Use of a Binary Search Pattern and Discriminator Analysis in the Radiologic Diagnosis of Arthritis

By Cohn Alexander

T HE LAST 30 years have seen substantial changes in the radiologic approach to the

diagnosis of arthritis. It is of interest to review

these changes, and in particular to look at the scale of the problem as it exists today and at the various diagnostic strategies used in the radio- logic approach to its solution.

In the 1930s radiology texts seldom men-

tioned more than two or three types of chronic

arthritis.’ There was no agreement on classifica-

tion, and information on the pathologic processes involved was sparse. In most x-ray departments, a differentiation between “atrophic” and “hyper-

trophic” types was regarded as the most that could be realistically expected.

Since that time, there has been a substantial

increase in the number of different categories of arthritis that have been recognized and in our knowledge of their radiologic manifestations. Today’s radiologist has good descriptions of the x-ray manifestations of approximately 25 dif-

ferent types of arthritis available. It is nevertheless true that if departmental

x-ray reports are reviewed, the more recently recognized entities are seldom mentioned in the differential. Radiologists appear reluctant to make suggestions outside the field of the three or four arthritides with which they are familiar. If this impression is correct, it suggests that the more recently acquired information is not being put to full use. It is not difficult to find a possible

explanation for this reluctance. With the new knowledge now available, the size and complex-

ity of the diagnostic problem has increased and has now reached a level that discourages the radiologist from attempting to sort out the most likely diagnosis. There are too many possibilities

From the Department of Radiology, Auckland Medical School, Auckland, New Zealand.

Cohn Alexander, MD, FRCR, FRACR, FACR: Professor of Radiology, Auckland Medical School, Auckland, New Zealand.

Address reprint requests to Colin J. Alexander, MD, FRCR. FRACR, FACR, Professor of Radiology, Auckland Medical School, Park Road, Auckland, New Zealand.

0 I986 By Grune & Stratton, Inc. 0049-0172/86/1602-0007$05.00/7

to be considered. The task of discriminating between them appears inhibitingly complex, and it seems that it is not attempted in many cases.

As a consequence the analysis is likely to be both truncated and cursory.

If this explanation is correct, it implies that

our traditional methodology may no longer be appropriate to the scale of the problem. This suggests that there is a need to examine those

traditional techniques to see if they involve any methodologic flaws that could render them inef-

fective for dealing with large scale diagnostic problems. This report consists largely in a search

for such flaws and for possible ways of overcom- ing them.

FACTORS LIMITING THE EFFECTIVENESS OF

THE STANDARD RADIOLOGIC METHOD

When the normal “pattern recognition”

approach of diagnostic radiology is critically examined, it is found to have several possible deficiencies. While these are probably not impor-

tant in simple problems, they could impair effec- tiveness when the problem is more complex. The first potential weakness is a defect in logical method.

An Inappropriate Logical Strategy

The traditional method taught to students of radiology is based on the Baconian concept of inductive reasoning: collect all the evidence first,

then inspect it as a whole in the hope that a recognizable pattern will be discernible. If such a pattern is recognized and fits the evidence rea-

sonably well, the analysis is over. If it does not, another will be tried. But in arthritis radiology, it is seldom that more than two or three diagnoses are considered.

This inductive approach to problem solving may work in simple problems, but for complex ones it is ineffective and has long been discred- ited. The methodologic analyses of modern scien- tists, particularly of Popper2 and Medawa? have made it plain that no scientist really works in this manner. Problems are solved by the sequential proposition and testing of hypotheses. This con- cept is supported by substantial research in cog-

104 Seminars in Arthritis and Rheumatism, Vol 16, No 2 (NovemberI, 1986: pp 104- 117

RADIOLOGIC DIAGNOSIS IN ARTHRITIS 105

nitive psychology,4 and its relevance to medical problem solving is fully established.s*6 The radiol- ogist considering more than one diagnosis is in fact using this method, but tends to regard it not as a primary approach but as indicating a failure of the normal pattern recognition.

The importance of this defect in logical method will clearly depend on the number of diagnoses that have to be considered. In the case of arthritis, where the number is large, the defect could be important. It can, however, readily be solved by the deliberate substitution of sequential hypothesis testing for the traditional inductive approach. However, implementing such a change immediately generates a second obstacle.

Problem Overload

There are more than 80 recognized causes of arthritis.’ Ten of these are common in any rheu- matology clinic, and another ten are not uncom- mon. It would be unrealistic to undertake the consideration of all these possible diagnoses in each case. The logistic problems involved would be unacceptable.

There is, however, a possible solution to this second difficulty if we use the standard computer approach to solving such problems. Considering 24 diagnoses seriatim is too laborious. However, if the diagnoses could by appropriate criteria be separated into two equal and distinguishable groups, only 12 diagnoses would remain after this first division. Two further subdivisions of this residue would leave only three residual diag- noses for consideration. The total number of tests required has been reduced from 25 to six. In this manner, the workload has been substantially lessened. The random iterative process normally used has been replaced by a structured process based not on individual diagnosis but on sub- groups.

If such a binary search pattern could be devised, it would simultaneously achieve the objectives of reducing the problem to a manage- able level without excluding any diagnosis from consideration, and adopting the hypothesis test- ing mode. Thus, a possible solution to the second problem is to set up a binary search tree. Adopt- ing this solution, however, depends on the suc- cessful solution of a third problem, stemming from the particular requirements of the binary method.

Lack of a Suitable Binary Classification of Arthritis Based on Radiologically Identifiable Characteristics

Most of the classifications of arthritis used in clinical practice are essentially binary (Table 1). However, they suffer from several deficiencies. The first is a poor discriminator. The second is impaired by a high ratio of false positive and negative findings and a 10% to 15% chance of subsequent change.8 The remainder are not based in any substantive way on the underlying pathology, and are not sufficiently discrimina- tory to serve a reliable taxonomic function. The clinician using the terms “erosive” or “inflam- matory”is using verbal shorthand and knows exactly what he means, but as both erosion and inflammation can occur in almost all arthroses, the terms are intrinsically of little merit.

