Simulating Cardiac Disease From Onset with a Simulating Cardiac Disease From Onset with a Minimal Cardiac Model Including Reflex ActionsMinimal Cardiac Model Including Reflex Actions

THE 12th INTERNATIONAL CONFERENCE ON BIOMEDICAL ENGINEERING

C. E. Hann1, J. G. Chase1, S. Andreassen2, B.W. Smith2, G. M. Shaw3,

1Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand2Centre for Model-based Medical Decision Support, Aalborg University, Aalborg, Denmark

3 Department of Intensive Care Medicine, Christchurch Hospital, Christchurch, New Zealand

• Cardiac disease state difficult to diagnose

- Limited data

- Reflex actions

• Minimal Cardiac Model

- primary parameters

- common ICU measurements

• Increased resistance in pulmonary artery – pulmonary embolism, atherosclerotic heart disease

• Optimize drug treatment on computer

-e.g. Warfarin

• Require fast parameter ID

Diagnosis and TreatmentDiagnosis and Treatment

Heart ModelHeart Model

D.E.’s and PV diagramD.E.’s and PV diagram

2

2232

2

1

1121

1

21

L

RQPPQ

L

RQPPQ

QQV

2

0

)375.0(80

)(02

)(

),1())(1()()(

t

VVdes

ete

ePteVVEteP

Reflex actionsReflex actions

• Vaso-constriction - contract veins

• Venous constriction – increase venous dead space

• Increased HR

• Increased ventricular contractility

Varying HR as a function of aoP

Disease StatesDisease States

• Pericardial Tamponade- build up of fluid in pericardium- dead space volume V0,pcd by 10 ml / 10 heart beats

• Pulmonary Embolism - Rpul 20% each time

• Cardiogenic shock- e.g. left ventricle infarction, blocked coronary artery- not enough oxygen to myocardium- Ees,lvf, P0,lvf

• Septic shock- blood poisoning- reduce systemic resistance

• Hypovolemic shock – severe drop in total blood volume

ResultsResults

Output Value

Volume in left ventricle 111.7/45.7 ml

Volume in right ventricle 112.2/46.1 ml

Cardiac output 5.3 L/min

Max Plv 119.2 mmHg

Max Prv 26.2 mmHg

Pressure in aorta 116.6/79.1 mmHg

Pressure in pulmonary artery 25.7/7.8 mmHg

Avg pressure in pulmonary vein 2.0 mmHg

Avg pressure in vena cava 2.0 mmHg

• Healthy human

ResultsResults

• Pericardial tamponade Ppu – 7.9 mmHgCO – 4.1 L/minMAP – 88.0 mmHg

• Pulmonary Embolism

• All other disease states capture physiological trends and magnitudes

IdentifiabilityIdentifiability

• Add 10% noise to outputs

• Apply integral-based optimization

Integral Method - ConceptIntegral Method - Concept

Discretised solution analogous to measured data

• Work backwards and find a,b,c

• Current method – solve D. E. numerically or analytically

8.0,2.0,5.0

1)0(,)sin(

cba

xctbaxx• (simple example with analytical solution )

R

PPq 21

12 13 14 15 16 17 18 191.4

1.45

1.5

1.55

1.6

1.65

1.7

1.75

1.8

1.85

time

x

))sincos(

)(()1(

1)(

22

322

ccatbatab

acaabcaeaa

tx at

- Find best least squares fit of x(t) to the data

- Non-linear, non-convex optimization, computationally intense

• integral method

– reformulate in terms of integrals

– linear, convex optimization, minimal computation

Integral Method - ConceptIntegral Method - Concept

0t• Integrate both sides from to t ( ) ,)sin( ctbaxx 4

0t

t

t

t

t

t

t

t

t

t

t

t

t

ttcttbdtxatxtx

dtcdttbdtxatxtx

dtctbaxdtx

0

0 0 0

00

)())cos()(cos()()(

1)sin()()(

))sin((

000

0

• Choose 10 values of t, between and form 10 equations in 3 unknowns a,b,c

40t 6

10,,1),()()())cos(1( 000

itxtxttctbdtxa iitt i

Integral Method - ConceptIntegral Method - Concept

)()(

)()(

)cos()cos(

)cos()cos(

010

01

010100

0110

10

0

1

0

txtx

txtx

c

b

a

ttttdtx

ttttdtx

tt

tt

• Linear least squares (unique solution)

Method Starting point CPU time (seconds) Solution

Integral - 0.003 [-0.5002, -0.2000, 0.8003]

Non-linear [-1, 1, 1] 4.6 [-0.52, -0.20, 0.83]

Non-linear [1, 1, 1] 20.8 [0.75, 0.32, -0.91]

• Integral method is at least 1000-10,000 times faster depending on starting point

• Thus very suitable for clinical application

IdentifiabilityIdentifiability

Change True value

(ml)

Optimized Value

Error (%)

First 180 176 2.22

Second 160 158 1.25

Third 140 138 1.43

Fourth 120 117 2.50

Fifth 100 100 0

• Pericardial tamponade (determining V0,pcd)

• Pulmonary Embolism (determining Rpul)

Change True value

(mmHg s ml-1)

Optimized Value

Error (%)

First 0.1862 0.1907 2.41

Second 0.2173 0.2050 5.67

Third 0.2483 0.2694 8.50

Fourth 0.2794 0.2721 2.60

Fifth 0.3104 0.2962 4.59

• Cardiogenic shock (determining [Ees,lvf, P0,lvf] (mmHg ml-1, mmHg)

Change True values Optimized Value

Error (%)

First [2.59,0.16] [2.61,0.15] [0.89,5.49]

Second [2.30,0.19] [2.30,0.18] [0.34,4.39]

Third [2.02,0.23] [2.02,0.21] [0.43,8.03]

Fourth [1.73,0.26] [1.70,0.24] [1.48,9.85]

Fifth [1.44,0.30] [1.43,0.27] [0.47,9.39]

Change True value

(mmHg s ml-1)

Optimized Value

Error (%)

First 1.0236 1.0278 0.41

Second 0.9582 0.9714 1.37

Third 0.8929 0.8596 3.73

Fourth 0.8276 0.8316 0.49

Fifth 0.7622 0.7993 4.86

IdentifiabilityIdentifiability

• Septic Shock (determining Rsys)

IdentifiabilityIdentifiability

• Hypovolemic Shock (determining stressed blood volume)

Change True value

(ml)

Optimized Value

Error (%)

First 1299.9 1206.5 7.18

Second 1177.3 1103.7 6.26

Third 1063.1 953.8 10.28

Fourth 967.8 1018.9 5.28

Fifth 928.5 853.4 8.10

ConclusionsConclusions

• Minimal cardiac model simulate time varying disease states

• Accurately captured physiological trends and magnitudes

capture wide range of dynamics

• Integral based parameter ID method

- errors from 0-10%, with 10% noise

- identifiable using common measurements

• Rapid feedback to medical staff

AcknowledgementsAcknowledgements

Questions ???

Engineers and Docs

Dr Geoff Chase Dr Geoff Shaw

AIC2, Kate, Carmen and Nick

The Danes

Steen Andreassen Dr Bram Smith

The honorary Danes