Simulating Cardiac Disease From Onset with a Minimal Cardiac Model Including Reflex Actions THE 12 th INTERNATIONAL CONFERENCE ON BIOMEDICAL ENGINEERING C. E. Hann 1, J. G. Chase 1, S. Andreassen 2, B.W. Smith 2, G. M. Shaw 3, 1 Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand 2 Centre 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 Treatment

Heart Model

D.E.’s and PV diagram

Reflex actions Vaso-constriction - contract veins Venous constriction – increase venous dead space Increased HR Increased ventricular contractility Varying HR as a function of

Disease 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

Results OutputValue Volume in left ventricle111.7/45.7 ml Volume in right ventricle112.2/46.1 ml Cardiac output5.3 L/min Max Plv119.2 mmHg Max Prv26.2 mmHg Pressure in aorta116.6/79.1 mmHg Pressure in pulmonary artery25.7/7.8 mmHg Avg pressure in pulmonary vein2.0 mmHg Avg pressure in vena cava2.0 mmHg Healthy human

Results Pericardial tamponadePpu – 7.9 mmHg CO – 4.1 L/min MAP – 88.0 mmHg Pulmonary Embolism All other disease states capture physiological trends and magnitudes

Identifiability Add 10% noise to outputs Apply integral-based optimization

Integral Method - Concept Discretised solution analogous to measured data Work backwards and find a,b,c Current method – solve D. E. numerically or analytically (simple example with analytical solution ) - 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 - Concept Integrate both sides from to t ( ) Choose 10 values of t, between and form 10 equations in 3 unknowns a,b,c

Integral Method - Concept Linear least squares (unique solution) MethodStarting pointCPU time (seconds)Solution Integral-0.003[ , , ] 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 ,000 times faster depending on starting point Thus very suitable for clinical application

Identifiability ChangeTrue value (ml) Optimized Value Error (%) First Second Third Fourth Fifth100 0 Pericardial tamponade (determining V0,pcd) Pulmonary Embolism (determining Rpul) ChangeTrue value (mmHg s ml -1 ) Optimized Value Error (%) First Second Third Fourth Fifth

Cardiogenic shock (determining [Ees,lvf, P0,lvf] (mmHg ml -1, mmHg) ChangeTrue valuesOptimized 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] ChangeTrue value (mmHg s ml -1 ) Optimized Value Error (%) First Second Third Fourth Fifth Identifiability Septic Shock (determining Rsys)

Identifiability Hypovolemic Shock (determining stressed blood volume) ChangeTrue value (ml) Optimized ValueError (%) First Second Third Fourth Fifth

Conclusions 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

Acknowledgements Questions ??? Engineers and Docs Dr Geoff ChaseDr Geoff Shaw AIC2, Kate, Carmen and Nick The Danes Steen Andreassen Dr Bram Smith The honorary Danes