Effect of resistive discontinuities on waveshape and velocity in a single cardiac fibre.
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Biomedical subjects
Publications and source records attributed to R Plonsey.
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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.
This paper reviews the literature on mathematical models of cardiac activation and evaluates these approaches against an analytical approach that includes both structure and membrane properties. The advantages and disadvantages of each methodology are described and directions for future research suggested.
The specific impedance of cardiac tissue cannot be measured directly. Instead, the investigator obtains voltage and current measurements and places them into a model of the tissue's structure to infer the impedances of elements of the model. If the model fails to describe major aspects of the real tissue, the results may be worthless, although possibly self-consistent. In the literature of impedance measurement in cardiac tissue, only rarely is the model explicitly described; more commonly, the tissue model is adopted implicitly when equations giving the impedance in terms of voltage and current measurements are adopted. This paper examines the series of models that have been used in specific impedance measurements of cardiac tissue and shows how the same or similar measurements can accurately describe tissue impedivity or can lead to significant errors when inadequate models such as isotropic and anisotropic monodomains (although a part of work of historical merit) are used.
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This paper studies the relative strength of sources associated with the cell and the junction between cells of an equivalent single cardiac fiber. It is shown that the junctional source is negligible compared to the cellular source. On the other hand, the junctional resistance affects the magnitude of the cellular source reducing it by possibly an order of magnitude. The significance of these results to cardiac electrophysiology is that the effect of the junctional resistance may have to be considered separate from that of the cellular resistance.
Cardiac tissue has been shown to function as an electrical syncytium in both intracellular and extracellular (interstitial) domains. Available experimental evidence and qualitative intuition about the complex anatomical structure support the viewpoint that different (average) conductivities are characteristic of the direction along the fiber axis, as compared with the cross-fiber direction, in intracellular as well as extracellular space. This report analyzes two-dimensional anisotropic cardiac tissue and achieves integral equations for finding intracellular and extracellular potentials, longitudinal currents, and membrane currents directly from a given description of the transmembrane voltage. These mathematical results are used as a basis for a numerical model of realistic (though idealized) two-dimensional cardiac tissue. A computer simulation based on the numerical model was executed for conductivity patterns including nominally normal ventricular muscle conductivities and a pattern having the intra- or extracellular conductivity ratio along x, the reciprocal of that along y. The computed results are based on assuming a simple spatial distribution for Vm, usually a circular isochrone, to isolate the effects on currents and potentials of variations in conductivities without confounding propagation differences. The results are in contrast to the many reports that explicity or implicitly assume isotropic conductivity or equal conductivity ratios along x and y. Specifically, with reciprocal conductivities, most current flows in large loops encompassing several millimeters, but only in the resting (polarized) region of the tissue; further, a given current flow path often includes four or more rather than two transmembrane excursions. The nominally normal results showed local currents predominantly with only two transmembrane passages; however, a substantial part of the current flow patterns in two-dimensional anisotropic bisyncytia may have qualitative as well as quantitative properties entirely different from those of one-dimensional strands.
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 Ohm's 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.
A wide spectrum of types of right bundle branch block (RBBB) were studied utilizing the body surface potential maps (BSPMs) of 37 children. Although the spectrum varied from very advanced RBBB to minimal partial RBBB, a common diagnostic feature was the absence of evidence for right ventricular breakthrough in the maps of all patients. Evidence for left ventricular breakthrough was usually seen, the exceptions being five patients with partial RBBB and one of 29 with advanced RBBB. The appearance of evidence for activation of the right ventricle by way of the septum was late in onset. In addition, especially in advanced RBBB, the BSPM pattern reflecting right ventricular activation was prolonged in such a manner that it appeared that utilization of right ventricular Purkinje tissue was minimal and inefficient. The BSPMs during ST-T, which were of inverse polarity, reflect repolarization that is determined by the sequence of depolarization to a greater degree than in the normal. In general, the more extensive the surgery, the more advanced the RBBB (as reflected in the BSPM), although there were exceptions. The one parameter that linked all patients with RBBB together was the absence of evidence for right ventricular epicardial breakthrough.
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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.
The goal of this paper is to examine the origins and relative importance of primary and secondary sources of electric and magnetic fields for excitable tissue. It is shown that for axonal and cardiac tissue a comparison of the relative field strength from both primary and secondary sources shows only the latter to be significant. Even if the divergence and curl of the primary source were independent (and hence were both needed to define the primary source), because the secondary sources all arise from the divergence of the primary source the magnetic field reflects the same source component as the electric field. As a consequence magnetic and electric fields arising from active tissue are strongly linked.
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The effect of increased lung conductivity on ECG potentials was studied in human subjects undergoing pulmonary lavage of a whole lung. In this procedure, the air in the lung is replaced by physiologic saline solution, which is a highly conductive fluid. The same situation was simulated theoretically with an eccentric spherical model of the heart and torso. Both the experimental results and theoretical simulations show a decrease in body-surface potentials as the lung conductivity increases. In particular, a large decrease was observed in the posterior vector and the scalar Z lead both experimentally and theoretically. The model simulation shows that the scalar Z lead is maximal at a conductivity value that is very close to the typical normal lung conductivity, so that low voltages are predicted for low lung conductivities as well.