Page 67 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 1 Multi-scale models of the heart for patient-specific simulations 37

implicitly accounting for the interface coupling conditions. This
approach typically requires the implementation of ad-hoc solvers,
and can be computationally demanding due to the sheer size of
the resulting system of equations. On the other hand, it generally
allows a more stable solution of the coupled problem. Partitioned
approaches have the advantage of allowing the use of off-the-shelf
solvers tailored to the individual problems (fluid dynamics and
elastodynamics). However, fulfilling the coupling conditions may
require iterative solution of the problem at each time step, poten-
tially resulting in significant computational overhead.
We focus our description on a partitioned approach. An il-
lustration of possible components for such an FSI computation
system is given in Fig. 1.13.Wenotetheinclusionof3Dvalvege-
ometry information, as relatively accurate models of the valves
(especially atrio-ventricular ones) are necessary for reproducing
many of the key features of the intraventricular flow field [183].

Figure 1.13. Fluid structure interaction system for cardiac haemodynamics
computation. The interactions between the electromechanical model, valves and
the computational fluid dynamics (CFD) model are controlled by the FSI interface
module.

An FSI module is, at its core, a coupling interface between
the myocardial electromechanical (EM) solver, the valves and the
3D computational fluid dynamics (CFD) solver, and controls the
proper exchange of information. Its usefulness is maximized when
one needs to integrate independent computational modules that
do not share data at a “deep” level, and need a special handler
of information between them. At each time step, the cardiac FSI
module would need to enable the following interactions:
• sending stress load information from fluid to the biomechanics
and valve modules
• sending endocardial wall and valve positions and velocities to
the CFD solver
• exchanging biomechanical and valve models stress and ana-
tomic constraint information.
In Chapter 2 we will look in detail at a possible realization of
a cardiac FSI system. We have discussed and described so far its
two main components: the biomechanical model and the 3D CFD