Identification of Time Varying Cardiac Disease State Using a Minimal Cardiac Model with Reflex Actions 14 th IFAC SYMPOSIUM ON SYSTEM IDENTIFICATION, SYSID-2006 C. E. Hann 1, S. Andreassen 2, B. W. Smith 2, G. M. Shaw 3, J. G. Chase 1, P. L. Jensen 4 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 4 Department of Cardiology, Aalborg Hospital, Denmark

Cardiac disturbances difficult to diagnose - Limited data - Reflex actions Minimal Cardiac Model - Interactions of simple models - primary parameters - common ICU measurements Increased resistance in pulmonary artery – pulmonary embolism, atherosclerotic heart disease 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. 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

Healthy Human Baseline 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

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

Add Noise to Identify Add 10% uniform distributed noise to outputs to identify 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

Identifying Disease State using All Variables - Simulated ChangeTrue value (ml) Optimized Value Error (%) First Second Third Fourth Fifth100 0 Capture disease states, assume Ppa, Pao, Vlv_max, Vlv_min, chamber flows. Pericardial tamponade (determining V0,pcd) Pulmonary Embolism (determining Rpul) ChangeTrue value (mmHg s ml -1 ) Optimized ValueError (%) 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 Septic Shock (determining Rsys) Identifying Disease State using All Variables - Simulated

Hypovolemic Shock (determining stressed blood volume) ChangeTrue value (ml) Optimized ValueError (%) First Second Third (hmm!) Fourth Fifth Identifying Disease State using All Variables - Simulated

Preliminary Animal Model Results Pulmonary embolism induced in pig (collaborators lab in Belgium) Identifying changes in pulmonary resistance, Rpul Left Ventricle 8 heartbeats Essential dynamics captured Remaining issues with sensor locations etc Aortic stenosis as well?

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 The Danes Steen Andreassen Dr Bram Smith The honorary Danes