Page 109 - Computational Modeling in Biomedical Engineering and Medical Physics

98 Computational Modeling in Biomedical Engineering and Medical Physics

Figure 4.3 Eindhoven triangle (left) and electrocardiogram signal (right).

Bioelectric sources. The direct ECG problem
As stated by experimental results (Schwan and Kay, 1957), in the frequency range of bio-
electric events, the capacitive and inductive properties of tissues are negligible as compared
to their resistive properties, therefore the human body is modeled here as a continuous
linear, homogeneous (by parts) medium. The bioelectrical activity of heart cells is the
result of a conversion of chemical energy into electrical energy, E i . The electric current
Þ,where σ is the electrical conductivity (Chapter 1: Physical,
density is then J 5 σ E i 1 Eð
Mathematical and Numerical Modeling). In quasistationary conditions, the electric field
produced by a current dipole p 5 lim I-N;l-0 Il,where I is the electric current intensity
and l is the oriented dipole length. Several representative dipole electric field sources are
found in the studies by Malmivuo and Plonsey (1995) and Morega (1999).
The electric potential, V, produced by dipolar sources in a nonhomogeneous
volume conductor, is the analytic solution to the direct ECG problem (D-ECG)
(Gesselowitz, 1967)

rU σrVÞ 5 rUJ 5 p; ð4:1Þ
ð

ð ð
1 X 1
4πσ V rðÞ 5 dv 1 0 UdS j ;
i σv j 2 σ Vr ð4:2Þ
j
J Ur
v r j S j r
|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
volume source primary sourceÞ
ð
ð
double layer sources secondary sourcesÞ