21 0321 0e

inference results can be explained using the graphicalcausality semantics as shown in Figure 1(b) Based on thesesemantics users can not only deduce the results but alsounderstand their logic

Based on the self-reliant chaining inference the missingparameters such as a3172 a7281 a112121 a10210D a9161and a6181 do not have an impact on the reasoning resultMoreover the most probable hypotheses could be typicallydetermined uniquely just within the logical reasoningprocess (before the probabilistic reasoning is performed)0us the causality structure that accurately represents thedisease pathogenesis is what really matters It is evident thatDUCG does not impose stringent requirements for com-pleteness of the parameters and clinical examination data0us it can be used to facilitate modeling through medicalknowledge and experience

22 Construction of Differential Diagnosis Model for BPPV

221 BPPV Characteristics

(1) Pathophysiology of BPPV0e vestibular receptor consistsof two otolith organs (the utricle and saccule) which overseelinear acceleration and gravity as well as three semicircularcanals (SCCs) that sense angular acceleration 0e SCCsinclude anterior SCCs (ASCCs) posterior SCCs (PSCCs)and lateral SCCs (LSCCs) 0e afferent nerves from otolithorgans and SCCs project symmetrical activities to the centralvestibular system to maintain the balance and spatial ori-entation BPPV results from misplaced calcium carbonatecrystals (otoconia) that are detached from utricle macula andcollected within the SCCs due to trauma infection or even

aging 0ese crystals either remain free-floating in the SCCsor become attached to the cupula Normally as the motionsensor of SCCs that are filled with endolymph cupula is agelatinous mass with the same density as endolymph Sincethe calcium particles are denser than the endolymph andcupula the SCCs become pathologically sensitive to linearacceleration and gravity the afferent nerves from SCCs thusfire asymmetrically leading to vertigo and nystagmusWhenmoving into the SCC the calcium carbonate crystal debrismay cause endolymph movement which consequentlystimulates the cupula of the affected canal during headmovement or while stationary (this is called canalithiasis)Similarly if adherent to the cupula the particles may alsoactivate it (this is called cupulolithiasis) [32]

(2) Clinical Characteristics of BPPV BPPV is characterizedby brief attacks of vertigo after lying down in bed looking upor bending down among others 0e vertigo attacks in mostcases last less than 1sim2 minutes and mostly occur at night orupon awakening [1] 0e diagnosis rests on the observationof characteristic nystagmus accompanying symptoms ofvertigo when a patientrsquos head is moved into a specific ori-entation with respect to gravity 0is is due to shred calciumcrystals from macula which may cause age-related changesin the protein and gelatinous matrix of the otolithicmembrane Although most of BPPV cases are idiopathic asignificant proportion can be associated with precedingtraumatic events including head trauma dental treatmentand ear surgery Other conditions such as viral vestibularneuritis otitis media Menierersquos disease idiopathic suddensensorineural hearing loss posterior circulation ischemiaand migraine can also trigger cases of BPPV

BPPV may affect each of the three SCCs Alternatively itcan affect more than one canal simultaneously resulting invarying nystagmus patterns [33] Notably due to its gravity-dependent position the most commonly affected semicir-cular canal is the posterior canal 0e positional and posi-tioning tests (eg DixndashHallpike diagnostic maneuver andsupine roll test) can provide an accurate diagnosis for thiscondition Furthermore the features of nystagmus in-cluding latency direction duration reversal and fatiga-bility are significant during diagnosis

(3) Subtype Differentiation of BPPV Based on the epide-miology causes of disease pathophysiology anatomy pa-thology clinical features and treatment outcomes a BPPVdisease may be classified into distinct categories along fourdimensions (1) depending on the localization of the par-ticles and the involved semicircular canals there are foursubtypes (PSCC ASCC LSCC and multiple-SCC (MSCC))(2) BPPV is subdivided into idiopathic BPPV and secondaryBPPV as it may occur as a primary disease or secondary toother otology disorders or systemic conditions [4] (3) BPPVcan be divided into canalithiasis and cupulolithiasisdepending on the nystagmus provoked characteristics fromthe positioning test based on the pathophysiology mecha-nism [32] and (4) based on the clinical features andtreatment outcomes BPPV falls into two categories typicaland atypical 0e atypical BPPV can be further identified as

Computational and Mathematical Methods in Medicine 5

subjective BPPV persistent BPPV and recurrent BPPVSubjective BPPV refers to the cases associated with a positivehistory of BPPV and DixndashHallpike or supine roll tests whichare positive for vertigo but negative for nystagmus [34] Apersistent BPPV refers to cases lasting for more than twoweeks while a recurrent BPPV indicates recurrence of BPPVin the same canal after a symptom-free interval of at leasttwo weeks from a previously successful treatment [35]

222 Constructed Model for Differential Diagnosis of BPPVAs a causality representation to the aforementioned path-ogenesis and pathophysiology of BPPV a new DUCG-basedcausality graph was constructed based on the vertigo modelpresented in [30] 0e BPPV differential diagnosis model isshown in Figure 2 it includes 125 variables (X-type 85 D-type 8 G-type 21 and B-type 11) and 286 arcs

(1) Modularized Modeling Scheme A modularized modelingscheme is applied in the construction of the causality graphshown in Figure 2 All BPPV subtypes are handled as in-dividual sub-DUCGs For example the three sub-DUCGsrepresenting the idiopathic PSCC LSCC and cupuloli-thiasis BPPV are demonstrated in Figures 3ndash5 respectivelyWhen the sub-DUCGs are merged solutions are proposedfor addressing the ambiguous contradictory and incom-plete information to ensure global coherence [30] Such amodularized modeling scheme reduces the difficulty inmodel construction using a divide-and-conquer approach

(2) Definition of Variables Based on the characteristics ofBPPV and the international diagnostic criteria [36] themedical information of patients including symptoms signsfindings of examinations medical histories etiology andpathogenesis pathophysiology and socio-psychological andenvironmental factors is incorporated into the model Table 2lists some of the variables of the model shown in Figure 2

(3) Representation of Causal Relationships In this repre-sentation arcs are established to represent and quantifycausal correlations among related symptoms and diseaseorigins complex causalities are denoted by a combination ofcausal functions via logic gates All causalities and param-eters in Figure 2 are determined by otoneurologists based ontheir knowledge experience epidemiology statistics andresearch achievements As stated before both the incom-pleteness of knowledge and imprecision of parameters havelittle impact on the reasoning accuracy thus DUCG is moreflexible for the model construction

23 e Algorithm of Differential Diagnostic ReasoningDifferential diagnosis aims at narrowing down the diseases tothe most probable one from a list of candidate diseases thatshow similar symptoms 0e differential diagnostic reasoningalgorithm is presented as Algorithm 1 which implements ahypothesis-driven process 0e posterior probability of thehypothesis event Hkj is used to quantify Hkjrsquos ability tointerpret the medical evidence E Notably a rare disease doesnot necessarily respond to a weak causality If a rare disease

(with a low prior probability) better explains a patientrsquossymptoms and medical evidence then the strength of thecausality functions can be high thus the disease will get ahigher ranked probability as a hypothesis event

231 New Causality Simplification Mechanisms Based onthe collected medical evidence E for a patient the process ofcausality simplifications is performed to the BPPV causalitygraph Causality simplification aims to eliminate the irrel-evant meaningless and impossible events and relationsfrom a causality graph 0erefore the model scale andcomplexity are both significantly decreased and the diseasehypothesis space converges0e root cause event can even bepreliminarily determined based on the simplified causalitygraph

As a complement to the original simplification rules ofDUCG [28 30] several new causality simplificationmechanisms including a pruning strategy and causalitytracking process are presented

Definition 1 (Pruning Strategy) 0e meaningless diseasehypothesis and its corresponding causalities are identifiedand pruned from the causality graph using a scheme ofcausality tracking for all the abnormal evidences

Definition 2 (Causality Tracking Process) 0e causalitytracking process starts from an observed event and traces itsupstream causality chains and ancestors back towards the B-type event(s) For any Bi only if all the abnormal evidence isreachable to it via a causality tracking process can it beidentified as a candidate hypothesis otherwise Bi should beeliminated from the hypothesis space and its correspondingcausalities should be pruned from the graph

232 Weighted Logic Inference Rules of Differential Diag-nosis for BPPV Based on the simplified causality graph andmedical evidence the process of logical inference is per-formed to obtain the hypothesis space according to (1)sim(3)Our earlier study showed that by applying event expandingand logical operations the logical inference can effectivelydecrease the complexity of probabilistic reasoning [28]However in response to BPPV differential diagnosis theweighted logic inference algorithm requires majormodifications

Some BPPV subtypes can be present in a patient si-multaneously For instance a diagnosis can be termed as anASCC-idiopathic-canalithiasis BPPV Such a case is knownas concurrency of subtypes Meanwhile the subtypes be-longing to the same category are mutually exclusive when adiagnostic conclusion is drawn Some examples of this arePSCC-BPPV (B231) LSCC-BPPV (B241) ASCC-BPPV(B251) and MSCC-BPPV (B261) 0erefore to deal withthese cases new weighted logic inference rules for exclusionand concurrency among others are developed as shownbelow

Rule 1 Suppose that the basic events (namely root causeevents) in a BPPV differential diagnosis model are

6 Computational and Mathematical Methods in Medicine

represented in terms of category sets as C1 B231 B241B251 B261 C2 B271 B281 C3 B291 B301 andC4 B311 B321 B331 State 1 of a B-type event indicatesthat the root cause event has occurred on the contrary state0 of a B-type event indicates that the root cause event has notoccurred 0e mutual exclusion rules for basic events inBPPV differential diagnosis can thus be defined asBi1Biprime 1 0 where Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 )

Proof From the definition the category sets C1 C2 and C3indicate different classification perspectives of BPPV0erefore all basic events within the same category set areexclusive and exhaustive Specifically there is B231B241 0

B231B251 0 B231B261 0 B241B251 0 B241B261 0B251B261 0 B271B281 0 and B291B301 0

Rule 2 Bi1Biprime 1 ne 0 for Bi Biprime isin C4 (ine iprime) and Bi1Biprime 1 ne 0 forBi1 isin Cm Biprime1 isin Cn(ine iprime mne n)

Proof 0e events in C4 describe the respective differenttypes of atypical BPPV in an overlapping manner Namelyall the basic events in B311 B321 B331 are likely to beconcurrent 0is sets the basis for Rule 2

Definition 3 (Maximizing Concurrent Basic Event SetStrategy) To obtain an ultimate disease hypothesis Hkj ifthe events that constitute Hkj are concurrent and consistentwith each other the maximum number of basic eventswithin the hypothesis space SH should be incorporated

It is essential to explore every possible outcome beforeruling out any basic event For example as SH B241 B281B301 is obtained for a case we should get only the correcthypothesis H11 B241B281B301 ne 0 in which the threeevents together interpret the observed symptoms ratherthan B241B281 B281B301 or so on

Rule 3 Given V isin B X G D jne jprime and integer yge 2then (Vij)

y Vij and VijVij 0

Figure 2 0e DUCG-based differential diagnostic causality graph for BPPV

Figure 3 Sub-DUCG for LSCC-idiopathic-recurrent BPPV

Figure 4 Sub-DUCG for PSCC-idiopathic-recurrent BPPV

Figure 5 0e sub-DUCG for cupulolithiasis BPPV

Computational and Mathematical Methods in Medicine 7

Rule 4 Given integer yge 2 kne kprime and jne jprime then(Fnkij)

y (rnirn)yAnkij FnkijFnkprimeij 0 FnkijFnkijprime 0 andFnkijFnkprimeijprime 0 if Bi1Biprime 1 0 is given Bi1 Biprime 1 isin Cm

ine iprime m isin 1 2 3 then it follows that Fnkiprime1Bi1 0 Fnki1Biprime1 0 and Fnki1Fnkiprime1 0

Proof 0e latter part of Rule 4 is based on Rule 1 and theother part has been proven in [28] From Rule 1 Bi1Biprime 1 0which implies that the basic events Bi1 and Biprime1 cannot beconcurrent and consequently brings about the mutual ex-clusions among the function events related to Bi1 and Biprime10erefore Anki1Ankiprime1 0 and Fnki1Fnkiprime1 0 as Anki1cannot be present in combination with Ankirsquo1 similarlythen Fnkiprime1Bi1 0 and Fnki1Biprime1 0 Notably Fnki1Fnkiprime0ne 0 is true because Anki1 and Ankiprime0 are independent ofeach other (since they are given independently)

Rule 5 1113936Mm11113937iisinSm

FnkijiViji

(1113936Mm11113937iisinSm

(rnirn))1113937

iisinS1AnkijiViji

where Sm denotes the set of variable number ina product item m isin 12 M and S1 sube S2 sube middot middot middot sube SM

Rule 6 Suppose that no mutually exclusive basic eventscoexist in the candidate hypothesis space thenFnkijVij(1113936iprimeFnkiprimej

iprimeViprimej

iprime) FnkijVij if j ji is given

Proof To complement the ordinary conditions of Rule 14discussed in [28] consider a situation related to mutuallyexclusive basic events Vij Bi1 and VijprimeBiprime1Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 ) as proposed in Rule 10eproposition of Rule 6 can thus be represented as

FnkijVij 1113944

iprime

FnkiprimejiprimeViprimej

iprime⎛⎝ ⎞⎠ FnkijVij middot FnkijVij

+ FnkijVij middot 1113944

iprime ne i

FnkiprimejiprimeViprimej

iprime

rnirn1113872 11138732AnkijVij

neFnkijVij

(8)

0e inclusion of mutually exclusive events leads to theaforementioned outcomes (ie the inconsistence betweenRule 1 and Rule 6) and the autonormalization feature nolonger holds 0erefore a solution for BPPV subtype dif-ferentiation known as a scheme of dummy basic variable(DBV) is proposed

233 Scheme of Dummy Basic Variable

Definition 4 (DBV) If mutually exclusive candidate hy-potheses coexist in the candidate hypothesis space ieBi1Biprime 1 0 Bi1 Biprime1 isin Cm(ine iprime m isin 1 2 3 ) Bi1 andBiprime1are converted into different states of a DBV each state of theDBV elicits an individual pathogenesis causality graphaccording to the hypothesis related to that state the specificcausalities of different diseases can be distinguished by theA-parameter values of DBV which can either be zero or not0e exclusive rules among basic events are thus transformedinto an inherent exclusive law among the states of an event

Table 2 Definition of variables for differential diagnosis of BPPV

Variables Descriptions

X1ndash3201ndash206

210ndash217

Pathophysiology of BPPV the lesion of theotolithic membrane of utricle macula thedegenerated otolith broken off from utriclemacula misplaced calcium carbonate crystalsdebris calcium free-floating particles enteringthe SCCs calcium particles adherent to the

cupula of SCC the endolymph movement withfree-floating particles that pathologicallystimulates the ampulla of canal and the

sensitivity to linear acceleration and gravityinduced by the abnormal deflection of cupula

X48ndash11

0e description of vertigo an illusion ofmovement the sensation that objects in the

environment is moving when the eyes are openand the sensation that a patient feels as if he or

she is moving when the eyes are closed

X1142454682

0e main accompanying symptomsspontaneous nystagmus and autonomic nerve

symptoms

X20-25

0e detailed description of the features ofvertigo attacks attack characteristics the onsetand duration of an attack causes of disease

frequency and severity

X26ndash28209

Changes in head position relative to gravityrotation of the head relative to the body while in

an upright position

X83ndash871300e feature of spontaneous nystagmus and the

Romberg test for vestibular function

X5249161163238

Other accompanying symptoms cochlearsymptoms hearing loss tinnitus the symptoms

of central nervous system and themanifestations of the primary and underlying

disordersX184185 Patientrsquos gender and age

X186189198234

0e typical and characteristic medical history amigraine hypertension head trauma and inner

ear pathology

X207ndash208

More than one semicircular canal is affectedsimultaneously (obtained statistically duringthe pretreatment process of medical data)

X218ndash221227228Positioning test vertigo and nystagmus when

the head is moving or rotating

X222ndash226

DixndashHallpike test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)

X229ndash233

Supine roll test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)X236 0e outcomes of the maneuver treatment

B23ndash33

PSCC-BPPV (B23) LSCC-BPPV (B24) ASCC-BPPV (B25) MSCC-BPPV (B26) secondary

BPPV (B27) idiopathic BPPV (B28)canalithiasis BPPV (B29) cupulolithiasis BPPV(B30) subjective BPPV (B31) persistent BPPV

(B32) and recurrent BPPV (B33)

8 Computational and Mathematical Methods in Medicine

0e problem of disobeying the autonormalization fea-ture can thus be addressed 0is method is illustrated via anexample in Figure 6(a) Suppose that B11 and B21 aremutually exclusive events 0ey are then combined into aDBV-Bv during the reasoning process corresponding to Bv1and Bv2 respectively From the definition of DBVa31v1 equiv a3111 a41v2 equiv a4121 a51v2 equiv a5121 and rnv equiv rniwhere i isin 1 2 and n isin 3 4 5 Figure 6(b) shows an ex-ample where an event (eg X3) is connected to more thanone basic event In this case rnv is defined as rnv equiv 1113936irni ifFnine 00us r3v r31 + r32 for the case in Figure 6(b) whichpoints out to a combination of basic events

In the context of differential diagnosis and upon thecompletion of causality simplifications the obtained can-didate hypotheses of C1 B231 B241 B251 B261 (there aremore than one basic event in the set) should be combinedinto a DBV-Bm with Bmk denoting Bi1 where k 1 2 3 4and i 23 24 25 26 PrBmk refers to the prior probabilityof Bi1 and Pr Bm01113966 1113967 1 minus 1113936kne0Pr Bmk1113966 1113967

Definition 5 (Ranked Independent Probability) 0e rankedindependent probability represents a new metric proposedfor quantifying the degree of confidence in whether a BPPVsubtype (eg Bi1 as a part of the hypothesis Hkj) can in-dependently interpret all the medical evidence in com-parison with the other subtypes coexisting in Hkj 0eranked independent probability of Bi1 is calculated as fol-lows (1) get hs

i1 of Bi1 according to (2) and (3) in which ζi isbased on the individual causality tracking graph of Bi1 and(2) for all the Bi1 within the set of Hkj hs

i1 is ranked byhs

i11113936ihsi1

24 eoretical Analysis of the Reasoning Complexity 0einference algorithm for the proposed method reduces thereasoning complexity in two ways First the causality graphsimplification and pruning strategy significantly decreases themodel scale 0e variables that are irrelevant or inconsistentwith the medical evidence are excluded from the reasoning

calculation 0is significantly reduces the computationalcomplexity Moreover the diagnostic reasoning conclusioncan even be accurately drawn solely via the causality sim-plification Second prior to probabilistic reasoning weightedlogic inference is performed based on the simplified causalitygraph 0us the multiple connected causalities can bedecomposed independently leading the chaining inference toexhibit high efficiency Furthermore the proposed logicalinference rules and logical operations can decrease thecomplexity and scale of logical event expressions

0e actual efficiency tests for the DUCG inference al-gorithm have been performed using online fault diagnosisdata from several large-scale industrial systems (eg nuclearpower plants) in which thousands of variables and causalityarcs are involved [28 31] 0e diagnostic reasoning cantypically be finished within 05ndash1 s (on a personal computer)Moreover the inference efficiency has been verified from ourpast clinical diagnosis applications that involved dozens ofdiseases such as jaundice and sellar region disease

3 Experiments and Analyses

31 Clinical Validation of the BPPV Differential DiagnosisMethod

311 Differential Diagnosis for BPPVmdashCase 1 Suppose thatthe medical evidence of a patient was observed in part asX41 X212 X243 X1844 X1852 X2094 X2292 X2302 X2070X2080 X2360 in Figure 2 and other X-type variables arenormal or unknown (incomplete medical information) 0emedical information in this experiment is from a 65-year-oldfemale patient who suffered from brief episodes of vertigowhen rolling over in bed for two weeks and was suspected tobe a BPPV case according to the supine roll test

Based on the evidence in this case Figure 2 can besimplified into the graph shown in Figure 7 by applying thecausality simplification rules and pruning strategy Manymeaningless relationships and events under current situa-tion are eliminated accordingly with SH B241 B281 B301

BeginFor a BPPV patientCollect medical evidence E including symptoms signs examination findings laboratory tests and medical historiesPerform causality simplification to the BPPV causality graph based on the evidence EApply the causality simplification mechanisms including the pruning strategy and causality tracking processObtain the simplified diagnostic causality graph

Perform the algorithms of weighted logic inference based on the simplified causality graphPerform the weighted logic event expansion to the evidence according to (1)Perform logic inference according to (2)

Apply the weighted logic inference rules 1sim6 of differential diagnosis for BPPVApply the scheme of dummy basic variablePerform the basic logic operations

Obtain the hypothesis event space SH Hkj1113966 1113967

Perform the probabilistic reasonings to obtain the posterior probability of Hkj conditioned on E hskj

Calculate the ranked independent probability of a BPPV subtypeEnd

ALGORITHM 1 Differential diagnostic reasoning method for BPPV

Computational and Mathematical Methods in Medicine 9

being inferred as the possible root causes 0e resultinghypothesis space SH is concise with all unlikely hypothesesbeing excluded from concern Moreover the individualcausality tracking graphs for the three root cause events B24B28 and B30 in Figure 7 are shown in Figure 8 whereby eachsubgraph independently covers all evidence0e graphs thusintuitively and faithfully represent the causalities underlyingthe pathogenesis of Case 1

By applying the algorithm of differential diagnosticreasoning for Case 1 the state probability ofH11 B241B281B301 can be obtained as hs

11

Pr H11 | E1113966 1113967 1 0e obtained ldquoranked independent prob-abilitiesrdquo of B241 B281 and B301 are listed in Table 3 0eLSCC-idiopathic-cupulolithiasis BPPV is therefore deter-mined as the diagnostic result of Case 1 this result isconsistent with the clinical conclusions confirmed byotoneurologists

312 Differential Diagnosis for BPPVmdashCase 2 A 72-year-old female patient complained about paroxysmal positionalvertigo for a month the attacks of vertigo were brief lastingfor one minute the vertigo frequently occurred whilelooking up or down0us the medical evidence for this caseis X41 X212 X243 X1844 X1852 X2070 X2080 X2093 X2223X2231 X2241 X2251 X2261 X2360 the other X-type variablesare normal or unknown (incomplete medical information)

By applying the algorithm of differential diagnosticreasoning the hypothesis event H11 B231B281B291B321 isuniquely determined as the origin of the disease whichindicates a PSCC-idiopathic-cupulolithiasis-persistentBPPV 0e diagnostic causality graph is shown in Figure 9which is based on the causality simplification of Figure 20e resulting ranked independent probabilities of B231B281 B291 and B321 are listed in Table 4 By explicitlyrepresenting the disease causes symptoms pathogenesisand the latent correlations among medical informationFigure 9 offers intuitive insights into the underlying path-ological mechanisms

313 Other Validated BPPV Subtype Cases A verificationexperiment on some other clinical cases was performed toevaluate the effectiveness of the proposed method 0ecorrectness was based on the otoneurologistsrsquo judgement onthe diagnostic outcomes in contrast to the practical con-clusions In the clinical center for vertigo in BeijingChaoyang Hospital BPPV cases are common howeverthere are multiple repetitions in the meaningful informationfor the BPPV patients on their medical histories and physicalexaminations regarding subtype differentiation Based on

this 75 typical BPPV cases were selected from the thousandsof cases containing medical records interviews and physicalassessments in the verification experiments 0e BPPVsubtypes involved are outlined in Table 5 0e selectionprinciple of BPPV cases was based on the internationaldiagnostic criteria for BPPV [36] and the typicality andrepresentativeness of BPPV subtype diseases Notably sincethe nystagmus cannot be observed for a subjective BPPVcase it is difficult to classify the case either as canalithiasisBPPV or cupulolithiasis BPPV

