1. Physiological Systems Modeling and Simulation Federica Caselli University of Rome “Tor Vergata” A.A. 2011/2012

2. Physiological Systems Modeling and Simulation Modeling Simulation

3. Purpose of modeling  Understanding physiology  Diagnosis  Prediction  Artificial organ design  Virtual medicine  … Modeling process:  Model formulation  Parameter identification  Model validation  Model simulation (iterative process!) Physiological Systems Modeling and Simulation Examples?

4. Type of models  Black or gray box (data or system modeling)  Linear or nonlinear  Stationary or time-dependent  Lumped or distributed parameters (ODE or PDE)  Deterministic or stochastic  …

5. LTI Models of Physiological Systems Example: linearized lung mechanics

6. System Identification Gray box Black box

7. Physiological CONTROL Systems Homeostasis!

8. Physiological CONTROL Systems Homeostasis!

9. Milestones 1952

10. Milestones 1938 1957 Huxley crossbridge model Hill model

11. Electric conduction in cells and tissues

12. Cell encapsulation Normalized drug mass in the container Drug delivery system modeling

13. Biomechanics

16. symmetry contact clamped

17. Biomechanics 100 % Stress free

18. Heart-lung machine Oxygen diffusion and transport, blood flow dynamics, stress on red blood cell and haemolysis...

19. Challenges  Complexity  Multiphysics & Multiscale models  Holistic approach  Growth and remodeling  Patient-Specific models  Noninvasive method for parameter identification  Computational efforts To name but a few!

20. References  Cobelli C. and Carson E., Introduction to Modeling in Physiology and Medicine, Elsevier/Academic Press, New York, 2007.  Holzapfel G.A., Nonlinear Solid Mechanics: A Continuum Approach for Engineering, Wiley, New York, 2000.  Humphrey J.D., Cardiovascular Solid Mechanics: cells, tissues and organs, Springer-Verlag, 2002.  Keener J. and Sneyd J., Mathematical Physiology – Systems Physiology, Springer.  Khoo M.C.K., Physiological Control Systems, IEEE Press, 2000.  Quarteroni A., Cardiovascular Mathematics, Springer, 2009.

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