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7.3 VULNERABILITY IN REGIONALLY ISCHEMIC HUMAN HEART: EFFECT OF THE EXTRACELLULAR POTASSIUM CONCENTRATION 129

7.3.2.2 Heart Model
The geometry of the biventricular heart (the atria have not been considered in the model) and the orientation of the
muscle fibers were obtained from DT-MRI from images acquired at Johns Hopkins University [35]. From the seg-
mented image, a regular volumetric mesh was constructed with hexahedral elements and a resolution of 0.4 0.4
0.4 mm, which gave rise to 1.43 million nodes and 1.29 million hexahedra.
Transmural heterogeneity of electrophysiological behavior across the heart is necessary for normal cardiac function,
with excessive heterogeneity contributing to arrhythmogenesis [66]. In this regard, transmural differences in the elec-
trophysiological behavior of the cells were introduced in order to obtain an APD gradient from the endocardium to the
epicardium, with the longest APD at the subendocardium [67]. This was achieved by defining a distribution in layers
of the three cell types defined in the TP06 models in a proportion of 20% of epicardial cells, 10% of endocardial cells,
and the remaining 70% is occupied by M-cells [68]. A recent study based on optical mapping of left-ventricular free
wall preparations of human hearts by Glukhov et al. [67] has identified islands of M-cells located at the subendocar-
dium, such as the distribution assumed in this work. These distributions resulted in a positive T wave in the pseudo-
ECG, as seen in the bottom panel in Fig. 7.5.

7.3.2.3 Electrophysiological Heterogeneities Under Acute Ischemia
The ischemic region was located in the inferolateral and posterior side of the left ventricle, mimicking the occlusion
of the circumflex artery (see Fig. 7.5A). The ischemic region was composed of realistically dimensioned transitional
BZs, a normal zone (NZ), and the central zone (CZ) of ischemia in agreement with experimental findings [28] during
+
the early stages of ischemia. In the CZ, [K ] o was set at three different values: 7.0, 8.0, and 9.0 in order to study three
+
different time frames during acute ischemia. The inward Na and L-type Ca 2+ currents were scaled by a factor of 0.85
to mimic the effect of acidosis [54, 69], whereas [ATP] i and [ADP] i concentrations were set to 5 and 99 mM, respectively
[30]. The BZ included a linear variation in electrophysiological properties between the NZ and the ischemic zone (IZ),
as shown in experiments [28]. In addition, the model includes a 1.0 mm washed zone (not affected by ischemia) in the
endocardium as a result of the interaction between the endocardial tissue and the blood in the ventricular cavities, as
suggested by Wilensky et al. [31] (see right panel in Fig. 7.5A). The resulting human ventricular model in acute regional
ischemia produced realistic pseudo-ECGs at the six derivations of the standard ECG (see bottom panel in Fig. 7.5),
exhibiting the ST elevation in V5–V6 with an acute T wave in V6 and ST depression in V1–V4 consistent with an infarc-
tion involving the inferior, lateral, and posterior walls caused by the occlusion of the proximal circumflex artery [70].

7.3.2.4 Stimulation Protocol
This work does not incorporate the specialized conduction system to stimulate the heart. However, Purkinje-like
stimulation was simulated by stimulating discrete zones of the endocardium according to the work performed by Dur-
rer et al. [71]. According to this work, endocardial stimulation in the left ventricle starts at three well-defined locations
within a time window of 5 ms: (i) a high area on the anterior paraseptal wall just below the attachment of the mitral
valve, (ii) a central area on the left surface of the interventricular septum, and (iii) the posterior paraseptal area at about
one-third of the distance from the apex to the base. For the right ventricle, we have defined a stimulation area near the
insertion of the anterior papillary muscle. In the right ventricle, stimulation starts 5 ms after the onset of the left ven-
tricular potential [71]. Fig. 7.5B shows the location of the four stimulation areas.
The model was preconditioned with endocardial stimulation (S1) consisting of 56 stimulations at a CL of 800 ms
(frequency of 1.25 Hz). Following the preconditioning, an extra stimulus, or premature stimulation, (S2) was applied
in the subendocardial BZ (see Fig. 7.5C) in agreement with the findings of Janse et al. [30]. The coupling intervals (CI),
for example, the time differences between S1 and S2, were varied with a resolution of 1 ms to determine the VW of
reentry. In this regard, a depolarization pattern was considered as a reentry if at least two cycles were completed
around the ischemic zone. Sustained reentrant patterns were studied for 3 s after the extra stimulus. Reentry patterns
and VWs were investigated for different values of extracellular potassium concentration in the CZ.

7.3.2.5 Numerical Simulations
Computations were performed with the GPU-based software TOR [59] using the operator splitting and a semiim-
plicit scheme with a fixed time step of 0.02 ms. Simulation of 1 s of electric activity took 1.5 h on a GPU Tesla M2090
(6 GB RAM DDR5).

I. BIOMECHANICS