Source-Field Relationships for Cardiac Generators on the Heart Surface Based on Their Transfer Coefficients

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Abstract
We consider three different types of equivalent sources over a closed surface enclosing all the electrical cardiac generators: the (in situ) potential, the (in situ) normal current density, and the (macroscopic) transmembrane potential on the heart surface. The last equivalent source, which behaves as a double layer, is derived from the bidomain (bisyncytia) model for anisotropic cardiac muscle. This model predicts that if ratios of intracellular to interstitial conductivity along all directions are equal, field potential can be calculated only using surface integrals. The volume integral arising from the tissue anisotropy of cardiac muscle vanishes in that case. For each type of source under study, we give the field potential in a bounded inhomogeneous volume conductor in the form of an integral equation. We also derive the conditions which the lead field (or the transfer coefficients) must satisfy. The in situ potential and normal current are related to the cardiac sources in a complex way, but their lead fields are independent of conductivity of heart muscle, whereas the transmembrane potential is directly involved as a source term, but the lead field depends on the anisotropy of the heart muscle.