The electrical field produced by the eccentric current dipole in the nonhomogeneous conductor

Abstract

T he problem investigated has important implications which bear on the electrical field which is produced by the heartbeat. For nearly 30 years1 the basic approach to human and animal electrocardiography has regarded the “heart generator” as a source-sink distribution which emanates from the heart muscle fibers. The most general viewpoint is that of treating the “heart generator” as a source-sink multipole in which the net pole strength is zero. In the general theory of multipoles the expansion for the potential includes a first term (tensor of rank zero) which vanishes when the net pole strength is zero. The second term of the expansion is the potential of a dipole or tensor of rank one. Additional terms are potentials of the quadripole, the octapole, and tensors of higher rank. At distances from the multipole large in comparison with its “circumference,” the cube and the higher powers of these distances enter the denominators of the terms which are components of tensors of rank two and higher, and the magnitudes of these terms may be neglected. Consequently, the potential field throughout the greater part of the body trunk is essentially equivalent to that produced by a dipole, or a tensor of rank one. Her5 the variations of body surface potentials are due to changes in strength of dipole moment &I and to rotations of the moment M-axis with each heartbeat. For the past 30 years the heart generator has been treated physically as though it produced the electrical field of a dipole in a homogeneous volume conductor.l This last simplification is, of course, a mere approximation of the truth. Nevertheless, this approximation has offered great advantages to both teachers and investigators. Recent investigations2-4 have naturally become more exacting and have introduced the general idea of different specific resistivities making up a nonhomogeneous conductor. It is the object of this article to help remove the foundations of electrocardiography from the approximate foundations of the homogeneous volume conductor to that of the more realistic nonhomogeneous volume conductor.