Page 116 - Artificial Intelligence for Computational Modeling of the Heart

86 Chapter 2 Implementation of a patient-specific cardiac model

CFD relative pressure field passed on to the FSI interface is pro-
cessed as follows:
• averaged inside the ventricle and subtracted from all points to
ensure zero mean
• extrapolated across the endocardial surface using a second or-
der accurate extrapolation method
• interpolated at the endocardial triangle barycenter locations.
This interpolated value, to which we add back the TLED pressure
for re-gauging, is the absolute pressure field applied as a load on
the endocardium.

Tests of the FSI module
We present here two simple verification tests of the FSI CFD
model, which compare results of the presented FSI solver to ana-
lytical solutions.
Test 1: Peristaltic transport
The experiment consists of imposing a time-periodic, wave-
like motion to a vessel geometry and in verifying the cross-
sectional flow at any time step (as originally described in [256]).
The wall deformation is changing both in time and space (along
the axial direction) and the flow variation at every time step is
computed analytically to depend on the wall movement as fol-
lows:
3φ 2
Θ = (2.37)
2 + φ
where 0 ≤ φ ≤ 1 represents the amplitude of the propagating wave,
with φ = 0 corresponding to total occlusion of the vessel and φ = 1
corresponding to a fully open vessel profile. Fig. 2.32 outlines the
favorable results obtained through numerical simulations. A total
of five values for φ were used, with flow rates compared against the
analytical solution. The experiments show excellent agreement
with the analytical solution.
Test 2: Expanding and contracting vessel
This experiment validates the implementation of mass-conser-
vation in the context of varying inlet and outlet boundary flows.
The geometry was generated synthetically by applying a defor-
mation function to a straight cylinder. It is given by the following
equations:

x = x
y = R(x,t)cosθ
z = R(x,t)sinθ
R(x,t) = R 0 + R max sin(2πt)sin(πx)