0e diagnostic outcomes of the DUCG-based modelagreed with the otoneurologistsrsquo conclusions with a cor-rectness index of 100 Based on the available publishedliterature no other research has reported a model-basedautomatic subtype differentiation of BPPV in the past

32 Comparative Analysis of DUCG and BN 0e maindifference between DUCG and BN in terms of the theoreticalframework is that the model structure and parameters ofDUCG are decoupled By virtue of such a feature the in-dependent causality representation by the weighted causalityfunction event Ankij in DUCG makes it possible to simplifythe original causality graph based on the collected medicalevidence 0e irrelevant and meaningless events and rela-tions are thus eliminated from the model Taking the sim-plified causality graph as the basis of diagnostic reasoningreduces the computational scale and complexity to a largeextent In contrast BN cannot be easily simplified owing tothe structural coupling feature among the variables thecausalities among the child-parent events in BN are typicallyrepresented through a joint probability distribution (eg aconditional probabilistic table CPT) in case any variablesand relations are removed from a BN the remaining pa-rameters in the CPTs may need major adjustments more-over the number of parameters specified in a CPTfor a BN isexponential to the number of the parent variables and statesinvolved while the parameters needed in the DUCG are lessthan the parameters in a BN

Others

B1X3

X4

X5

Others

X3

X4

X5

B2

BV

(a)

Others

X3

X4

Others

X3

X4

BV

B1

B2

(b)

Figure 6 Example of DBV (a) Example 1 (b) Example 2

Figure 7 Diagnostic causality graph for Case 1

10 Computational and Mathematical Methods in Medicine

Furthermore by the independence representation andautomatic normalization feature for the weighted logic eventexpansion the ldquoself-reliantrdquo chaining inference and logicoperations can be performed in DUCG 0e parameters andinformation that are eliminated during the causality simpli-fication and those that are not involved in the chaining in-ference can all be missing (or some parameters which are notof concern are thus not provided) during this reasoningprocess and do not affect the diagnostic accuracy 0e diag-nostic inference method under incomplete information in-dicates that some unnecessary clinical tests and inappropriatemedications can be omitted thereby decreasing the patientsrsquo

medical costs For a BN the reasoning accuracy depends onthe completeness of the parameters in the CPTs

33 Application Analysis 0e proposed method can be de-veloped as an automatic diagnostic system for clinicians Basedon the compact independent and graphical causality repre-sentation using DUCG the model construction and diagnosis

(a) (b)

(c)

Figure 8 Individual causality tracking graphs of the hypotheses for Case 1 (a) LSCC-BPPV (B24) (b) Idiopathic BPPV (B28) (c)Cupulolithiasis BPPV (B30)

Table 3 Diagnostic reasoning results of Case 1

BPPVsubtype Description Ranked independent

probabilityB241 LSCC-BPPV 00388B281 Idiopathic BPPV 09542

B301Cupulolithiasis

BPPV 0007

H11 B241B281B301 1

Figure 9 Diagnostic causality graph for Case 2

Table 4 Diagnostic reasoning results of Case 2

BPPVsubtype Description Ranked independent

probabilityB231 PSCC-BPPV 01435B281 Idiopathic BPPV 07653

B291Canalithiasis

BPPV 00091

B321 Persistent BPPV 00821H11 B231B281B291B321 1

Table 5 BPPV subtypes involved in the validated cases

BPPV subtype No of casesPSCC 53ASCC 1LSCC 16MSCC 5Idiopathic 55Secondary 16Canalithiasis 61Cupulolithiasis 8Subjective 4Persistent 4Recurrent 8Typical 59

Computational and Mathematical Methods in Medicine 11

application are both easy to implement For a patient theclinical data through can be obtained through inquiry physicalexamination and auxiliary examination among others Nextthe clinical data including symptoms signs examination andtest data are input into the diagnostic reasoning interface ofthe system and the diagnosis results can be obtained throughreasoning calculation 0e clinical application of this methodis thus very convenient 0rough incorporation into the au-tomatic medical devices this method could improve the ef-ficiency of BPPV diagnosis and therapy especially for generalpractitioners in primary health care institutions In additionthe system can also be used inmobile and Internet terminals asa secondary tool for telemedicine finally it can serve as ateaching tool for doctor training in related disciplines

4 Summary

0is study proposes a DUCG method for differential di-agnosis of BPPV To distinguish among various causes ofvertiginous disorders with similar symptoms the proposedmethod involves a graphical and compact representation inaddition to logical reasoning algorithms for pathologicalmechanisms and related uncertain causalities New algo-rithms of differential diagnostic reasoning are proposed byintegrating a pruning strategy in the causality simplificationprocess a maximizing concurrent basic event set strategy inthe formulation of hypothesis space and the weighted logicinference rules for subtype differentiation of BPPV Fur-thermore a scheme of dummy basic variable is introduced tosettle the problems related to mutually exclusive root causeevents 0e model manifests higher correctness favorablerobustness to incomplete evidence and satisfactory dis-criminatory power for BPPV subtypes Furthermore usingthe diagnostic reasoning method and graphical represen-tation mechanism not only provides a diagnostic result butalso explains the rationale for suggesting the diseases whichjustifies the probability results

In light of these encouraging preliminary results moreclinical studies will be performed Furthermore a newmethod of probabilistic prediction for the vestibular dys-function-induced fall risk will be the subject of our futureresearch endeavors

Data Availability

0e data used to support the findings of this study are se-lected from the clinical cases of Department of Otorhino-laryngology Head and Neck Surgery Beijing Chaoyanghospital Requests for access to these data should be made toYanjun Wang (docwyjn163com Beijing Chaoyanghospital)

Disclosure

Chunling Dong and Yanjun Wang are cofirst authors

Conflicts of Interest

0e authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

0is work was supported in part by the National NaturalScience Foundation of China under Grant no 71671103 andin part by the Fundamental Research Funds for the CentralUniversities under Grant nos CUC2019B023CUC19ZD008 and CUC19ZD007

References

[1] N Bhattacharyya R F Baugh L Orvidas et al ldquoClinicalpractice guideline benign paroxysmal positional vertigordquoOtolaryngologymdashHead and Neck Surgery vol 139 no 5_suppl pp S47ndashS81 2008

[2] J S Oghalai S Manolidis J L Barth M G Stewart andH A Jenkins ldquoUnrecognized benign paroxysmal positionalvertigo in elderly patientsrdquo OtolaryngologymdashHead and NeckSurgery vol 122 no 5 pp 630ndash634 2000

[3] M P Prim-Espada J I De Diego-Sastre and E Perez-Fernandez ldquoEstudio metaanalıtico de la eficacia de la man-iobra de Epley en el vertigo posicional paroxıstico benignordquoNeurologıa vol 25 no 5 pp 295ndash299 2010

[4] L S Parnes S K Agrawal and J Atlas ldquoDiagnosis andmanagement of benign paroxysmal positional vertigo(BPPV)rdquo Canadian Medical Association Journal vol 169no 7 pp 681ndash693 2003

[5] J C Li and J Epley ldquo0e 360-degree maneuver for treatmentof benign positional vertigordquo Otology amp Neurotology vol 27no 1 pp 71ndash77 2006

[6] R Isola R Carvalho and A K Tripathy ldquoKnowledge dis-covery in medical systems using differential diagnosisLAMSTAR and $k$-NNrdquo IEEE Transactions on InformationTechnology in Biomedicine vol 16 no 6 pp 1287ndash1295 2012

[7] A L Barabasi N Gulbahce and J Loscalzo ldquoNetworkmedicine a network-based approach to human diseaserdquoNature Reviews Genetics vol 12 no 1 pp 56ndash68 2011

[8] E Mira A Buizza G Magenes M Manfrin and R SchmidldquoExpert systems as a diagnostic aid in otoneurologyrdquo Journalfor Oto-Rhino-Laryngology and Its Related Specialties (ORL)vol 52 no 2 pp 96ndash103 1990

[9] C E S Gavilan J E Gallego and J Gavilan ldquoCarnisel anexpert system for vestibular diagnosisrdquo Acta Oto-Lar-yngologica vol 110 no 3-4 pp 161ndash167 1990

[10] E Kentala I Pyykko Y Auramo J Laurikkala andM Juhola ldquoOtoneurological expert system for vertigordquo ActaOto-Laryngologica vol 119 no 5 pp 517ndash521 1999

[11] E Kentala K Viikki I Pyykko andM Juhola ldquoProduction ofdiagnostic rules from a neurotologic database with decisiontreesrdquo Annals of Otology Rhinology and Laryngology vol 109no 2 pp 170ndash176 2000

[12] J W Song J H Lee J H Choi and S J Chun ldquoAutomaticdifferential diagnosis of pancreatic serous and mucinouscystadenomas based on morphological featuresrdquo Computersin Biology and Medicine vol 43 no 1 pp 1ndash15 2013

[13] M H Lopes N R Ortega P S Silveira E Massad R Higaand F Marin Hde ldquoFuzzy cognitive map in differential di-agnosis of alterations in urinary elimination a nursing ap-proachrdquo International Journal of Medical Informatics vol 82no 3 pp 201ndash208 2013

[14] C Salvatore A Cerasa I Castiglioni et al ldquoMachine learningon brain MRI data for differential diagnosis of Parkinsonrsquosdisease and Progressive Supranuclear Palsyrdquo Journal ofNeuroscience Methods vol 222 pp 230ndash237 2014

12 Computational and Mathematical Methods in Medicine

E A3172A7281A112121A10210DA9161A6181A8121B21

middot12

1113874 1113875A5121B21 +12

1113874 1113875A5141A4181A8121B211113874 1113875

12

1113874 1113875A3172A7281A112121A10210DA9161A6181A8121

middot A5121B21 +12

1113874 1113875A3172A7281A112121A10210DA9161

middot A6181A5141A4181A8121B21

(6)

Similarly the expanding expression of E in the causalitycontext of B11 is

E A3172A7281A112121A10210DA9161A6181A5141

middot A4181A8111B11

(7)

Finally hypothesis space SH under evidence E is ob-tained as follows SH H11 H211113966 1113967 where H11 equiv B11 andH21 equiv B21 0erefore the two hypotheses are determined asthe probable causes of the observed evidence as both canindependently interpret all the symptoms 0e probabilisticcalculation results are hs

11 0679 and hs21 0321 0e

inference results can be explained using the graphicalcausality semantics as shown in Figure 1(b) Based on thesesemantics users can not only deduce the results but alsounderstand their logic

Based on the self-reliant chaining inference the missingparameters such as a3172 a7281 a112121 a10210D a9161and a6181 do not have an impact on the reasoning resultMoreover the most probable hypotheses could be typicallydetermined uniquely just within the logical reasoningprocess (before the probabilistic reasoning is performed)0us the causality structure that accurately represents thedisease pathogenesis is what really matters It is evident thatDUCG does not impose stringent requirements for com-pleteness of the parameters and clinical examination data0us it can be used to facilitate modeling through medicalknowledge and experience

22 Construction of Differential Diagnosis Model for BPPV

221 BPPV Characteristics

(1) Pathophysiology of BPPV0e vestibular receptor consistsof two otolith organs (the utricle and saccule) which overseelinear acceleration and gravity as well as three semicircularcanals (SCCs) that sense angular acceleration 0e SCCsinclude anterior SCCs (ASCCs) posterior SCCs (PSCCs)and lateral SCCs (LSCCs) 0e afferent nerves from otolithorgans and SCCs project symmetrical activities to the centralvestibular system to maintain the balance and spatial ori-entation BPPV results from misplaced calcium carbonatecrystals (otoconia) that are detached from utricle macula andcollected within the SCCs due to trauma infection or even

aging 0ese crystals either remain free-floating in the SCCsor become attached to the cupula Normally as the motionsensor of SCCs that are filled with endolymph cupula is agelatinous mass with the same density as endolymph Sincethe calcium particles are denser than the endolymph andcupula the SCCs become pathologically sensitive to linearacceleration and gravity the afferent nerves from SCCs thusfire asymmetrically leading to vertigo and nystagmusWhenmoving into the SCC the calcium carbonate crystal debrismay cause endolymph movement which consequentlystimulates the cupula of the affected canal during headmovement or while stationary (this is called canalithiasis)Similarly if adherent to the cupula the particles may alsoactivate it (this is called cupulolithiasis) [32]

(2) Clinical Characteristics of BPPV BPPV is characterizedby brief attacks of vertigo after lying down in bed looking upor bending down among others 0e vertigo attacks in mostcases last less than 1sim2 minutes and mostly occur at night orupon awakening [1] 0e diagnosis rests on the observationof characteristic nystagmus accompanying symptoms ofvertigo when a patientrsquos head is moved into a specific ori-entation with respect to gravity 0is is due to shred calciumcrystals from macula which may cause age-related changesin the protein and gelatinous matrix of the otolithicmembrane Although most of BPPV cases are idiopathic asignificant proportion can be associated with precedingtraumatic events including head trauma dental treatmentand ear surgery Other conditions such as viral vestibularneuritis otitis media Menierersquos disease idiopathic suddensensorineural hearing loss posterior circulation ischemiaand migraine can also trigger cases of BPPV

BPPV may affect each of the three SCCs Alternatively itcan affect more than one canal simultaneously resulting invarying nystagmus patterns [33] Notably due to its gravity-dependent position the most commonly affected semicir-cular canal is the posterior canal 0e positional and posi-tioning tests (eg DixndashHallpike diagnostic maneuver andsupine roll test) can provide an accurate diagnosis for thiscondition Furthermore the features of nystagmus in-cluding latency direction duration reversal and fatiga-bility are significant during diagnosis

(3) Subtype Differentiation of BPPV Based on the epide-miology causes of disease pathophysiology anatomy pa-thology clinical features and treatment outcomes a BPPVdisease may be classified into distinct categories along fourdimensions (1) depending on the localization of the par-ticles and the involved semicircular canals there are foursubtypes (PSCC ASCC LSCC and multiple-SCC (MSCC))(2) BPPV is subdivided into idiopathic BPPV and secondaryBPPV as it may occur as a primary disease or secondary toother otology disorders or systemic conditions [4] (3) BPPVcan be divided into canalithiasis and cupulolithiasisdepending on the nystagmus provoked characteristics fromthe positioning test based on the pathophysiology mecha-nism [32] and (4) based on the clinical features andtreatment outcomes BPPV falls into two categories typicaland atypical 0e atypical BPPV can be further identified as

Computational and Mathematical Methods in Medicine 5

subjective BPPV persistent BPPV and recurrent BPPVSubjective BPPV refers to the cases associated with a positivehistory of BPPV and DixndashHallpike or supine roll tests whichare positive for vertigo but negative for nystagmus [34] Apersistent BPPV refers to cases lasting for more than twoweeks while a recurrent BPPV indicates recurrence of BPPVin the same canal after a symptom-free interval of at leasttwo weeks from a previously successful treatment [35]

222 Constructed Model for Differential Diagnosis of BPPVAs a causality representation to the aforementioned path-ogenesis and pathophysiology of BPPV a new DUCG-basedcausality graph was constructed based on the vertigo modelpresented in [30] 0e BPPV differential diagnosis model isshown in Figure 2 it includes 125 variables (X-type 85 D-type 8 G-type 21 and B-type 11) and 286 arcs

(1) Modularized Modeling Scheme A modularized modelingscheme is applied in the construction of the causality graphshown in Figure 2 All BPPV subtypes are handled as in-dividual sub-DUCGs For example the three sub-DUCGsrepresenting the idiopathic PSCC LSCC and cupuloli-thiasis BPPV are demonstrated in Figures 3ndash5 respectivelyWhen the sub-DUCGs are merged solutions are proposedfor addressing the ambiguous contradictory and incom-plete information to ensure global coherence [30] Such amodularized modeling scheme reduces the difficulty inmodel construction using a divide-and-conquer approach

(2) Definition of Variables Based on the characteristics ofBPPV and the international diagnostic criteria [36] themedical information of patients including symptoms signsfindings of examinations medical histories etiology andpathogenesis pathophysiology and socio-psychological andenvironmental factors is incorporated into the model Table 2lists some of the variables of the model shown in Figure 2

(3) Representation of Causal Relationships In this repre-sentation arcs are established to represent and quantifycausal correlations among related symptoms and diseaseorigins complex causalities are denoted by a combination ofcausal functions via logic gates All causalities and param-eters in Figure 2 are determined by otoneurologists based ontheir knowledge experience epidemiology statistics andresearch achievements As stated before both the incom-pleteness of knowledge and imprecision of parameters havelittle impact on the reasoning accuracy thus DUCG is moreflexible for the model construction

23 e Algorithm of Differential Diagnostic ReasoningDifferential diagnosis aims at narrowing down the diseases tothe most probable one from a list of candidate diseases thatshow similar symptoms 0e differential diagnostic reasoningalgorithm is presented as Algorithm 1 which implements ahypothesis-driven process 0e posterior probability of thehypothesis event Hkj is used to quantify Hkjrsquos ability tointerpret the medical evidence E Notably a rare disease doesnot necessarily respond to a weak causality If a rare disease

(with a low prior probability) better explains a patientrsquossymptoms and medical evidence then the strength of thecausality functions can be high thus the disease will get ahigher ranked probability as a hypothesis event

231 New Causality Simplification Mechanisms Based onthe collected medical evidence E for a patient the process ofcausality simplifications is performed to the BPPV causalitygraph Causality simplification aims to eliminate the irrel-evant meaningless and impossible events and relationsfrom a causality graph 0erefore the model scale andcomplexity are both significantly decreased and the diseasehypothesis space converges0e root cause event can even bepreliminarily determined based on the simplified causalitygraph

As a complement to the original simplification rules ofDUCG [28 30] several new causality simplificationmechanisms including a pruning strategy and causalitytracking process are presented

Definition 1 (Pruning Strategy) 0e meaningless diseasehypothesis and its corresponding causalities are identifiedand pruned from the causality graph using a scheme ofcausality tracking for all the abnormal evidences

Definition 2 (Causality Tracking Process) 0e causalitytracking process starts from an observed event and traces itsupstream causality chains and ancestors back towards the B-type event(s) For any Bi only if all the abnormal evidence isreachable to it via a causality tracking process can it beidentified as a candidate hypothesis otherwise Bi should beeliminated from the hypothesis space and its correspondingcausalities should be pruned from the graph

232 Weighted Logic Inference Rules of Differential Diag-nosis for BPPV Based on the simplified causality graph andmedical evidence the process of logical inference is per-formed to obtain the hypothesis space according to (1)sim(3)Our earlier study showed that by applying event expandingand logical operations the logical inference can effectivelydecrease the complexity of probabilistic reasoning [28]However in response to BPPV differential diagnosis theweighted logic inference algorithm requires majormodifications

Some BPPV subtypes can be present in a patient si-multaneously For instance a diagnosis can be termed as anASCC-idiopathic-canalithiasis BPPV Such a case is knownas concurrency of subtypes Meanwhile the subtypes be-longing to the same category are mutually exclusive when adiagnostic conclusion is drawn Some examples of this arePSCC-BPPV (B231) LSCC-BPPV (B241) ASCC-BPPV(B251) and MSCC-BPPV (B261) 0erefore to deal withthese cases new weighted logic inference rules for exclusionand concurrency among others are developed as shownbelow

Rule 1 Suppose that the basic events (namely root causeevents) in a BPPV differential diagnosis model are

6 Computational and Mathematical Methods in Medicine

represented in terms of category sets as C1 B231 B241B251 B261 C2 B271 B281 C3 B291 B301 andC4 B311 B321 B331 State 1 of a B-type event indicatesthat the root cause event has occurred on the contrary state0 of a B-type event indicates that the root cause event has notoccurred 0e mutual exclusion rules for basic events inBPPV differential diagnosis can thus be defined asBi1Biprime 1 0 where Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 )

Proof From the definition the category sets C1 C2 and C3indicate different classification perspectives of BPPV0erefore all basic events within the same category set areexclusive and exhaustive Specifically there is B231B241 0

B231B251 0 B231B261 0 B241B251 0 B241B261 0B251B261 0 B271B281 0 and B291B301 0

Rule 2 Bi1Biprime 1 ne 0 for Bi Biprime isin C4 (ine iprime) and Bi1Biprime 1 ne 0 forBi1 isin Cm Biprime1 isin Cn(ine iprime mne n)

Proof 0e events in C4 describe the respective differenttypes of atypical BPPV in an overlapping manner Namelyall the basic events in B311 B321 B331 are likely to beconcurrent 0is sets the basis for Rule 2

Definition 3 (Maximizing Concurrent Basic Event SetStrategy) To obtain an ultimate disease hypothesis Hkj ifthe events that constitute Hkj are concurrent and consistentwith each other the maximum number of basic eventswithin the hypothesis space SH should be incorporated

It is essential to explore every possible outcome beforeruling out any basic event For example as SH B241 B281B301 is obtained for a case we should get only the correcthypothesis H11 B241B281B301 ne 0 in which the threeevents together interpret the observed symptoms ratherthan B241B281 B281B301 or so on

Rule 3 Given V isin B X G D jne jprime and integer yge 2then (Vij)

y Vij and VijVij 0

Figure 2 0e DUCG-based differential diagnostic causality graph for BPPV

Figure 3 Sub-DUCG for LSCC-idiopathic-recurrent BPPV

Figure 4 Sub-DUCG for PSCC-idiopathic-recurrent BPPV

Figure 5 0e sub-DUCG for cupulolithiasis BPPV

Computational and Mathematical Methods in Medicine 7

Rule 4 Given integer yge 2 kne kprime and jne jprime then(Fnkij)

y (rnirn)yAnkij FnkijFnkprimeij 0 FnkijFnkijprime 0 andFnkijFnkprimeijprime 0 if Bi1Biprime 1 0 is given Bi1 Biprime 1 isin Cm

ine iprime m isin 1 2 3 then it follows that Fnkiprime1Bi1 0 Fnki1Biprime1 0 and Fnki1Fnkiprime1 0

Proof 0e latter part of Rule 4 is based on Rule 1 and theother part has been proven in [28] From Rule 1 Bi1Biprime 1 0which implies that the basic events Bi1 and Biprime1 cannot beconcurrent and consequently brings about the mutual ex-clusions among the function events related to Bi1 and Biprime10erefore Anki1Ankiprime1 0 and Fnki1Fnkiprime1 0 as Anki1cannot be present in combination with Ankirsquo1 similarlythen Fnkiprime1Bi1 0 and Fnki1Biprime1 0 Notably Fnki1Fnkiprime0ne 0 is true because Anki1 and Ankiprime0 are independent ofeach other (since they are given independently)

Rule 5 1113936Mm11113937iisinSm

FnkijiViji

(1113936Mm11113937iisinSm

(rnirn))1113937

iisinS1AnkijiViji

where Sm denotes the set of variable number ina product item m isin 12 M and S1 sube S2 sube middot middot middot sube SM

Rule 6 Suppose that no mutually exclusive basic eventscoexist in the candidate hypothesis space thenFnkijVij(1113936iprimeFnkiprimej

iprimeViprimej

iprime) FnkijVij if j ji is given

Proof To complement the ordinary conditions of Rule 14discussed in [28] consider a situation related to mutuallyexclusive basic events Vij Bi1 and VijprimeBiprime1Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 ) as proposed in Rule 10eproposition of Rule 6 can thus be represented as

FnkijVij 1113944

iprime

FnkiprimejiprimeViprimej

iprime⎛⎝ ⎞⎠ FnkijVij middot FnkijVij

+ FnkijVij middot 1113944

iprime ne i

FnkiprimejiprimeViprimej

iprime

rnirn1113872 11138732AnkijVij

neFnkijVij

(8)

