Project C4: Coupling between reaction-diffusion waves and mechanical deformations in elastic excitable media.

The main goal of the project is to develop one- and two-dimensional models
wherein reaction-diffusion waves are coupled with mechanical deformations in
systems with fixed and moving boundaries. The elastic parameters of pheno-
menological models shall be determined by comparison with experimental
data either obtained from in-vitro measurements in layers of cardiac muscle
cells or from in-vivo magnetic resonance imaging.
We plan to start from realistic physiological model as well as simplified equa-
tions obtained by fitting of the more realistic model. These models are stan-
dard reaction-diffusion equations and need to be extended by coupling to
mechano-elastical equations describing stress generation in the medium. In
addition, stationary and moving boundary conditions in one- and two dimen-
sional geometries shall be realized. The model should contain one partial
differential equation for the transmembrane voltage in the cardiac tissue and
equations describing the ionic channel dynamics and the calcium concentration.
To describe the electro-mechanical coupling, an equation for the active stress
generated by changes in potential and calcium concentration has to be added. 
These equations are then supplemented by the relation between active stress
and mechanical deformation. We also plan to explore simplified models derived
from the original equations, namely reaction-diffusion equations with nonlocal
coupling terms. All models will first be studied by systematic direct simulations
and by numerical bifurcation and stability analysis. In a second step, we will use
such model equations to determine elastic parameters from experiments on
moving heart tissue by employing inverse methods.

Project leaders: Prof. Dr. M. Bär [1], Prof. Dr. H. Engel [2]