Heart Wall - Tissue Functioning and Remodeling in the Circulatory and Ventilatory Systems - page 340

propagation. During the relative refractory period (RRP), the potential propagates
when the stimulus is supraliminal. The supernormal period (SPN) is a short phase
at the end of repolarization, during which the potential initiated by an infraliminal
stimulus propagates. The excitability is maximal and decreases to its rest value at
the end of the total recovery period . Refractory periods vary with excitation rate.

6.6.9 Electromechanical Modeling

Advances in signal and image acquisition and processing enable measurements
of electrical and mechanical (cardiac wall motion, cardiac chamber flow patterns,
and coronary perfusion) quantities and improve clinical outcome. Nevertheless,
anatomical and functional data must be combined in a consistent framework.
In addition, personalized treatment remains difficult to optimize.
Mathematical models and associated multimodel, multiscale, and multiphysics
computational coupling platforms are aimed at integrating produced measurements,
visualizing evolution of quantities of interest during the cardiac cycle, as well as
deriving indicators that are not directly observable to assist treatment decisions.
Continuum-based simulation codes rely on high-performance computing.
Three-dimensional ventricular electromechanical models primarily rely on 2
submodels that treat the electrical and mechanical activity, respectively. Ventric-
ular geometry is obtained from high-resolution magnetic resonance imaging and
computerized tomography. The cardiac geometry is extracted using automatic and
semi-automatic segmentation techniques that can be based on atlases computed
from population data or statistical shape models that can be applied to heart images.
Manual correction tools are available when the segmentation is not accurate enough.
Once the ventricular geometry is reconstructed, an appropriate spatial discretiza-
tion of the cardiac geometry yields the computational mesh. Mesh adaptation and
adaptivity allow to match physical requirements and to follow proper propagation
of physical quantities. As the governing equations of electrical and mechanical
problems differ, mesh element type and size fit each problem requirements.
The electrical model simulates the propagation of a depolarization wave in the
cardiac wall. The electrical model describes the ionic current using a simplified
representation with a low number of parameters (Vol. 7 - Chap. 8. Numerical
Simulations). High-resolution tetrahedral meshes can be employed for detailed elec-
trophysiological analysis. Further information on the nodal network can be added.
An organ-level problem is described by reaction-transport equations. A reduced
electrophysiological model such as the one proposed by Mitchell and Schaeffer
can be used. Incorporating heterogeneous electrical conductivities of the thorax and
its content, the propagation of depolarization wave can be computed on the body
surface to yield an ECG trace. A sensitivity analysis of the effect of mesh size,
initial stimulation points, and conduction velocity, among other parametyers, can