a virtual glucose homeostasis model for verification...

A Virtual Glucose Homeostasis Model for Verification,Simulation and Clinical Trials

Neeraj Kumar Singh

INPT-ENSEEIHT/IRITUniversity of Toulouse, France

September 14, 2016

Neeraj Kumar Singh A Perspective on Environment Modelling September 14, 2016 1 / 25

Outline

1 Critical Systems

2 Context and Problems

3 Glucose Homeostasis Models

4 Formalization of GH

5 GH Simulator Framework

6 Hardware Implementation of GH

7 Conclusion & Future Work


Critical Systems

Definition

A system whose failure may result in injury, loss of life, economical loss orserious environmental damage. These systems require interaction betweencomputational and physical elements.


System Failures

System Failures

Therac-25 (1985-1987): six people overexposed to radiation.

Pacemaker and ICD (1990-2002): 17,323 pacemakers and ICDs wereexplanted that includes 61 deaths.

Insulin Infusion Pump (IIP) (2010): 5000 adverse events that includes30 deaths.

Missing Malaysian Plane MH370 (8 March, 2014): Unknown.

Satellite Failure:+150: http://www.sat-nd.com/failures/.


http://www.sat-nd.com/failures/

Context and Problems

Context

Development of virtual model for verification, simulation and clinical trialsthat can be used in the development process of medical devices.

Current Challenges

Increasing complexity of the critical medical systems.

Lack of biological simulation/environment for medical devices.

Better techniques for requirement analysis.

Needs some sound techniques to meet regulators, and certificationstandards.

Modelling critical medical systems using human-in-loop architecture.


Insulin Infusion Pump

Insulin Infusion Pump

An insulin pump is a small, complex, software-intensive medical device thatallows controllable, continuous subcutaneous infusion of insulin to patients.


IIP Requirements

REQ1: The device must undergo a power-on-self-test (POST) whenever devicepower is turned on.REQ2: The device must suspend all active basal delivery or bolus deliver duringpump refilling and in the case of system failure.REQ3: The device shall allow the user to manage system functionalities relatedto: stopping insulin delivery; validating basal profiles parameters; remindermanagement; and validating bolus preset parameters.REQ4: The device shall allow the user to define a basal profile that consists of anordered set of basal rates, ordered over a 24 hour day, as well as a temporarybasal, that consists of a basal rate for a specified duration of time within a 24hour day.REQ5: The device can contain several basal profiles, but only one basal profilecan be active at any single point in time.REQ6: The device must allow the user to override an active basal profile with atemporary basal, without changing the existing basal profile.REQ7: The device shall resume the active basal profile after the temporary basalterminates.


IIP Requirements

REQ8: The device shall enforce a maximum dosage for the normal bolus orextended bolus.REQ9: The user shall be able to stop the active normal or extended bolus.REQ10: The device must maintain an electronic log of every operationassociated with an user alert, such as an audio alarm.REQ11: The device shall maintain a history of basal and bolus dosages over thepast n days. n always differs among brands, though most store up to 90 days ofdata.REQ12: The device shall enable the user to create a food database that can beused to store food or meal descriptions and the carbs associated with them.REQ13: The device shall allow to the user to change parameter settings of basalprofile, bolus preset, and temporary basal.REQ14: The device shall provide feedback to the user regarding system anddelivery status.


Objectives

To identify gaps or inconsistencies in the IIP requirements.

Developing a closed-loop model for verification and validation of IIP.

Analysing system interaction between the GH model and IIP.

Developing a simulation model from the formal virtual GH model.

Developing a test bench using the virtual GH model and simulationfor clinical trials of IIPs.

Generating test cases to test the functional correctness of IIPsoftware.

Developing patient specific model at various level of systemdevelopment.

The virtual environment model can be used by medical industriesduring the product development.

The virtual GH environment model can be used by regulators forvalidating and certifying the medical devices.