0e inclusion of mutually exclusive events leads to theaforementioned outcomes (ie the inconsistence betweenRule 1 and Rule 6) and the autonormalization feature nolonger holds 0erefore a solution for BPPV subtype dif-ferentiation known as a scheme of dummy basic variable(DBV) is proposed

233 Scheme of Dummy Basic Variable

Definition 4 (DBV) If mutually exclusive candidate hy-potheses coexist in the candidate hypothesis space ieBi1Biprime 1 0 Bi1 Biprime1 isin Cm(ine iprime m isin 1 2 3 ) Bi1 andBiprime1are converted into different states of a DBV each state of theDBV elicits an individual pathogenesis causality graphaccording to the hypothesis related to that state the specificcausalities of different diseases can be distinguished by theA-parameter values of DBV which can either be zero or not0e exclusive rules among basic events are thus transformedinto an inherent exclusive law among the states of an event

Table 2 Definition of variables for differential diagnosis of BPPV

Variables Descriptions

X1ndash3201ndash206

210ndash217

Pathophysiology of BPPV the lesion of theotolithic membrane of utricle macula thedegenerated otolith broken off from utriclemacula misplaced calcium carbonate crystalsdebris calcium free-floating particles enteringthe SCCs calcium particles adherent to the

cupula of SCC the endolymph movement withfree-floating particles that pathologicallystimulates the ampulla of canal and the

sensitivity to linear acceleration and gravityinduced by the abnormal deflection of cupula

X48ndash11

0e description of vertigo an illusion ofmovement the sensation that objects in the

environment is moving when the eyes are openand the sensation that a patient feels as if he or

she is moving when the eyes are closed

X1142454682

0e main accompanying symptomsspontaneous nystagmus and autonomic nerve

symptoms

X20-25

0e detailed description of the features ofvertigo attacks attack characteristics the onsetand duration of an attack causes of disease

frequency and severity

X26ndash28209

Changes in head position relative to gravityrotation of the head relative to the body while in

an upright position

X83ndash871300e feature of spontaneous nystagmus and the

Romberg test for vestibular function

X5249161163238

Other accompanying symptoms cochlearsymptoms hearing loss tinnitus the symptoms

of central nervous system and themanifestations of the primary and underlying

disordersX184185 Patientrsquos gender and age

X186189198234

0e typical and characteristic medical history amigraine hypertension head trauma and inner

ear pathology

X207ndash208

More than one semicircular canal is affectedsimultaneously (obtained statistically duringthe pretreatment process of medical data)

X218ndash221227228Positioning test vertigo and nystagmus when

the head is moving or rotating

X222ndash226

DixndashHallpike test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)

X229ndash233

Supine roll test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)X236 0e outcomes of the maneuver treatment

B23ndash33

PSCC-BPPV (B23) LSCC-BPPV (B24) ASCC-BPPV (B25) MSCC-BPPV (B26) secondary

BPPV (B27) idiopathic BPPV (B28)canalithiasis BPPV (B29) cupulolithiasis BPPV(B30) subjective BPPV (B31) persistent BPPV

(B32) and recurrent BPPV (B33)

8 Computational and Mathematical Methods in Medicine

0e problem of disobeying the autonormalization fea-ture can thus be addressed 0is method is illustrated via anexample in Figure 6(a) Suppose that B11 and B21 aremutually exclusive events 0ey are then combined into aDBV-Bv during the reasoning process corresponding to Bv1and Bv2 respectively From the definition of DBVa31v1 equiv a3111 a41v2 equiv a4121 a51v2 equiv a5121 and rnv equiv rniwhere i isin 1 2 and n isin 3 4 5 Figure 6(b) shows an ex-ample where an event (eg X3) is connected to more thanone basic event In this case rnv is defined as rnv equiv 1113936irni ifFnine 00us r3v r31 + r32 for the case in Figure 6(b) whichpoints out to a combination of basic events

In the context of differential diagnosis and upon thecompletion of causality simplifications the obtained can-didate hypotheses of C1 B231 B241 B251 B261 (there aremore than one basic event in the set) should be combinedinto a DBV-Bm with Bmk denoting Bi1 where k 1 2 3 4and i 23 24 25 26 PrBmk refers to the prior probabilityof Bi1 and Pr Bm01113966 1113967 1 minus 1113936kne0Pr Bmk1113966 1113967

Definition 5 (Ranked Independent Probability) 0e rankedindependent probability represents a new metric proposedfor quantifying the degree of confidence in whether a BPPVsubtype (eg Bi1 as a part of the hypothesis Hkj) can in-dependently interpret all the medical evidence in com-parison with the other subtypes coexisting in Hkj 0eranked independent probability of Bi1 is calculated as fol-lows (1) get hs

i1 of Bi1 according to (2) and (3) in which ζi isbased on the individual causality tracking graph of Bi1 and(2) for all the Bi1 within the set of Hkj hs

i1 is ranked byhs

i11113936ihsi1

24 eoretical Analysis of the Reasoning Complexity 0einference algorithm for the proposed method reduces thereasoning complexity in two ways First the causality graphsimplification and pruning strategy significantly decreases themodel scale 0e variables that are irrelevant or inconsistentwith the medical evidence are excluded from the reasoning

calculation 0is significantly reduces the computationalcomplexity Moreover the diagnostic reasoning conclusioncan even be accurately drawn solely via the causality sim-plification Second prior to probabilistic reasoning weightedlogic inference is performed based on the simplified causalitygraph 0us the multiple connected causalities can bedecomposed independently leading the chaining inference toexhibit high efficiency Furthermore the proposed logicalinference rules and logical operations can decrease thecomplexity and scale of logical event expressions

0e actual efficiency tests for the DUCG inference al-gorithm have been performed using online fault diagnosisdata from several large-scale industrial systems (eg nuclearpower plants) in which thousands of variables and causalityarcs are involved [28 31] 0e diagnostic reasoning cantypically be finished within 05ndash1 s (on a personal computer)Moreover the inference efficiency has been verified from ourpast clinical diagnosis applications that involved dozens ofdiseases such as jaundice and sellar region disease

3 Experiments and Analyses

31 Clinical Validation of the BPPV Differential DiagnosisMethod

311 Differential Diagnosis for BPPVmdashCase 1 Suppose thatthe medical evidence of a patient was observed in part asX41 X212 X243 X1844 X1852 X2094 X2292 X2302 X2070X2080 X2360 in Figure 2 and other X-type variables arenormal or unknown (incomplete medical information) 0emedical information in this experiment is from a 65-year-oldfemale patient who suffered from brief episodes of vertigowhen rolling over in bed for two weeks and was suspected tobe a BPPV case according to the supine roll test

Based on the evidence in this case Figure 2 can besimplified into the graph shown in Figure 7 by applying thecausality simplification rules and pruning strategy Manymeaningless relationships and events under current situa-tion are eliminated accordingly with SH B241 B281 B301

BeginFor a BPPV patientCollect medical evidence E including symptoms signs examination findings laboratory tests and medical historiesPerform causality simplification to the BPPV causality graph based on the evidence EApply the causality simplification mechanisms including the pruning strategy and causality tracking processObtain the simplified diagnostic causality graph

Perform the algorithms of weighted logic inference based on the simplified causality graphPerform the weighted logic event expansion to the evidence according to (1)Perform logic inference according to (2)

Apply the weighted logic inference rules 1sim6 of differential diagnosis for BPPVApply the scheme of dummy basic variablePerform the basic logic operations

Obtain the hypothesis event space SH Hkj1113966 1113967

Perform the probabilistic reasonings to obtain the posterior probability of Hkj conditioned on E hskj

Calculate the ranked independent probability of a BPPV subtypeEnd

ALGORITHM 1 Differential diagnostic reasoning method for BPPV

Computational and Mathematical Methods in Medicine 9

being inferred as the possible root causes 0e resultinghypothesis space SH is concise with all unlikely hypothesesbeing excluded from concern Moreover the individualcausality tracking graphs for the three root cause events B24B28 and B30 in Figure 7 are shown in Figure 8 whereby eachsubgraph independently covers all evidence0e graphs thusintuitively and faithfully represent the causalities underlyingthe pathogenesis of Case 1

By applying the algorithm of differential diagnosticreasoning for Case 1 the state probability ofH11 B241B281B301 can be obtained as hs

11

Pr H11 | E1113966 1113967 1 0e obtained ldquoranked independent prob-abilitiesrdquo of B241 B281 and B301 are listed in Table 3 0eLSCC-idiopathic-cupulolithiasis BPPV is therefore deter-mined as the diagnostic result of Case 1 this result isconsistent with the clinical conclusions confirmed byotoneurologists

312 Differential Diagnosis for BPPVmdashCase 2 A 72-year-old female patient complained about paroxysmal positionalvertigo for a month the attacks of vertigo were brief lastingfor one minute the vertigo frequently occurred whilelooking up or down0us the medical evidence for this caseis X41 X212 X243 X1844 X1852 X2070 X2080 X2093 X2223X2231 X2241 X2251 X2261 X2360 the other X-type variablesare normal or unknown (incomplete medical information)

By applying the algorithm of differential diagnosticreasoning the hypothesis event H11 B231B281B291B321 isuniquely determined as the origin of the disease whichindicates a PSCC-idiopathic-cupulolithiasis-persistentBPPV 0e diagnostic causality graph is shown in Figure 9which is based on the causality simplification of Figure 20e resulting ranked independent probabilities of B231B281 B291 and B321 are listed in Table 4 By explicitlyrepresenting the disease causes symptoms pathogenesisand the latent correlations among medical informationFigure 9 offers intuitive insights into the underlying path-ological mechanisms

313 Other Validated BPPV Subtype Cases A verificationexperiment on some other clinical cases was performed toevaluate the effectiveness of the proposed method 0ecorrectness was based on the otoneurologistsrsquo judgement onthe diagnostic outcomes in contrast to the practical con-clusions In the clinical center for vertigo in BeijingChaoyang Hospital BPPV cases are common howeverthere are multiple repetitions in the meaningful informationfor the BPPV patients on their medical histories and physicalexaminations regarding subtype differentiation Based on

this 75 typical BPPV cases were selected from the thousandsof cases containing medical records interviews and physicalassessments in the verification experiments 0e BPPVsubtypes involved are outlined in Table 5 0e selectionprinciple of BPPV cases was based on the internationaldiagnostic criteria for BPPV [36] and the typicality andrepresentativeness of BPPV subtype diseases Notably sincethe nystagmus cannot be observed for a subjective BPPVcase it is difficult to classify the case either as canalithiasisBPPV or cupulolithiasis BPPV

0e diagnostic outcomes of the DUCG-based modelagreed with the otoneurologistsrsquo conclusions with a cor-rectness index of 100 Based on the available publishedliterature no other research has reported a model-basedautomatic subtype differentiation of BPPV in the past

32 Comparative Analysis of DUCG and BN 0e maindifference between DUCG and BN in terms of the theoreticalframework is that the model structure and parameters ofDUCG are decoupled By virtue of such a feature the in-dependent causality representation by the weighted causalityfunction event Ankij in DUCG makes it possible to simplifythe original causality graph based on the collected medicalevidence 0e irrelevant and meaningless events and rela-tions are thus eliminated from the model Taking the sim-plified causality graph as the basis of diagnostic reasoningreduces the computational scale and complexity to a largeextent In contrast BN cannot be easily simplified owing tothe structural coupling feature among the variables thecausalities among the child-parent events in BN are typicallyrepresented through a joint probability distribution (eg aconditional probabilistic table CPT) in case any variablesand relations are removed from a BN the remaining pa-rameters in the CPTs may need major adjustments more-over the number of parameters specified in a CPTfor a BN isexponential to the number of the parent variables and statesinvolved while the parameters needed in the DUCG are lessthan the parameters in a BN

Others

B1X3

X4

X5

Others

X3

X4

X5

B2

BV

(a)

Others

X3

X4

Others

X3

X4

BV

B1

B2

(b)

Figure 6 Example of DBV (a) Example 1 (b) Example 2

Figure 7 Diagnostic causality graph for Case 1

10 Computational and Mathematical Methods in Medicine

Furthermore by the independence representation andautomatic normalization feature for the weighted logic eventexpansion the ldquoself-reliantrdquo chaining inference and logicoperations can be performed in DUCG 0e parameters andinformation that are eliminated during the causality simpli-fication and those that are not involved in the chaining in-ference can all be missing (or some parameters which are notof concern are thus not provided) during this reasoningprocess and do not affect the diagnostic accuracy 0e diag-nostic inference method under incomplete information in-dicates that some unnecessary clinical tests and inappropriatemedications can be omitted thereby decreasing the patientsrsquo

medical costs For a BN the reasoning accuracy depends onthe completeness of the parameters in the CPTs

33 Application Analysis 0e proposed method can be de-veloped as an automatic diagnostic system for clinicians Basedon the compact independent and graphical causality repre-sentation using DUCG the model construction and diagnosis

(a) (b)

(c)

Figure 8 Individual causality tracking graphs of the hypotheses for Case 1 (a) LSCC-BPPV (B24) (b) Idiopathic BPPV (B28) (c)Cupulolithiasis BPPV (B30)

Table 3 Diagnostic reasoning results of Case 1

BPPVsubtype Description Ranked independent

probabilityB241 LSCC-BPPV 00388B281 Idiopathic BPPV 09542

B301Cupulolithiasis

BPPV 0007

H11 B241B281B301 1

Figure 9 Diagnostic causality graph for Case 2

Table 4 Diagnostic reasoning results of Case 2

BPPVsubtype Description Ranked independent

probabilityB231 PSCC-BPPV 01435B281 Idiopathic BPPV 07653

B291Canalithiasis

BPPV 00091

B321 Persistent BPPV 00821H11 B231B281B291B321 1

Table 5 BPPV subtypes involved in the validated cases

BPPV subtype No of casesPSCC 53ASCC 1LSCC 16MSCC 5Idiopathic 55Secondary 16Canalithiasis 61Cupulolithiasis 8Subjective 4Persistent 4Recurrent 8Typical 59

Computational and Mathematical Methods in Medicine 11

application are both easy to implement For a patient theclinical data through can be obtained through inquiry physicalexamination and auxiliary examination among others Nextthe clinical data including symptoms signs examination andtest data are input into the diagnostic reasoning interface ofthe system and the diagnosis results can be obtained throughreasoning calculation 0e clinical application of this methodis thus very convenient 0rough incorporation into the au-tomatic medical devices this method could improve the ef-ficiency of BPPV diagnosis and therapy especially for generalpractitioners in primary health care institutions In additionthe system can also be used inmobile and Internet terminals asa secondary tool for telemedicine finally it can serve as ateaching tool for doctor training in related disciplines

4 Summary

0is study proposes a DUCG method for differential di-agnosis of BPPV To distinguish among various causes ofvertiginous disorders with similar symptoms the proposedmethod involves a graphical and compact representation inaddition to logical reasoning algorithms for pathologicalmechanisms and related uncertain causalities New algo-rithms of differential diagnostic reasoning are proposed byintegrating a pruning strategy in the causality simplificationprocess a maximizing concurrent basic event set strategy inthe formulation of hypothesis space and the weighted logicinference rules for subtype differentiation of BPPV Fur-thermore a scheme of dummy basic variable is introduced tosettle the problems related to mutually exclusive root causeevents 0e model manifests higher correctness favorablerobustness to incomplete evidence and satisfactory dis-criminatory power for BPPV subtypes Furthermore usingthe diagnostic reasoning method and graphical represen-tation mechanism not only provides a diagnostic result butalso explains the rationale for suggesting the diseases whichjustifies the probability results

In light of these encouraging preliminary results moreclinical studies will be performed Furthermore a newmethod of probabilistic prediction for the vestibular dys-function-induced fall risk will be the subject of our futureresearch endeavors

Data Availability

0e data used to support the findings of this study are se-lected from the clinical cases of Department of Otorhino-laryngology Head and Neck Surgery Beijing Chaoyanghospital Requests for access to these data should be made toYanjun Wang (docwyjn163com Beijing Chaoyanghospital)

Disclosure

Chunling Dong and Yanjun Wang are cofirst authors

Conflicts of Interest

0e authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

0is work was supported in part by the National NaturalScience Foundation of China under Grant no 71671103 andin part by the Fundamental Research Funds for the CentralUniversities under Grant nos CUC2019B023CUC19ZD008 and CUC19ZD007

References

[1] N Bhattacharyya R F Baugh L Orvidas et al ldquoClinicalpractice guideline benign paroxysmal positional vertigordquoOtolaryngologymdashHead and Neck Surgery vol 139 no 5_suppl pp S47ndashS81 2008

[2] J S Oghalai S Manolidis J L Barth M G Stewart andH A Jenkins ldquoUnrecognized benign paroxysmal positionalvertigo in elderly patientsrdquo OtolaryngologymdashHead and NeckSurgery vol 122 no 5 pp 630ndash634 2000

[3] M P Prim-Espada J I De Diego-Sastre and E Perez-Fernandez ldquoEstudio metaanalıtico de la eficacia de la man-iobra de Epley en el vertigo posicional paroxıstico benignordquoNeurologıa vol 25 no 5 pp 295ndash299 2010

[4] L S Parnes S K Agrawal and J Atlas ldquoDiagnosis andmanagement of benign paroxysmal positional vertigo(BPPV)rdquo Canadian Medical Association Journal vol 169no 7 pp 681ndash693 2003

[5] J C Li and J Epley ldquo0e 360-degree maneuver for treatmentof benign positional vertigordquo Otology amp Neurotology vol 27no 1 pp 71ndash77 2006

[6] R Isola R Carvalho and A K Tripathy ldquoKnowledge dis-covery in medical systems using differential diagnosisLAMSTAR and $k$-NNrdquo IEEE Transactions on InformationTechnology in Biomedicine vol 16 no 6 pp 1287ndash1295 2012

[7] A L Barabasi N Gulbahce and J Loscalzo ldquoNetworkmedicine a network-based approach to human diseaserdquoNature Reviews Genetics vol 12 no 1 pp 56ndash68 2011

[8] E Mira A Buizza G Magenes M Manfrin and R SchmidldquoExpert systems as a diagnostic aid in otoneurologyrdquo Journalfor Oto-Rhino-Laryngology and Its Related Specialties (ORL)vol 52 no 2 pp 96ndash103 1990

[9] C E S Gavilan J E Gallego and J Gavilan ldquoCarnisel anexpert system for vestibular diagnosisrdquo Acta Oto-Lar-yngologica vol 110 no 3-4 pp 161ndash167 1990

[10] E Kentala I Pyykko Y Auramo J Laurikkala andM Juhola ldquoOtoneurological expert system for vertigordquo ActaOto-Laryngologica vol 119 no 5 pp 517ndash521 1999

[11] E Kentala K Viikki I Pyykko andM Juhola ldquoProduction ofdiagnostic rules from a neurotologic database with decisiontreesrdquo Annals of Otology Rhinology and Laryngology vol 109no 2 pp 170ndash176 2000

[12] J W Song J H Lee J H Choi and S J Chun ldquoAutomaticdifferential diagnosis of pancreatic serous and mucinouscystadenomas based on morphological featuresrdquo Computersin Biology and Medicine vol 43 no 1 pp 1ndash15 2013

[13] M H Lopes N R Ortega P S Silveira E Massad R Higaand F Marin Hde ldquoFuzzy cognitive map in differential di-agnosis of alterations in urinary elimination a nursing ap-proachrdquo International Journal of Medical Informatics vol 82no 3 pp 201ndash208 2013

[14] C Salvatore A Cerasa I Castiglioni et al ldquoMachine learningon brain MRI data for differential diagnosis of Parkinsonrsquosdisease and Progressive Supranuclear Palsyrdquo Journal ofNeuroscience Methods vol 222 pp 230ndash237 2014

12 Computational and Mathematical Methods in Medicine

subjective BPPV persistent BPPV and recurrent BPPVSubjective BPPV refers to the cases associated with a positivehistory of BPPV and DixndashHallpike or supine roll tests whichare positive for vertigo but negative for nystagmus [34] Apersistent BPPV refers to cases lasting for more than twoweeks while a recurrent BPPV indicates recurrence of BPPVin the same canal after a symptom-free interval of at leasttwo weeks from a previously successful treatment [35]

222 Constructed Model for Differential Diagnosis of BPPVAs a causality representation to the aforementioned path-ogenesis and pathophysiology of BPPV a new DUCG-basedcausality graph was constructed based on the vertigo modelpresented in [30] 0e BPPV differential diagnosis model isshown in Figure 2 it includes 125 variables (X-type 85 D-type 8 G-type 21 and B-type 11) and 286 arcs

(1) Modularized Modeling Scheme A modularized modelingscheme is applied in the construction of the causality graphshown in Figure 2 All BPPV subtypes are handled as in-dividual sub-DUCGs For example the three sub-DUCGsrepresenting the idiopathic PSCC LSCC and cupuloli-thiasis BPPV are demonstrated in Figures 3ndash5 respectivelyWhen the sub-DUCGs are merged solutions are proposedfor addressing the ambiguous contradictory and incom-plete information to ensure global coherence [30] Such amodularized modeling scheme reduces the difficulty inmodel construction using a divide-and-conquer approach

(2) Definition of Variables Based on the characteristics ofBPPV and the international diagnostic criteria [36] themedical information of patients including symptoms signsfindings of examinations medical histories etiology andpathogenesis pathophysiology and socio-psychological andenvironmental factors is incorporated into the model Table 2lists some of the variables of the model shown in Figure 2

(3) Representation of Causal Relationships In this repre-sentation arcs are established to represent and quantifycausal correlations among related symptoms and diseaseorigins complex causalities are denoted by a combination ofcausal functions via logic gates All causalities and param-eters in Figure 2 are determined by otoneurologists based ontheir knowledge experience epidemiology statistics andresearch achievements As stated before both the incom-pleteness of knowledge and imprecision of parameters havelittle impact on the reasoning accuracy thus DUCG is moreflexible for the model construction

23 e Algorithm of Differential Diagnostic ReasoningDifferential diagnosis aims at narrowing down the diseases tothe most probable one from a list of candidate diseases thatshow similar symptoms 0e differential diagnostic reasoningalgorithm is presented as Algorithm 1 which implements ahypothesis-driven process 0e posterior probability of thehypothesis event Hkj is used to quantify Hkjrsquos ability tointerpret the medical evidence E Notably a rare disease doesnot necessarily respond to a weak causality If a rare disease

(with a low prior probability) better explains a patientrsquossymptoms and medical evidence then the strength of thecausality functions can be high thus the disease will get ahigher ranked probability as a hypothesis event

231 New Causality Simplification Mechanisms Based onthe collected medical evidence E for a patient the process ofcausality simplifications is performed to the BPPV causalitygraph Causality simplification aims to eliminate the irrel-evant meaningless and impossible events and relationsfrom a causality graph 0erefore the model scale andcomplexity are both significantly decreased and the diseasehypothesis space converges0e root cause event can even bepreliminarily determined based on the simplified causalitygraph

As a complement to the original simplification rules ofDUCG [28 30] several new causality simplificationmechanisms including a pruning strategy and causalitytracking process are presented

Definition 1 (Pruning Strategy) 0e meaningless diseasehypothesis and its corresponding causalities are identifiedand pruned from the causality graph using a scheme ofcausality tracking for all the abnormal evidences

Definition 2 (Causality Tracking Process) 0e causalitytracking process starts from an observed event and traces itsupstream causality chains and ancestors back towards the B-type event(s) For any Bi only if all the abnormal evidence isreachable to it via a causality tracking process can it beidentified as a candidate hypothesis otherwise Bi should beeliminated from the hypothesis space and its correspondingcausalities should be pruned from the graph

