Page 82 - Artificial Intelligence for Computational Modeling of the Heart

52 Chapter 2 Implementation of a patient-specific cardiac model

tions with minimal communication between neighboring nodes,
which makes the algorithm inherently well suited for parallel ar-
chitecture. Unlike the FDM which is also based on a Cartesian
lattice, the spatial derivatives are not explicitly computed but are
obtained implicitly as part of the algorithm.
The Lattice-Boltzmann method was recently proposed [217]as
an alternate approach for fast solution of general, monodomain
electrophysiology models (the LBM-EP method), and was ap-
plied to real patient anatomies (Fig. 2.11). Its implementation
on Graphical Processing Units (GPUs) showed nearly real-time
performance on a regular workstation with off-the-shelf GPUs
[218,219]. This computational performance enabled fast patient-
specific calibration of a cardiac electrophysiology model from im-
ages and 12-lead ECG signals [220] and this model was success-
fully applied on 19 real patients with Dilated Cardiomyopathy
(DCM).

Figure 2.11. (Left) Snapshot of the activation potential propagation through the
myocardial tissue and (right) the resulting map of the activation times, computed
by solving the monodomain model of tissue electrophysiology with M-S cellular
model and LBM computational method.

In contrast to the finite element and finite difference formu-
lations, which solve the governing equations for the action po-
tential, the lattice-Boltzmann method solves a more fundamental
kinetic equation, i.e., the Boltzmann equation. This method has
its origins in the approaches based on cellular automata, and tries
to utilize the simplicity of the physics at the microscopic scale
to produce emergent macroscopic behavior. The fundamental ki-
netic variable is the distribution function f(x,e,t), which gives the
probability of finding a particle at location (x,t) traveling with a
velocity e. The lattice Boltzmann method is a special discretiza-
tion of the kinetic model in the velocity space, where the particle
velocities are restricted to belong to a small set of discrete veloc-
ities e i ={e 1 ,e 2 ,...,e N }. This results in a vector of distribution