Glucose Homeostasis Models

Clinical Models

Models for

diagnostic tests

control

progression

complications

Non-Clinical Models

Models for

insulin-glucose, hepatic glucose, glucagon, and insulin receptordynamics

beta-cell insulin release

brain glucose homeostasis


Glucose Homeostasis Models

Use of the Models

To present a simulation of the glucose homeostasis system tounderstand the actual behavior.

To assist the medical experts for simulation purpose of the glucosedynamics.

Disadvantages

Existing models are based on complex mathematics, therefore thesemodels

are difficult and make simulation very time-consuming.

are not suitable for presenting an abstract behavior of GH.

are not suitable for verification purpose.


Glucose Homeostasis System

HighCPlasmaCGlucoseCLevel

LowCPlasmaCGlucoseCLevel

NormalCGlucoseCLevelCMaintainedC

α-cellsβ-cells

GlucagonRelease

InsulinRelease

GlucoseCUtilizationCandCStorageCinCLiverC

asCGlycogen

LiverCConvertsCGlycogenCtoC

Glucose

GlucoseCLevelCDrops

GlucoseCLevelCRises

Pancreas


Glucose Homeostasis Automata

Glucose Level Drops

Glucose Level Rises

Hi No Lo

AcBc

Li

St Tr

Insulin Release

GlucagonRelease

Figure: The Glucose Homeostasis AutomataNeeraj Kumar Singh A Perspective on Environment Modelling September 14, 2016 13 / 25

The Glucose Homeostasis Definition

Definition 1 (The Glucose Homeostasis System)

Given a set of nodes N, a transition T is a pair (i, j), with i, j ∈ N . A transition is denoted by i j. The glucose homeostasis system is a tuple GHS = (N, T, N0) where:

• N = { Hi, No, Lo, Ac, Bc, Li, St, Tr } is a finite set of landmark nodes in the glucosehomeostasis network;

• T ⊆ N × N = {No 7→ Hi, Hi 7→ No, No 7→ Lo, Lo 7→ No, Hi 7→ Hi, No 7→ No, Lo 7→ Lo, Hi7→ Bc, Lo 7→ Ac, Bc 7→ Li, Ac 7→ Li, Li 7→ St, Li 7→ Tr, St 7→ No, Tr 7→ No, St 7→ Hi, Tr 7→ Lo,Tr 7→ Hi} is a set of transitions to present data flow between two landmark nodes;

• N0 = No is the initial landmark node (normal glucose level);


Abnormal Glucose Homeostasis System

HighbPlasmabGlucosebLevel

LowbPlasmabGlucosebLevel

NormalbGlucosebLevelbMaintainedb

Alpha-CellsbDefect;Abnormalb

GlucagonbRelease

InsulinRelease

Beta-CellsbDefect;InsufficientborbnoInsulinbSecretion

InsufficientborbnobGlucagonb

SecretionPancreas

InsulinbResistanceinbCellsb

ExcessbInsulinborbExtreambExercise

ExcessbGlucagonbSecretion

PersistentHighbPlasmab

GlucosebLevel

Hyperglyoemia-inducedDiabetesbComplications

PersistentLowbPlasmab

GlucosebLevel

PersistentHighbPlasmab

GlucosebLevel

β-cells α-cells

Figure: Abnormal Glucose Homeostasis System


Blood Glucose Level

Property 1 (Blood Glucose Level)The blood glucose level defines different stages, such as hyperglycemia, hypoglycemia andnormal. The glucose level is low (hypoglycemia) if FPG ∈ [0,70) or OGTT ∈ [0,70), and theglucose level is high (hyperglycemia) if FPG ≥ 125 or OGTT ≥ 200, and the glucose level isnormal if FPG ∈ [70,100) or OGTT ∈ [70,140). We classify pre-diabetes to be the range whereFPG ∈ [100,125) or OGTT ∈ [140,200).

