14 th IFAC SYMPOSIUM ON SYSTEM IDENTIFICATION, SYSID-2006

1. Identification of Time Varying Cardiac Disease State Using a Minimal Cardiac Model with Reflex Actions 14th IFAC SYMPOSIUM ON SYSTEM IDENTIFICATION, SYSID-2006 C. E. Hann1, S. Andreassen2, B. W. Smith2, G. M. Shaw3, J. G. Chase1, P. L. Jensen4 1Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand 2Centre 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. Diagnosis and Treatment • 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

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 • Healthy human

8. Model Simulation Results • Pericardial tamponade Ppu – 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. (simple example with analytical solution ) Integral Method - Concept Work backwards and find a,b,c Current method – solve D. E. numerically or analytically Discretised solution analogous to measured data • 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) 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 • Capture disease states, assume Ppa, Pao, Vlv_max, Vlv_min, chamber flows. • Pericardial tamponade (determining V0,pcd) • Pulmonary Embolism (determining Rpul)

14. Identifying Disease State using All Variables - Simulated • Cardiogenic shock (determining [Ees,lvf, P0,lvf] (mmHg ml-1, mmHg) • Septic Shock (determining Rsys)

15. Identifying Disease State using All Variables - Simulated • Hypovolemic Shock (determining stressed blood volume)

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 Engineers and Docs The Danes The honorary Danes Steen Andreassen Dr Bram Smith Dr Geoff Chase Dr Geoff Shaw Questions ???