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5. ELELCTROPHYSIOLOGIC SUBSTRATE

OF THE HUMAN HEART

In the previous sections of this monograph, we described electrophysiologic processes

at the molecular, cellular and tissue levels. These processes interact across scales, giving rise to
emergent behaviors at the whole-heart level. These behaviors include normal excitation and
abnormal rhythms (arrhythmias) that can be life threatening and result in sudden cardiac death.

It is crucial for improved diagnosis and treatment to understand the mechanisms of human
cardiac arrhythmias and properties of the arrhythmic substrate in patients. In recent years, a novel
functional imaging modality was developed that can map noninvasively the electrical activity of
the human heart in situ. This method, called Electrocardiographic Imaging (ECGI), was applied in
various cardiac pathologies and provided mechanistic insights to the arrhythmic substrate at the

level of the whole heart of patients. We summarize these insights below.

5.1 The ECGI Method

The physical basis for ECGI is the property that the electric potential field, Φ, generated by
the cardiac electrical excitation in the surrounding passive (not electrically excited) tissues of the
torso (between the epicardium and the body surface) obeys Laplace’s equation:

2
▼ Φ = 0 (5.1)

Subject to the following boundary conditions on the body surface:

Φ = Φ (5.2)
T

Where Φ is the known (recorded) electrocardiographic potentials on the torso surface, and
T

∂ Φ/∂n = 0 (5.3)

Where n is normal to the torso surface, stating that no current can flow from the torso into the

surrounding air, an insulating medium that cannot conduct current. This mathematical
formulation is known as Cauchy problem. ECGI seeks to compute Φ on the epicardial surface of
the heart, Φ , from the measured Φ on the torso surface.
E T

Because the heart and torso surfaces are irregular, the problem must be solved

numerically. The first step in this procedure is to discretize the relationship between the epicardial
potentials and the torso surface potentials. We used two methods to discretize the relationship:
the boundary elements method (BEM) 260 and the method of fundamental solutions (MFS) .
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