Page 119 - Computational Modeling in Biomedical Engineering and Medical Physics

108 Computational Modeling in Biomedical Engineering and Medical Physics

Figure 4.10 Discordant AP alternans duration produced by an ectopic stimulus (arrow) at the cable
end followed by 240 ms pacing at the bottom end of the cable (left). AP alternans duration are
21
suppressed by reducing the Ca current by 25% (right) (Mocanu et al., 2007).
AP duration at the end, is strongly dependent on the coupling interval of the abnor-
mal beat and the frequency of the sinus stimuli. At lower sinus rates, only concordant
alternans were seen.
When the Ca 21 current is reduced by 25% the sinus excitations does not lead to
discordant or concordant alternans, but rather a {1:1} periodic rhythm with a shorter
APD occurs (Fig. 4.10, right).

Two-dimensional action potential propagation
A simplified model of the excitable cardiac tissue, which involves a fast variable u and a
slow variable w, is introduced trough the continuous media, coupled PDEs (Aliev and
Panfilov, 1996)

2
2
@u @ u @ u
5 1 2 ku u 2 aÞ u 2 1Þ 2 uw 1 i stim ;
2
ð
@t @x 2 @y |fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |{z} ð4:14Þ
ð
applied stimulus
ð
fast process AP upstrokeÞ
2 3
@w 6 7
6 7 ފ:
1
2
6
½
5 ε 0 1 μ w= μ 1 u 7 2w 2 ku u 2 a 2 1ð ð4:15Þ
@t 4 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}5
recovery phase
The four parameters have no specific physiological meaning, and they are adjusted to
render the dynamics of a square L3 L excitable cell—here, k5 8, a5 0.15, ε 0 5 0.002,
μ 1 5 0.2, μ 2 5 0.3. Thetimeand thetransmembrane potential are related to the model