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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]
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