From the point of view of the radiologist, these traditional classifications have the further disad- vantage in that they were designed for other purposes and have little relevance to the radio- logic problem. They do not correlate with radio- logically identifiable characteristics, and for this reason they do not provide an appropriate basis for radiologic analysis.

It would help if there were a classification specifically designed to permit radiologic distri- bution into binary subsegments. Such a classifi- cation could be based on the observation that there are in fact only two basic types of arthritis; those in which the initial lesion is a synovitis and those due to some abnormality in the articular cartilage. If we accept the premise that in its early stages the disease process is dominant in the key tissue, and if this tissue can be identified radiologically, then a binary analysis could be feasible.

In fact, evidence of the feasibility of making this distinction already exists. The credit for first using this approach radiologically should proba- bly go to Martel et al.’ In their report contrasting

Table 1. Classifications of Arthritis

Classification Basis

Polyarticular/monarticular

Seropositive/seronegative

Clinical

Atrophic/hypertrophic

Erosive/nonerosive

Inflammatory/degenerative

Inflammatory/degenerative/metabolic

Pathologic

Pathologic

Etiologic

Etiologic

106 COLIN ALEXANDER

the radiologic appearances of psoriatic and ero- sive osteoarthritis, they point out how the anat- omy of the joint surfaces modifies the response to

arthritis, and describe the erosions in the area not covered by articular cartilage-the “bare area”-as characteristic of psoriasis. This is an

important observation; but this area is not actu-

ally bare, but covered by synovium, and an

erosion at this site is the primary marker of any synovial arthritis. Similarly, the osteoarthritic erosions at the thinner cartilage sites are markers for a chondropathic arthritis. The terminology used by Martel et al, such as “mouse’s ears” and “gull’s wings” erosions, is picturesque, but it is

evident that this difference in radiologic appear- ance relates to a fundamental difference in the

underlying pathologic process. The different location of erosions is a manifestation of a major discriminant factor, which is generally valid

throughout the field of arthritis. It has recently been reemphasized in synovial arthritis of the hip

by Goldberg et al,” and potentially provides the

necessary basis for a binary classification.

arthroses potentially negate the possibility of

setting up an effective binary analysis based on tissue location. Before such an analysis can pro- ceed, it is necessary that they be separated from the remainder. In this report, they are classified

as “depositional arthroses,” borrowing the term used by Brown.” They are defined as diseases

characterized by the macroscopic focal deposi- tion of a metabolic surplus.

Almost all arthroses can be put readily into one of two categories, synovial or chondropathic, depending on the site of the primary pathologic process, but when this exercise is carried out, there remains a small subgroup of four diseases that do not fit the classification. This subgroup consists of those arthroses in which the initial

lesion is not restricted to a particular tissue. It can occur in any of the three joint components;

bone, synovium, or cartilage. These four

Using this pathologic basis, it is possible to derive a classification that could serve the special needs of radiologic analysis better than those currently used clinically. Such a classification is illustrated in Table 2. Although it is based differ- ently, it does not provide significantly different groupings from those listed in Table 1. The main divisions correspond roughly with the traditional

classes of “inflammatory” and “degenerative,” but as virtually all arthroses eventually show

both these changes, this terminology is too imprecise to be useful. The old “metabolic” listing, which included gout, amyloid, pyrophos-

phate arthritis, and the cation diseases, in fact contains two disparate groups with different pathologic and radiologic characteristics. There- fore, it is advantageous for the purpose of this analysis to split it into two by separating the

depositional group. As Gardner” points out, classifications are

essentially artificial devices and none can be completely satisfactory and free from ambiguity.

The one derived above is no exception. Some of the assumptions on which it is based depend on

Table 2. A Classification of Arthritis Based on the Site of Primary Tissue Involvement

Tissue/Category

Synovium/Synovial

RA

Lupus arthritis

Mixed CT disease

Villonodular synovitis (MI

Haemophilia. etc (MI

Systemic sclerosis

Jacoud arthritis

Reactive arthritis

Synovial chondromatosis (MI

Infective arthritis (Ml

Hyperparathyrodism 1 O, 2 ’

Spondylarthritis

Ankylosing spondylitis

Reiter syndrome

Psoriasis

Colitic arthritis

Cartilage/Chondropathic

Degenerative

OA

Acromegaly

Neurotrophic

Metabolic

Pyrophosphate arthropathy

Hyperparathyroidism (primary)

Haemochromatosis

Wilson disease

Ochronosis

Keitel syndrome

Senile chondrocalcinosis

Unrestricted, Any Tissue/Depositional

Gout

Hyperlipidaemia

Amyloid

Multicentric reticula histiocytosis

Abbreviations: M, mono- or pauci-articular; CT, connective tissue.

RADIOLOGIC DIAGNOSIS IN ARTHRITIS 107

evidence that is incomplete. They may in time prove incorrect and need revision. The classifica- tion assumes, for example, that the chondrocalci- nosis of old age is primarily a manifestation of failed pyrophosphate homeostasis rather than a complication of degenerative arthrosis, basing this on the reported observation that its correla- tion with age is linear while its correlation with osteoarthritis (OA) is not.13 In addition, the classification accepts the chondropathic rather than the osseous theory of the etiology of 0A14 on the grounds that even if the latter was correct, it is the cartilage changes that lead to the clinical and radiologic manifestations. “Seronegative spondylarthritis” is preferred to the misleading term “rheumatoid variant,” and one arthritis (primary hyperparathyroidism) appears in both main divisions. This decision could be challenged on the grounds that the synovitis of hyperpara- thyroidism may be secondary rather than prima- ry,” but it is justifiable in a radiologic context because the erosions seen radiologically are indistinguishable from those of a primary synovi- tis.16 Similarly, it has been shown that hemo- philia has both synovial and cartilaginous com- ponents,” but it is classified as synovial in Table 2 because the former dominate the early radio- logic picture for which the classification is designed.

