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Biomedical subjects

R Plonsey

Publications and source records attributed to R Plonsey.

At least 37 records · Page 2Linked to original sources
PubMed1991

One-dimensional model of cardiac defibrillation.

The response of a single strand of cardiac cells to a uniform defibrillatory shock assuming steady-state linear conditions is examined. It is argued that the effect of this current is quantitatively described by the induced transmembrane potential even under passive conditions. The characteristics of the single strand are those that would exist if the heart was a system of equivalent parallel pathways from apex to base. It is shown that essentially every cell is both hyperpolarized and depolarised from the shock by an amount proportional to the stimulus intensity and the intercellular junctional resistance. For physiological values of model parameters the evaluated depolarisations are consistent with levels necessary to affect electrophysiological behaviour.

Electric Countershock↗
PubMed1991

Implications of macroscopic source strength on cardiac cellular activation models.

This paper compares several cellular-level models of cardiac activation according to the sources that are generated and their macroscopic fields. Since macroscopic field patterns and strengths are well documented, by comparing the models of cardiac activation, the more controversial microscopic processes can be evaluated. The results show that it is most likely that both macroscopic and microscopic activation of cardiac tissue are uniform processes, and in a direction that is transverse to the fiber axis.

Animals↗
PubMed1991

The Brody effect revisited.

This paper reexamines the Brody effect, both in the far-field and in the near-field approximation. It stresses the fact that near an inhomogeneity the Brody factor is not a constant but a function of space. A full documentation of this function for realistic values of the inhomogeneity as relevant to electrocardiography is included. The existence of a zone having "anomalous" Brody factors is demonstrated. Moreover, the importance for this problem of the zero reference point is stressed.

Blood Volume↗
PubMed1990

A planar slab bidomain model for cardiac tissue.

A fully three-dimensional model of the ventricular or atrial free wall will involve a planar geometry of finite thickness. The governing equations for the interstitial and extracellular potential of a planar slab of cardiac tissue comprised of parallel fibers undergoing uniform plane-wave activation are presented. A comparison with a bidomain of cylindrical geometry with the same half-thickness shows that the potentials in the planar bidomain (as a function of depth) approach core-conductor behavior more quickly.

Animals↗
PubMed1990

Extracellular potentials and currents of a single active fiber in a restricted volume conductor.

Based on mathematical expressions governing the electric field, the extracellular potentials generated by a single active fiber in a restricted circular cylindrical volume conductor are evaluated. This paper examines the effect of the extent of the volume conductor, with radius b, on the extracellular potentials at different field points. For values of b less than 1.5 times the fiber radius, the extracellular potentials in the volume conductor are always the core conductor potentials, independent of the shape and amplitude of the transmembrane potential. For b greater than a critical radius (a value that depends on the transmembrane potential waveform), the extracellular potentials at and near the membrane are the same as if the volume conductor were unbounded. Near the boundary with the insulator, the amplitude of the extracellular potentials is equal to the core conductor amplitude, although the potentials are much broader than the core conductor potential.

Action Potentials↗
PubMed1990

Analysis of excitable cell activation: relative effects of external electrical stimuli.

In the functional electrical stimulation of nerve an expression defined as the 'activating function' has been introduced to evaluate the propensity for a particular fibre to excite. This approach to determine resulting activation is only an approximation as it neglects the presence of the fibres on the applied field, in contrast to activity determined from a rigorous solution to the core conductor/excitable membrane equations. An alternative approach to determining relative excitability based on the induced transmembrane potential is presented, thereby allowing for current redistribution via the space constant of the target fibre. The paper critically examines the approximations made with activating functions, and concludes that as currently formulated the activating function has limitations in predicting relative excitability under a number of important conditions. In contrast, it is the induced (passive) transmembrane potential that provides a quantitatively reliable estimate of the tendency for fibres to excite.

Electric Stimulation↗
PubMed1990

Effect of intracellular anisotropy on electrical source determination in a muscle fibre.

Expressions are available for describing, quantitatively, the source associated with an action potential propagating along an excitable fibre. For a nerve fibre one such expression defines an equivalent volume dipole density function tau(x) = -delta/delta x (sigma i phi i (x) - sigma e phi e (x)) ax (where x is the axial co-ordinate, i is the intracellular and e the extracellular region, sigma i and sigma e are isotropic conductivities, phi the potential at the membrane, while axial symmetry is assumed), and this source fills the intracellular region. This source, as distinct from transmembrane current formulations, lies in a uniform, isotropic, extracellular, medium. Consequently, for a fibre bundle a simple superposition of sources, all lying in a uniform, isotropic, extracellular space, can be accomplished. However, for muscle fibres the presence of non-conducting myofibrils causes the intracellular space to be anisotropic. The paper describes the modification in the aforementioned expressions for the case of longitudinal and transverse propagation and extrapolation to an arbitrary angle of propagation. The resultant source continues to be expressed relative to a uniform, isotropic, extracellular medium.

