Page 112 - Artificial Intelligence for Computational Modeling of the Heart

82 Chapter 2 Implementation of a patient-specific cardiac model

ELBM framework the simulation is stabilized by automatically
tuning the α parameter, which allows the simulation to run at very
high Reynolds numbers without becoming unstable or requiring
large grid resolution.

2.4.2 3D fluid structure interaction

In this section we give specific implementation details for a
Fluid Structure Interaction (FSI) cardiac computation system (see
Fig. 2.30). As a reminder, the computation system is comprised of
the TLED solver, handling the biomechanics computations, the
3D CFD solver, in this case LBM-CFD being used, and the valve
module, which has two components, the reduced order one (part
of TLED) and the 3D one. At any given time step of the computa-
tion the FSI algorithm proceeds as follows:
1. execute one step of TLED, updating the biomechanics (my-
ocardial walls kinematics) and the 0D valve state (opening of
the valve)
2. map 0D valve phase to the 3D valve kinematic phase, as con-
strained also by the myocardium (generating new 3D valve
positions)
3. run 3D CFD using the new myocardial positions and veloci-
ties, and the new 3D valve positions and velocities
4. send 3D CFD pressures to myocardial walls and mean pressure
to 0D valve modules.
The two main systems (TLED and LBM-CFD) run at different time
steps, and the so-called “sub-cycling” approach ensures that in-
formation exchange is done at the appropriate time stamps. In
practice, as TLED runs at coarser time steps (step 1 in the al-
gorithm), the LBM-CFD solver is run for several time steps (the
“sub-cycles”, repeatedly executing step 3) with unchanged bound-
ary conditions, until its time stamp gets in sync with TLED. We give
more details in the following for each of the FSI steps.

Preparatory step
Some useful pre-computations need to occur first. The end-
diastolic (at time t = 0) myocardial tetra mesh is provided with
LV and LVOT tags that are used to extract an endocardial surface
whose topology remains unchanged over the course of the cardiac
cycle. The endocardial surface boundary edges are separated into
the mitral and aortic contours, which are then tessellated to create
the mitral and aortic virtual boundaries (outlets) for the use of the
CFD code. Each endocardial mesh vertex is associated to a (closest
at t = 0) tetra mesh vertex and follows rigidly its motion over the
course of the cardiac cycle. As the endocardial mesh gets updated