232 Weighted Logic Inference Rules of Differential Diag-nosis for BPPV Based on the simplified causality graph andmedical evidence the process of logical inference is per-formed to obtain the hypothesis space according to (1)sim(3)Our earlier study showed that by applying event expandingand logical operations the logical inference can effectivelydecrease the complexity of probabilistic reasoning [28]However in response to BPPV differential diagnosis theweighted logic inference algorithm requires majormodifications

Some BPPV subtypes can be present in a patient si-multaneously For instance a diagnosis can be termed as anASCC-idiopathic-canalithiasis BPPV Such a case is knownas concurrency of subtypes Meanwhile the subtypes be-longing to the same category are mutually exclusive when adiagnostic conclusion is drawn Some examples of this arePSCC-BPPV (B231) LSCC-BPPV (B241) ASCC-BPPV(B251) and MSCC-BPPV (B261) 0erefore to deal withthese cases new weighted logic inference rules for exclusionand concurrency among others are developed as shownbelow

Rule 1 Suppose that the basic events (namely root causeevents) in a BPPV differential diagnosis model are

6 Computational and Mathematical Methods in Medicine

represented in terms of category sets as C1 B231 B241B251 B261 C2 B271 B281 C3 B291 B301 andC4 B311 B321 B331 State 1 of a B-type event indicatesthat the root cause event has occurred on the contrary state0 of a B-type event indicates that the root cause event has notoccurred 0e mutual exclusion rules for basic events inBPPV differential diagnosis can thus be defined asBi1Biprime 1 0 where Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 )

Proof From the definition the category sets C1 C2 and C3indicate different classification perspectives of BPPV0erefore all basic events within the same category set areexclusive and exhaustive Specifically there is B231B241 0

B231B251 0 B231B261 0 B241B251 0 B241B261 0B251B261 0 B271B281 0 and B291B301 0

Rule 2 Bi1Biprime 1 ne 0 for Bi Biprime isin C4 (ine iprime) and Bi1Biprime 1 ne 0 forBi1 isin Cm Biprime1 isin Cn(ine iprime mne n)

Proof 0e events in C4 describe the respective differenttypes of atypical BPPV in an overlapping manner Namelyall the basic events in B311 B321 B331 are likely to beconcurrent 0is sets the basis for Rule 2

Definition 3 (Maximizing Concurrent Basic Event SetStrategy) To obtain an ultimate disease hypothesis Hkj ifthe events that constitute Hkj are concurrent and consistentwith each other the maximum number of basic eventswithin the hypothesis space SH should be incorporated

It is essential to explore every possible outcome beforeruling out any basic event For example as SH B241 B281B301 is obtained for a case we should get only the correcthypothesis H11 B241B281B301 ne 0 in which the threeevents together interpret the observed symptoms ratherthan B241B281 B281B301 or so on

Rule 3 Given V isin B X G D jne jprime and integer yge 2then (Vij)

y Vij and VijVij 0

Figure 2 0e DUCG-based differential diagnostic causality graph for BPPV

Figure 3 Sub-DUCG for LSCC-idiopathic-recurrent BPPV

Figure 4 Sub-DUCG for PSCC-idiopathic-recurrent BPPV

Figure 5 0e sub-DUCG for cupulolithiasis BPPV

Computational and Mathematical Methods in Medicine 7

Rule 4 Given integer yge 2 kne kprime and jne jprime then(Fnkij)

y (rnirn)yAnkij FnkijFnkprimeij 0 FnkijFnkijprime 0 andFnkijFnkprimeijprime 0 if Bi1Biprime 1 0 is given Bi1 Biprime 1 isin Cm

ine iprime m isin 1 2 3 then it follows that Fnkiprime1Bi1 0 Fnki1Biprime1 0 and Fnki1Fnkiprime1 0

Proof 0e latter part of Rule 4 is based on Rule 1 and theother part has been proven in [28] From Rule 1 Bi1Biprime 1 0which implies that the basic events Bi1 and Biprime1 cannot beconcurrent and consequently brings about the mutual ex-clusions among the function events related to Bi1 and Biprime10erefore Anki1Ankiprime1 0 and Fnki1Fnkiprime1 0 as Anki1cannot be present in combination with Ankirsquo1 similarlythen Fnkiprime1Bi1 0 and Fnki1Biprime1 0 Notably Fnki1Fnkiprime0ne 0 is true because Anki1 and Ankiprime0 are independent ofeach other (since they are given independently)

Rule 5 1113936Mm11113937iisinSm

FnkijiViji

(1113936Mm11113937iisinSm

(rnirn))1113937

iisinS1AnkijiViji

where Sm denotes the set of variable number ina product item m isin 12 M and S1 sube S2 sube middot middot middot sube SM

Rule 6 Suppose that no mutually exclusive basic eventscoexist in the candidate hypothesis space thenFnkijVij(1113936iprimeFnkiprimej

iprimeViprimej

iprime) FnkijVij if j ji is given

Proof To complement the ordinary conditions of Rule 14discussed in [28] consider a situation related to mutuallyexclusive basic events Vij Bi1 and VijprimeBiprime1Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 ) as proposed in Rule 10eproposition of Rule 6 can thus be represented as

FnkijVij 1113944

iprime

FnkiprimejiprimeViprimej

iprime⎛⎝ ⎞⎠ FnkijVij middot FnkijVij

+ FnkijVij middot 1113944

iprime ne i

FnkiprimejiprimeViprimej

iprime

rnirn1113872 11138732AnkijVij

neFnkijVij

(8)

0e inclusion of mutually exclusive events leads to theaforementioned outcomes (ie the inconsistence betweenRule 1 and Rule 6) and the autonormalization feature nolonger holds 0erefore a solution for BPPV subtype dif-ferentiation known as a scheme of dummy basic variable(DBV) is proposed

233 Scheme of Dummy Basic Variable

Definition 4 (DBV) If mutually exclusive candidate hy-potheses coexist in the candidate hypothesis space ieBi1Biprime 1 0 Bi1 Biprime1 isin Cm(ine iprime m isin 1 2 3 ) Bi1 andBiprime1are converted into different states of a DBV each state of theDBV elicits an individual pathogenesis causality graphaccording to the hypothesis related to that state the specificcausalities of different diseases can be distinguished by theA-parameter values of DBV which can either be zero or not0e exclusive rules among basic events are thus transformedinto an inherent exclusive law among the states of an event

Table 2 Definition of variables for differential diagnosis of BPPV

Variables Descriptions

X1ndash3201ndash206

210ndash217

Pathophysiology of BPPV the lesion of theotolithic membrane of utricle macula thedegenerated otolith broken off from utriclemacula misplaced calcium carbonate crystalsdebris calcium free-floating particles enteringthe SCCs calcium particles adherent to the

cupula of SCC the endolymph movement withfree-floating particles that pathologicallystimulates the ampulla of canal and the

sensitivity to linear acceleration and gravityinduced by the abnormal deflection of cupula

X48ndash11

0e description of vertigo an illusion ofmovement the sensation that objects in the

environment is moving when the eyes are openand the sensation that a patient feels as if he or

she is moving when the eyes are closed

X1142454682

0e main accompanying symptomsspontaneous nystagmus and autonomic nerve

symptoms

X20-25

0e detailed description of the features ofvertigo attacks attack characteristics the onsetand duration of an attack causes of disease

frequency and severity

X26ndash28209

Changes in head position relative to gravityrotation of the head relative to the body while in

an upright position

X83ndash871300e feature of spontaneous nystagmus and the

Romberg test for vestibular function

X5249161163238

Other accompanying symptoms cochlearsymptoms hearing loss tinnitus the symptoms

of central nervous system and themanifestations of the primary and underlying

disordersX184185 Patientrsquos gender and age

X186189198234

0e typical and characteristic medical history amigraine hypertension head trauma and inner

ear pathology

X207ndash208

More than one semicircular canal is affectedsimultaneously (obtained statistically duringthe pretreatment process of medical data)

X218ndash221227228Positioning test vertigo and nystagmus when

the head is moving or rotating

X222ndash226

DixndashHallpike test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)

X229ndash233

Supine roll test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)X236 0e outcomes of the maneuver treatment

B23ndash33

PSCC-BPPV (B23) LSCC-BPPV (B24) ASCC-BPPV (B25) MSCC-BPPV (B26) secondary

BPPV (B27) idiopathic BPPV (B28)canalithiasis BPPV (B29) cupulolithiasis BPPV(B30) subjective BPPV (B31) persistent BPPV

(B32) and recurrent BPPV (B33)

8 Computational and Mathematical Methods in Medicine

0e problem of disobeying the autonormalization fea-ture can thus be addressed 0is method is illustrated via anexample in Figure 6(a) Suppose that B11 and B21 aremutually exclusive events 0ey are then combined into aDBV-Bv during the reasoning process corresponding to Bv1and Bv2 respectively From the definition of DBVa31v1 equiv a3111 a41v2 equiv a4121 a51v2 equiv a5121 and rnv equiv rniwhere i isin 1 2 and n isin 3 4 5 Figure 6(b) shows an ex-ample where an event (eg X3) is connected to more thanone basic event In this case rnv is defined as rnv equiv 1113936irni ifFnine 00us r3v r31 + r32 for the case in Figure 6(b) whichpoints out to a combination of basic events

In the context of differential diagnosis and upon thecompletion of causality simplifications the obtained can-didate hypotheses of C1 B231 B241 B251 B261 (there aremore than one basic event in the set) should be combinedinto a DBV-Bm with Bmk denoting Bi1 where k 1 2 3 4and i 23 24 25 26 PrBmk refers to the prior probabilityof Bi1 and Pr Bm01113966 1113967 1 minus 1113936kne0Pr Bmk1113966 1113967

Definition 5 (Ranked Independent Probability) 0e rankedindependent probability represents a new metric proposedfor quantifying the degree of confidence in whether a BPPVsubtype (eg Bi1 as a part of the hypothesis Hkj) can in-dependently interpret all the medical evidence in com-parison with the other subtypes coexisting in Hkj 0eranked independent probability of Bi1 is calculated as fol-lows (1) get hs

i1 of Bi1 according to (2) and (3) in which ζi isbased on the individual causality tracking graph of Bi1 and(2) for all the Bi1 within the set of Hkj hs

i1 is ranked byhs

i11113936ihsi1

24 eoretical Analysis of the Reasoning Complexity 0einference algorithm for the proposed method reduces thereasoning complexity in two ways First the causality graphsimplification and pruning strategy significantly decreases themodel scale 0e variables that are irrelevant or inconsistentwith the medical evidence are excluded from the reasoning

calculation 0is significantly reduces the computationalcomplexity Moreover the diagnostic reasoning conclusioncan even be accurately drawn solely via the causality sim-plification Second prior to probabilistic reasoning weightedlogic inference is performed based on the simplified causalitygraph 0us the multiple connected causalities can bedecomposed independently leading the chaining inference toexhibit high efficiency Furthermore the proposed logicalinference rules and logical operations can decrease thecomplexity and scale of logical event expressions

0e actual efficiency tests for the DUCG inference al-gorithm have been performed using online fault diagnosisdata from several large-scale industrial systems (eg nuclearpower plants) in which thousands of variables and causalityarcs are involved [28 31] 0e diagnostic reasoning cantypically be finished within 05ndash1 s (on a personal computer)Moreover the inference efficiency has been verified from ourpast clinical diagnosis applications that involved dozens ofdiseases such as jaundice and sellar region disease

3 Experiments and Analyses

31 Clinical Validation of the BPPV Differential DiagnosisMethod

311 Differential Diagnosis for BPPVmdashCase 1 Suppose thatthe medical evidence of a patient was observed in part asX41 X212 X243 X1844 X1852 X2094 X2292 X2302 X2070X2080 X2360 in Figure 2 and other X-type variables arenormal or unknown (incomplete medical information) 0emedical information in this experiment is from a 65-year-oldfemale patient who suffered from brief episodes of vertigowhen rolling over in bed for two weeks and was suspected tobe a BPPV case according to the supine roll test

Based on the evidence in this case Figure 2 can besimplified into the graph shown in Figure 7 by applying thecausality simplification rules and pruning strategy Manymeaningless relationships and events under current situa-tion are eliminated accordingly with SH B241 B281 B301

BeginFor a BPPV patientCollect medical evidence E including symptoms signs examination findings laboratory tests and medical historiesPerform causality simplification to the BPPV causality graph based on the evidence EApply the causality simplification mechanisms including the pruning strategy and causality tracking processObtain the simplified diagnostic causality graph

Perform the algorithms of weighted logic inference based on the simplified causality graphPerform the weighted logic event expansion to the evidence according to (1)Perform logic inference according to (2)

Apply the weighted logic inference rules 1sim6 of differential diagnosis for BPPVApply the scheme of dummy basic variablePerform the basic logic operations

Obtain the hypothesis event space SH Hkj1113966 1113967

Perform the probabilistic reasonings to obtain the posterior probability of Hkj conditioned on E hskj

Calculate the ranked independent probability of a BPPV subtypeEnd

ALGORITHM 1 Differential diagnostic reasoning method for BPPV

Computational and Mathematical Methods in Medicine 9

being inferred as the possible root causes 0e resultinghypothesis space SH is concise with all unlikely hypothesesbeing excluded from concern Moreover the individualcausality tracking graphs for the three root cause events B24B28 and B30 in Figure 7 are shown in Figure 8 whereby eachsubgraph independently covers all evidence0e graphs thusintuitively and faithfully represent the causalities underlyingthe pathogenesis of Case 1

By applying the algorithm of differential diagnosticreasoning for Case 1 the state probability ofH11 B241B281B301 can be obtained as hs

11

Pr H11 | E1113966 1113967 1 0e obtained ldquoranked independent prob-abilitiesrdquo of B241 B281 and B301 are listed in Table 3 0eLSCC-idiopathic-cupulolithiasis BPPV is therefore deter-mined as the diagnostic result of Case 1 this result isconsistent with the clinical conclusions confirmed byotoneurologists

312 Differential Diagnosis for BPPVmdashCase 2 A 72-year-old female patient complained about paroxysmal positionalvertigo for a month the attacks of vertigo were brief lastingfor one minute the vertigo frequently occurred whilelooking up or down0us the medical evidence for this caseis X41 X212 X243 X1844 X1852 X2070 X2080 X2093 X2223X2231 X2241 X2251 X2261 X2360 the other X-type variablesare normal or unknown (incomplete medical information)

By applying the algorithm of differential diagnosticreasoning the hypothesis event H11 B231B281B291B321 isuniquely determined as the origin of the disease whichindicates a PSCC-idiopathic-cupulolithiasis-persistentBPPV 0e diagnostic causality graph is shown in Figure 9which is based on the causality simplification of Figure 20e resulting ranked independent probabilities of B231B281 B291 and B321 are listed in Table 4 By explicitlyrepresenting the disease causes symptoms pathogenesisand the latent correlations among medical informationFigure 9 offers intuitive insights into the underlying path-ological mechanisms

313 Other Validated BPPV Subtype Cases A verificationexperiment on some other clinical cases was performed toevaluate the effectiveness of the proposed method 0ecorrectness was based on the otoneurologistsrsquo judgement onthe diagnostic outcomes in contrast to the practical con-clusions In the clinical center for vertigo in BeijingChaoyang Hospital BPPV cases are common howeverthere are multiple repetitions in the meaningful informationfor the BPPV patients on their medical histories and physicalexaminations regarding subtype differentiation Based on

this 75 typical BPPV cases were selected from the thousandsof cases containing medical records interviews and physicalassessments in the verification experiments 0e BPPVsubtypes involved are outlined in Table 5 0e selectionprinciple of BPPV cases was based on the internationaldiagnostic criteria for BPPV [36] and the typicality andrepresentativeness of BPPV subtype diseases Notably sincethe nystagmus cannot be observed for a subjective BPPVcase it is difficult to classify the case either as canalithiasisBPPV or cupulolithiasis BPPV

0e diagnostic outcomes of the DUCG-based modelagreed with the otoneurologistsrsquo conclusions with a cor-rectness index of 100 Based on the available publishedliterature no other research has reported a model-basedautomatic subtype differentiation of BPPV in the past

32 Comparative Analysis of DUCG and BN 0e maindifference between DUCG and BN in terms of the theoreticalframework is that the model structure and parameters ofDUCG are decoupled By virtue of such a feature the in-dependent causality representation by the weighted causalityfunction event Ankij in DUCG makes it possible to simplifythe original causality graph based on the collected medicalevidence 0e irrelevant and meaningless events and rela-tions are thus eliminated from the model Taking the sim-plified causality graph as the basis of diagnostic reasoningreduces the computational scale and complexity to a largeextent In contrast BN cannot be easily simplified owing tothe structural coupling feature among the variables thecausalities among the child-parent events in BN are typicallyrepresented through a joint probability distribution (eg aconditional probabilistic table CPT) in case any variablesand relations are removed from a BN the remaining pa-rameters in the CPTs may need major adjustments more-over the number of parameters specified in a CPTfor a BN isexponential to the number of the parent variables and statesinvolved while the parameters needed in the DUCG are lessthan the parameters in a BN

Others

B1X3

X4

X5

Others

X3

X4

X5

B2

BV

(a)

Others

X3

X4

Others

X3

X4

BV

B1

B2

(b)

Figure 6 Example of DBV (a) Example 1 (b) Example 2

Figure 7 Diagnostic causality graph for Case 1

10 Computational and Mathematical Methods in Medicine

Furthermore by the independence representation andautomatic normalization feature for the weighted logic eventexpansion the ldquoself-reliantrdquo chaining inference and logicoperations can be performed in DUCG 0e parameters andinformation that are eliminated during the causality simpli-fication and those that are not involved in the chaining in-ference can all be missing (or some parameters which are notof concern are thus not provided) during this reasoningprocess and do not affect the diagnostic accuracy 0e diag-nostic inference method under incomplete information in-dicates that some unnecessary clinical tests and inappropriatemedications can be omitted thereby decreasing the patientsrsquo

medical costs For a BN the reasoning accuracy depends onthe completeness of the parameters in the CPTs

33 Application Analysis 0e proposed method can be de-veloped as an automatic diagnostic system for clinicians Basedon the compact independent and graphical causality repre-sentation using DUCG the model construction and diagnosis

(a) (b)

(c)

Figure 8 Individual causality tracking graphs of the hypotheses for Case 1 (a) LSCC-BPPV (B24) (b) Idiopathic BPPV (B28) (c)Cupulolithiasis BPPV (B30)

Table 3 Diagnostic reasoning results of Case 1

BPPVsubtype Description Ranked independent

probabilityB241 LSCC-BPPV 00388B281 Idiopathic BPPV 09542

B301Cupulolithiasis

BPPV 0007

H11 B241B281B301 1

Figure 9 Diagnostic causality graph for Case 2

Table 4 Diagnostic reasoning results of Case 2

BPPVsubtype Description Ranked independent

probabilityB231 PSCC-BPPV 01435B281 Idiopathic BPPV 07653

B291Canalithiasis

BPPV 00091

B321 Persistent BPPV 00821H11 B231B281B291B321 1

Table 5 BPPV subtypes involved in the validated cases

BPPV subtype No of casesPSCC 53ASCC 1LSCC 16MSCC 5Idiopathic 55Secondary 16Canalithiasis 61Cupulolithiasis 8Subjective 4Persistent 4Recurrent 8Typical 59

Computational and Mathematical Methods in Medicine 11

application are both easy to implement For a patient theclinical data through can be obtained through inquiry physicalexamination and auxiliary examination among others Nextthe clinical data including symptoms signs examination andtest data are input into the diagnostic reasoning interface ofthe system and the diagnosis results can be obtained throughreasoning calculation 0e clinical application of this methodis thus very convenient 0rough incorporation into the au-tomatic medical devices this method could improve the ef-ficiency of BPPV diagnosis and therapy especially for generalpractitioners in primary health care institutions In additionthe system can also be used inmobile and Internet terminals asa secondary tool for telemedicine finally it can serve as ateaching tool for doctor training in related disciplines

4 Summary

0is study proposes a DUCG method for differential di-agnosis of BPPV To distinguish among various causes ofvertiginous disorders with similar symptoms the proposedmethod involves a graphical and compact representation inaddition to logical reasoning algorithms for pathologicalmechanisms and related uncertain causalities New algo-rithms of differential diagnostic reasoning are proposed byintegrating a pruning strategy in the causality simplificationprocess a maximizing concurrent basic event set strategy inthe formulation of hypothesis space and the weighted logicinference rules for subtype differentiation of BPPV Fur-thermore a scheme of dummy basic variable is introduced tosettle the problems related to mutually exclusive root causeevents 0e model manifests higher correctness favorablerobustness to incomplete evidence and satisfactory dis-criminatory power for BPPV subtypes Furthermore usingthe diagnostic reasoning method and graphical represen-tation mechanism not only provides a diagnostic result butalso explains the rationale for suggesting the diseases whichjustifies the probability results

In light of these encouraging preliminary results moreclinical studies will be performed Furthermore a newmethod of probabilistic prediction for the vestibular dys-function-induced fall risk will be the subject of our futureresearch endeavors

Data Availability

0e data used to support the findings of this study are se-lected from the clinical cases of Department of Otorhino-laryngology Head and Neck Surgery Beijing Chaoyanghospital Requests for access to these data should be made toYanjun Wang (docwyjn163com Beijing Chaoyanghospital)

Disclosure

Chunling Dong and Yanjun Wang are cofirst authors

Conflicts of Interest

0e authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

0is work was supported in part by the National NaturalScience Foundation of China under Grant no 71671103 andin part by the Fundamental Research Funds for the CentralUniversities under Grant nos CUC2019B023CUC19ZD008 and CUC19ZD007

References

[1] N Bhattacharyya R F Baugh L Orvidas et al ldquoClinicalpractice guideline benign paroxysmal positional vertigordquoOtolaryngologymdashHead and Neck Surgery vol 139 no 5_suppl pp S47ndashS81 2008

[2] J S Oghalai S Manolidis J L Barth M G Stewart andH A Jenkins ldquoUnrecognized benign paroxysmal positionalvertigo in elderly patientsrdquo OtolaryngologymdashHead and NeckSurgery vol 122 no 5 pp 630ndash634 2000

[3] M P Prim-Espada J I De Diego-Sastre and E Perez-Fernandez ldquoEstudio metaanalıtico de la eficacia de la man-iobra de Epley en el vertigo posicional paroxıstico benignordquoNeurologıa vol 25 no 5 pp 295ndash299 2010

[4] L S Parnes S K Agrawal and J Atlas ldquoDiagnosis andmanagement of benign paroxysmal positional vertigo(BPPV)rdquo Canadian Medical Association Journal vol 169no 7 pp 681ndash693 2003

[5] J C Li and J Epley ldquo0e 360-degree maneuver for treatmentof benign positional vertigordquo Otology amp Neurotology vol 27no 1 pp 71ndash77 2006

[6] R Isola R Carvalho and A K Tripathy ldquoKnowledge dis-covery in medical systems using differential diagnosisLAMSTAR and $k$-NNrdquo IEEE Transactions on InformationTechnology in Biomedicine vol 16 no 6 pp 1287ndash1295 2012

[7] A L Barabasi N Gulbahce and J Loscalzo ldquoNetworkmedicine a network-based approach to human diseaserdquoNature Reviews Genetics vol 12 no 1 pp 56ndash68 2011

[8] E Mira A Buizza G Magenes M Manfrin and R SchmidldquoExpert systems as a diagnostic aid in otoneurologyrdquo Journalfor Oto-Rhino-Laryngology and Its Related Specialties (ORL)vol 52 no 2 pp 96ndash103 1990

