Page 91 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 2 Implementation of a patient-specific cardiac model 61

Algorithm 2 Modeling high-speed conducting tissue with a space-
dependent conductivity field σ.
Require: Volume V discretized in a Cartesian grid with N h points
x i , level-set representation φ of septal endocardium, user-
defined threshold h, grid spacings x and ξ, conductivity for
normal tissue σ normal and for high-speed conducting system
σ purkinje .
1: φ h = φ| V
2: candidates := {}
√
3
3: h ext := h + x
2
4: for i = 1 → N h do
5: if 0 ≤ φ h (x i ) ≤ h ext then
6: candidates = { candidates, i }
7: end if
8: end for
9: for j ∈ candidates do
10: count = 0;
11: compute
φ ξ = φ| subdividing voxel
v j in N ξ lattice

v j
points ξ k
12: for k = 1 → N ξ do
13: if 0 ≤ φ ξ (ξ ) ≤ t then
k
14: ++count;
15: end if
16: end for
17: ψ j = count /N ξ
18: σ(x j ) = ψσ purkinje + (1 − ψ) σ normal
19: end for
20: return Σ

2.2.3 Graph-EP: fast computation of tissue activation
time
When the focus is on the very fast computation of the pattern
of electrical activation, and it is not required to model the details
of cellular electrophysiology, Eikonal models offer a convenient al-
ternative to monodomain or bidomain models. The Eikonal equa-
tion describes the propagation of a wave front in a domain Ω,
givenaninitial configurationonasubdomain Γ ⊂ Ω:

√

T
∇a R∇a = 1 in Ω
(2.7)
a = a 0 on Γ
where the unknown a is the activation time, Ω represents the my-
ocardium, Γ represent the regions of earliest activation in the my-