Page 224 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 6 Additional clinical applications 197

be very small, resulting in very high computational cost. Alter-
native formulations of the method, such as the entropic Lattice-
Boltzmann method (ELBM) [444] can be considered to reduce the
computational complexity of simulating physiological aortic flow.
Since LBM operates on a Cartesian grid and the 3D model of
the aorta is a surface mesh, it is embedded in the grid by com-
puting a signed distance function φ(x) for each location x in the
grid, i.e. φ(x) is the signed distance from the grid node x to the
closest point on the surface mesh. The sign is computed such that
φ(x) ≤ 0 for grid nodes located inside the vessel, and φ(x)> 0 for
nodes located outside of the vessel, hence the surface location
can be accurately identified as φ(x) = 0. The surface mesh also
contains a label associated to each polygon, depending on the
boundary condition that needs to be applied, i.e. inlet, outlet or
no-slip wall. The surface labels are associated to each grid node
along with φ during the pre-processing step. Thus, the boundary
nodes can be identified, and the type of boundary condition that
needs to be applied is determined.
Since a large number of flow computations are required, per-
formance becomes an important aspect. Being LBM readily par-
allelizable, it is possible to resort to optimized GPU-based imple-
mentations [445–448].
The purpose of the flow computations is to find a correlation
between geometric features of the vessel and pressure drop. All
computations were performed under a steady state configuration,
i.e. a constant flow rate was imposed at the inlet, and the flow
computation was run until convergence was reached. Unsteady
flow computations were shown to have a limited impact on global
hemodynamic quantities, including pressure drop, at the expense
of very time-consuming computations [429,449].
For each synthetic surface a total of six computations were per-
formed, varying the inlet Reynolds number between 500 and 5000.
To ensure that the resulting flow rate and pressures lie in a phys-
iologically plausible range, the inlet flow rate was constrained to
be smaller than 32 L/min, and the resulting pressure drop below
60 mmHg. Since the pressure drop cannot be determined a priori,
it was estimated using the Young-Tsai model [438] as a function of
inlet flow rate and the CoA degree. Thus, the inlet flow rates for a
case were chosen as follows:
1. The initial inlet flow rates are computed such that the Reynolds
numbers are 500,1000,2000,...,5000 respectively:

ReA inlet ν
Q = , (6.7)
2r inlet