[9] C E S Gavilan J E Gallego and J Gavilan ldquoCarnisel anexpert system for vestibular diagnosisrdquo Acta Oto-Lar-yngologica vol 110 no 3-4 pp 161ndash167 1990

[10] E Kentala I Pyykko Y Auramo J Laurikkala andM Juhola ldquoOtoneurological expert system for vertigordquo ActaOto-Laryngologica vol 119 no 5 pp 517ndash521 1999

[11] E Kentala K Viikki I Pyykko andM Juhola ldquoProduction ofdiagnostic rules from a neurotologic database with decisiontreesrdquo Annals of Otology Rhinology and Laryngology vol 109no 2 pp 170ndash176 2000

[12] J W Song J H Lee J H Choi and S J Chun ldquoAutomaticdifferential diagnosis of pancreatic serous and mucinouscystadenomas based on morphological featuresrdquo Computersin Biology and Medicine vol 43 no 1 pp 1ndash15 2013

[13] M H Lopes N R Ortega P S Silveira E Massad R Higaand F Marin Hde ldquoFuzzy cognitive map in differential di-agnosis of alterations in urinary elimination a nursing ap-proachrdquo International Journal of Medical Informatics vol 82no 3 pp 201ndash208 2013

[14] C Salvatore A Cerasa I Castiglioni et al ldquoMachine learningon brain MRI data for differential diagnosis of Parkinsonrsquosdisease and Progressive Supranuclear Palsyrdquo Journal ofNeuroscience Methods vol 222 pp 230ndash237 2014

12 Computational and Mathematical Methods in Medicine

represented in terms of category sets as C1 B231 B241B251 B261 C2 B271 B281 C3 B291 B301 andC4 B311 B321 B331 State 1 of a B-type event indicatesthat the root cause event has occurred on the contrary state0 of a B-type event indicates that the root cause event has notoccurred 0e mutual exclusion rules for basic events inBPPV differential diagnosis can thus be defined asBi1Biprime 1 0 where Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 )

Proof From the definition the category sets C1 C2 and C3indicate different classification perspectives of BPPV0erefore all basic events within the same category set areexclusive and exhaustive Specifically there is B231B241 0

B231B251 0 B231B261 0 B241B251 0 B241B261 0B251B261 0 B271B281 0 and B291B301 0

Rule 2 Bi1Biprime 1 ne 0 for Bi Biprime isin C4 (ine iprime) and Bi1Biprime 1 ne 0 forBi1 isin Cm Biprime1 isin Cn(ine iprime mne n)

Proof 0e events in C4 describe the respective differenttypes of atypical BPPV in an overlapping manner Namelyall the basic events in B311 B321 B331 are likely to beconcurrent 0is sets the basis for Rule 2

Definition 3 (Maximizing Concurrent Basic Event SetStrategy) To obtain an ultimate disease hypothesis Hkj ifthe events that constitute Hkj are concurrent and consistentwith each other the maximum number of basic eventswithin the hypothesis space SH should be incorporated

It is essential to explore every possible outcome beforeruling out any basic event For example as SH B241 B281B301 is obtained for a case we should get only the correcthypothesis H11 B241B281B301 ne 0 in which the threeevents together interpret the observed symptoms ratherthan B241B281 B281B301 or so on

Rule 3 Given V isin B X G D jne jprime and integer yge 2then (Vij)

y Vij and VijVij 0

Figure 2 0e DUCG-based differential diagnostic causality graph for BPPV

Figure 3 Sub-DUCG for LSCC-idiopathic-recurrent BPPV

Figure 4 Sub-DUCG for PSCC-idiopathic-recurrent BPPV

Figure 5 0e sub-DUCG for cupulolithiasis BPPV

Computational and Mathematical Methods in Medicine 7

Rule 4 Given integer yge 2 kne kprime and jne jprime then(Fnkij)

y (rnirn)yAnkij FnkijFnkprimeij 0 FnkijFnkijprime 0 andFnkijFnkprimeijprime 0 if Bi1Biprime 1 0 is given Bi1 Biprime 1 isin Cm

ine iprime m isin 1 2 3 then it follows that Fnkiprime1Bi1 0 Fnki1Biprime1 0 and Fnki1Fnkiprime1 0

Proof 0e latter part of Rule 4 is based on Rule 1 and theother part has been proven in [28] From Rule 1 Bi1Biprime 1 0which implies that the basic events Bi1 and Biprime1 cannot beconcurrent and consequently brings about the mutual ex-clusions among the function events related to Bi1 and Biprime10erefore Anki1Ankiprime1 0 and Fnki1Fnkiprime1 0 as Anki1cannot be present in combination with Ankirsquo1 similarlythen Fnkiprime1Bi1 0 and Fnki1Biprime1 0 Notably Fnki1Fnkiprime0ne 0 is true because Anki1 and Ankiprime0 are independent ofeach other (since they are given independently)

Rule 5 1113936Mm11113937iisinSm

FnkijiViji

(1113936Mm11113937iisinSm

(rnirn))1113937

iisinS1AnkijiViji

where Sm denotes the set of variable number ina product item m isin 12 M and S1 sube S2 sube middot middot middot sube SM

Rule 6 Suppose that no mutually exclusive basic eventscoexist in the candidate hypothesis space thenFnkijVij(1113936iprimeFnkiprimej

iprimeViprimej

iprime) FnkijVij if j ji is given

Proof To complement the ordinary conditions of Rule 14discussed in [28] consider a situation related to mutuallyexclusive basic events Vij Bi1 and VijprimeBiprime1Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 ) as proposed in Rule 10eproposition of Rule 6 can thus be represented as

FnkijVij 1113944

iprime

FnkiprimejiprimeViprimej

iprime⎛⎝ ⎞⎠ FnkijVij middot FnkijVij

+ FnkijVij middot 1113944

iprime ne i

FnkiprimejiprimeViprimej

iprime

rnirn1113872 11138732AnkijVij

neFnkijVij

(8)

0e inclusion of mutually exclusive events leads to theaforementioned outcomes (ie the inconsistence betweenRule 1 and Rule 6) and the autonormalization feature nolonger holds 0erefore a solution for BPPV subtype dif-ferentiation known as a scheme of dummy basic variable(DBV) is proposed

233 Scheme of Dummy Basic Variable

Definition 4 (DBV) If mutually exclusive candidate hy-potheses coexist in the candidate hypothesis space ieBi1Biprime 1 0 Bi1 Biprime1 isin Cm(ine iprime m isin 1 2 3 ) Bi1 andBiprime1are converted into different states of a DBV each state of theDBV elicits an individual pathogenesis causality graphaccording to the hypothesis related to that state the specificcausalities of different diseases can be distinguished by theA-parameter values of DBV which can either be zero or not0e exclusive rules among basic events are thus transformedinto an inherent exclusive law among the states of an event

Table 2 Definition of variables for differential diagnosis of BPPV

Variables Descriptions

X1ndash3201ndash206

210ndash217

Pathophysiology of BPPV the lesion of theotolithic membrane of utricle macula thedegenerated otolith broken off from utriclemacula misplaced calcium carbonate crystalsdebris calcium free-floating particles enteringthe SCCs calcium particles adherent to the

cupula of SCC the endolymph movement withfree-floating particles that pathologicallystimulates the ampulla of canal and the

sensitivity to linear acceleration and gravityinduced by the abnormal deflection of cupula

X48ndash11

0e description of vertigo an illusion ofmovement the sensation that objects in the

environment is moving when the eyes are openand the sensation that a patient feels as if he or

she is moving when the eyes are closed

X1142454682

0e main accompanying symptomsspontaneous nystagmus and autonomic nerve

symptoms

X20-25

0e detailed description of the features ofvertigo attacks attack characteristics the onsetand duration of an attack causes of disease

frequency and severity

X26ndash28209

Changes in head position relative to gravityrotation of the head relative to the body while in

an upright position

X83ndash871300e feature of spontaneous nystagmus and the

Romberg test for vestibular function

X5249161163238

Other accompanying symptoms cochlearsymptoms hearing loss tinnitus the symptoms

of central nervous system and themanifestations of the primary and underlying

disordersX184185 Patientrsquos gender and age

X186189198234

0e typical and characteristic medical history amigraine hypertension head trauma and inner

ear pathology

X207ndash208

More than one semicircular canal is affectedsimultaneously (obtained statistically duringthe pretreatment process of medical data)

X218ndash221227228Positioning test vertigo and nystagmus when

the head is moving or rotating

X222ndash226

DixndashHallpike test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)

X229ndash233

Supine roll test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)X236 0e outcomes of the maneuver treatment

B23ndash33

PSCC-BPPV (B23) LSCC-BPPV (B24) ASCC-BPPV (B25) MSCC-BPPV (B26) secondary

BPPV (B27) idiopathic BPPV (B28)canalithiasis BPPV (B29) cupulolithiasis BPPV(B30) subjective BPPV (B31) persistent BPPV

(B32) and recurrent BPPV (B33)

8 Computational and Mathematical Methods in Medicine

0e problem of disobeying the autonormalization fea-ture can thus be addressed 0is method is illustrated via anexample in Figure 6(a) Suppose that B11 and B21 aremutually exclusive events 0ey are then combined into aDBV-Bv during the reasoning process corresponding to Bv1and Bv2 respectively From the definition of DBVa31v1 equiv a3111 a41v2 equiv a4121 a51v2 equiv a5121 and rnv equiv rniwhere i isin 1 2 and n isin 3 4 5 Figure 6(b) shows an ex-ample where an event (eg X3) is connected to more thanone basic event In this case rnv is defined as rnv equiv 1113936irni ifFnine 00us r3v r31 + r32 for the case in Figure 6(b) whichpoints out to a combination of basic events

In the context of differential diagnosis and upon thecompletion of causality simplifications the obtained can-didate hypotheses of C1 B231 B241 B251 B261 (there aremore than one basic event in the set) should be combinedinto a DBV-Bm with Bmk denoting Bi1 where k 1 2 3 4and i 23 24 25 26 PrBmk refers to the prior probabilityof Bi1 and Pr Bm01113966 1113967 1 minus 1113936kne0Pr Bmk1113966 1113967

Definition 5 (Ranked Independent Probability) 0e rankedindependent probability represents a new metric proposedfor quantifying the degree of confidence in whether a BPPVsubtype (eg Bi1 as a part of the hypothesis Hkj) can in-dependently interpret all the medical evidence in com-parison with the other subtypes coexisting in Hkj 0eranked independent probability of Bi1 is calculated as fol-lows (1) get hs

i1 of Bi1 according to (2) and (3) in which ζi isbased on the individual causality tracking graph of Bi1 and(2) for all the Bi1 within the set of Hkj hs

i1 is ranked byhs

i11113936ihsi1

24 eoretical Analysis of the Reasoning Complexity 0einference algorithm for the proposed method reduces thereasoning complexity in two ways First the causality graphsimplification and pruning strategy significantly decreases themodel scale 0e variables that are irrelevant or inconsistentwith the medical evidence are excluded from the reasoning

calculation 0is significantly reduces the computationalcomplexity Moreover the diagnostic reasoning conclusioncan even be accurately drawn solely via the causality sim-plification Second prior to probabilistic reasoning weightedlogic inference is performed based on the simplified causalitygraph 0us the multiple connected causalities can bedecomposed independently leading the chaining inference toexhibit high efficiency Furthermore the proposed logicalinference rules and logical operations can decrease thecomplexity and scale of logical event expressions

0e actual efficiency tests for the DUCG inference al-gorithm have been performed using online fault diagnosisdata from several large-scale industrial systems (eg nuclearpower plants) in which thousands of variables and causalityarcs are involved [28 31] 0e diagnostic reasoning cantypically be finished within 05ndash1 s (on a personal computer)Moreover the inference efficiency has been verified from ourpast clinical diagnosis applications that involved dozens ofdiseases such as jaundice and sellar region disease

3 Experiments and Analyses

31 Clinical Validation of the BPPV Differential DiagnosisMethod

311 Differential Diagnosis for BPPVmdashCase 1 Suppose thatthe medical evidence of a patient was observed in part asX41 X212 X243 X1844 X1852 X2094 X2292 X2302 X2070X2080 X2360 in Figure 2 and other X-type variables arenormal or unknown (incomplete medical information) 0emedical information in this experiment is from a 65-year-oldfemale patient who suffered from brief episodes of vertigowhen rolling over in bed for two weeks and was suspected tobe a BPPV case according to the supine roll test

Based on the evidence in this case Figure 2 can besimplified into the graph shown in Figure 7 by applying thecausality simplification rules and pruning strategy Manymeaningless relationships and events under current situa-tion are eliminated accordingly with SH B241 B281 B301

BeginFor a BPPV patientCollect medical evidence E including symptoms signs examination findings laboratory tests and medical historiesPerform causality simplification to the BPPV causality graph based on the evidence EApply the causality simplification mechanisms including the pruning strategy and causality tracking processObtain the simplified diagnostic causality graph

Perform the algorithms of weighted logic inference based on the simplified causality graphPerform the weighted logic event expansion to the evidence according to (1)Perform logic inference according to (2)

Apply the weighted logic inference rules 1sim6 of differential diagnosis for BPPVApply the scheme of dummy basic variablePerform the basic logic operations

Obtain the hypothesis event space SH Hkj1113966 1113967

Perform the probabilistic reasonings to obtain the posterior probability of Hkj conditioned on E hskj

Calculate the ranked independent probability of a BPPV subtypeEnd

ALGORITHM 1 Differential diagnostic reasoning method for BPPV

Computational and Mathematical Methods in Medicine 9

being inferred as the possible root causes 0e resultinghypothesis space SH is concise with all unlikely hypothesesbeing excluded from concern Moreover the individualcausality tracking graphs for the three root cause events B24B28 and B30 in Figure 7 are shown in Figure 8 whereby eachsubgraph independently covers all evidence0e graphs thusintuitively and faithfully represent the causalities underlyingthe pathogenesis of Case 1

By applying the algorithm of differential diagnosticreasoning for Case 1 the state probability ofH11 B241B281B301 can be obtained as hs

11

Pr H11 | E1113966 1113967 1 0e obtained ldquoranked independent prob-abilitiesrdquo of B241 B281 and B301 are listed in Table 3 0eLSCC-idiopathic-cupulolithiasis BPPV is therefore deter-mined as the diagnostic result of Case 1 this result isconsistent with the clinical conclusions confirmed byotoneurologists

312 Differential Diagnosis for BPPVmdashCase 2 A 72-year-old female patient complained about paroxysmal positionalvertigo for a month the attacks of vertigo were brief lastingfor one minute the vertigo frequently occurred whilelooking up or down0us the medical evidence for this caseis X41 X212 X243 X1844 X1852 X2070 X2080 X2093 X2223X2231 X2241 X2251 X2261 X2360 the other X-type variablesare normal or unknown (incomplete medical information)

By applying the algorithm of differential diagnosticreasoning the hypothesis event H11 B231B281B291B321 isuniquely determined as the origin of the disease whichindicates a PSCC-idiopathic-cupulolithiasis-persistentBPPV 0e diagnostic causality graph is shown in Figure 9which is based on the causality simplification of Figure 20e resulting ranked independent probabilities of B231B281 B291 and B321 are listed in Table 4 By explicitlyrepresenting the disease causes symptoms pathogenesisand the latent correlations among medical informationFigure 9 offers intuitive insights into the underlying path-ological mechanisms

313 Other Validated BPPV Subtype Cases A verificationexperiment on some other clinical cases was performed toevaluate the effectiveness of the proposed method 0ecorrectness was based on the otoneurologistsrsquo judgement onthe diagnostic outcomes in contrast to the practical con-clusions In the clinical center for vertigo in BeijingChaoyang Hospital BPPV cases are common howeverthere are multiple repetitions in the meaningful informationfor the BPPV patients on their medical histories and physicalexaminations regarding subtype differentiation Based on

this 75 typical BPPV cases were selected from the thousandsof cases containing medical records interviews and physicalassessments in the verification experiments 0e BPPVsubtypes involved are outlined in Table 5 0e selectionprinciple of BPPV cases was based on the internationaldiagnostic criteria for BPPV [36] and the typicality andrepresentativeness of BPPV subtype diseases Notably sincethe nystagmus cannot be observed for a subjective BPPVcase it is difficult to classify the case either as canalithiasisBPPV or cupulolithiasis BPPV

0e diagnostic outcomes of the DUCG-based modelagreed with the otoneurologistsrsquo conclusions with a cor-rectness index of 100 Based on the available publishedliterature no other research has reported a model-basedautomatic subtype differentiation of BPPV in the past

32 Comparative Analysis of DUCG and BN 0e maindifference between DUCG and BN in terms of the theoreticalframework is that the model structure and parameters ofDUCG are decoupled By virtue of such a feature the in-dependent causality representation by the weighted causalityfunction event Ankij in DUCG makes it possible to simplifythe original causality graph based on the collected medicalevidence 0e irrelevant and meaningless events and rela-tions are thus eliminated from the model Taking the sim-plified causality graph as the basis of diagnostic reasoningreduces the computational scale and complexity to a largeextent In contrast BN cannot be easily simplified owing tothe structural coupling feature among the variables thecausalities among the child-parent events in BN are typicallyrepresented through a joint probability distribution (eg aconditional probabilistic table CPT) in case any variablesand relations are removed from a BN the remaining pa-rameters in the CPTs may need major adjustments more-over the number of parameters specified in a CPTfor a BN isexponential to the number of the parent variables and statesinvolved while the parameters needed in the DUCG are lessthan the parameters in a BN

Others

B1X3

X4

X5

Others

X3

X4

X5

B2

BV

(a)

Others

X3

X4

Others

X3

X4

BV

B1

B2

(b)

Figure 6 Example of DBV (a) Example 1 (b) Example 2

Figure 7 Diagnostic causality graph for Case 1

10 Computational and Mathematical Methods in Medicine

Furthermore by the independence representation andautomatic normalization feature for the weighted logic eventexpansion the ldquoself-reliantrdquo chaining inference and logicoperations can be performed in DUCG 0e parameters andinformation that are eliminated during the causality simpli-fication and those that are not involved in the chaining in-ference can all be missing (or some parameters which are notof concern are thus not provided) during this reasoningprocess and do not affect the diagnostic accuracy 0e diag-nostic inference method under incomplete information in-dicates that some unnecessary clinical tests and inappropriatemedications can be omitted thereby decreasing the patientsrsquo

medical costs For a BN the reasoning accuracy depends onthe completeness of the parameters in the CPTs

33 Application Analysis 0e proposed method can be de-veloped as an automatic diagnostic system for clinicians Basedon the compact independent and graphical causality repre-sentation using DUCG the model construction and diagnosis

(a) (b)

(c)

Figure 8 Individual causality tracking graphs of the hypotheses for Case 1 (a) LSCC-BPPV (B24) (b) Idiopathic BPPV (B28) (c)Cupulolithiasis BPPV (B30)

Table 3 Diagnostic reasoning results of Case 1

BPPVsubtype Description Ranked independent

probabilityB241 LSCC-BPPV 00388B281 Idiopathic BPPV 09542

B301Cupulolithiasis

BPPV 0007

H11 B241B281B301 1

Figure 9 Diagnostic causality graph for Case 2

Table 4 Diagnostic reasoning results of Case 2

BPPVsubtype Description Ranked independent

probabilityB231 PSCC-BPPV 01435B281 Idiopathic BPPV 07653

B291Canalithiasis

BPPV 00091

B321 Persistent BPPV 00821H11 B231B281B291B321 1

Table 5 BPPV subtypes involved in the validated cases

BPPV subtype No of casesPSCC 53ASCC 1LSCC 16MSCC 5Idiopathic 55Secondary 16Canalithiasis 61Cupulolithiasis 8Subjective 4Persistent 4Recurrent 8Typical 59

Computational and Mathematical Methods in Medicine 11

application are both easy to implement For a patient theclinical data through can be obtained through inquiry physicalexamination and auxiliary examination among others Nextthe clinical data including symptoms signs examination andtest data are input into the diagnostic reasoning interface ofthe system and the diagnosis results can be obtained throughreasoning calculation 0e clinical application of this methodis thus very convenient 0rough incorporation into the au-tomatic medical devices this method could improve the ef-ficiency of BPPV diagnosis and therapy especially for generalpractitioners in primary health care institutions In additionthe system can also be used inmobile and Internet terminals asa secondary tool for telemedicine finally it can serve as ateaching tool for doctor training in related disciplines

4 Summary

0is study proposes a DUCG method for differential di-agnosis of BPPV To distinguish among various causes ofvertiginous disorders with similar symptoms the proposedmethod involves a graphical and compact representation inaddition to logical reasoning algorithms for pathologicalmechanisms and related uncertain causalities New algo-rithms of differential diagnostic reasoning are proposed byintegrating a pruning strategy in the causality simplificationprocess a maximizing concurrent basic event set strategy inthe formulation of hypothesis space and the weighted logicinference rules for subtype differentiation of BPPV Fur-thermore a scheme of dummy basic variable is introduced tosettle the problems related to mutually exclusive root causeevents 0e model manifests higher correctness favorablerobustness to incomplete evidence and satisfactory dis-criminatory power for BPPV subtypes Furthermore usingthe diagnostic reasoning method and graphical represen-tation mechanism not only provides a diagnostic result butalso explains the rationale for suggesting the diseases whichjustifies the probability results

In light of these encouraging preliminary results moreclinical studies will be performed Furthermore a newmethod of probabilistic prediction for the vestibular dys-function-induced fall risk will be the subject of our futureresearch endeavors

Data Availability

0e data used to support the findings of this study are se-lected from the clinical cases of Department of Otorhino-laryngology Head and Neck Surgery Beijing Chaoyanghospital Requests for access to these data should be made toYanjun Wang (docwyjn163com Beijing Chaoyanghospital)

Disclosure

Chunling Dong and Yanjun Wang are cofirst authors

Conflicts of Interest

0e authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

0is work was supported in part by the National NaturalScience Foundation of China under Grant no 71671103 andin part by the Fundamental Research Funds for the CentralUniversities under Grant nos CUC2019B023CUC19ZD008 and CUC19ZD007

References

[1] N Bhattacharyya R F Baugh L Orvidas et al ldquoClinicalpractice guideline benign paroxysmal positional vertigordquoOtolaryngologymdashHead and Neck Surgery vol 139 no 5_suppl pp S47ndashS81 2008

[2] J S Oghalai S Manolidis J L Barth M G Stewart andH A Jenkins ldquoUnrecognized benign paroxysmal positionalvertigo in elderly patientsrdquo OtolaryngologymdashHead and NeckSurgery vol 122 no 5 pp 630ndash634 2000

[3] M P Prim-Espada J I De Diego-Sastre and E Perez-Fernandez ldquoEstudio metaanalıtico de la eficacia de la man-iobra de Epley en el vertigo posicional paroxıstico benignordquoNeurologıa vol 25 no 5 pp 295ndash299 2010

[4] L S Parnes S K Agrawal and J Atlas ldquoDiagnosis andmanagement of benign paroxysmal positional vertigo(BPPV)rdquo Canadian Medical Association Journal vol 169no 7 pp 681ndash693 2003

[5] J C Li and J Epley ldquo0e 360-degree maneuver for treatmentof benign positional vertigordquo Otology amp Neurotology vol 27no 1 pp 71ndash77 2006

[6] R Isola R Carvalho and A K Tripathy ldquoKnowledge dis-covery in medical systems using differential diagnosisLAMSTAR and $k$-NNrdquo IEEE Transactions on InformationTechnology in Biomedicine vol 16 no 6 pp 1287ndash1295 2012