Action Potentials↗
PubMed1990

Limitations of approximate solutions for computing the extracellular potential of single fibers and bundle equivalents.

The mathematical description of the extracellular field generated by activity in an excitable fiber in an unbounded volume conductor will depend on assumptions made about the sources and the source-field relationship. This paper examines and compares the rigorous and conventional approximate solutions of Laplace's equation used to evaluate the extracellular potential of a single, cylindrical fiber. The single fiber is considered as both a prototypical element (such as a nerve or muscle fiber) and an elementary model of an entire multicellular preparation (e.g., nerve bundle or Purkinje strand). The effects of the fiber radius, the intracellular and extracellular conductivities, and the shape and extent of the source function (either the transmembrane potential or the intracellular potential) on the solutions are discussed. The results show that, in general, the approximate solutions are unsatisfactory for computing the surface extracellular potential when the single fiber is used to represent a large bundle (greater than 300 microns).

Fourier Analysis↗
PubMed1990

Point source nerve bundle stimulation: effects of fiber diameter and depth on simulated excitation.

Excitation response of different diameter myelinated nerve fibers situated at various depths within a cylindrical nerve bundle from the applied field of a point source electrode are analytically evaluated. For the potential field calculation, the fiber bundle is considered to be immersed in an infinite isotropic conductive medium and is idealized as an infinitely extending cylinder represented as an anisotropic bidomain (where electrical coupling from interstitial to intracellular space is included). Myelinated nerve fiber excitation is determined from a core-conductor nerve model, whose nodal currents are described by the Frankenhaeuser-Huxley kinetics and the aforementioned field providing the applied potentials. Stimulation level necessary for a nerve fiber to reach threshold is quantified in response to four descriptions of the volume conductor: the isotropic homogeneous case, the monodomain case, the bidomain case, and the "modified monodomain" case (where axial current is considered to flow through a parallel combination of longitudinal interstitial and intracellular resistive pathways, i.e., "complete" current redistribution). Model results indicate the importance of a bidomain representation of the nerve bundle, and provide insight into the relationship between the physical medium and the physiological properties of nerve fiber excitation.

Electric Conductivity↗
PubMed1990

Simulation of propagation along a cylindrical bundle of cardiac tissue--I: Mathematical formulation.

This paper presents a mathematical description based on a three-dimensional model for studying propagation in cardiac muscle. The model makes use of the bidomain concept to construct a representation of a cylindrical, multicellular bundle lying in an extensive volume conductor. The equations for the cylindrical bidomain are derived here for different combinations of boundary conditions and simplifying assumptions. The analysis shows that an analytic model for propagation can be set up if one assumes that the ratio of the intracellular and interstitial bidomain conductivities in the radial and axial direction are the same (i.e., equal anisotropy) and the intracellular radial current density vanishes at the surface. The simulation of this model will be discussed in a subsequent paper. As a point of reference, the classical one-dimensional cable model is also examined and the expressions governing propagation are reformulated to account for the extracellular medium, a factor ignored in most simulation studies.

Action Potentials↗
PubMed1990

Simulation of propagation along a cylindrical bundle of cardiac tissue--II: Results of simulation.

Previous evaluations of the cylindrical bidomain model of a bundle of cardiac tissue, have been obtained by using an analytic function for the transmembrane potential and assuming the activating wavefront through the bundle cross section is planar. In this paper, nonlinear membrane kinetics are introduced into the bidomain membrane and equal anisotropy ratios are assumed, permitting the transmembrane potential to be computed and its behavior examined at different depths in the bundle and for different values of conductivity and bundle diameters. In contrast with single fiber models, the bundle model reveals that the shape of the action potential is influenced by tissue resistivities. In addition, the steady-state activation wavefront through the cross-section perpendicular to the long axis of the bundle is not planar and propagates with a velocity that lies between that of a single fiber in an unbounded volume and a single fiber in a restricted extracellular space. In general, the bundle model is shown to be significantly better than the classical single fiber model in describing the behavior of real cardiac tissue.

Action Potentials↗
PubMed1990

Mechanism of cardiac defibrillation in open-chest dogs with unipolar DC-coupled simultaneous activation and shock potential recordings.

