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

Physiological Systems Modeling and Simulation Modeling Simulation

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?

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  …

LTI Models of Physiological Systems Example: linearized lung mechanics

System Identification Gray box Black box

Physiological CONTROL Systems Homeostasis!

Physiological CONTROL Systems Homeostasis!

Milestones 1952

Milestones Huxley crossbridge model Hill model

Electric conduction in cells and tissues

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

Biomechanics

symmetry contact clamped

Biomechanics 100 % Stress free

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

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!

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

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