The main objective of this course is the detailed study of the mathematical models dscribing the ionic currents, the action potential of the different cells of the heart, and the models describing the propagation of the electric signal in the heart. The course look in detail the numerical solution of the resulting equations as well as the implementation in the computer favoring the interaction of the student with computer codes implemented in a user friendly environment. These modeling and simulation tools are then applied to the study of arrhythmias in particular those associated with acute regional ischemia.

By the end of the course, the student

• will be able to use the acquired knowledge to understand and describe complex engineerng problem
• will be able to formulate and solve complex problems in the field of biomedical engineering
• will be able to apply engineering methods to the field of biology and biotechnology
• will be able to perform continuous learning and develop strategies for autonomous learning
• will be able to communicate the results of his activity in clear and concise manner.

Basic physiology of the heart: functioning and structure. Modeling cardiac excitation and excitability: The cardiac action potential. Models of cardiac action potential. The contractile behavior of the cardiac myocyte: active and passive elasticity of the cardiac myocyte. The muscle structure of the heart: mathematical models of cardiac anatomy. Modeling propagation in excitable media: Monodomain and bidomain equations. The extracellular potential and the model of the Torso. Mechanics of the heart: Kinematics relations, stress equilibrium, constitutive model of the cardiac tissue: passive and active behavior. Material parameter estimation. The Finite Element method for modeling Impulse propagation: algorithms, numerical implementation, convergence, stability and performance. Computational mechanics of the heart: The finite element method for nonlinear problems, implementation, and computer simulations. Stress analysis of the diastolic heart. Simulation aspects of the electro-mechanical simulation of the heart, i.e., influence of space and time dicretization.

Course material:

Handouts, presentations, (accessible) papers on computational biology of the heart. For model implementation, the software package Matlab wil be used for modeling the electric and electromechanical models in 1D and 2D cases. 

There is no mandatory prerequisite. However, sound background on linear algebra, basic concepts of physics and physiology of the heart and numerical methods are desirable

Students will be evaluated at the end of the course on the basis of a written examination on the theoretical parts of the course and the reports from practical sessions.

Final exam: 70%

Report of Laboratory sessions and Project: 30%