The term “reactive arthritis” is normally understood to include colitic and Reiter arthritis, but is retained in the synovial section of the classification to exemplify those that are not in the spondylarthritis subgroup.

Notwithstanding these reservations, the classi- fication does meet the objective of a binary division as long as the depositional group is excluded from the primary analysis. However, its use depends on the assumption that synovial and chondropathic arthroses can be distinguished radiologically.

This conceptual framework is critical to the efficacy of the proposed binary analysis. It is not, however, an established concept, and it has not yet been shown that evidence permitting this distinction exists.

Lack of Accepted Criteria for Distinguishing Chondropathic and Synovial Arthroses

The common denominator of the chondro- pathic arthroses is a change in the chemical constitution and structural organization of carti-

lage and a failure of its function of protecting bone under dynamic load. When the radiologic characteristics of this group of arthroses are examined, three radiologic markers are consis- tently found to be present: (1) increased density of subchondral bone, (2) marginal osteophyte formation, and (3) subchondral bone erosion.

The increased density is regularly seen and is probably due to augmented stress stimulation of osteoblasts.” The radiologic osteophyte is one of the earliest changes in the chondropathic arthroses. It is seen as early as three days after surgery in experimental OA18 occurring simulta- neously with biochemical changes before surface fibrillation appears. l9 In most cases, it is due to cartilage proliferation followed by subchondral ossification, and it is accordingly called by some an osteochondrophyte.20 The radiologist sees only the central bone core, but when present it is a strong discriminator.

This osteochondrophyte starts at the articular margin (Fig l), and normally can only grow laterally to an extent determined by local pres- sure constraints. Occasionally, when central pressures are reduced by subluxation, the osteo- phyte can grow centrally to cover the articular cartilage (Fig 2). This central osteophyte is uncommon except in the hip and shoulder, and it has been shown by Harrison et a121 that it is not due to the recrudescence of central subchondral ossification, although this commonly coexists.

It is essential to differentiate between this marginal osteophyte, which is a cartilage phe- nomenon unrelated to capsule or ligaments, and two other spurs occurring at tendon, capsule, and ligament attachments: the traction spur, which is a semiphysiologic or posttraumatic phenomenon of no discriminant value in arthritis (Fig 1 B), and the inflammatory spur at an enthesis, which is a strong marker for spondylarthritis.22

Traction spurs may occur in association with OA,23 but the great majority seen radiologically are not due to arthritis and accordingly have to be identified and ignored. It was failure to make this distinction between traction spurs and osteo- phytes that had led to the misconception that OA is common in the ankles of soccer players. The critical observation was made many years ago by McMurray,24 but failure to make the distinction is still a potent cause for misunderstanding and misdiagnosis.

By contrast, the inflammatory spur is always

COLIN ALEXANDER

Fig 1. (A) An osteophyte at the anterior articular margin of the talus, indicating that a chondropethic arthritis is present. In this cese it is OA. (6) A normal traction spur arising at the ridge for insertion of the ankle and telonavicu- lar ligaments. It is separated by a concave depression from the anterior articular margin. Large spurs may develop at this site as a normal variant, a concomitant of idiopathic skeletal hyperostosis, a response to trauma, or to abnormal dynamic loading as in subtaler synostosis. Distinction of these two spurs depends critically on a knowledge of the anatomy.

pathologic, and if it can be recognized, it is a strong but not infallible marker for spondylar- thritis. The term “enthesopathy,” used by Ball” to describe this lesion, is in the reporter’s view best restricted to this inflammatory group. To use it indiscriminately for both types of spur is to destroy its usefulness. Other investigators, how- ever, do not accept the validity of this restric- tion.25

Subchondral bone erosion may consist of superficial stress attrition, small subchondral pseudocysts, or large geodes.26,27 These distinc-

Fig 2. A central osteophyte on the humerus. The osteophyte has been able to grow centrally over the cartilage because upward and outward subluxation of the humerel head has resulted in a low pressure area in the lower half of the joint. There is gross attrition of the rotator cuff.

tions are unhelpful and irrelevant, but identifica- tion of the site as subchondral is critical (Fig 3). The term erosion is commonly used in arthritis to imply superficial synovial destruction, but the radiologist cannot identify the pathologic pro- cess, only the site. Therefore, it is more practical in radiology to use the term erosion in its nonspe- cific etymologic sense of indolent destruction, irrespective of cause. The only factor of discrimi-

nant value to the radiologist is whether it started under a cartilage-or synovial-covered surface.

When the literature describing the synovial

arthroses is reviewed, a different pattern emerges. Again, three main but different mark- ers are reported: (1) synovial erosions, (2) osteo- porosis, and (3) periostitis. Of these, the latter two are variable, and it appears that the first is the prime marker (Fig 4). In this group of arthroses, the marginal cartilage, which is the source of the osteophyte in OA, is commonly destroyed by synovitis. As a consequence, osteo- phytes (at least in the early stages of the disease) are rare. There are other markers, such as uni- form cartilage loss, which favor a synovial arthri- tis, but this is not reliable at all joints” and does occur in metabolic arthrosis, so it is a weak discriminator.29

RADIOLOGIC DIAGNOSIS IN ARTHRITIS 109

Fig 3. (A) The frontal film of a metacarpophalangeal joint showing an erosion that could be either synovial or subchondral. In this view, the ero- sion is unlooalized and has no discrimi- nant value. (B) The oblique view con- firms that it is subchondral.

COLIN ALEXANDER

Fig 4. Typical synovial erosion in a great toe.

