1. Clinical cardiovascular identification with limited data and fast forward simulation 6 th IFAC SYMPOSIUM ON MODELLING AND CONTROL IN BIOMEDICAL SYSTEMS C. E. Hann 1, J. G. Chase 1, G. M. Shaw 2, S. Andreassen 3, B. W. Smith 3 1 Department 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. 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, …) Diagnosis and Treatment

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 (P 1 >P 2, P 2 ): (close on flow)

6. Fast Forward Simulation Ventricular interaction  solve every time step (slow) Substitute: Linear in V spt  Analytical solution  very fast Method (20 Heart beats)CPU time (s)Speed increase factor Event solver101.9 First Heaviside36.82.8 Simpler Heaviside18.85.4 Simpler Heaviside + V spt formula3.132.9

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  P ao  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 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

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

11. 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

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) 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

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 ChangeTrue value (ml) Optimized Value Error (%) First1801762.22 Second1601581.25 Third1401381.43 Fourth1201172.50 Fifth100 0 Pericardial Tamponade: Find all parameters, look for change in V0,pcd Pulmonary Embolism: Find all parameters, look for change in 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 All other variables effectively unchanged from baseline

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

17. Hypovolemic Shock: Find all parameters, look for change in total stressed blood volume ChangeTrue value (ml) Optimized Value Error (%) 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 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 Left Ventricle (30 mins) Right Ventricle (30 mins) Use only: Pao, Ppa, min/max(Vlv, Vrv) to ID all parameters Far fewer measurements than in simulation

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 Septum Volume (Pig 2) Right ventricle expansion index (Pig 2) Pulmonary resistance (Pig 2) Reflex actions (Pig 2) PV loops (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 Questions ??? Engineers and Docs Dr Geoff ChaseDr Geoff Shaw The Danes Prof Steen Andreassen Dr Bram Smith The Honorary Danes Belgium Honorary Kiwis Dr Thomas Desaive Christina Starfinger