Blood Sugar Level Fasting Plasma Glucose (FPG) Oral Glucose Tolerance Test(mg/dL) (mg/dL)

Normal 70..99 70..139Pre-Diabetes 100..125 140..199High glucose 126 or above 200 or aboveLow glucose 0..69 0..69

Table: FPG and OGTT Test Values for Glucose Level


Abstract Model

Context

axm1 : Glucose level , {Normal}, {High}, {Low})axm2 : partition(GHS , {OK}, {KO})

NoHi Lo

Figure: Automata of an Abstract Model


Abstract Machine

inv1 : Current Glucose Level ∈ Glucose levelinv2 : Diabetic Condition ∈ GHSinv3 : Diabetic Condition = KO⇔

Current Glucose Level = High ∨ Current Glucose Level = Lowinv4 : Current Glucose Level = Normal ⇔ Diabetic Condition = OK

EVENT Normal GlucoseWHENgrd1 : Current Glucose Level = Normal∨

Current Glucose Level = Low∨Current Glucose Level = High

THENact1 : Current Glucose Level := Normalact2 : Diabetic Condition := OK

END


Abstract Machine

EVENT High GlucoseWHENgrd1 : Current Glucose Level = Normal ∨ Current Glucose Level = High

THENact1 : Current Glucose Level := Highact2 : Diabetic Condition := KO

END

EVENT Low GlucoseWHENgrd1 : Current Glucose Level = Normal ∨ Current Glucose Level = Low

THENact1 : Current Glucose Level := Lowact2 : Diabetic Condition := KO

END

N. K. Singh, Hao Wang, Mark Lawford, Thomas S. E. Maibaum, and Alan Wassyng “Formalizing the Glucose HomeostasisMechanism”, 16th International Conference on Human-Computer Interaction (HCI 2014), LNCS, Springer InternationalPublishing, pp. 460–4271, Vol-8529, 2014.


Progressive Refinements

Refinement

Gradually introduce details and complexity to the specification byremoving non-determinism and by adding more events.

Refinement 1 : To introduce the α-cells and β-cells of Pancreasincluding their releasing functions and defects.

Refinement 2 : To define the liver behaviour for converting orstoring the glucose in the body.

Refinement 3 : To add the abnormal conditions of Pancreas,diabetic conditions, and diabetes complications.

Refinement 4 : To introduce the Blood Sugar Concentration forassessing the Diabetes and Pre-diabetes.


GH Simulator Framework

Physiology of GH

Physiology of the Pancreas

Physiology of the Liver

Insulin-glucose Dynamics

Glucagon-glucose Dynamics

GH Abnormality

Physiology of pancreatic alpha-cells and beta-cell

Modeling Toolsand

Computation Tools

SimulationKernel

Required Parameters

User Interface and

Visualization of GH

Formal Specification

of GH

Finite elements,Finite differences,Lumped elements,etc.


Hardware Implementation of GH

User Interface and

Visualization of GH

Formal Specification

of GH

GHSimulation

Modeling and Implementation

of GH Model

HardwarePlatform

FPGA, Arduino, Snickerdoodle, etc

Matlab orLabVIEW


Usage Scenarios of Environment Model

Behavioural Requirements

To Discover Essential Safety Properties

Patient Safety in Closed-loop

To Generate Automatic Test Cases

Test Bench for Clinical Trials of IIPs


Conclusion & Future Work

Conclusion

Logic based mathematical modelling of the GH (Normal andAbnormal)

Developed a stepwise formal model of GH environment model

Applying model checking and theorem prover to prove safetyproperties.

Proposed Simulation framework

Proposed Hardware Implementation framework

To meet the V&V requirements of certification standards like FDAetc.

Future Work

Integration of GH model and IIP for developing the closed-loop model

Development of GH simulator

Test bench for IIPs through developing the hardware platform of GH


a virtual glucose homeostasis model for verification...

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