Anatomical requirements for marker recogni- tion. Thus, it seems that the most useful dis- criminator between these two groups is the nature of the tissue covering the surface at the site of any erosions. This can only be determined if the radiologist is aware of the extent of the cartilage and synovial covered surfaces and the site of the capsule insertion, as they relate to the projections used. This requirement is illustrated in Fig 5. Without this knowledge, it is impossible to determine whether an erosion is subchondral, synovial, or extraarticular.

This information is also necessary to permit distinction between traction spur, enthesitic spur, and osteophyte. The osteophyte arises from the edge of the articular cartilage; the others are capsular or extraarticular. When the capsule or tendon insertion is remote from cartilage, as on the patella or femoral head, distinction between the three types of spur is simple. However, in

Fig 5. The influence of capsule insertion on interpreta- tion of radiographic manifestations of arthritis. Unless the location of the capsule insertion is known. synoviel erosions (Al cannot be distinguished from extracapsular erosions, end traction spurs, which have no discriminant value in arthritis, can be mistaken for osteophytes. (Bl E = extra articular erosion: 0 - osteophyte: TS = traction spur.

situations in which the capsule insertion is close to the cartilage, as at the other lower tibia1 margin, distinction between the two entities is less easy and posttraumatic traction spurs can be misinterpreted as evidence of OA (Fig 1). In the small hand joints, the osteophyte commonly invades the capsule and the distinction cannot be made.‘* The work of Resnick30331 in the wrist, ankle, and other areas, of Martel et al in the hand,32 of Foster et al inthe elbow,33 and of Weston in many other sites34 graphically shows the degree to which comprehension advances when the anatomy is thoroughly understood.

Even if this anatomic information is available, the discrimination between the two classes can still only be made if the erosions can be detected and localized. It is not uncommon for a further deficiency at this level to prevent effective analy- sis.

A Low Signal to Noise Ratio in the Evidence

The radiologist examining a film of the hand for arthritis will examine each joint for changes in the soft tissues, alignment, cartilage thickness, bone density, periostitis, and bone erosion, and will then note the distribution of the abnormali- ties found. In other words, he is looking for at least seven bits of information. If there were two manifestations of each variable, the possible combinations would be 27 = 128. In fact, the above analysis is too simplistic. It assumes a binary system, with only two possible manifesta- tions of each factor, but this premise is false. There are four possible manifestations of erosion

RADIOLOGIC DIAGNOSIS IN ARTHRITIS 111

(absent, subchondral, synovial, extraarticular), at least three of periostitis (absent, linear, spicu- lated), five of soft tissue change (atrophy, artic- ular swelling, nonarticular symmetric swelling, asymmetric swelling, calcification), four of carti- lage change, at least six for distribution, and so on. The number of possible combinations is not 128, but approximately 5,000. If a spine/sacroil- iac film is added to the hand examination, the number of possible combinations approaches 30,000. The radiologist is suffering from infor- mation overload. This difficulty is compounded when it is realized that the problem must be solved, not by inductive reasoning, but by hypothesis testing, for at any particular stage of the testing process only a small part of the mass of evidence available will be germane to the actual hypothesis being tested. This component of the evidence constitutes the signal. The rest of the evidence is not relevant at this stage, and serves only to confuse the issue. Statistically speaking, it is noise. If this problem is to be overcome, it will be necessary to reduce the noise: in other words, to restrict consideration at each stage of the analysis to evidence of value at that particular stage. This involves a further con- straint on the analytic process.

Reducing the noise. In a binary search pat- tern, a piece of evidence has no intrinsic merit. Its usefulness depends solely on whether or not it is useful in sorting a particular population of possi- bilities into two groups. This leads to the concept of the discriminator, defined as a bit of positive evidence that allows differentiation between two alternative diagnostic groupings with a high probability of that differentiation being correct. If only valid discriminators are used at each step, noise is excluded. When the radiologic literature is searched for valid discriminators, certain use- ful concepts emerge. Absence of a discriminator is weak evidence and has little discriminant value. The value of a discriminator is not abso- lute, but depends on the differentiation required. For example, the typical syndesmophyte is a strong discriminator in distinguishing rheuma- toid arthritis (RA) from ankylosing spondylitis, but is valueless if we are trying to distinguish the latter from psoriatic spondylitis. The floating syndesmophyte is strong in this situation, but of no value in distinguishing psoriasis from Reiter spondylitis.35 In other words, the same bit of

evidence may be a crucial discriminaator at one stage of the analysis, and mere noise at another. The six markers described above seem to estab- lish themselves as the key discriminators in arthritis radiology.

Increasing the signal. Signal strength de- pends on the resolving power of the technique (its capacity to detect erosions) and on the number of regions examined and views taken.

With regard to the first, Mall et aP6 have shown the superiority of nonscreen over screen techniques, and further advantages accrue from the use of optical or geometric magnification.37 Erosions are not only of primary importance in making the initial synovial/chondropathic dis- crimination, they are also in many cases the only effective tool for quantifying and monitoring the progress of the disease.3s”9 Over-reading and under-reading can occur even with good quality films?’ and suboptimal techniques can only increase the likelihood of error.

Aside from technique, there remains some dispute as to whether simple positioning tech- niques suffice.4’ If the nature of the arthritis is known and the examination is primarily for staging and surveillance, there is good evidence that taking extra views, such as oblique films of the hands, is unproductive and contributes little to patient care.42 The situation is different when the objective is diagnosis. In this case, if reliance is placed on frontal films of the hands alone, then erosions that are critical to the diagnosis will not be detected in a proportion of cases.41943*44 This false negative rate is of the order of lo%, a misrate that is acceptable in a monitoring situa- tion, but probably not in a diagnostic one if a high standard of accuracy is to be achieved.

Apart from the increased probability of detecting erosions if further views are taken, these views contribute materially to the ability to determine whether erosions are subchondral or synovial. An unlocalized erosion has no discrim- ninat value, and if only one view is available, it is often impossible to establish this localization (Figs 3 and 6).

