Current and Potential Fields Generated by Two Dipoles

Abstract

The distribution of currents and potentials in a circular conducting medium surrounding two eccentric dipoles was studied to establish how much information on the number, location, and orientation of the dipoles could be deduced from measurements of potential in the medium at various distances from the generators. When a single, eccentric dipole was active, the curve illustrating the distribution of potentials along the boundary exhibited different kinds of asymmetry, which revealed that the dipole was eccentric and gave some information about its orientation. When both dipoles were active, two maxima and two minima, revealing the presence of two generators, appeared along the boundary when the angle between dipole moments was 150° or more. Along internal circumferences two maxima and two minima appeared at smaller angles between dipole moments and the location of the maxima was closely related to that of the dipole anodes. When the dipoles lay on the same diameter and had opposite polarity, the presence of two generators was clearly detectable from boundary measurements, whereas vector representation was zero. These data improve our understanding of electrical signals recorded from the body surface, whether in the form of electrocardiograms, vectorcardiograms, or equipotential contour maps.ADDITIONAL KEY WORDS mathematical-physical models electrocardiography vectorcardiography electromaps• Recent investigations on the distribution of cardiac potentials on the body surface of normal subjects and cardiac patients have shown that multiple maxima and minima are simultaneously present on the chest walls during some phases of the cardiac cycle. During the other phases, only one maximum and one minimum were observed (1-5). The number, location and time-course of surface maxima and minima exhibited typical changes in various heart diseases (6-8).Electrophysiological interpretation of chest maps requires the surface potential patterns to be correlated with the intracardiac location of active fibers at the various instants considered. Knowledge of this correlation may be gained in different ways: (1) The distribution of chest potentials and the location of intracardiac generators can be determined experimenFrom Istituto Simes di Cardiologia Sperimentale, Via Bellerio, 41, Milano, Italy 20161. . Received May 14, 1970; accepted for publication October 6, 1970. tally in the same animal (9); and (2) the distribution of potentials in a conducting medium can be established for any number and location of current generators by physical or mathematical models (10)(11)(12)(13)(14)(15)(16)(17)(18)(19). This paper reports an investigation on the current and potential fields generated by two dipoles located eccentrically in a circular, homogeneous conducting lamina. This model has been chosen because it simulates electrical situations actually occurring in the heart when two excitation waves travel simultaneously in different directions through the ventricular or atrial walls.The distribution of potentials generated by t...

High-resolution noncontact charge-density mapping of endocardial activation

“…The heart's potential field results from the summation of many tiny electric dipoles that are defined as charge sources (q + ) closely coupled with equivalent sinks (q -) (2, 6, 7, 32). These microscopic sources arise from ion channels within the membrane of myocardial cells and are understood as the origin of the macroscopic distribution of potentials that are responsible for both the intracardiac EGM and the body-surface ECG (1,4,6). Localizing the sources (also called equivalent generators) of bioelectric fields has long been seen as desirable (6,33), even though the earliest theoretical studies of electric fields from nerve or muscle established that it would not be physically possible to measure such sources directly (2,20).…”

“…Since the 1960s, source models have evolved to include distributions of current density that extend from all active ion channels and flow throughout the entire extracellular torso-volume. This is an ohmic model that assumes a source current as the origin of the extracellular potential field that manifests from the flow of current across the volume-conductor impedance (1,2,35,36,40). However, such a view is inconsistent with first principles of electrostatic field theory (4,21,22,34,41), which state that a distribution of current density (charge in motion) generates a magnetic field, while an electric field arises from a static (or quasi-static) distribution of CD (4,21,34).…”

“…The study of electric fields has been central to understanding the normal heartbeat (1)(2)(3)(4) and has underpinned clinical cardiology through interpretation of surface electrocardiograms (ECGs) (5)(6)(7)(8). The clinical discipline of cardiac electrophysiology has relied on recording and mapping intracardiac electrograms (EGMs) to identify targets for interventional therapy (9,10).…”

A comparison of volume conductor and source geometry effects on body surface and epicardial potentials.

“…The smoothing effect was also demonstrated by Taccardi et al (1951Taccardi et al ( , 1958Taccardi et al ( , 1972 in tank studies of the potential distribution surrounding isolated turtle and dog hearts, as well as in a study of the potential field generated experimentally by two dipoles in a circular homogeneous conducting medium (DeAmbroggi and Taccardi, 1970). An isolated, perfused rabbit heart technique was used by Mirvis et al (1977) to assess the ability to detect and localize multiple discrete epicardial events from body surface potential distributions.…”

Πειραματικαι Παρατηρησεις Επι Του Ηλεκτροκαρδιογραφηματος Κατα Την Ηλεκτρικην Μονωσιν Καρδιας Κυνος

“…έργασίαι εις μαθηματικά ή φυσικά πρότυπα (models) ύπεστήριξαν, δτι ή δλη ήλεκτρεργετική δύναμις τής καρδίας δύ ναται να παρασταθή δια πολλαπλών δίπολων (Holt καί συν. 46 , Okada 63 , Ambroggi καί Taccardi 3 , Selvester καί συν. 77 , 78 ) ή δια πο>υπόλων (Plonsey 66 , Geselowitz 34 ).…”