Robert Plonsey

Considerations of quasi-stationarity in electrophysiological systems

Conditions under which a time varying electromagnetic field problem (such as arises in electrophysiology, electrocardiography, etc.) can be reduced to the conventional quasistatic problem are summarized. These conditions are discussed for typical physiological parameters.

The active fiber in a volume conductor

This paper considers the quantitative description of intracellular and extracellular fields of a single circular cylindrical fiber resulting from the propagation of an action potential (AP). Several formulations are noted, but one, which permits identification of free-space source-sink relationships, is examined in some detail; the physical models which it gives rise to are described and developed. Desirable approximations are considered and the conditions of their validity are discussed. A convolution integral formulation to field patterns (from their sources) is presented. Axially symmetric anisotropic media are also considered.

The effects of variations in conductivity and geometrical parameters on the electrocardiogram, using an eccentric spheres model.

The effects of variations in the volume conductor properties of the torso on the electrocardiogram were studied by means of a theoretical eccentric spheres model. The model includes a blood cavity, cardiac muscle layer, pericardium, lung region, skeletal muscle layer, and subcutaneous fat. The source of the field is a double-layer spherical cap located within the myocardium. The following effects regarding the electrocardiogram (ECG) potentials were determined: (1) blood augments the potential, but less than predicted by simpler published models; (2) in anemia, high potentials are expected, whereas in polycythemia, voltages are reduced; (3) abnormally low lung conductivity (emphysema) causes low surface potentials whose magnitude is controlled by the low conductivity skeletal muscle layer; (4) low voltages result both from low and high pericardial conductivities; (5) the surface potential increases with increasing myocardial conductivity; (6) low skeletal muscle conductivity (Pompes disease) causes high surface potentials; (7) obesity lowers the potential only slightly; (8) a thick myocardium, protruding into the lung region, slightly augments the potential; (9) an increase in the thickness of the myocardium at the expense of the blood cavity causes a decrease in potential; (10) the potential increases with increasing heart size; and (11) the location of the heart within the torso has a very significant effect on the surface potential distribution. cire Res 104-111, 1979

The Four-Electrode Resistivity Technique as Applied to Cardiac Muscle

Cardiac tissue consists of two conducting regions, the intracellular and the interstitial, which are separated by a plasma membrane. It therefore constitutes a bidomain, as distinct from a single (monodomain) conducting region. Each cardiac domain is anisotropic.

Action potential sources and their volume conductor fields

This essentially tutorial paper describes, quantitatively, the bioelectric sources corresponding to a propagated action potential with particular emphasis on a cylindrical nerve or muscle fiber of infinite or finite length. Based on this source description, the resulting volume conductor fields are described and discussed.

Propagation of excitation in idealized anisotropic two-dimensional tissue.

This paper reports on a simulation of propagation for anisotropic two-dimensional cardiac tissue. The tissue structure assumed was that of a Hodgin-Huxley membrane separating inside and outside anisotropic media, obeying Ohms law in each case. Membrane current was found by an integral expression involving partial spatial derivatives of Vm weighted by a function of distance. Numerical solutions for transmembrane voltage as a function of time following excitation at a single central site were computed using an algorithm that examined only the portion of the tissue undergoing excitation at each moment; thereby, the number of calculations required was reduced to a large but achievable number. Results are shown for several combinations of the four conductivity values: With isotropic tissue, excitation spread in circles, as expected. With tissue having nominally normal ventricular conductivities, excitation spread in patterns close to ellipses. With reciprocal conductivities, isochrones approximated a diamond shape, and were in conflict with the theoretical predictions of Muler and Markin; the time constant of the foot of the action potentials, as computed, varied between sites along axes as compared with sites along the diagonals, even though membrane properties were identical everywhere. Velocity of propagation changed for several milliseconds following the stimulus. Patterns that would have been expected from well-known studies in one dimension did not always occur in two dimensions, with the magnitude of the difference varying from nil for isotropic conductivities to quite large for reciprocal conductivities.

Stimulation of Spheroidal Cells - The Role of Cell Shape

The behavior of spheroidal cells in an applied uniform field is examined in order to gain insight into the role of cell shape in the electrical activity of biological cells. The responses of cells having different eccentricities but the same height in the direction of stimulation are compared. The effect of a change in the direction of stimulation is discussed. In the process of obtaining the results an approximate method for calculating biopotentials during extracellular stimulation is presented and justified.

Intercalated discs as a cause for discontinuous propagation in cardiac muscle: a theoretical simulation.

A theoretical model of a cardiac muscle fiber (strand) based on core conductor principles and which includes a periodic intercalated disc structure has been developed. The model allows for examination of the mechanism of electrical propagation in cardiac muscle on a microscopic cell-to-cell level. The results of the model simulations demonstrate the discontinuous nature of electrical propagation in cardiac muscle and the inability of classical continuous cable theory to adequately describe propagation phenomena in cardiac muscle.

Capability and Limitations of Electrocardiography and Magnetocardiography

The capabilities and limitations of electrocardiography and magnetocardiography are discussed. Representing the electrical activity of the heart by an impressed current density ji, electrocardiography determines the spherical harmonic multipole expansion of its divergence (flux source), while magnetocardiography determines the spherical harmonic multipole expansion of the radial component of its curl (vortex source).

Interstitial potentials and their change with depth into cardiac tissue

The electrical source strength for an isolated, active, excitable fiber can be taken to be its transmembrane current as an excellent approximation. The transmembrane current can be determined from intracellular potentials only. But for multicellular preparations, particularly cardiac ventricular muscle, the electrical source strength may be changed significantly by the presence of the interstitial potential field. This report examines the size of the interstitial potential field as a function of depth into a semi-infinite tissue structure of cardiac muscle regarded as syncytial. A uniform propagating plane wave of excitation is assumed and the interstitial potential field is found based on consideration of the medium as a continuum (bidomain model). As a whole, the results are inconsistent with any of the limiting cases normally used to represent the volume conductor, and suggest that in only the thinnest of tissue (less than 200 micron) can the interstitial potentials be ignored.