The scope of the examination is also impor- tant. It is not uncommon for involved joints to be clinically silent,45 and if a survey is necessary it needs to be broad enough to include the sites of predilection: the feet for gout and RA, the knees and hands for chondrocalcinosis, the spine and

COLIN ALEXANDER

sacroiliac joints for spondylarthritis. However, this poses a further problem. To include all these areas in each case would hardly be good practice, and it therefore seems best if such surveys are not

routine, but tailored to the likely diagnosis, as

indicated by the clinical presentation and the evidence from the first films taken. These first

films will usually allow a ready solution to the synovial/chondropathic question, and hence determine the optimum direction for the rest of the survey. This involves converting what is currently a routine procedure into a supervised one. It may legitimately be questioned whether this use of radiologic manpower can be justified, and views on this will differ. If it can be achieved,

it does seem likely that it could produce better results, with maximum signal to noise ratio and less unnecessary elaboration of techniques than the present method of routine views and dele- gated technique selection.

With these precautions to augment the signal to noise ratio, it is possible to set up a binary search tree, using the classification in Table 2, the major discriminators noted above, and minor ones appropriate to the different stages of the

search pattern.

A BINARY SEARCH PAlTERN

FOR RADIOLOGIC DIAGNOSIS

This involves the sequential proposition of four or five of seven possible questions, using at each

Fig 6. A metacarpophalan- geal joint grossly damaged by arthritis. The frontal film sug- gests that the destruction is subchondral, but the oblique view demonstrates synovial erosions and allows accurate categorization of the arthritis.

stage only those discriminators appropriate to the question. The first is the fundamental ques-

tion in arthritis radiology (Table 3). Usually, it is readily answered, and if the

answer is correct, the scale of the subsequent

analysis is halved and the chances of being seriously in error are much reduced. Occasional- ly, the answer will be “both.” There are three

possible explanations for this: a double patholo- gy, typically RA, plus pyrophosphate or OA; late degenerative changes in a chronic synovial arthritis; or gout, manifesting as a multi-tissue arthritis, but without other typical features.

If the answer is “chondropathic,” the next step is to descend the chondropathic limb of the tree

(Table 4). The OA group is usually readily analyzed. The

seven possibilities in the metabolic group pose a greater problem, but it is narrowed down to the point where it can be tackled by matrix analysis using known markers.28V45A9 Diffuse chondrocal- cinosis occurs in the cation diseases as well as in pyrophosphate disease, and hence, does not dis- criminate within the group. The assumption that diffuse chondrocalcinosis, when it is found in OA, is a reflection of age and not a complication of the arthrosis may prove incorrect, but the reasons for this conclusion are noted above. The status of “hydroxyapatite disease”” as an entity is unclear, and it is not at this stage included in the analysis.

RADIOLOGIC DIAGNOSIS IN ARTHRITIS 113

Table 3. Is This Arthritis Chondropathic or Synovial?

Discriminators

Chondropathic

Subchondral erosion

Sclerosis

Osteophyte

Local cartilage narrowing

Chondrocalcinosis, local

or diffuse

Random phalanx devia-

tions

Synovial

Synovial erosion

Osteoporosis

Periostitis

Subtendinous erosion

Syndesmophyte

Early cartilage loss

Boutonniere/swan

neck deformity

Flexion deformity

Uniform ulnar devia-

tion of fingers

If the answer to the question posed in Table 3 was “synovial,” then the analysis proceeds down the second limb of the tree (Table 5).

It is at this stage that the evidence from the feet and the spine and sacroiliac joints become helpful. If the choice falls in the spondylarthritis group, it remains to determine whether or not the condition fits the diagnosis of ankylosing spondy- litis (Table 6).

If it is not likely to be ankylosing spondylitis, it remains to decide whether Reiter arthritis or psoriasis best fits the evidence (Table 7).

The nonspondylarthritis group is a large one and needs to be broken down to a manageable level. The next question with a single discrimina- tor aims to achieve this end: Is the arthritis polyarticular or mono/pauci-articular?

Table 4. If Chondropathic, Is It a Degenerative or a

Metabolic Arthrosis?

Discriminators

Degenerative

Typical OA distribution

Localized cartilage loss

Marginal flecks of carti-

lage calcification

OA prototype:

Metabolic

Atypical distribution for

OA (shoulders, MCP,

radiocarpal)

Uniform cartilage loss

Diffuse chondrocalcinosis

Disproportionate erosion

Excessive geode forma-

tion

Rapid progression

Acute synovial swelling

Multiple disc/annulus in-

volvement

Sacroiliac erosion

Symphysis erosion

Synovial calcification

Tendon calcification

Pyrophosphate disease

Table 5. If Synovial, Is This Arthritis One of the Spondylerthritis Group?

Discriminators

Seronegative spondylarthritis

Asymmetric predilection for

Terminal interphalangeal joints

lnterphalangeal great toe

Florid periostitis

Spiculated periostitis

Sacroileitis withsclerosis

Vertebral syndesmophytes

Ray distribution

Calcaneal sclerosis

Terminal phalanx sclerosis

Extraspinal enthesopathy

lnterphalangeal ankylosis

Diffuse dactvlitis

Joint space thickening

Subungual hyperkeratosis

lschial erosion

Not spondylarthritis

Symmetrical

MCP-PIP Distribution

Progressive osteoporosis

Large erosions (geodes)

Soft tissue nodules

Ankylosing spondylitis prototype: RA

These two subgroups are identified in Table 2. The polyarticular group remains large, but in practice the great majority of patients in this group have RA, and diagnostic difficulties due to the other entities are uncommon. However, the discriminator is not infallible, as both RA and reactive arthritis can have a monoarticular pre- sentation.

By this time, the arthritis has been classified into a group and identified with a prototype. This prototype is, however, provisional and two fur- ther steps are necessary. First, it is now appropri- ate to recall that the depositional group has not yet been considered, and the possibility should be explored by looking for discrepancies that would support that possibility (Table 8).