The automatic implantable cardioverter-defibrillator has been shown to dramatically improve survival. The future refinement of these devices requires a clear understanding of their mechanism of action. We performed the following study to test two hypotheses: 1) When defibrillation is successful, fibrillating activity must be annihilated in a critical mass of both ventricles; and 2) when defibrillation is unsuccessful, at least one area of the ventricular mass has been left fibrillating. Unipolar Ag/AgCl sintered electrodes were directly coupled from triangular arrays at 40 epicardial locations (total, 120 recording sites) that covered both right and left ventricular surfaces and were designed to measure the voltage gradient generated by the shock at each triangular array as well as the underlying myocardial electrical activity before and immediately after the shock. An algorithm was developed and tested that reliably scored whether a postshock activation was a continuation of the immediately previous fibrillating activity. This technique was applied to 203 defibrillation attempts in six open-chest dogs during electrically induced ventricular fibrillation. There were 139 successful defibrillation attempts and 64 unsuccessful attempts. Monophasic truncated exponential 10-msec defibrillation shocks (0.5-35 J) were delivered through an anodal patch on the right atrium and a cathodal patch on the left ventricular apex. In all cases of unsuccessful defibrillation, at least one ventricular site could be clearly identified that failed to be defibrillated. In cases of successful defibrillation two distinct patterns were observed: 1) complete annihilation of fibrillating activity at all sites or 2) nearly complete cessation of fibrillating activity with a single area of persistent fibrillation that subsequently self-extinguished within one to three activations. This single site in the second form of successful defibrillation was located in the region of minimum voltage gradient produced by the defibrillating waveform and was occasionally accompanied by dynamic encapsulation with refractory tissue as a result of a wavefront emanating from a region that had undergone successful defibrillation. These results support the hypothesis that a critical mass of myocardium must be affected for successful defibrillation and that unsuccessful defibrillation is always accompanied by residual fibrillating activity in at least one site. The results also demonstrate that the size of the critical mass required for successful defibrillation can be less than 100%.

Animals↗
PubMed1989

Analysis of the longitudinal and radial resistivity measurements of the nerve trunk.

Of the many models of peripheral nerve in the literature, essentially all have relied on experimentally derived values for the anisotropic resistivity of the nerve bundle interstitial space. This paper is a comprehensive mathematical analysis of the most referenced experiment for the longitudinal and radial resistivity measurements of the nerve trunk, namely that of Tasaki. For the analysis of the longitudinal measurements we introduce intracellular as well as interstitial current pathways (not considered by Tasaki). For the radial measurement the resistivity is expected to depend on the geometric packing of fibers within the trunk. Since Tasaki's paper did not include a histological examination of the nerve trunk these measurements are difficult to evaluate. However, our analysis indicates the importance of including the above factors, in addition to the epineurial (and perineurial) sheath as a resistive pathway. Our mathematical analysis supports the experimental measurements and confirms an assumed nerve trunk composition with theoretically derived values for the interstitial resistivities. It is therefore concluded that, at present, an appropriate procedure in determining resistivity values for use in modeling is to derive these values for an idealized nerve bundle based on the microscopic (electrolytic) resistivity of the interstitial medium.

Animals↗
PubMed1988

Bioelectric sources arising in excitable fibers (ALZA lecture).

This paper reviews the evaluation of bioelectric source strength and source field relationships for excitable fibers. For the single fiber, quantitative expressions describing the source may be derived which are independent of the fields produced by the sources. Rigorous expressions describe the equivalent elemental sources as discs, while the approximate line source is frequently satisfactory under physiological conditions. For fiber bundles the source associated with each fiber cannot be evaluated by the approximate isolated fiber expressions. However, when the bundle can be approximated as a bidomain and if the activation is planar, then mathematical expressions can be obtained. The resulting field behaves as if its origin was an equivalent single fiber. When the bidomain simplification and equal anisotropy ratio approximation is made, the planar waveform assumption can be removed and the resultant source and field can be evaluated. However, the latter are no longer independent.

Action Potentials↗
PubMed1988

Potential and current distributions in a cylindrical bundle of cardiac tissue.

The intracellular and interstitial potentials associated with each cell or fiber in multicellular preparations carrying a uniformly propagating wave are important for characterizing the electrophysiological behavior of the preparation and in particular, for evaluating the source contributed by each fiber. The aforementioned potentials depend on a number of factors including the conductivities characterizing the intracellular, interstitial, and extracellular domains, the thickness of the tissue, and the distance (depth) of the field point from the surface of the tissue. A model study is presented describing the extracellular and interstitial potential distribution and current flow in a cylindrical bundle of cardiac muscle arising from a planar wavefront. For simplicity, the bundle is considered as a bidomain. Using typical values of conductivity, the results show that the intracellular and interstitial potential of fibers near the center of a very large bundle (greater than 10 mm) may be approximated by the potentials of a single fiber surrounded by a limited extracellular space (a fiber in oil), hence justifying a core-conductor model. For smaller bundles, the peak interstitial potential is less than that predicted by the core-conductor model but still large enough to affect the overall source strength. The magnitude of the source strength is greatest for fibers lying near the center of the bundle and diminishes sharply for fibers within 50 microns of the surface.

Animals↗