The computational biology of the heart is one of the most important recent applications of mathematical modeling and simulation in bioengineering. In this regard, the main research directions and the most important for engineering, biological and medical applications are the development of a realist model of the whole mammalian heart. The realization of such a model has become feasible thanks to recent advances in computer technology and experiments on cardiac tissue. The present course, which has a heavily computational orientation, considers an integral description of the heart. The first third of the course is dedicated to establish the electro-mechanical model of the organ. Starting from the basic physiology of the ion channels; the electric and mechanical functioning of the cardiac myocyte is presented. These models are couple to a model of the cardiac tissue upon which the model of the entire organ is developed. The remaining of the course is dedicated to the numerical modeling and simulation of the cardiac electromechanics. The basis for solving the governing equations for the electrical and mechanical behavior of the heart using the finite element method will be discussed in detail along with their implementation in different computational softwares.

Learning objectives:

By the end of the course, an active participant is capable of reading literature regarding the electric and mechanical behavior of the heart. Furthermore, he or she will be able to implement a model and perform calculations with it, as well as will be able to interface with existing software to perform advanced simulations.

Contents:

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. The software Abaqus will be used for the stress analysis of the diastolic heart.

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.