[7] A L Barabasi N Gulbahce and J Loscalzo ldquoNetworkmedicine a network-based approach to human diseaserdquoNature Reviews Genetics vol 12 no 1 pp 56ndash68 2011

[8] E Mira A Buizza G Magenes M Manfrin and R SchmidldquoExpert systems as a diagnostic aid in otoneurologyrdquo Journalfor Oto-Rhino-Laryngology and Its Related Specialties (ORL)vol 52 no 2 pp 96ndash103 1990

[9] C E S Gavilan J E Gallego and J Gavilan ldquoCarnisel anexpert system for vestibular diagnosisrdquo Acta Oto-Lar-yngologica vol 110 no 3-4 pp 161ndash167 1990

[10] E Kentala I Pyykko Y Auramo J Laurikkala andM Juhola ldquoOtoneurological expert system for vertigordquo ActaOto-Laryngologica vol 119 no 5 pp 517ndash521 1999

[11] E Kentala K Viikki I Pyykko andM Juhola ldquoProduction ofdiagnostic rules from a neurotologic database with decisiontreesrdquo Annals of Otology Rhinology and Laryngology vol 109no 2 pp 170ndash176 2000

[12] J W Song J H Lee J H Choi and S J Chun ldquoAutomaticdifferential diagnosis of pancreatic serous and mucinouscystadenomas based on morphological featuresrdquo Computersin Biology and Medicine vol 43 no 1 pp 1ndash15 2013

[13] M H Lopes N R Ortega P S Silveira E Massad R Higaand F Marin Hde ldquoFuzzy cognitive map in differential di-agnosis of alterations in urinary elimination a nursing ap-proachrdquo International Journal of Medical Informatics vol 82no 3 pp 201ndash208 2013

[14] C Salvatore A Cerasa I Castiglioni et al ldquoMachine learningon brain MRI data for differential diagnosis of Parkinsonrsquosdisease and Progressive Supranuclear Palsyrdquo Journal ofNeuroscience Methods vol 222 pp 230ndash237 2014

12 Computational and Mathematical Methods in Medicine

Rule 4 Given integer yge 2 kne kprime and jne jprime then(Fnkij)

y (rnirn)yAnkij FnkijFnkprimeij 0 FnkijFnkijprime 0 andFnkijFnkprimeijprime 0 if Bi1Biprime 1 0 is given Bi1 Biprime 1 isin Cm

ine iprime m isin 1 2 3 then it follows that Fnkiprime1Bi1 0 Fnki1Biprime1 0 and Fnki1Fnkiprime1 0

Proof 0e latter part of Rule 4 is based on Rule 1 and theother part has been proven in [28] From Rule 1 Bi1Biprime 1 0which implies that the basic events Bi1 and Biprime1 cannot beconcurrent and consequently brings about the mutual ex-clusions among the function events related to Bi1 and Biprime10erefore Anki1Ankiprime1 0 and Fnki1Fnkiprime1 0 as Anki1cannot be present in combination with Ankirsquo1 similarlythen Fnkiprime1Bi1 0 and Fnki1Biprime1 0 Notably Fnki1Fnkiprime0ne 0 is true because Anki1 and Ankiprime0 are independent ofeach other (since they are given independently)

Rule 5 1113936Mm11113937iisinSm

FnkijiViji

(1113936Mm11113937iisinSm

(rnirn))1113937

iisinS1AnkijiViji

where Sm denotes the set of variable number ina product item m isin 12 M and S1 sube S2 sube middot middot middot sube SM

Rule 6 Suppose that no mutually exclusive basic eventscoexist in the candidate hypothesis space thenFnkijVij(1113936iprimeFnkiprimej

iprimeViprimej

iprime) FnkijVij if j ji is given

Proof To complement the ordinary conditions of Rule 14discussed in [28] consider a situation related to mutuallyexclusive basic events Vij Bi1 and VijprimeBiprime1Bi1 Biprime 1 isin Cm(ine iprime m isin 1 2 3 ) as proposed in Rule 10eproposition of Rule 6 can thus be represented as

FnkijVij 1113944

iprime

FnkiprimejiprimeViprimej

iprime⎛⎝ ⎞⎠ FnkijVij middot FnkijVij

+ FnkijVij middot 1113944

iprime ne i

FnkiprimejiprimeViprimej

iprime

rnirn1113872 11138732AnkijVij

neFnkijVij

(8)

0e inclusion of mutually exclusive events leads to theaforementioned outcomes (ie the inconsistence betweenRule 1 and Rule 6) and the autonormalization feature nolonger holds 0erefore a solution for BPPV subtype dif-ferentiation known as a scheme of dummy basic variable(DBV) is proposed

233 Scheme of Dummy Basic Variable

Definition 4 (DBV) If mutually exclusive candidate hy-potheses coexist in the candidate hypothesis space ieBi1Biprime 1 0 Bi1 Biprime1 isin Cm(ine iprime m isin 1 2 3 ) Bi1 andBiprime1are converted into different states of a DBV each state of theDBV elicits an individual pathogenesis causality graphaccording to the hypothesis related to that state the specificcausalities of different diseases can be distinguished by theA-parameter values of DBV which can either be zero or not0e exclusive rules among basic events are thus transformedinto an inherent exclusive law among the states of an event

Table 2 Definition of variables for differential diagnosis of BPPV

Variables Descriptions

X1ndash3201ndash206

210ndash217

Pathophysiology of BPPV the lesion of theotolithic membrane of utricle macula thedegenerated otolith broken off from utriclemacula misplaced calcium carbonate crystalsdebris calcium free-floating particles enteringthe SCCs calcium particles adherent to the

cupula of SCC the endolymph movement withfree-floating particles that pathologicallystimulates the ampulla of canal and the

sensitivity to linear acceleration and gravityinduced by the abnormal deflection of cupula

X48ndash11

0e description of vertigo an illusion ofmovement the sensation that objects in the

environment is moving when the eyes are openand the sensation that a patient feels as if he or

she is moving when the eyes are closed

X1142454682

0e main accompanying symptomsspontaneous nystagmus and autonomic nerve

symptoms

X20-25

0e detailed description of the features ofvertigo attacks attack characteristics the onsetand duration of an attack causes of disease

frequency and severity

X26ndash28209

Changes in head position relative to gravityrotation of the head relative to the body while in

an upright position

X83ndash871300e feature of spontaneous nystagmus and the

Romberg test for vestibular function

X5249161163238

Other accompanying symptoms cochlearsymptoms hearing loss tinnitus the symptoms

of central nervous system and themanifestations of the primary and underlying

disordersX184185 Patientrsquos gender and age

X186189198234

0e typical and characteristic medical history amigraine hypertension head trauma and inner

ear pathology

X207ndash208

More than one semicircular canal is affectedsimultaneously (obtained statistically duringthe pretreatment process of medical data)

X218ndash221227228Positioning test vertigo and nystagmus when

the head is moving or rotating

X222ndash226

DixndashHallpike test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)

X229ndash233

Supine roll test the feature of evokednystagmus (latency duration directionamplitude frequency fatigability and

reversibility)X236 0e outcomes of the maneuver treatment

B23ndash33

PSCC-BPPV (B23) LSCC-BPPV (B24) ASCC-BPPV (B25) MSCC-BPPV (B26) secondary

BPPV (B27) idiopathic BPPV (B28)canalithiasis BPPV (B29) cupulolithiasis BPPV(B30) subjective BPPV (B31) persistent BPPV

(B32) and recurrent BPPV (B33)

8 Computational and Mathematical Methods in Medicine

0e problem of disobeying the autonormalization fea-ture can thus be addressed 0is method is illustrated via anexample in Figure 6(a) Suppose that B11 and B21 aremutually exclusive events 0ey are then combined into aDBV-Bv during the reasoning process corresponding to Bv1and Bv2 respectively From the definition of DBVa31v1 equiv a3111 a41v2 equiv a4121 a51v2 equiv a5121 and rnv equiv rniwhere i isin 1 2 and n isin 3 4 5 Figure 6(b) shows an ex-ample where an event (eg X3) is connected to more thanone basic event In this case rnv is defined as rnv equiv 1113936irni ifFnine 00us r3v r31 + r32 for the case in Figure 6(b) whichpoints out to a combination of basic events

In the context of differential diagnosis and upon thecompletion of causality simplifications the obtained can-didate hypotheses of C1 B231 B241 B251 B261 (there aremore than one basic event in the set) should be combinedinto a DBV-Bm with Bmk denoting Bi1 where k 1 2 3 4and i 23 24 25 26 PrBmk refers to the prior probabilityof Bi1 and Pr Bm01113966 1113967 1 minus 1113936kne0Pr Bmk1113966 1113967

Definition 5 (Ranked Independent Probability) 0e rankedindependent probability represents a new metric proposedfor quantifying the degree of confidence in whether a BPPVsubtype (eg Bi1 as a part of the hypothesis Hkj) can in-dependently interpret all the medical evidence in com-parison with the other subtypes coexisting in Hkj 0eranked independent probability of Bi1 is calculated as fol-lows (1) get hs

i1 of Bi1 according to (2) and (3) in which ζi isbased on the individual causality tracking graph of Bi1 and(2) for all the Bi1 within the set of Hkj hs

i1 is ranked byhs

i11113936ihsi1

24 eoretical Analysis of the Reasoning Complexity 0einference algorithm for the proposed method reduces thereasoning complexity in two ways First the causality graphsimplification and pruning strategy significantly decreases themodel scale 0e variables that are irrelevant or inconsistentwith the medical evidence are excluded from the reasoning

calculation 0is significantly reduces the computationalcomplexity Moreover the diagnostic reasoning conclusioncan even be accurately drawn solely via the causality sim-plification Second prior to probabilistic reasoning weightedlogic inference is performed based on the simplified causalitygraph 0us the multiple connected causalities can bedecomposed independently leading the chaining inference toexhibit high efficiency Furthermore the proposed logicalinference rules and logical operations can decrease thecomplexity and scale of logical event expressions

0e actual efficiency tests for the DUCG inference al-gorithm have been performed using online fault diagnosisdata from several large-scale industrial systems (eg nuclearpower plants) in which thousands of variables and causalityarcs are involved [28 31] 0e diagnostic reasoning cantypically be finished within 05ndash1 s (on a personal computer)Moreover the inference efficiency has been verified from ourpast clinical diagnosis applications that involved dozens ofdiseases such as jaundice and sellar region disease

3 Experiments and Analyses

31 Clinical Validation of the BPPV Differential DiagnosisMethod

311 Differential Diagnosis for BPPVmdashCase 1 Suppose thatthe medical evidence of a patient was observed in part asX41 X212 X243 X1844 X1852 X2094 X2292 X2302 X2070X2080 X2360 in Figure 2 and other X-type variables arenormal or unknown (incomplete medical information) 0emedical information in this experiment is from a 65-year-oldfemale patient who suffered from brief episodes of vertigowhen rolling over in bed for two weeks and was suspected tobe a BPPV case according to the supine roll test

Based on the evidence in this case Figure 2 can besimplified into the graph shown in Figure 7 by applying thecausality simplification rules and pruning strategy Manymeaningless relationships and events under current situa-tion are eliminated accordingly with SH B241 B281 B301

BeginFor a BPPV patientCollect medical evidence E including symptoms signs examination findings laboratory tests and medical historiesPerform causality simplification to the BPPV causality graph based on the evidence EApply the causality simplification mechanisms including the pruning strategy and causality tracking processObtain the simplified diagnostic causality graph

Perform the algorithms of weighted logic inference based on the simplified causality graphPerform the weighted logic event expansion to the evidence according to (1)Perform logic inference according to (2)

Apply the weighted logic inference rules 1sim6 of differential diagnosis for BPPVApply the scheme of dummy basic variablePerform the basic logic operations

Obtain the hypothesis event space SH Hkj1113966 1113967

Perform the probabilistic reasonings to obtain the posterior probability of Hkj conditioned on E hskj

Calculate the ranked independent probability of a BPPV subtypeEnd

ALGORITHM 1 Differential diagnostic reasoning method for BPPV

Computational and Mathematical Methods in Medicine 9

being inferred as the possible root causes 0e resultinghypothesis space SH is concise with all unlikely hypothesesbeing excluded from concern Moreover the individualcausality tracking graphs for the three root cause events B24B28 and B30 in Figure 7 are shown in Figure 8 whereby eachsubgraph independently covers all evidence0e graphs thusintuitively and faithfully represent the causalities underlyingthe pathogenesis of Case 1

By applying the algorithm of differential diagnosticreasoning for Case 1 the state probability ofH11 B241B281B301 can be obtained as hs

11

Pr H11 | E1113966 1113967 1 0e obtained ldquoranked independent prob-abilitiesrdquo of B241 B281 and B301 are listed in Table 3 0eLSCC-idiopathic-cupulolithiasis BPPV is therefore deter-mined as the diagnostic result of Case 1 this result isconsistent with the clinical conclusions confirmed byotoneurologists

312 Differential Diagnosis for BPPVmdashCase 2 A 72-year-old female patient complained about paroxysmal positionalvertigo for a month the attacks of vertigo were brief lastingfor one minute the vertigo frequently occurred whilelooking up or down0us the medical evidence for this caseis X41 X212 X243 X1844 X1852 X2070 X2080 X2093 X2223X2231 X2241 X2251 X2261 X2360 the other X-type variablesare normal or unknown (incomplete medical information)

By applying the algorithm of differential diagnosticreasoning the hypothesis event H11 B231B281B291B321 isuniquely determined as the origin of the disease whichindicates a PSCC-idiopathic-cupulolithiasis-persistentBPPV 0e diagnostic causality graph is shown in Figure 9which is based on the causality simplification of Figure 20e resulting ranked independent probabilities of B231B281 B291 and B321 are listed in Table 4 By explicitlyrepresenting the disease causes symptoms pathogenesisand the latent correlations among medical informationFigure 9 offers intuitive insights into the underlying path-ological mechanisms

313 Other Validated BPPV Subtype Cases A verificationexperiment on some other clinical cases was performed toevaluate the effectiveness of the proposed method 0ecorrectness was based on the otoneurologistsrsquo judgement onthe diagnostic outcomes in contrast to the practical con-clusions In the clinical center for vertigo in BeijingChaoyang Hospital BPPV cases are common howeverthere are multiple repetitions in the meaningful informationfor the BPPV patients on their medical histories and physicalexaminations regarding subtype differentiation Based on

this 75 typical BPPV cases were selected from the thousandsof cases containing medical records interviews and physicalassessments in the verification experiments 0e BPPVsubtypes involved are outlined in Table 5 0e selectionprinciple of BPPV cases was based on the internationaldiagnostic criteria for BPPV [36] and the typicality andrepresentativeness of BPPV subtype diseases Notably sincethe nystagmus cannot be observed for a subjective BPPVcase it is difficult to classify the case either as canalithiasisBPPV or cupulolithiasis BPPV

0e diagnostic outcomes of the DUCG-based modelagreed with the otoneurologistsrsquo conclusions with a cor-rectness index of 100 Based on the available publishedliterature no other research has reported a model-basedautomatic subtype differentiation of BPPV in the past

32 Comparative Analysis of DUCG and BN 0e maindifference between DUCG and BN in terms of the theoreticalframework is that the model structure and parameters ofDUCG are decoupled By virtue of such a feature the in-dependent causality representation by the weighted causalityfunction event Ankij in DUCG makes it possible to simplifythe original causality graph based on the collected medicalevidence 0e irrelevant and meaningless events and rela-tions are thus eliminated from the model Taking the sim-plified causality graph as the basis of diagnostic reasoningreduces the computational scale and complexity to a largeextent In contrast BN cannot be easily simplified owing tothe structural coupling feature among the variables thecausalities among the child-parent events in BN are typicallyrepresented through a joint probability distribution (eg aconditional probabilistic table CPT) in case any variablesand relations are removed from a BN the remaining pa-rameters in the CPTs may need major adjustments more-over the number of parameters specified in a CPTfor a BN isexponential to the number of the parent variables and statesinvolved while the parameters needed in the DUCG are lessthan the parameters in a BN

Others

B1X3

X4

X5

Others

X3

X4

X5

B2

BV

(a)

Others

X3

X4

Others

X3

X4

BV

B1

B2

(b)

Figure 6 Example of DBV (a) Example 1 (b) Example 2

Figure 7 Diagnostic causality graph for Case 1

10 Computational and Mathematical Methods in Medicine

Furthermore by the independence representation andautomatic normalization feature for the weighted logic eventexpansion the ldquoself-reliantrdquo chaining inference and logicoperations can be performed in DUCG 0e parameters andinformation that are eliminated during the causality simpli-fication and those that are not involved in the chaining in-ference can all be missing (or some parameters which are notof concern are thus not provided) during this reasoningprocess and do not affect the diagnostic accuracy 0e diag-nostic inference method under incomplete information in-dicates that some unnecessary clinical tests and inappropriatemedications can be omitted thereby decreasing the patientsrsquo

medical costs For a BN the reasoning accuracy depends onthe completeness of the parameters in the CPTs

33 Application Analysis 0e proposed method can be de-veloped as an automatic diagnostic system for clinicians Basedon the compact independent and graphical causality repre-sentation using DUCG the model construction and diagnosis

(a) (b)

(c)

Figure 8 Individual causality tracking graphs of the hypotheses for Case 1 (a) LSCC-BPPV (B24) (b) Idiopathic BPPV (B28) (c)Cupulolithiasis BPPV (B30)

Table 3 Diagnostic reasoning results of Case 1

BPPVsubtype Description Ranked independent

probabilityB241 LSCC-BPPV 00388B281 Idiopathic BPPV 09542

B301Cupulolithiasis

BPPV 0007

H11 B241B281B301 1

Figure 9 Diagnostic causality graph for Case 2

Table 4 Diagnostic reasoning results of Case 2

BPPVsubtype Description Ranked independent

probabilityB231 PSCC-BPPV 01435B281 Idiopathic BPPV 07653

B291Canalithiasis

BPPV 00091

B321 Persistent BPPV 00821H11 B231B281B291B321 1

Table 5 BPPV subtypes involved in the validated cases

BPPV subtype No of casesPSCC 53ASCC 1LSCC 16MSCC 5Idiopathic 55Secondary 16Canalithiasis 61Cupulolithiasis 8Subjective 4Persistent 4Recurrent 8Typical 59

Computational and Mathematical Methods in Medicine 11

application are both easy to implement For a patient theclinical data through can be obtained through inquiry physicalexamination and auxiliary examination among others Nextthe clinical data including symptoms signs examination andtest data are input into the diagnostic reasoning interface ofthe system and the diagnosis results can be obtained throughreasoning calculation 0e clinical application of this methodis thus very convenient 0rough incorporation into the au-tomatic medical devices this method could improve the ef-ficiency of BPPV diagnosis and therapy especially for generalpractitioners in primary health care institutions In additionthe system can also be used inmobile and Internet terminals asa secondary tool for telemedicine finally it can serve as ateaching tool for doctor training in related disciplines

4 Summary

0is study proposes a DUCG method for differential di-agnosis of BPPV To distinguish among various causes ofvertiginous disorders with similar symptoms the proposedmethod involves a graphical and compact representation inaddition to logical reasoning algorithms for pathologicalmechanisms and related uncertain causalities New algo-rithms of differential diagnostic reasoning are proposed byintegrating a pruning strategy in the causality simplificationprocess a maximizing concurrent basic event set strategy inthe formulation of hypothesis space and the weighted logicinference rules for subtype differentiation of BPPV Fur-thermore a scheme of dummy basic variable is introduced tosettle the problems related to mutually exclusive root causeevents 0e model manifests higher correctness favorablerobustness to incomplete evidence and satisfactory dis-criminatory power for BPPV subtypes Furthermore usingthe diagnostic reasoning method and graphical represen-tation mechanism not only provides a diagnostic result butalso explains the rationale for suggesting the diseases whichjustifies the probability results

In light of these encouraging preliminary results moreclinical studies will be performed Furthermore a newmethod of probabilistic prediction for the vestibular dys-function-induced fall risk will be the subject of our futureresearch endeavors

Data Availability

0e data used to support the findings of this study are se-lected from the clinical cases of Department of Otorhino-laryngology Head and Neck Surgery Beijing Chaoyanghospital Requests for access to these data should be made toYanjun Wang (docwyjn163com Beijing Chaoyanghospital)

Disclosure

Chunling Dong and Yanjun Wang are cofirst authors

Conflicts of Interest

0e authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

0is work was supported in part by the National NaturalScience Foundation of China under Grant no 71671103 andin part by the Fundamental Research Funds for the CentralUniversities under Grant nos CUC2019B023CUC19ZD008 and CUC19ZD007

References

[1] N Bhattacharyya R F Baugh L Orvidas et al ldquoClinicalpractice guideline benign paroxysmal positional vertigordquoOtolaryngologymdashHead and Neck Surgery vol 139 no 5_suppl pp S47ndashS81 2008

[2] J S Oghalai S Manolidis J L Barth M G Stewart andH A Jenkins ldquoUnrecognized benign paroxysmal positionalvertigo in elderly patientsrdquo OtolaryngologymdashHead and NeckSurgery vol 122 no 5 pp 630ndash634 2000

[3] M P Prim-Espada J I De Diego-Sastre and E Perez-Fernandez ldquoEstudio metaanalıtico de la eficacia de la man-iobra de Epley en el vertigo posicional paroxıstico benignordquoNeurologıa vol 25 no 5 pp 295ndash299 2010

[4] L S Parnes S K Agrawal and J Atlas ldquoDiagnosis andmanagement of benign paroxysmal positional vertigo(BPPV)rdquo Canadian Medical Association Journal vol 169no 7 pp 681ndash693 2003

[5] J C Li and J Epley ldquo0e 360-degree maneuver for treatmentof benign positional vertigordquo Otology amp Neurotology vol 27no 1 pp 71ndash77 2006

[6] R Isola R Carvalho and A K Tripathy ldquoKnowledge dis-covery in medical systems using differential diagnosisLAMSTAR and $k$-NNrdquo IEEE Transactions on InformationTechnology in Biomedicine vol 16 no 6 pp 1287ndash1295 2012

[7] A L Barabasi N Gulbahce and J Loscalzo ldquoNetworkmedicine a network-based approach to human diseaserdquoNature Reviews Genetics vol 12 no 1 pp 56ndash68 2011

[8] E Mira A Buizza G Magenes M Manfrin and R SchmidldquoExpert systems as a diagnostic aid in otoneurologyrdquo Journalfor Oto-Rhino-Laryngology and Its Related Specialties (ORL)vol 52 no 2 pp 96ndash103 1990

[9] C E S Gavilan J E Gallego and J Gavilan ldquoCarnisel anexpert system for vestibular diagnosisrdquo Acta Oto-Lar-yngologica vol 110 no 3-4 pp 161ndash167 1990

[10] E Kentala I Pyykko Y Auramo J Laurikkala andM Juhola ldquoOtoneurological expert system for vertigordquo ActaOto-Laryngologica vol 119 no 5 pp 517ndash521 1999

[11] E Kentala K Viikki I Pyykko andM Juhola ldquoProduction ofdiagnostic rules from a neurotologic database with decisiontreesrdquo Annals of Otology Rhinology and Laryngology vol 109no 2 pp 170ndash176 2000

[12] J W Song J H Lee J H Choi and S J Chun ldquoAutomaticdifferential diagnosis of pancreatic serous and mucinouscystadenomas based on morphological featuresrdquo Computersin Biology and Medicine vol 43 no 1 pp 1ndash15 2013

[13] M H Lopes N R Ortega P S Silveira E Massad R Higaand F Marin Hde ldquoFuzzy cognitive map in differential di-agnosis of alterations in urinary elimination a nursing ap-proachrdquo International Journal of Medical Informatics vol 82no 3 pp 201ndash208 2013

