Page 113 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 2 Implementation of a patient-specific cardiac model 83

Figure 2.30. Fluid structure interaction system for cardiac haemodynamics
computation. The interactions between the electromechanical model, valves and
the CFD model are controlled by the FSI interface module.

at any time t, the aortic and mitral outlet surface barycenters are
updated accordingly. The displacement rate of the endocardial
vertices is the velocity information being sent to the CFD solver.
Furthermore, each of the valve ring boundary vertices is kinemat-
ically linked to a closest myocardial tetra mesh vertex, computed
at end-diastolic time (t = 0). During simulation, as the tetra mesh
moves over time, the new tetra mesh position is imposed as a rigid
constraint to the valve boundary vertices. This ensures that the
valve boundary travels along with the mesh as it moves over time.
Another valve constraint is ensured using a 0D–3D kinematics
mapping. As a reminder, the 0D valve model uses a valve phase
function which is proportional to the effective area opening. In
Fig. 2.31 we give an illustrative example of how the valve phases
can be mapped to 3D valve mesh sequences over the course of the
cardiac cycle, in this pre-computation stage. In practice one can
start from a kinematic sequence of topologically consistent (i.e.
satisfying point-to-point correspondence) 3D valve meshes (see
section 2.1.1) and first compute their phases as the areas of the
minimal surfaces spanning their rim boundaries. By focusing then
on a given cardiac stage (e.g. systole), one can create a valve-mesh-
over-systolic-time function by an interpolation method of choice.
For example, a Fourier transform for each of the mesh nodes has
also the benefit of smoothing any high frequency noise in the ini-
tial mesh sequence. The 0D–3D mapping is then used during the
computation step to provide the 3D valve mesh corresponding to
any 0D opening phase.

Step 1
This step has already been discussed in the biomechanics sec-
tion. As a reminder (see section 1.4.1), the 0D valves use the ven-