The prototype of this group is gout, and if the answer is positive, it remains to distinguish it from the other three depositional arthroses. The overhanging margin, or roof, described by Mar- te15’ is a strong marker for this group, indicating the action of periosteum, and therefore an extraarticular erosion (Fig 7). However, it is occasionally seen in late RA. The others are rare and can usually be identified clinically or by analysis using known discriminators.52-54

114 COLIN ALEXANDER

Table 6. If Spondylarthritis, Is It Ankylosing Spondylitis or Table 6. Are There Any Inconsistencies That Suggest a

ReiterIPsoriasis? Depositional Arthritis?

Discriminators

Ankylosing spondylitis

Axial presentation

Bilateral sacroiliac ankylo-

sis

Symmetric sacroileitis

Widespread symmetrical

spondylitis

Hip and shoulder involve-

ment

lschial erosion

Reiter/psoriasis

Peripheral presentation

Distal IP joint presenta-

tion

Tuft absorption

Asymmetric syndesmo-

phytes

Hypertrophic syndasmo-

phytas “Floating” syndesmo-

phytes

Selective involvement 1 P

great toe

Widening 1 P joint space

Arthritis mutilans

Sclerosis calcaneum

Asymmetric sacroileitis

Focal spondylitis

Sclerosis terminal pha-

langes

Subungual hyperkeratosis

Even when this question has been answered, the diagnosis is still not secure, because the prototype has not been vigorously tested against the evidence, and a number of alternative diag- noses have not yet been considered. For this, one last question is needed (Table 9).

This question is essential, no matter how strong the diagnosis may appear. It consists essentially in a ruthless search for inconsisten- cies, which may be the clue to a nonprototype diagnosis. It is at this stage that the rich store of knowledge available helps the radiologist to refine his diagnosis within a field narrowed down to manageable proportions by the binary search process.

Table 7. If Not Ankylosing Spondylitis, Is It Psoriasis or

Reiter Arthritis?

Discriminatws

Psoriasis

Sclerosis terminal pha-

langes

Multiple TIP involvement

Terminal tuft absorption

Sclerosis inferior calca-

neum

One hand involvement

One ray involvement

Spiculated periostitis

Reiter Arthritis

Acute presentation

Transient paraarticular

porosis

Acute linear periostitis

Reversibility

Foot predominance

Discriminators

Random distribution

Normal bone density

Retained articular cartilage

Soft tissue masses

Erosions that are

Multi-tissue

Extraarticular

Roofed

Mass related

Endosteal calcification

DISCUSSION

This is not the first attempt to simplify the radiologic diagnosis of arthritis. Although there are many excellent descriptions of the radiologic manifestations of arthritis, those of Genant” and of Resnick and Niwayama56*57 for example, these rely basically on pattern recognition and do not attempt to derive a diagnostic pathway. As Edeiken7 pointed out, the scale of the problem is too great for ready solution by this simple recog- nition technique.

This is particularly true when different arthroses have points of similarity, and this has led several investigators to search for reliable

Fig 7. A patient with classical changes of gout. Both synoviel and subchondral erosions are present, which coufd indicate a double pathology. but the presence of other erosions, whioh are roofed. mama related, end extrearticu- lar, confirms that this is a depositional arthritis.

RADIOLOGIC DIAGNOSIS IN ARTHRITIS

Table 9. Are There Any Other Discrepancies Inconsistent

With the Provisional Diagnosis?

Disproportionate features

Distribution incompatability

lncompatability with the clinical findings

markers that would allow distinction in such cases. The concept of the “discriminator” is implicit, if not explicitly stated, in such studies. Examples are the frequency matrices used by Martel et al9 in distinguishing psoriatic arthritis and OA, and by Adamson et alz9 in their report comparing pyrophosphate arthritis and hemoch- romatosis. Valid discriminators can be derived from these matrices. The obscuring effect of statistical noise in the diagnosis, and the advan- tage of confining attention to discriminators as a means of combating this, have not been previ- ously discussed.

Resnick and Niwayama56*57 tackled the prob- lem by emphasizing a “compartmental” or “tar- get area” approach, based on identification of the joint compartments for which particular ar- throses have a predilection. This emphasis on distribution as a key diagnostic factor is unques- tionably valid, but it is only one factor and not an infallible one. Most arthroses can involve most joints, and excessive reliance on distribution alone has long been recognized as a potential source of error. The illustrations in the classic text by these two investigator? show consider- able overlap in the target areas, and illustrate the

Fig 9. A diagnostic algo- rithm approach to the radio- logic diagnosis of arthritis.

115

limitation as well as the use of distribution as a discriminator.

Edeiken7 divides the arthroses into clinically and radiologically predominant subgroups, and suggests the use of deossification as a useful marker allowing division into two further subdi- visions. Brown” uses a diagnostic algorithm with monarthritis/polyarthritis as the root of his search tree, subsequently dividing the latter into the conventional metabolic, inflammatory, and degenerative subgroups. This does result in an orderly approach, but it has to be questioned whether the first discriminator is strong enough for use as an initial, and therefore critical, dis- criminator. In the investigator’s hands, it has been misleading rather too often to be reliable and it suffers from the further disadvantage that the answer to this key question may not be available to the radiologist. The fact that these approaches have been made is nevertheless an indication that a diagnostic problem does exist. It is clear that there is a need to convert the traditional random pattern recognition into some more logical diagnostic pathway. It is hoped that the optimized binary search tree proposed above may solve some of these problems (Fig 8). It does seem advantageous to use (if possible) some form of sequential hypothesis testing, and to base it on pathologic processes that can be identified radio- logically. There may be better algorithms, and experience may lead to further refinements, but so far the approach shown in Fig 8 has proved

DEPOSITIONAL? 1 I

[ OTHER DISCREPANCIES ? 1

116 COLIN ALEXANDER

superior to others tried. The technique does lead to a presumptive diagnosis after three or four questions, and also provides the basis for select- ing an appropriate diagnostic survey if one is needed. It is particularly helpful in patients with double pathology, in mixed RA and pyrophos- phate arthritis, for example, allowing confident identification of both the synovial and the chon- dropathic components. The approach is readily taught, and radiologic trainees using the system quickly gain confidence and show rapid improve- ment in knowledge and accuracy.

