Page 116 - Computational Modeling in Biomedical Engineering and Medical Physics

Electrical activity of the heart 105

The normal cardiac electrical activity manifests through electric field waves that
propagate throughout atria and ventricles as synchronized APs. Arrhythmias are
deviations from this self-sustained pattern of theAPwaveinitiationorpropagation.
The alternans is a long short long cycle of the AP duration, APD, during rapid
pacing (Chialvo et al., 1990), and it is perceived as a forerunner of severe ventricular
arrhythmias, such as ventricular tachycardia and ventricular fibrillation (Pastore et al.,
1999). The origins of alternans, either concordant (in phase everywhere in the tissue)
or discordant (in opposition in distinct spatial regions) APD (Watanabe et al., 2001),
and accompanying reentries may be touched using one- and two-dimensional car-
diac propagation models (Mocanu et al., 2007). The diastolic interval, DI, shortens
the cell APD and, below a critical DI value, the cell no longer responds with an AP
(Qu et al., 1999).
Alternans, called a “{2:2} rhythm”, occur when two stimuli elicit two APs of dif-
ferent duration and shape. Increasing the stimulation frequency leads to conduction
block and {2:1} synchronization, in which the cardiac tissue responds to every other
stimulus (Mocanu et al., 2007). They are produced during high heart rates (pacing fre-
quencies) when the inclination of the restitution curve is above one (Guevara et al.,
1984; Strumillo and Ruta, 2002). Calcium channel blockers may contribute to flatten
it and thus suppress the alternans (Garfinkel et al., 2000).

One-dimension action potential propagation
The AP transmitted by a one-dimensional filament of ventricular muscle has been
1
modeled using an adaption of the cylindrical cable theory (Mocanu et al., 2007;
Schierwagen and Ohme, 2020), which yields the transmembrane voltage that may be
calculated using

2
@V m r @ V m
C m 1 I ion 5 2 ; ð4:10Þ
@t 2ρ @x
with the boundary conditions

1 @V m 1 @V m
52 I stim ; 5 0: ð4:11Þ
ρ @x x50 ρ @x x5L

2
For the example shown here, C m 5 1 μF/cm is the membrane capacitance per
unit area, ρ 5 0.25 kΩ cm is the intracellular axial resistivity per unit length, r 5
5 μm is the cell radius, and L 5 7 cm is the length of the cable. The ionic current
2
density through the cell membrane, I ion [μA/cm ], sums up the contributions of all
1
The telegraphist’s (cable) equation was introduced in 1855 by Lord Kelvin, for the transatlantic
telegraph cable.