Clinical cardiovascular identification with limited data and fast forward simulation

1. Clinical cardiovascular identification with limited data and fast forward simulation 6th IFAC SYMPOSIUM ON MODELLING AND CONTROL IN BIOMEDICAL SYSTEMS C. E. Hann1, J. G. Chase1, G. M. Shaw2, S. Andreassen3, B. W. Smith3 1Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand 2 Department of Intensive Care Medicine, Christchurch Hospital, Christchurch, New Zealand 3 Centre for Model-based Medical Decision Support, Aalborg University, Aalborg, Denmark

2. Diagnosis and Treatment • Problem: Cardiac disturbances difficult to diagnose • Limited data • Reflex actions • Solution: Minimal Model + Patient-Specific Parameter ID • Interactions of simple models to create complex dynamics • Primary parameters • Identification must use common ICU measurements • E.g. increased resistance in pulmonary artery  pulmonary embolism, atherosclerotic heart disease • However: Identification for diagnosis requires fast parameter ID • Must occur in “clinical real-time” • Limits model and method complexity (e.g. parameter numbers, non-linearities, …)

3. Heart Model

4. D.E.’s and PV diagram

5. Fast Forward Simulation • Formulate in terms of Heaviside functions: • No looking for sign changes and restarting DE solver done automatically • E.g. filling (P1>P2, P2 ): (close on flow)

6. Fast Forward Simulation • Ventricular interaction  solve every time step (slow) Substitute: • Linear in Vspt Analytical solution  very fast

7. Reflex Actions • Vaso-constriction - contract veins • Venous constriction – increase venous dead space • Increased HR • Increased ventricular contractility Varying HR as a linear function of DPao  Simple interactions to create overall complex dynamic behaviour in the full system model

8. Disease States • Pericardial Tamponade: • Build up of fluid in pericardium • Decrease: dead space volume V0,pcd • Pulmonary Embolism: • Increase: Rpul • Cardiogenic shock: • Not enough oxygen to myocardium (e.g. from blocked coronary artery) • Decrease: Ees,lvf, Increase: P0,lvf  A more complex set of changes/interactions • Septic shock: • Blood poisoning • Decrease: Rsys = systemic resistance • Hypovolemic shock: • Severe decrease in total blood volume = sum of individual volumes Current Status: • Clinical results for Pulmonary Embolism • Simulated results for others

9. A Healthy Human Baseline

10. Simulation of Disease States • Pericardial Tamponade Ppu – 7.9 mmHg CO – 4.1 L/min MAP – 88.0 mmHg • Pulmonary Embolism: Rpul increases as embolism induced ~60-75% change in mean value • All other disease states similarly capture physiological trends and magnitudes

11. (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

12. 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

13. 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

14. Adding Noise & ID • Add 10% uniform distributed noise to outputs to identify • Conservative value that is larger than what has been encountered clinically • Sample at 100-200 Hz Capture disease states, assume Ppa, Pao, Vlv_max, Vlv_min, chamber flows.

15. Identifying Disease State Using All Variables - Simulated • Pericardial Tamponade: Find all parameters, look for change in V0,pcd All other variables effectively unchanged from baseline • Pulmonary Embolism: Find all parameters, look for change in Rpul All other variables effectively unchanged from baseline

16. Identifying Disease State Using All Variables - Simulated • Cardiogenic shock: Find all parameters, look for change in [Ees,lvf, P0,lvf] All other variables effectively unchanged from baseline • Septic Shock: Find all parameters, look for change in Rsys All other variables effectively unchanged from baseline

17. Identifying Disease State using All Variables - Simulated • Hypovolemic Shock: Find all parameters, look for change in totalstressed blood volume All other variables effectively unchanged from baseline

18. New for MCBMS! Clinical Results • Pulmonary embolism induced in pigs (collaborators in Liege, Belgium) • Identify changes in Rpul including reflex actions and all variables • Use only: Pao, Ppa, min/max(Vlv, Vrv) to ID all parameters • Far fewer measurements than in simulation Right Ventricle (30 mins) Left Ventricle (30 mins)

19. Animal Model Results – PV loops Left Ventricle (120 mins) Right Ventricle (120 mins) Left Ventricle (180 mins) Right Ventricle (120 mins)

20. Animal Model Results Over Time PV loops (Pig 2) Pulmonary resistance (Pig 2) Reflex actions (Pig 2) Right ventricle expansion index (Pig 2) Septum Volume (Pig 2) Rpul – All pigs

21. Conclusions • Minimal cardiac model simulate time varying disease states • Accurately captures physiological trends and magnitudes • Accurately captures a wide range of dynamics • Fast simulation methods available • Integral-based parameter ID  patient specific models • Simulation: ID errors from 0-10%, with 10% noise • Animal model:Pressures (Total Error) =2.22±2.17 mmHg (< 5%) Volumes (Total Error) = 2.37±2.01 ml (< 5%) • Identifiable using a minimal number of common measurements • Rapid ID method, easily implemented in Matlab • Rapid ID = Rapid diagnostic feedback • Future Work = septic shock (Dec 2006), and other disease states (2007)

22. Acknowledgements Engineers and Docs Honorary Kiwis Belgium Dr Thomas Desaive Dr Geoff Chase Dr Geoff Shaw The Honorary Danes The Danes Christina Starfinger Questions ??? Prof Steen Andreassen Dr Bram Smith