It is none the less necessary to recognize the limitations of the synovial/chondropathic ap- proach.

First, the discriminators become less useful as the arthritis progresses. Erosions do not remain confined to their site of origin. Synovial erosions extend under cartilage, and chondropathic ero- sions under synovium covered surfaces. In the late stages of any arthritic process, all the tissues become to some degree involved, and the primary distinction between synovial and chondropathic groups may become obscured by secondary changes. Second, any such algorithm has a built in limitation in that it is only effective if the discriminators are present, in particular, those for the crucial first question, which is the root of the search tree. If they are absent, or if the tissue origin of the erosions cannot be accurately identi- fied, the primary distinction cannot be made. If only synovial or chondropathic erosions are pres- ent in a depositional arthritis, it may be impossi- ble to detect its true nature. For example, Figs 3 and 4 were chosen as examples of typical sub-

chondral and synovial erosions. In fact, both patients were suffering from gout. In both cases, confirmatory evidence of a depositional arthritis is lacking, and a firm radiologic diagnosis of gout cannot be made. Similarly, if the technique is inadequate, or the radiologist unaware of the capsular anatomy of the joint in question, then the firm pathologic base necessary for such a diagnostic approach may be lacking. The major contribution of all such approaches is in early arthritis, before secondary changes have ob- scured the picture. Fortunately, this is the time when clinical criteria and immunologic markers may be misleading,” and any help that can be derived from the x-ray is likely to be more useful than in late disease.

It is appropriate at this stage to acknowledge the work of the many workers who have provided the data base necessary for such a system to be practical; important too to acknowledge more remote contributions. The theoretical concept stems in the main from three men: the German, Popper, who laid the foundation of modern con- cepts of hypothesis testing*; the Englishman, Babbage, who designed the first digital com- puter; and the ninth century Arab mathemati- cian, Abu Jafar al-Khowarizmi, whose name is enshrined in our modern derivative, the algo- rithm.59 Paradoxically, it is also necessary to now pay homage to the same 17th century philoso- pher whose scientific method was discarded as inadequate at the start of this paper; for it was the same Francis Bacon who as far as is known, was the first man to make practical use of the binary system.60

REFERENCES

1. Golden R: Diagnostic Roentgenology. New York,

Thomas Nelson and Sons, 1936, p 448

2. Popper KR: The Logic of Scientific Discovery. London,

Hutchinson, 1972

3. Medawar P: Induction and Intuition in Scientific

Thought, in Pluto’s Republic. Oxford, England, Oxford

University Press, 1982, pp 73-114

4. Kassirer JP, Kuipers BJ, Gerry GA: Toward a theory of

clinical expertise. Am J Med 73:251-259, 1982

5. Kassirer JP, Gorry GA: Clinical problem solving: A

behavioural analysis. Ann Intern Med 89:245-255, 1978

6. Sherwood T: Science in radiology. Lancet 1:594, 1978

7. Edeiken J: Radiologic approach to arthritis. Semin

Roentgen01 17:8-15, 1982

8. Wright V, Mall JMH: Seronegative polyarthritis.

Amsterdam, Elsevier/North Holland Biomedical, 1976, pp

9, 15

9. Martel W, Stuck KJ, Dworin AM, et al: Erosive

osteoarthritis and psoriatic arthritis: A radiologic comparison

in the hand, wrist and foot. AJR 134: 125-I 35.1980

10. Goldberg RP, Weissman BN, Naimark A, et al:

Femoral neck erosions: Sign of hip joint synovial disease.

AJR 141:107-111,1983

11. Brown JC: The differential diagnosis of arthritis, in

Forrester DM, Brown JC, Nesson JW (eds): The Radiology

of Joint Disease (ed 2). Philadelphia, Saunders, 1978, p 602

12. Gardner DL: General pathology of the peripheral

joints, in Sokoloff L (ed): The Joints and Synovial Fluid, vol

2. Orlando, Fla, Academic, 1980, p 321

13. Wilkins E, Dieppe P, Maddison P, et al: Osteoarthritis

and articular chondrocalcinosis in the elderly. Ann Rheum

Dis 42:28&284,1983

14. Radin EL, Paul IL, Rose RM: Role of mechanical

117

factors in pathogenesis of primary osteoarthritis. Lancet

1:519-522,1972 15. Bywaters EGL, Dixon AS, Scott JT: Joint lesions of

hyperparathyroidism. Ann Rheum Dis 22:171-187, 1963 16. Hamilton S, Knickerhocks WJ: Periarticular erosions

in the hands and wrists in haemodialysis patients. Clin Radio1

33:19-24.1982 17. Sokoloff L: The Biology of Degenerative Joint Dis-

ease. Chicago, University of Chicago, 1969, pp l&l 1

18. Gilbertson EMM: Development of peri-articular

osteophytes in experimentally induced osteoarthritis in the

dog. Ann Rheum Dis 34: 12-25, 1975

19. McDevitt C, Gilbertson E, Muir H: An experimental

model of osteoarthritis; early morphological and biochemical

changes. J Bone Joint Surg [Br] 59B:24-35, 1977

20. Moskowitz RW: Introduction, in Moskowitz RW,

Howell DS, Goldberg VM, et al (eds): Osteoarthritis: Diag-

nosis and Management. Philadelphia, Saunders, 1984, pp l-5

21. Harrison MHM, Schajowicz F, Trueta J: Osteoarthri-

tis of the hip: Study of nature and evolution of disease. J Bone

Joint Surg [Br] 35B3598-626, 1953 22. Ball J: Enthesopathy of rheumatoid and ankylosing

