On Bioelectric Potentials in an Inhomogeneous Volume Conductor

Green's theorem is used to derive two sets of expressions for the quasi-static potential distribution in an inhomogeneous volume conductor. The current density in passive regions is assumed to be linearly related instantaneously to the electric field. Two equations are derived relating potentials to an arbitrary distribution of impressed currents. In one, surfaces of discontinuity in electrical conductivity are replaced by double layers and in the other, by surface charges. A multipole equivalent generator is defined and related both to the potential distribution on the outer surface of the volume conductor and to the current sources. An alternative result involves the electric field at the outer surface rather than the potential. Finally, the impressed currents are related to electrical activity at the membranes of active cells. The normal component of membrane current density is assumed to be equal at both membrane surfaces. One expression is obtained involving the potentials at the inner and outer surfaces of the membrane. A second expression involves the transmembrane potential and the normal component of membrane current

Model Studies of the Magnetocardiogram

A general expression is developed for the quasi-static magnetic field outside an inhomogeneous nonmagnetic volume conductor containing internal electromotive forces. Multipole expansions for both the electric and magnetic fields are derived. It is shown that the external magnetic field vanishes under conditions of axial symmetry. The magnetic field for a dipole current source in a sphere is derived, and the effect of an eccentric spherical inhomogeneity is analyzed. Finally the magnetic dipole moment is calculated for a current dipole in a conducting prolate spheroid

Simulation studies of the electrocardiogram

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