Electro-mechanical coupling
Module: tutorials.04_EM_tissue.04_EM_coupling.run
Section author: Gernot Plank <gernot.plank@medunigraz.at> and Christoph Augustin <christoph.augustin@medunigraz.at
This tutorial elucidates the setting up of electro-mechanically coupled tisue simulations. As an example we use a simpliefied model of a left ventricular wedge preparation. For the sake of computational efficiency the apico-basal and circumferential dimension of the wedge are chosen by default to be small and the resolution of the model is coarse. As in the matching single cell stretcher experiment the same EP models (TT2, GPB) and stress models (TanhStress, LandStress, GPB-LandStress-model) are available which cover all three coupling modes (activation-time based ECC, weak calcium-driven ECC and strong calcium-driven ECC). The differences between coupling modes are illustrated in Fig. 52.
Fig. 138 The setup uses a simple LV wedge preparation where the apicobasal and
circumferential dimension can be chosen by setting the
--length
and --width
input parameters.
The wedge is mechanically fixated through homogeneous Dirichlet boundary
conditions at the apical face of the wedge.
At the anterior and posterior faces homogeneous Dirichlet boundary
conditions are also applied, preventing any displacement in radial
(z-axis) and circumferential (x-axis) direction,
but allowing the wedge to slide along the apico-basal (y-axis) direction.
Fiber rotation is set to standard values with -60 degrees at the
epicardial face and +60 degrees at the endocardial face.
The wedge is electrically stimulated epicardially at the center of the
preparation.
To run the examples of this tutorial do
cd ${TUTORIALS}/04_EM>_tissue/04_EM_coupling
To inquire the exposed experimental input parameters run
./run.py --help
which yields the following options:
--EP {TT2,GPB} pick human EP model (default is TT2)
--Stress {LandStress,TanhStress}
pick stress model (default is TanhStress)
--width WIDTH choose circumferential width of wedge in mm
--resolution RESOLUTION
choose mesh resolution in mm (default is 2.0 mm)
--duration DURATION duration of simulation (ms) (default: 500.0 ms)
--mechanics-off switch off mechanics to generate activation vectors
Simulation results computed at a higher spatial resolution of
are shown in the following for a full
contraction-relaxation cycle.
Specifically, the activation sequence is shown in terms of all relevant
signals involved in active force generation in
fig-ecc-wedge
.
Fig. 139 Shown are signals involved in the
excitation-contraction coupling cascade.
A stimulus is delivered at the center of the epicardial surface to
initiate the propagation of action potentials.
The leftmost panels shows transmebrane voltages
(blue: -90 mV, red: +50 mV).
Propagating action potentials initiate Calcium transients which drive the
generation of active stress.
The mid-left panel shows the intracellular Calcium transients
(blue: 0.
, red: 1.2
).
Due to fiber rotation a significant heterogeneity in fiber stretch,
, is wittnessed,
which is shown in the mid-right panel
(blue: 0.7, red: 1.3).
The rightmost panel shows active tension
(black: 0.0 kPa, red: 40 kPa).
In a first step we solve only the EP problem with the active stress plug-in
enabled to verify that activation sequence and force generation are working
properly.
Solving of the mechanics problems is turned off by adding the
--mechanics-off
flag,
thus fiber stretch remains constant at
for the entire simulation.
Tension therefore is not modulated by length-dependence.
The
--visualize
option shows transmembrane voltage ,
active stress
and fiber stretch
.
./run.py --EP TT2 --Stress TanhStress --ID exp-em-ti-01 --mechanics-off --visualize
Omitting the --mechanics-off
flag turns on the computation of deformation.
Using the default settings for --length
, --width
and --resolution
leads to a fairly coarse discretization, but allows for sufficiently short
simulation cycles.
EP in this simulation is driven by a reaction-eikonal approach
(see Neic et al [1] for details)
which yields undistorted propagation patterns even on coarse meshes.
For the sake of saving compute time we use a resolution of 4 mm.
./run.py --EP TT2 --Stress TanhStress --resolution 4 --ID exp-em-ti-02 --visualize
As before in experiment exp01, we solve only the EP problem with the active stress plug-in enabled
to verify that activation sequence and force generation are working as expected.
As we are using a Calcium-driven active stress model the --visualize
option shows also the Calcium signals which serve as input for driving the
active stress model.
./run.py --EP TT2 --Stress LandStress --ID exp-em-ti-03 --mechanics-off --visualize
We repeat experiment exp03 with deformation enabled now.
Due to the weak coupling approach used the Calcium signals remain unaltered
as compared to experiment exp03 without deformation (i.e. ).
./run.py --EP TT2 --Stress LandStress --resolution 4 --ID exp-em-ti-04 --visualize
This experiment repeats exp03, but with strong coupling For the sake of saving compute time only 80 ms activity are simulated to observe the onset of contraction.
./run.py --EP GPB --Stress LandStress --mechanics-off --ID exp-em-ti-05 --visualize
./run.py --EP GPB --Stress LandStress --resolution 4 --ID exp-em-ti-06 --visualize