spondylitis. Ann Rheum Dis 30:213-223, 197 1

23. Ball J, Sharp J: Osteoarthrosis, in Scott JT (ed):

Copeman’s Textbook of the Rheumatic Diseases (ed 5). New

York, Churchill Livingstone, 1978, pp 605,609

24. McMurray TB: Footballers ankle. J Bone Joint Surg

[Br] 32B:68-69, 1950

25. Resnick D, Niwayama G: Entheses and enthesopathy.

Radiology 146:1-9, 1983

26. Resnick D, Niwayama G, Coutts RD: Subchondral

cysts (geodes) in arthritic disorders: Pathologic and radio-

graphic appearance of the hip joint. AJR 128:799-806, 1977

27. Gerber NJ, Dixon A: Synovial cysts and juxtaarticu-

lar bone cysts (geodes). Semin Arthritis Rheum 3:323-348,

1974

28. Martel W, Snarr JW, Horn JR: The metacarpopha-

langeal joints in interphalangeal osteoarthritis. Radiology

108:1-7, 1973

29. Adamson JC, Resnick CS, Guerra J, et al: Hand and

wrist arthropathies of hemochromatosis and calcium pyro-

phosphate deposition disease: Distinct radiographic features.

Radiology 147:377-381, 1983

30. Resnick D: Rheumatoid arthritis of the wrist: The

compartmental approach. Photogr 52:50-88, 1976

31. Resnick D: Talar ridges, osteophytes and beaks: A

radiologic commentary. Radiology 151:329-332, 1984

32. Martel W, Hayes JT, Duff IF: The pattern of bone

erosion of the hand and wrist in rheumatoid arthritis. Radi-

ology 84:20&214, 1965

33. Foster DR, Park WM, McCall IW, et al: The supina-

tor notch sign in rheumatoid arthritis. Clin Radio1 31:195-

199.1980

34. Weston WJ: Traumatic effusions of the ankle and

posterior subtaloid joints. Br J Radio1 31:445-447, 1958

35. Sundaram M, Patton JT: Paravertebral ossification in

psoriasis and Reiter’s disease. Br J Radio1 48:628633, 1975

36. Mall JC, Genant HK, Silcox DC, et al: The efficacy of

fine detail radiography in the evaluation of patients with

rheumatoid arthritis. Radiology 112:37-42, 1974

37. Genant HK, Doi K, Mall JC, et al: Direct radio-

graphic magnification for skeletal radiology. Radiology

123147-55.1977

38. Genant HK: Methods of assessing radiographic

change in rheumatoid arthritis. Am J Med 75:35-47, 1983

39. Weisman MH, Hannifin DM, Guerra J, et al: Analy-

sis of Auranofin as a rheumatoid remitting agent. J Rheuma-

tol 132-136, 1982 (suppl8)

40. Stelling CB, Keats MM, Keats TE: Irregularities at

the base of the proximal phalanges: False indicator of early

rheumatoid arthritis. AJR 138:695698, 1982

41. De Smet AA, Martin NL, Fritz SL, et al: Radio-

graphic projections for the diagnosis of arthritis in the hands

and wrists. Radiology 139:577-58 I, 198 1

42. Edwards JCW, Edwards SE, Huskisson EC: The

value of radiography in the management of rheumatoid

arthritis. Radiology 34:413416, 1982

43. Norgaard F: Earliest roentgen changes in polyarthritis

of the rheumatoid type. Radiology 92:299-303, 1969

44. Resnick D: Early abnormalities of pisiform and tri-

quetrum in rheumatoid arthritis. Ann Rheum Dis 35:46-50,

1976

45. Barthelemy CR, Nakayama DA, Carrera GF: Gouty

arthritis: A prospective radiographic evaluation of sixty

patients. Skeletal Radio1 II:]-8, 1984

46. Martel W, McCarter DK, Solkky MA, et al: Further

observations on the arthropathy of calcium pyrophosphate

crystal deposition disease. Radiology 141:1-l 5, 1981

47. Resnick CS, Resnick D: Crystal deposition disease.

Semin Arthritis Rheum 12:390-403, 1983

48. Dalinka MK, Reginat AJ, Golden DA: Calcium depo-

sition diseases. Semin Roentgen01 17:39-48, 1982

49. Hirsch JH, Killien FC, Troupin RH: The arthropathy

of hemochromatosis. Radiology 118:591-596, 1976

50. Bonavita JA, Dalinka MK, Schumacher HR: Hy-

droxyapatite deposition disease. Radiology 134:621-625,

1980

5 1. Martel W: The overhanging margin of bone: A roent-

genologic manifestation of gout. Radiology 91:755-856,

1968

52. Goldman AB: Some miscellaneous joint diseases.

Semin Roentgen01 17:60-80, 1980

53. Gold RH, Bassett LW, Theros EG: Radiologic com-

parison of erosive polyarthritides with prominent interpha-

langeal involvement. Skeletal Radio1 8:89-97, 1982

54. Resnick D, Broderick TW: Intra-osseous calcitica-

tions in tophaceous gout. AJR 137:1157-1161, 1981

55. Genant HK: Radiology of rheumatic diseases, in

McCarty DJ (ed): Arthritis and Allied Conditions (ed 9).

Philadelphia, Lea & Febiger, 1979, pp &I 30

56. Resnick D: Rheumatoid arthritis of the wrist: The

compartmental approach. Med Radiogr Photogr 52:50-88,

1976

57. Resnick D, Niwayama G: Diagnosis of Bone and Joint

Disorders. Philadelphia, Saunders, 1981, pp 3228-3254

58. Sack KE, Genant HK: Radiologist’s guide to the use

of the laboratory in diagnosing rheumatic diseases. Radiol-

ogy 139:585-592,198 1

59. Knuth DE: Algorithms. Sci Am 236:63-80, 1977

60. Heath FG: Origins of the binary code. Sci Am 227:76-

83, 1972