[14] C Salvatore A Cerasa I Castiglioni et al ldquoMachine learningon brain MRI data for differential diagnosis of Parkinsonrsquosdisease and Progressive Supranuclear Palsyrdquo Journal ofNeuroscience Methods vol 222 pp 230ndash237 2014

12 Computational and Mathematical Methods in Medicine

0e problem of disobeying the autonormalization fea-ture can thus be addressed 0is method is illustrated via anexample in Figure 6(a) Suppose that B11 and B21 aremutually exclusive events 0ey are then combined into aDBV-Bv during the reasoning process corresponding to Bv1and Bv2 respectively From the definition of DBVa31v1 equiv a3111 a41v2 equiv a4121 a51v2 equiv a5121 and rnv equiv rniwhere i isin 1 2 and n isin 3 4 5 Figure 6(b) shows an ex-ample where an event (eg X3) is connected to more thanone basic event In this case rnv is defined as rnv equiv 1113936irni ifFnine 00us r3v r31 + r32 for the case in Figure 6(b) whichpoints out to a combination of basic events

In the context of differential diagnosis and upon thecompletion of causality simplifications the obtained can-didate hypotheses of C1 B231 B241 B251 B261 (there aremore than one basic event in the set) should be combinedinto a DBV-Bm with Bmk denoting Bi1 where k 1 2 3 4and i 23 24 25 26 PrBmk refers to the prior probabilityof Bi1 and Pr Bm01113966 1113967 1 minus 1113936kne0Pr Bmk1113966 1113967

Definition 5 (Ranked Independent Probability) 0e rankedindependent probability represents a new metric proposedfor quantifying the degree of confidence in whether a BPPVsubtype (eg Bi1 as a part of the hypothesis Hkj) can in-dependently interpret all the medical evidence in com-parison with the other subtypes coexisting in Hkj 0eranked independent probability of Bi1 is calculated as fol-lows (1) get hs

i1 of Bi1 according to (2) and (3) in which ζi isbased on the individual causality tracking graph of Bi1 and(2) for all the Bi1 within the set of Hkj hs

i1 is ranked byhs

i11113936ihsi1

24 eoretical Analysis of the Reasoning Complexity 0einference algorithm for the proposed method reduces thereasoning complexity in two ways First the causality graphsimplification and pruning strategy significantly decreases themodel scale 0e variables that are irrelevant or inconsistentwith the medical evidence are excluded from the reasoning

calculation 0is significantly reduces the computationalcomplexity Moreover the diagnostic reasoning conclusioncan even be accurately drawn solely via the causality sim-plification Second prior to probabilistic reasoning weightedlogic inference is performed based on the simplified causalitygraph 0us the multiple connected causalities can bedecomposed independently leading the chaining inference toexhibit high efficiency Furthermore the proposed logicalinference rules and logical operations can decrease thecomplexity and scale of logical event expressions

0e actual efficiency tests for the DUCG inference al-gorithm have been performed using online fault diagnosisdata from several large-scale industrial systems (eg nuclearpower plants) in which thousands of variables and causalityarcs are involved [28 31] 0e diagnostic reasoning cantypically be finished within 05ndash1 s (on a personal computer)Moreover the inference efficiency has been verified from ourpast clinical diagnosis applications that involved dozens ofdiseases such as jaundice and sellar region disease

3 Experiments and Analyses

31 Clinical Validation of the BPPV Differential DiagnosisMethod

311 Differential Diagnosis for BPPVmdashCase 1 Suppose thatthe medical evidence of a patient was observed in part asX41 X212 X243 X1844 X1852 X2094 X2292 X2302 X2070X2080 X2360 in Figure 2 and other X-type variables arenormal or unknown (incomplete medical information) 0emedical information in this experiment is from a 65-year-oldfemale patient who suffered from brief episodes of vertigowhen rolling over in bed for two weeks and was suspected tobe a BPPV case according to the supine roll test

Based on the evidence in this case Figure 2 can besimplified into the graph shown in Figure 7 by applying thecausality simplification rules and pruning strategy Manymeaningless relationships and events under current situa-tion are eliminated accordingly with SH B241 B281 B301

BeginFor a BPPV patientCollect medical evidence E including symptoms signs examination findings laboratory tests and medical historiesPerform causality simplification to the BPPV causality graph based on the evidence EApply the causality simplification mechanisms including the pruning strategy and causality tracking processObtain the simplified diagnostic causality graph

Perform the algorithms of weighted logic inference based on the simplified causality graphPerform the weighted logic event expansion to the evidence according to (1)Perform logic inference according to (2)

Apply the weighted logic inference rules 1sim6 of differential diagnosis for BPPVApply the scheme of dummy basic variablePerform the basic logic operations

Obtain the hypothesis event space SH Hkj1113966 1113967

Perform the probabilistic reasonings to obtain the posterior probability of Hkj conditioned on E hskj

Calculate the ranked independent probability of a BPPV subtypeEnd

ALGORITHM 1 Differential diagnostic reasoning method for BPPV

Computational and Mathematical Methods in Medicine 9

being inferred as the possible root causes 0e resultinghypothesis space SH is concise with all unlikely hypothesesbeing excluded from concern Moreover the individualcausality tracking graphs for the three root cause events B24B28 and B30 in Figure 7 are shown in Figure 8 whereby eachsubgraph independently covers all evidence0e graphs thusintuitively and faithfully represent the causalities underlyingthe pathogenesis of Case 1

By applying the algorithm of differential diagnosticreasoning for Case 1 the state probability ofH11 B241B281B301 can be obtained as hs

11

Pr H11 | E1113966 1113967 1 0e obtained ldquoranked independent prob-abilitiesrdquo of B241 B281 and B301 are listed in Table 3 0eLSCC-idiopathic-cupulolithiasis BPPV is therefore deter-mined as the diagnostic result of Case 1 this result isconsistent with the clinical conclusions confirmed byotoneurologists

312 Differential Diagnosis for BPPVmdashCase 2 A 72-year-old female patient complained about paroxysmal positionalvertigo for a month the attacks of vertigo were brief lastingfor one minute the vertigo frequently occurred whilelooking up or down0us the medical evidence for this caseis X41 X212 X243 X1844 X1852 X2070 X2080 X2093 X2223X2231 X2241 X2251 X2261 X2360 the other X-type variablesare normal or unknown (incomplete medical information)

By applying the algorithm of differential diagnosticreasoning the hypothesis event H11 B231B281B291B321 isuniquely determined as the origin of the disease whichindicates a PSCC-idiopathic-cupulolithiasis-persistentBPPV 0e diagnostic causality graph is shown in Figure 9which is based on the causality simplification of Figure 20e resulting ranked independent probabilities of B231B281 B291 and B321 are listed in Table 4 By explicitlyrepresenting the disease causes symptoms pathogenesisand the latent correlations among medical informationFigure 9 offers intuitive insights into the underlying path-ological mechanisms

313 Other Validated BPPV Subtype Cases A verificationexperiment on some other clinical cases was performed toevaluate the effectiveness of the proposed method 0ecorrectness was based on the otoneurologistsrsquo judgement onthe diagnostic outcomes in contrast to the practical con-clusions In the clinical center for vertigo in BeijingChaoyang Hospital BPPV cases are common howeverthere are multiple repetitions in the meaningful informationfor the BPPV patients on their medical histories and physicalexaminations regarding subtype differentiation Based on

this 75 typical BPPV cases were selected from the thousandsof cases containing medical records interviews and physicalassessments in the verification experiments 0e BPPVsubtypes involved are outlined in Table 5 0e selectionprinciple of BPPV cases was based on the internationaldiagnostic criteria for BPPV [36] and the typicality andrepresentativeness of BPPV subtype diseases Notably sincethe nystagmus cannot be observed for a subjective BPPVcase it is difficult to classify the case either as canalithiasisBPPV or cupulolithiasis BPPV

0e diagnostic outcomes of the DUCG-based modelagreed with the otoneurologistsrsquo conclusions with a cor-rectness index of 100 Based on the available publishedliterature no other research has reported a model-basedautomatic subtype differentiation of BPPV in the past

32 Comparative Analysis of DUCG and BN 0e maindifference between DUCG and BN in terms of the theoreticalframework is that the model structure and parameters ofDUCG are decoupled By virtue of such a feature the in-dependent causality representation by the weighted causalityfunction event Ankij in DUCG makes it possible to simplifythe original causality graph based on the collected medicalevidence 0e irrelevant and meaningless events and rela-tions are thus eliminated from the model Taking the sim-plified causality graph as the basis of diagnostic reasoningreduces the computational scale and complexity to a largeextent In contrast BN cannot be easily simplified owing tothe structural coupling feature among the variables thecausalities among the child-parent events in BN are typicallyrepresented through a joint probability distribution (eg aconditional probabilistic table CPT) in case any variablesand relations are removed from a BN the remaining pa-rameters in the CPTs may need major adjustments more-over the number of parameters specified in a CPTfor a BN isexponential to the number of the parent variables and statesinvolved while the parameters needed in the DUCG are lessthan the parameters in a BN

Others

B1X3

X4

X5

Others

X3

X4

X5

B2

BV

(a)

Others

X3

X4

Others

X3

X4

BV

B1

B2

(b)

Figure 6 Example of DBV (a) Example 1 (b) Example 2

Figure 7 Diagnostic causality graph for Case 1

10 Computational and Mathematical Methods in Medicine

Furthermore by the independence representation andautomatic normalization feature for the weighted logic eventexpansion the ldquoself-reliantrdquo chaining inference and logicoperations can be performed in DUCG 0e parameters andinformation that are eliminated during the causality simpli-fication and those that are not involved in the chaining in-ference can all be missing (or some parameters which are notof concern are thus not provided) during this reasoningprocess and do not affect the diagnostic accuracy 0e diag-nostic inference method under incomplete information in-dicates that some unnecessary clinical tests and inappropriatemedications can be omitted thereby decreasing the patientsrsquo

medical costs For a BN the reasoning accuracy depends onthe completeness of the parameters in the CPTs

33 Application Analysis 0e proposed method can be de-veloped as an automatic diagnostic system for clinicians Basedon the compact independent and graphical causality repre-sentation using DUCG the model construction and diagnosis

(a) (b)

(c)

Figure 8 Individual causality tracking graphs of the hypotheses for Case 1 (a) LSCC-BPPV (B24) (b) Idiopathic BPPV (B28) (c)Cupulolithiasis BPPV (B30)

Table 3 Diagnostic reasoning results of Case 1

BPPVsubtype Description Ranked independent

probabilityB241 LSCC-BPPV 00388B281 Idiopathic BPPV 09542

B301Cupulolithiasis

BPPV 0007

H11 B241B281B301 1

Figure 9 Diagnostic causality graph for Case 2

Table 4 Diagnostic reasoning results of Case 2

BPPVsubtype Description Ranked independent

probabilityB231 PSCC-BPPV 01435B281 Idiopathic BPPV 07653

B291Canalithiasis

BPPV 00091

B321 Persistent BPPV 00821H11 B231B281B291B321 1

Table 5 BPPV subtypes involved in the validated cases

BPPV subtype No of casesPSCC 53ASCC 1LSCC 16MSCC 5Idiopathic 55Secondary 16Canalithiasis 61Cupulolithiasis 8Subjective 4Persistent 4Recurrent 8Typical 59

Computational and Mathematical Methods in Medicine 11

application are both easy to implement For a patient theclinical data through can be obtained through inquiry physicalexamination and auxiliary examination among others Nextthe clinical data including symptoms signs examination andtest data are input into the diagnostic reasoning interface ofthe system and the diagnosis results can be obtained throughreasoning calculation 0e clinical application of this methodis thus very convenient 0rough incorporation into the au-tomatic medical devices this method could improve the ef-ficiency of BPPV diagnosis and therapy especially for generalpractitioners in primary health care institutions In additionthe system can also be used inmobile and Internet terminals asa secondary tool for telemedicine finally it can serve as ateaching tool for doctor training in related disciplines

4 Summary

0is study proposes a DUCG method for differential di-agnosis of BPPV To distinguish among various causes ofvertiginous disorders with similar symptoms the proposedmethod involves a graphical and compact representation inaddition to logical reasoning algorithms for pathologicalmechanisms and related uncertain causalities New algo-rithms of differential diagnostic reasoning are proposed byintegrating a pruning strategy in the causality simplificationprocess a maximizing concurrent basic event set strategy inthe formulation of hypothesis space and the weighted logicinference rules for subtype differentiation of BPPV Fur-thermore a scheme of dummy basic variable is introduced tosettle the problems related to mutually exclusive root causeevents 0e model manifests higher correctness favorablerobustness to incomplete evidence and satisfactory dis-criminatory power for BPPV subtypes Furthermore usingthe diagnostic reasoning method and graphical represen-tation mechanism not only provides a diagnostic result butalso explains the rationale for suggesting the diseases whichjustifies the probability results

In light of these encouraging preliminary results moreclinical studies will be performed Furthermore a newmethod of probabilistic prediction for the vestibular dys-function-induced fall risk will be the subject of our futureresearch endeavors

Data Availability

0e data used to support the findings of this study are se-lected from the clinical cases of Department of Otorhino-laryngology Head and Neck Surgery Beijing Chaoyanghospital Requests for access to these data should be made toYanjun Wang (docwyjn163com Beijing Chaoyanghospital)

Disclosure

Chunling Dong and Yanjun Wang are cofirst authors

Conflicts of Interest

0e authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

0is work was supported in part by the National NaturalScience Foundation of China under Grant no 71671103 andin part by the Fundamental Research Funds for the CentralUniversities under Grant nos CUC2019B023CUC19ZD008 and CUC19ZD007

References

[1] N Bhattacharyya R F Baugh L Orvidas et al ldquoClinicalpractice guideline benign paroxysmal positional vertigordquoOtolaryngologymdashHead and Neck Surgery vol 139 no 5_suppl pp S47ndashS81 2008

[2] J S Oghalai S Manolidis J L Barth M G Stewart andH A Jenkins ldquoUnrecognized benign paroxysmal positionalvertigo in elderly patientsrdquo OtolaryngologymdashHead and NeckSurgery vol 122 no 5 pp 630ndash634 2000

[3] M P Prim-Espada J I De Diego-Sastre and E Perez-Fernandez ldquoEstudio metaanalıtico de la eficacia de la man-iobra de Epley en el vertigo posicional paroxıstico benignordquoNeurologıa vol 25 no 5 pp 295ndash299 2010

[4] L S Parnes S K Agrawal and J Atlas ldquoDiagnosis andmanagement of benign paroxysmal positional vertigo(BPPV)rdquo Canadian Medical Association Journal vol 169no 7 pp 681ndash693 2003

[5] J C Li and J Epley ldquo0e 360-degree maneuver for treatmentof benign positional vertigordquo Otology amp Neurotology vol 27no 1 pp 71ndash77 2006

[6] R Isola R Carvalho and A K Tripathy ldquoKnowledge dis-covery in medical systems using differential diagnosisLAMSTAR and $k$-NNrdquo IEEE Transactions on InformationTechnology in Biomedicine vol 16 no 6 pp 1287ndash1295 2012

[7] A L Barabasi N Gulbahce and J Loscalzo ldquoNetworkmedicine a network-based approach to human diseaserdquoNature Reviews Genetics vol 12 no 1 pp 56ndash68 2011

[8] E Mira A Buizza G Magenes M Manfrin and R SchmidldquoExpert systems as a diagnostic aid in otoneurologyrdquo Journalfor Oto-Rhino-Laryngology and Its Related Specialties (ORL)vol 52 no 2 pp 96ndash103 1990

[9] C E S Gavilan J E Gallego and J Gavilan ldquoCarnisel anexpert system for vestibular diagnosisrdquo Acta Oto-Lar-yngologica vol 110 no 3-4 pp 161ndash167 1990

[10] E Kentala I Pyykko Y Auramo J Laurikkala andM Juhola ldquoOtoneurological expert system for vertigordquo ActaOto-Laryngologica vol 119 no 5 pp 517ndash521 1999

[11] E Kentala K Viikki I Pyykko andM Juhola ldquoProduction ofdiagnostic rules from a neurotologic database with decisiontreesrdquo Annals of Otology Rhinology and Laryngology vol 109no 2 pp 170ndash176 2000

[12] J W Song J H Lee J H Choi and S J Chun ldquoAutomaticdifferential diagnosis of pancreatic serous and mucinouscystadenomas based on morphological featuresrdquo Computersin Biology and Medicine vol 43 no 1 pp 1ndash15 2013

[13] M H Lopes N R Ortega P S Silveira E Massad R Higaand F Marin Hde ldquoFuzzy cognitive map in differential di-agnosis of alterations in urinary elimination a nursing ap-proachrdquo International Journal of Medical Informatics vol 82no 3 pp 201ndash208 2013

[14] C Salvatore A Cerasa I Castiglioni et al ldquoMachine learningon brain MRI data for differential diagnosis of Parkinsonrsquosdisease and Progressive Supranuclear Palsyrdquo Journal ofNeuroscience Methods vol 222 pp 230ndash237 2014

12 Computational and Mathematical Methods in Medicine

being inferred as the possible root causes 0e resultinghypothesis space SH is concise with all unlikely hypothesesbeing excluded from concern Moreover the individualcausality tracking graphs for the three root cause events B24B28 and B30 in Figure 7 are shown in Figure 8 whereby eachsubgraph independently covers all evidence0e graphs thusintuitively and faithfully represent the causalities underlyingthe pathogenesis of Case 1

By applying the algorithm of differential diagnosticreasoning for Case 1 the state probability ofH11 B241B281B301 can be obtained as hs

11

Pr H11 | E1113966 1113967 1 0e obtained ldquoranked independent prob-abilitiesrdquo of B241 B281 and B301 are listed in Table 3 0eLSCC-idiopathic-cupulolithiasis BPPV is therefore deter-mined as the diagnostic result of Case 1 this result isconsistent with the clinical conclusions confirmed byotoneurologists

312 Differential Diagnosis for BPPVmdashCase 2 A 72-year-old female patient complained about paroxysmal positionalvertigo for a month the attacks of vertigo were brief lastingfor one minute the vertigo frequently occurred whilelooking up or down0us the medical evidence for this caseis X41 X212 X243 X1844 X1852 X2070 X2080 X2093 X2223X2231 X2241 X2251 X2261 X2360 the other X-type variablesare normal or unknown (incomplete medical information)

By applying the algorithm of differential diagnosticreasoning the hypothesis event H11 B231B281B291B321 isuniquely determined as the origin of the disease whichindicates a PSCC-idiopathic-cupulolithiasis-persistentBPPV 0e diagnostic causality graph is shown in Figure 9which is based on the causality simplification of Figure 20e resulting ranked independent probabilities of B231B281 B291 and B321 are listed in Table 4 By explicitlyrepresenting the disease causes symptoms pathogenesisand the latent correlations among medical informationFigure 9 offers intuitive insights into the underlying path-ological mechanisms

313 Other Validated BPPV Subtype Cases A verificationexperiment on some other clinical cases was performed toevaluate the effectiveness of the proposed method 0ecorrectness was based on the otoneurologistsrsquo judgement onthe diagnostic outcomes in contrast to the practical con-clusions In the clinical center for vertigo in BeijingChaoyang Hospital BPPV cases are common howeverthere are multiple repetitions in the meaningful informationfor the BPPV patients on their medical histories and physicalexaminations regarding subtype differentiation Based on

this 75 typical BPPV cases were selected from the thousandsof cases containing medical records interviews and physicalassessments in the verification experiments 0e BPPVsubtypes involved are outlined in Table 5 0e selectionprinciple of BPPV cases was based on the internationaldiagnostic criteria for BPPV [36] and the typicality andrepresentativeness of BPPV subtype diseases Notably sincethe nystagmus cannot be observed for a subjective BPPVcase it is difficult to classify the case either as canalithiasisBPPV or cupulolithiasis BPPV

0e diagnostic outcomes of the DUCG-based modelagreed with the otoneurologistsrsquo conclusions with a cor-rectness index of 100 Based on the available publishedliterature no other research has reported a model-basedautomatic subtype differentiation of BPPV in the past

32 Comparative Analysis of DUCG and BN 0e maindifference between DUCG and BN in terms of the theoreticalframework is that the model structure and parameters ofDUCG are decoupled By virtue of such a feature the in-dependent causality representation by the weighted causalityfunction event Ankij in DUCG makes it possible to simplifythe original causality graph based on the collected medicalevidence 0e irrelevant and meaningless events and rela-tions are thus eliminated from the model Taking the sim-plified causality graph as the basis of diagnostic reasoningreduces the computational scale and complexity to a largeextent In contrast BN cannot be easily simplified owing tothe structural coupling feature among the variables thecausalities among the child-parent events in BN are typicallyrepresented through a joint probability distribution (eg aconditional probabilistic table CPT) in case any variablesand relations are removed from a BN the remaining pa-rameters in the CPTs may need major adjustments more-over the number of parameters specified in a CPTfor a BN isexponential to the number of the parent variables and statesinvolved while the parameters needed in the DUCG are lessthan the parameters in a BN

Others

B1X3

X4

X5

Others

X3

X4

X5

B2

BV

(a)

Others

X3

X4

Others

X3

X4

BV

B1

B2

(b)

Figure 6 Example of DBV (a) Example 1 (b) Example 2

Figure 7 Diagnostic causality graph for Case 1

10 Computational and Mathematical Methods in Medicine

Furthermore by the independence representation andautomatic normalization feature for the weighted logic eventexpansion the ldquoself-reliantrdquo chaining inference and logicoperations can be performed in DUCG 0e parameters andinformation that are eliminated during the causality simpli-fication and those that are not involved in the chaining in-ference can all be missing (or some parameters which are notof concern are thus not provided) during this reasoningprocess and do not affect the diagnostic accuracy 0e diag-nostic inference method under incomplete information in-dicates that some unnecessary clinical tests and inappropriatemedications can be omitted thereby decreasing the patientsrsquo

medical costs For a BN the reasoning accuracy depends onthe completeness of the parameters in the CPTs

33 Application Analysis 0e proposed method can be de-veloped as an automatic diagnostic system for clinicians Basedon the compact independent and graphical causality repre-sentation using DUCG the model construction and diagnosis

(a) (b)

(c)

Figure 8 Individual causality tracking graphs of the hypotheses for Case 1 (a) LSCC-BPPV (B24) (b) Idiopathic BPPV (B28) (c)Cupulolithiasis BPPV (B30)

Table 3 Diagnostic reasoning results of Case 1

BPPVsubtype Description Ranked independent

probabilityB241 LSCC-BPPV 00388B281 Idiopathic BPPV 09542

B301Cupulolithiasis

BPPV 0007

H11 B241B281B301 1

Figure 9 Diagnostic causality graph for Case 2

Table 4 Diagnostic reasoning results of Case 2

BPPVsubtype Description Ranked independent

probabilityB231 PSCC-BPPV 01435B281 Idiopathic BPPV 07653

B291Canalithiasis

BPPV 00091

B321 Persistent BPPV 00821H11 B231B281B291B321 1

Table 5 BPPV subtypes involved in the validated cases

BPPV subtype No of casesPSCC 53ASCC 1LSCC 16MSCC 5Idiopathic 55Secondary 16Canalithiasis 61Cupulolithiasis 8Subjective 4Persistent 4Recurrent 8Typical 59

