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R Plonsey

Publications and source records attributed to R Plonsey.

At least 19 recordsLinked to original sources
PubMed1992

Active response of a one-dimensional cardiac model with gap junctions to extracellular stimulation.

To study the response of cardiac tissue to electrical stimulation, a one-dimensional model of cardiac tissue has been developed using linear core-conductor theory and the DiFrancesco-Noble model of Purkinje tissue. The cable lies in a restricted extracellular medium and includes a representation of the junctional resistances known to interconnect cardiac cells. Two electrode geometries are considered: (a) a semi-infinite cable with a monopolar electrode at the end of the cable and (b) a terminated cable with one electrode at each end of the cable. In a series of simulations, stimuli of varying magnitude and polarity are applied at three different times during the plateau of the action potential. The results at the stimulus site show that the action potential duration may either decrease or increase in response to the stimulus, depending on the polarity and application time of the stimulus. The spatial behaviour of the cable in response to the stimulus indicates that sites greater than 200 cells from the stimulating electrode are not affected by the stimulus.

Electric Stimulation↗
PubMed1992

Electrophysiological interaction through the interstitial space between adjacent unmyelinated parallel fibers.

The influence of interstitial or extracellular potentials on propagation usually has been ignored, often through assuming these potentials to be insignificantly different from zero, presumably because both measurements and calculations become much more complex when interstitial interactions are included. This study arose primarily from an interest in cardiac muscle, where it has been well established that substantial interstitial potentials occur in tightly packed structures, e.g., tens of millivolts within the ventricular wall. We analyzed the electrophysiological interaction between two adjacent unmyelinated fibers within a restricted extracellular space. Numerical evaluations made use of two linked core-conductor models and Hodgkin-Huxley membrane properties. Changes in transmembrane potentials induced in the second fiber ranged from nonexistent with large intervening volumes to large enough to initiate excitation when fibers were coupled by interstitial currents through a small interstitial space. With equal interstitial and intracellular longitudinal conductivities and close coupling, the interaction was large enough (induced Vm approximately 20 mV peak-to-peak) that action potentials from one fiber initiated excitation in the other, for the 40-microns radius evaluated. With close coupling but no change in structure, propagation velocity in the first fiber varied from 1.66 mm/ms (when both fibers were simultaneously stimulated) to 2.84 mm/ms (when the second fiber remained passive). Although normal propagation through interstitial interaction is unlikely, the magnitudes of the electrotonic interactions were large and may have a substantial modulating effect on function.

Animals↗
PubMed1992

The transient subthreshold response of spherical and cylindrical cell models to extracellular stimulation.

The effect of extracellular stimulation on excitable tissue is evaluated using analytical models. Primary emphasis is placed on the determination of the rate of rise of the membrane potential in response to subthreshold stimulation. Three models are studied: 1) a spherical cell in a uniform electric field, 2) an infinite cylindrical fiber with a point source stimulus, and 3) a finite length cable with sealed ends and a stimulus electrode at each end. Results show that the rate of rise of the transmembrane potential was more rapid than the step response of a space-clamped membrane for all geometries considered. The response of the cylindrical fiber to extracellular stimulation is compared to previously reported studies of the cylindrical fiber response to intracellular stimulation. It is found that the location of the stimulus has little effect on the infinite fiber response. For terminated cables, however, an accurate model of stimulus response must discriminate between intracellular and extracellular stimulation.

Cell Physiological Phenomena↗
PubMed1992

The effect of cellular discontinuities on the transient subthreshold response of a one-dimensional cardiac model.

Previous studies have examined the influence of the gap-junction discontinuity on the steady-state response of a cardiac cable to electrical defibrillation. It is important to understand when steady-state conditions may be assumed. For this reason, the transient, subthreshold behavior of a discontinuous cardiac cable is examined in this study. The behavior of the cable reflects two characteristics: 1) the continuous nature of the entire cable and 2) the isolated behavior of individual cells imposed by the junction discontinuity. The results show two effective time constants of activation: a large time constant corresponding to the time constant of a continuous cable of equivalent length, and a small time constant reflecting the rapid activation of an isolated cell. The rapid activation establishes a voltage gradient across each cell of the cable with one end of the cell hyperpolarized and the opposite end depolarized. This pattern of hyperpolarization and depolarization reaches a maximum value in approximately 3 microseconds and may play an important role in the mechanism of defibrillation.

Intercellular Junctions↗
PubMed1991

The quantitative investigation of the binding process of calcium blocking drugs in a sinoatrial node.

Application of existing models of sinoatrial node pacemaker activity and of channel-drug interaction allow us to reproduce action potential changes as a result of the blocking effect of drugs. Two calcium antagonistic drugs, nifedipine and mesudipine, were investigated and as a result averaged rate constants of binding and unbinding were evaluated. The procedure applied which is based on experimental results and on computer simulations, can be used as an initial step for comparison of different drugs.

Action Potentials↗
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↗