1. 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

2. 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

3. Heart Model

4. D.E.’s and PV diagram

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

6. 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

7. 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

8. 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

9. Add Noise to Identify Add 10% uniform distributed noise to outputs to identify Apply integral-based optimization

10. 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

11. 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

12. Integral Method - Concept Linear least squares (unique solution) MethodStarting pointCPU 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

13. Identifying Disease State using All Variables - Simulated ChangeTrue value (ml) Optimized Value Error (%) First1801762.22 Second1601581.25 Third1401381.43 Fourth1201172.50 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 (%) First0.18620.19072.41 Second0.21730.20505.67 Third0.24830.26948.50 Fourth0.27940.27212.60 Fifth0.31040.29624.59

14. 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 (%) First1.02361.02780.41 Second0.95820.97141.37 Third0.89290.85963.73 Fourth0.82760.83160.49 Fifth0.76220.79934.86 Septic Shock (determining Rsys) Identifying Disease State using All Variables - Simulated

15. Hypovolemic Shock (determining stressed blood volume) ChangeTrue value (ml) Optimized ValueError (%) First1299.91206.57.18 Second1177.31103.76.26 Third1063.1953.810.28 (hmm!) Fourth967.81018.95.28 Fifth928.5853.48.10 Identifying Disease State using All Variables - Simulated

16. 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?

17. 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

18. Acknowledgements Questions ??? Engineers and Docs Dr Geoff ChaseDr Geoff Shaw The Danes Steen Andreassen Dr Bram Smith The honorary Danes