Computational and Mathematical Methods in Medicine 11

application are both easy to implement For a patient theclinical data through can be obtained through inquiry physicalexamination and auxiliary examination among others Nextthe clinical data including symptoms signs examination andtest data are input into the diagnostic reasoning interface ofthe system and the diagnosis results can be obtained throughreasoning calculation 0e clinical application of this methodis thus very convenient 0rough incorporation into the au-tomatic medical devices this method could improve the ef-ficiency of BPPV diagnosis and therapy especially for generalpractitioners in primary health care institutions In additionthe system can also be used inmobile and Internet terminals asa secondary tool for telemedicine finally it can serve as ateaching tool for doctor training in related disciplines

4 Summary

0is study proposes a DUCG method for differential di-agnosis of BPPV To distinguish among various causes ofvertiginous disorders with similar symptoms the proposedmethod involves a graphical and compact representation inaddition to logical reasoning algorithms for pathologicalmechanisms and related uncertain causalities New algo-rithms of differential diagnostic reasoning are proposed byintegrating a pruning strategy in the causality simplificationprocess a maximizing concurrent basic event set strategy inthe formulation of hypothesis space and the weighted logicinference rules for subtype differentiation of BPPV Fur-thermore a scheme of dummy basic variable is introduced tosettle the problems related to mutually exclusive root causeevents 0e model manifests higher correctness favorablerobustness to incomplete evidence and satisfactory dis-criminatory power for BPPV subtypes Furthermore usingthe diagnostic reasoning method and graphical represen-tation mechanism not only provides a diagnostic result butalso explains the rationale for suggesting the diseases whichjustifies the probability results

In light of these encouraging preliminary results moreclinical studies will be performed Furthermore a newmethod of probabilistic prediction for the vestibular dys-function-induced fall risk will be the subject of our futureresearch endeavors

Data Availability

0e data used to support the findings of this study are se-lected from the clinical cases of Department of Otorhino-laryngology Head and Neck Surgery Beijing Chaoyanghospital Requests for access to these data should be made toYanjun Wang (docwyjn163com Beijing Chaoyanghospital)

Disclosure

Chunling Dong and Yanjun Wang are cofirst authors

Conflicts of Interest

0e authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

0is work was supported in part by the National NaturalScience Foundation of China under Grant no 71671103 andin part by the Fundamental Research Funds for the CentralUniversities under Grant nos CUC2019B023CUC19ZD008 and CUC19ZD007

References

[1] N Bhattacharyya R F Baugh L Orvidas et al ldquoClinicalpractice guideline benign paroxysmal positional vertigordquoOtolaryngologymdashHead and Neck Surgery vol 139 no 5_suppl pp S47ndashS81 2008

[2] J S Oghalai S Manolidis J L Barth M G Stewart andH A Jenkins ldquoUnrecognized benign paroxysmal positionalvertigo in elderly patientsrdquo OtolaryngologymdashHead and NeckSurgery vol 122 no 5 pp 630ndash634 2000

[3] M P Prim-Espada J I De Diego-Sastre and E Perez-Fernandez ldquoEstudio metaanalıtico de la eficacia de la man-iobra de Epley en el vertigo posicional paroxıstico benignordquoNeurologıa vol 25 no 5 pp 295ndash299 2010

[4] L S Parnes S K Agrawal and J Atlas ldquoDiagnosis andmanagement of benign paroxysmal positional vertigo(BPPV)rdquo Canadian Medical Association Journal vol 169no 7 pp 681ndash693 2003

[5] J C Li and J Epley ldquo0e 360-degree maneuver for treatmentof benign positional vertigordquo Otology amp Neurotology vol 27no 1 pp 71ndash77 2006

[6] R Isola R Carvalho and A K Tripathy ldquoKnowledge dis-covery in medical systems using differential diagnosisLAMSTAR and $k$-NNrdquo IEEE Transactions on InformationTechnology in Biomedicine vol 16 no 6 pp 1287ndash1295 2012

[7] A L Barabasi N Gulbahce and J Loscalzo ldquoNetworkmedicine a network-based approach to human diseaserdquoNature Reviews Genetics vol 12 no 1 pp 56ndash68 2011

[8] E Mira A Buizza G Magenes M Manfrin and R SchmidldquoExpert systems as a diagnostic aid in otoneurologyrdquo Journalfor Oto-Rhino-Laryngology and Its Related Specialties (ORL)vol 52 no 2 pp 96ndash103 1990

[9] C E S Gavilan J E Gallego and J Gavilan ldquoCarnisel anexpert system for vestibular diagnosisrdquo Acta Oto-Lar-yngologica vol 110 no 3-4 pp 161ndash167 1990

[10] E Kentala I Pyykko Y Auramo J Laurikkala andM Juhola ldquoOtoneurological expert system for vertigordquo ActaOto-Laryngologica vol 119 no 5 pp 517ndash521 1999

[11] E Kentala K Viikki I Pyykko andM Juhola ldquoProduction ofdiagnostic rules from a neurotologic database with decisiontreesrdquo Annals of Otology Rhinology and Laryngology vol 109no 2 pp 170ndash176 2000

[12] J W Song J H Lee J H Choi and S J Chun ldquoAutomaticdifferential diagnosis of pancreatic serous and mucinouscystadenomas based on morphological featuresrdquo Computersin Biology and Medicine vol 43 no 1 pp 1ndash15 2013

[13] M H Lopes N R Ortega P S Silveira E Massad R Higaand F Marin Hde ldquoFuzzy cognitive map in differential di-agnosis of alterations in urinary elimination a nursing ap-proachrdquo International Journal of Medical Informatics vol 82no 3 pp 201ndash208 2013

[14] C Salvatore A Cerasa I Castiglioni et al ldquoMachine learningon brain MRI data for differential diagnosis of Parkinsonrsquosdisease and Progressive Supranuclear Palsyrdquo Journal ofNeuroscience Methods vol 222 pp 230ndash237 2014

12 Computational and Mathematical Methods in Medicine

Furthermore by the independence representation andautomatic normalization feature for the weighted logic eventexpansion the ldquoself-reliantrdquo chaining inference and logicoperations can be performed in DUCG 0e parameters andinformation that are eliminated during the causality simpli-fication and those that are not involved in the chaining in-ference can all be missing (or some parameters which are notof concern are thus not provided) during this reasoningprocess and do not affect the diagnostic accuracy 0e diag-nostic inference method under incomplete information in-dicates that some unnecessary clinical tests and inappropriatemedications can be omitted thereby decreasing the patientsrsquo

medical costs For a BN the reasoning accuracy depends onthe completeness of the parameters in the CPTs

33 Application Analysis 0e proposed method can be de-veloped as an automatic diagnostic system for clinicians Basedon the compact independent and graphical causality repre-sentation using DUCG the model construction and diagnosis

(a) (b)

(c)

Figure 8 Individual causality tracking graphs of the hypotheses for Case 1 (a) LSCC-BPPV (B24) (b) Idiopathic BPPV (B28) (c)Cupulolithiasis BPPV (B30)

Table 3 Diagnostic reasoning results of Case 1

BPPVsubtype Description Ranked independent

probabilityB241 LSCC-BPPV 00388B281 Idiopathic BPPV 09542

B301Cupulolithiasis

BPPV 0007

H11 B241B281B301 1

Figure 9 Diagnostic causality graph for Case 2

Table 4 Diagnostic reasoning results of Case 2

BPPVsubtype Description Ranked independent

probabilityB231 PSCC-BPPV 01435B281 Idiopathic BPPV 07653

B291Canalithiasis

BPPV 00091

B321 Persistent BPPV 00821H11 B231B281B291B321 1

Table 5 BPPV subtypes involved in the validated cases

BPPV subtype No of casesPSCC 53ASCC 1LSCC 16MSCC 5Idiopathic 55Secondary 16Canalithiasis 61Cupulolithiasis 8Subjective 4Persistent 4Recurrent 8Typical 59

Computational and Mathematical Methods in Medicine 11

application are both easy to implement For a patient theclinical data through can be obtained through inquiry physicalexamination and auxiliary examination among others Nextthe clinical data including symptoms signs examination andtest data are input into the diagnostic reasoning interface ofthe system and the diagnosis results can be obtained throughreasoning calculation 0e clinical application of this methodis thus very convenient 0rough incorporation into the au-tomatic medical devices this method could improve the ef-ficiency of BPPV diagnosis and therapy especially for generalpractitioners in primary health care institutions In additionthe system can also be used inmobile and Internet terminals asa secondary tool for telemedicine finally it can serve as ateaching tool for doctor training in related disciplines

4 Summary

0is study proposes a DUCG method for differential di-agnosis of BPPV To distinguish among various causes ofvertiginous disorders with similar symptoms the proposedmethod involves a graphical and compact representation inaddition to logical reasoning algorithms for pathologicalmechanisms and related uncertain causalities New algo-rithms of differential diagnostic reasoning are proposed byintegrating a pruning strategy in the causality simplificationprocess a maximizing concurrent basic event set strategy inthe formulation of hypothesis space and the weighted logicinference rules for subtype differentiation of BPPV Fur-thermore a scheme of dummy basic variable is introduced tosettle the problems related to mutually exclusive root causeevents 0e model manifests higher correctness favorablerobustness to incomplete evidence and satisfactory dis-criminatory power for BPPV subtypes Furthermore usingthe diagnostic reasoning method and graphical represen-tation mechanism not only provides a diagnostic result butalso explains the rationale for suggesting the diseases whichjustifies the probability results

In light of these encouraging preliminary results moreclinical studies will be performed Furthermore a newmethod of probabilistic prediction for the vestibular dys-function-induced fall risk will be the subject of our futureresearch endeavors

Data Availability

0e data used to support the findings of this study are se-lected from the clinical cases of Department of Otorhino-laryngology Head and Neck Surgery Beijing Chaoyanghospital Requests for access to these data should be made toYanjun Wang (docwyjn163com Beijing Chaoyanghospital)

Disclosure

Chunling Dong and Yanjun Wang are cofirst authors

Conflicts of Interest

0e authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

0is work was supported in part by the National NaturalScience Foundation of China under Grant no 71671103 andin part by the Fundamental Research Funds for the CentralUniversities under Grant nos CUC2019B023CUC19ZD008 and CUC19ZD007

References

[1] N Bhattacharyya R F Baugh L Orvidas et al ldquoClinicalpractice guideline benign paroxysmal positional vertigordquoOtolaryngologymdashHead and Neck Surgery vol 139 no 5_suppl pp S47ndashS81 2008

[2] J S Oghalai S Manolidis J L Barth M G Stewart andH A Jenkins ldquoUnrecognized benign paroxysmal positionalvertigo in elderly patientsrdquo OtolaryngologymdashHead and NeckSurgery vol 122 no 5 pp 630ndash634 2000

[3] M P Prim-Espada J I De Diego-Sastre and E Perez-Fernandez ldquoEstudio metaanalıtico de la eficacia de la man-iobra de Epley en el vertigo posicional paroxıstico benignordquoNeurologıa vol 25 no 5 pp 295ndash299 2010

[4] L S Parnes S K Agrawal and J Atlas ldquoDiagnosis andmanagement of benign paroxysmal positional vertigo(BPPV)rdquo Canadian Medical Association Journal vol 169no 7 pp 681ndash693 2003

[5] J C Li and J Epley ldquo0e 360-degree maneuver for treatmentof benign positional vertigordquo Otology amp Neurotology vol 27no 1 pp 71ndash77 2006

[6] R Isola R Carvalho and A K Tripathy ldquoKnowledge dis-covery in medical systems using differential diagnosisLAMSTAR and $k$-NNrdquo IEEE Transactions on InformationTechnology in Biomedicine vol 16 no 6 pp 1287ndash1295 2012

[7] A L Barabasi N Gulbahce and J Loscalzo ldquoNetworkmedicine a network-based approach to human diseaserdquoNature Reviews Genetics vol 12 no 1 pp 56ndash68 2011

[8] E Mira A Buizza G Magenes M Manfrin and R SchmidldquoExpert systems as a diagnostic aid in otoneurologyrdquo Journalfor Oto-Rhino-Laryngology and Its Related Specialties (ORL)vol 52 no 2 pp 96ndash103 1990

[9] C E S Gavilan J E Gallego and J Gavilan ldquoCarnisel anexpert system for vestibular diagnosisrdquo Acta Oto-Lar-yngologica vol 110 no 3-4 pp 161ndash167 1990

[10] E Kentala I Pyykko Y Auramo J Laurikkala andM Juhola ldquoOtoneurological expert system for vertigordquo ActaOto-Laryngologica vol 119 no 5 pp 517ndash521 1999

[11] E Kentala K Viikki I Pyykko andM Juhola ldquoProduction ofdiagnostic rules from a neurotologic database with decisiontreesrdquo Annals of Otology Rhinology and Laryngology vol 109no 2 pp 170ndash176 2000

[12] J W Song J H Lee J H Choi and S J Chun ldquoAutomaticdifferential diagnosis of pancreatic serous and mucinouscystadenomas based on morphological featuresrdquo Computersin Biology and Medicine vol 43 no 1 pp 1ndash15 2013

[13] M H Lopes N R Ortega P S Silveira E Massad R Higaand F Marin Hde ldquoFuzzy cognitive map in differential di-agnosis of alterations in urinary elimination a nursing ap-proachrdquo International Journal of Medical Informatics vol 82no 3 pp 201ndash208 2013

[14] C Salvatore A Cerasa I Castiglioni et al ldquoMachine learningon brain MRI data for differential diagnosis of Parkinsonrsquosdisease and Progressive Supranuclear Palsyrdquo Journal ofNeuroscience Methods vol 222 pp 230ndash237 2014

12 Computational and Mathematical Methods in Medicine

application are both easy to implement For a patient theclinical data through can be obtained through inquiry physicalexamination and auxiliary examination among others Nextthe clinical data including symptoms signs examination andtest data are input into the diagnostic reasoning interface ofthe system and the diagnosis results can be obtained throughreasoning calculation 0e clinical application of this methodis thus very convenient 0rough incorporation into the au-tomatic medical devices this method could improve the ef-ficiency of BPPV diagnosis and therapy especially for generalpractitioners in primary health care institutions In additionthe system can also be used inmobile and Internet terminals asa secondary tool for telemedicine finally it can serve as ateaching tool for doctor training in related disciplines

4 Summary

0is study proposes a DUCG method for differential di-agnosis of BPPV To distinguish among various causes ofvertiginous disorders with similar symptoms the proposedmethod involves a graphical and compact representation inaddition to logical reasoning algorithms for pathologicalmechanisms and related uncertain causalities New algo-rithms of differential diagnostic reasoning are proposed byintegrating a pruning strategy in the causality simplificationprocess a maximizing concurrent basic event set strategy inthe formulation of hypothesis space and the weighted logicinference rules for subtype differentiation of BPPV Fur-thermore a scheme of dummy basic variable is introduced tosettle the problems related to mutually exclusive root causeevents 0e model manifests higher correctness favorablerobustness to incomplete evidence and satisfactory dis-criminatory power for BPPV subtypes Furthermore usingthe diagnostic reasoning method and graphical represen-tation mechanism not only provides a diagnostic result butalso explains the rationale for suggesting the diseases whichjustifies the probability results

In light of these encouraging preliminary results moreclinical studies will be performed Furthermore a newmethod of probabilistic prediction for the vestibular dys-function-induced fall risk will be the subject of our futureresearch endeavors

Data Availability

0e data used to support the findings of this study are se-lected from the clinical cases of Department of Otorhino-laryngology Head and Neck Surgery Beijing Chaoyanghospital Requests for access to these data should be made toYanjun Wang (docwyjn163com Beijing Chaoyanghospital)

Disclosure

Chunling Dong and Yanjun Wang are cofirst authors

Conflicts of Interest

0e authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

0is work was supported in part by the National NaturalScience Foundation of China under Grant no 71671103 andin part by the Fundamental Research Funds for the CentralUniversities under Grant nos CUC2019B023CUC19ZD008 and CUC19ZD007

References

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[2] J S Oghalai S Manolidis J L Barth M G Stewart andH A Jenkins ldquoUnrecognized benign paroxysmal positionalvertigo in elderly patientsrdquo OtolaryngologymdashHead and NeckSurgery vol 122 no 5 pp 630ndash634 2000

[3] M P Prim-Espada J I De Diego-Sastre and E Perez-Fernandez ldquoEstudio metaanalıtico de la eficacia de la man-iobra de Epley en el vertigo posicional paroxıstico benignordquoNeurologıa vol 25 no 5 pp 295ndash299 2010

[4] L S Parnes S K Agrawal and J Atlas ldquoDiagnosis andmanagement of benign paroxysmal positional vertigo(BPPV)rdquo Canadian Medical Association Journal vol 169no 7 pp 681ndash693 2003

[5] J C Li and J Epley ldquo0e 360-degree maneuver for treatmentof benign positional vertigordquo Otology amp Neurotology vol 27no 1 pp 71ndash77 2006

[6] R Isola R Carvalho and A K Tripathy ldquoKnowledge dis-covery in medical systems using differential diagnosisLAMSTAR and $k$-NNrdquo IEEE Transactions on InformationTechnology in Biomedicine vol 16 no 6 pp 1287ndash1295 2012

[7] A L Barabasi N Gulbahce and J Loscalzo ldquoNetworkmedicine a network-based approach to human diseaserdquoNature Reviews Genetics vol 12 no 1 pp 56ndash68 2011

[8] E Mira A Buizza G Magenes M Manfrin and R SchmidldquoExpert systems as a diagnostic aid in otoneurologyrdquo Journalfor Oto-Rhino-Laryngology and Its Related Specialties (ORL)vol 52 no 2 pp 96ndash103 1990

[9] C E S Gavilan J E Gallego and J Gavilan ldquoCarnisel anexpert system for vestibular diagnosisrdquo Acta Oto-Lar-yngologica vol 110 no 3-4 pp 161ndash167 1990

[10] E Kentala I Pyykko Y Auramo J Laurikkala andM Juhola ldquoOtoneurological expert system for vertigordquo ActaOto-Laryngologica vol 119 no 5 pp 517ndash521 1999

[11] E Kentala K Viikki I Pyykko andM Juhola ldquoProduction ofdiagnostic rules from a neurotologic database with decisiontreesrdquo Annals of Otology Rhinology and Laryngology vol 109no 2 pp 170ndash176 2000

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[13] M H Lopes N R Ortega P S Silveira E Massad R Higaand F Marin Hde ldquoFuzzy cognitive map in differential di-agnosis of alterations in urinary elimination a nursing ap-proachrdquo International Journal of Medical Informatics vol 82no 3 pp 201ndash208 2013

[14] C Salvatore A Cerasa I Castiglioni et al ldquoMachine learningon brain MRI data for differential diagnosis of Parkinsonrsquosdisease and Progressive Supranuclear Palsyrdquo Journal ofNeuroscience Methods vol 222 pp 230ndash237 2014

12 Computational and Mathematical Methods in Medicine

[15] D Mudali L K Teune R J Renken K L Leenders andJ B Roerdink ldquoClassification of Parkinsonian syndromesfrom FDG-PET brain data using decision trees with SSMPCA featuresrdquo Computational and Mathematical Methods inMedicine vol 2015 Article ID 136921 10 pages 2015

[16] M Ota Y Nakata K Ito et al ldquoDifferential diagnosis tool forparkinsonian syndrome using multiple structural brainmeasuresrdquo Computational and Mathematical Methods inMedicine vol 2013 Article ID 571289 10 pages 2013

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[18] S Ceccon D F Garway-Heath D P Crabb and A TuckerldquoExploring early glaucoma and the visual field test classifi-cation and clustering using Bayesian networksrdquo IEEE Journalof Biomedical and Health Informatics vol 18 no 3pp 1008ndash1014 2013

[19] J D Rodriguez A Perez D Arteta D Tejedor andJ A Lozano ldquoUsing multidimensional bayesian networkclassifiers to assist the treatment of multiple sclerosisrdquo IEEETransactions on Systems Man and Cybernetics Part C Ap-plications and Reviews vol 42 no 6 pp 1705ndash1715 2012

[20] L He D Hu M Wan Y Wen K M Von Deneen andM Zhou ldquoCommon bayesian network for classification ofEEG-basedmulticlass motor imagery BCIrdquo IEEE Transactionson Systems Man and Cybernetics Systems vol 46 no 6pp 843ndash854 2016

[21] J Oliva J I Serrano M D del Castillo and A Iglesias ldquoAmethodology for the characterization and diagnosis of cog-nitive impairmentsmdashapplication to specific language im-pairmentrdquo Artificial Intelligence in Medicine vol 61pp 89ndash96 2014

[22] P Melin J Amezcua F Valdez and O Castillo ldquoA newneural network model based on the LVQ algorithm for multi-class classification of arrhythmiasrdquo Information Sciencesvol 279 pp 483ndash497 2014

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[24] J Nahar T Imam K S Tickle and Y-P P Chen ldquoCom-putational intelligence for heart disease diagnosis a medicalknowledge driven approachrdquo Expert Systems with Applica-tions vol 40 no 1 pp 96ndash104 2013

[25] K Yue Q Fang X Wang J Li and W Liu ldquoA parallel andincremental approach for data-intensive learning of bayesiannetworksrdquo IEEE Transactions on Cybernetics vol 45 no 12pp 2890ndash2904 2015

[26] A Cano A R Masegosa and S Moral ldquoA method for in-tegrating expert knowledge when learning bayesian networksfrom datardquo IEEE Transactions on Systems Man and Cy-bernetics Part B Cybernetics vol 41 no 5 pp 1382ndash13942011

[27] S Guessoum M T Laskri and J Lieber ldquoRespiDiag a case-based reasoning system for the diagnosis of chronic ob-structive pulmonary diseaserdquo Expert Systems with Applica-tions vol 41 no 2 pp 267ndash273 2014

[28] Q Zhang C L Dong Y Cui and Z H Yang ldquoDynamicUncertain Causality Graph for knowledge representation andprobabilistic reasoning statistics base matrix and applica-tionrdquo IEEE Transactions on Neural Networks and LearningSystems vol 25 no 4 pp 645ndash663 2014

[29] Q Zhang ldquoDynamic Uncertain Causality Graph for knowl-edge representation and probabilistic reasoning directedcyclic graph and joint probability distributionrdquo IEEETransactions on Neural Networks and Learning Systemsvol 26 no 7 pp 1503ndash1517 2015

[30] C Dong Y Wang Q Zhang and N Wang ldquo0e method-ology of Dynamic Uncertain Causality Graph for intelligentdiagnosis of vertigordquo Computer Methods and Programs inBiomedicine vol 113 no 1 pp 162ndash174 2014

[31] C Dong Z Zhou and Q Zhang ldquoCubic dynamic uncertaincausality graph a new methodology for modeling and rea-soning about complex faults with negative feedbacksrdquo IEEETransactions on Reliability vol 67 no 3 pp 920ndash932 2018

[32] T D Fife ldquoBenign paroxysmal positional vertigordquo SeminarsIn Neurology vol 29 no 5 pp 500ndash508 2009

[33] S G Korres D G Balatsouras S Papouliakos andE Ferekidis ldquoBenign paroxysmal positional vertigo and itsmanagementrdquo Medical Science Monitor vol 13 no 6pp CR275ndash82 2007

[34] D G Balatsouras and S G Korres ldquoSubjective benign par-oxysmal positional vertigordquo OtolaryngologymdashHead and NeckSurgery vol 146 no 1 pp 98ndash103 2012

[35] S J Choi J B Lee H J Lim et al ldquoClinical features ofrecurrent or persistent benign paroxysmal positional vertigordquoOtolaryngologymdashHead and Neck Surgery vol 147 pp 919ndash924 2012

[36] M von Brevern P Bertholon T Brandt et al ldquoBenignparoxysmal positional vertigo diagnostic criteriardquo Journal ofVestibular Research vol 25 no 3-4 pp 105ndash117 2015

Computational and Mathematical Methods in Medicine 13