Page 122 - Computational Modeling in Biomedical Engineering and Medical Physics

Electrical activity of the heart 111

Dowle et al., 1997; Scrale, 2009, Dobre et al., 2011a), that go back to Turing
(1952) and Shiferaw and Karma (2006), and generic reaction-diffusion nonlinear
chemical excitable systems of diffusing species (Alonso et al., 2013)

@V
Þ;
5 kI V; w; p i Þ 1 rU D V rVð ð4:16Þ
ð
@t
@w
Þ;
5 RV; w; p i Þ 1 rU D w rVð ð4:17Þ
ð
@t
where I(V,w,p i ) and R(V,w,p i ) are nonlinear functions and p i are tuning parameters,
which are typically solved in square (cubic) computational domains with homoge-
neous Neumann boundary conditions.
The tuning parameters are a limiting, arbitrary factor and their trial-and-error “tun-
ing” may question the physical grounds of such endeavor. It is the price for using
homogenization techniques needed to introduce continuous media. Nevertheless,
numerical modeling on detailed “twins” of the actual electrophysiologic processes may
have the ability to accurately render the complex responses of cardiac cells under nor-
mal and abnormal conditions.

4.4 Coupling the action potential with the electric field diffusion
in the thorax

One of the applications of the direct problem of electrocardiography is to simulate
the propagation of cardiac depolarization fronts with the aim to investigate arrhyth-
mias, in the attempt to investigate common heart disorders, as seen before. Another
important application is the modeling of electrical defibrillation, as emergency inter-
ventional therapy against extreme heart condition. Ventricular fibrillation is a cardiac
arrhythmia that can be fatal if left untreated within minutes. The most effective ther-
apy for ending ventricular fibrillation is the electric shock. The internal defibrillator
is an electronic device that is implanted in cardiac patients prone to such arrhythmias
with the aim to deliver on demand electric shocks. This device detects and termi-
nates cardiac arrhythmias using electrodes inserted into the SVC and the right ventri-
cle. A good model of the electrical activity of the heart is based on the adequate
mathematical equations that best fit the studied phenomena. Choosing the right
boundary and initial conditions are crucial too for tuning the numerical computation
results (Mocanu et al., 2002).
The numerical study of the ECG problem starts with the AP propagation at
the heart level, which is then coupled to the electric field diffusion within the
thorax that is monitored using electrical signals numerically evaluated on the
chest’ssurface.