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C S Henriquez

Publications and source records attributed to C S Henriquez.

13 recordsLinked to original sources
PubMed1992

Cardiac propagation simulation.

We have completed a range of membrane-based simulations of action potential propagation in two- and three-dimensional models of ventricular myocardium. The two-dimensional simulations included a bidomain representation of the myocardium which explicitly characterized the component volume conductors in the intracellular, interstitial, and extracellular spaces. With these simulations, we studied the contribution of the extracellular volume conductor to transmural myocardial propagation during depolarization. We also used two-dimensional bidomain simulations to study the effect of the interstitial volume conductor in the setting of planar myocardial depolarization with nominal and extreme tissue conductivities. Our three-dimensional simulations included a monodomain representation of the myocardium which characterized the three component volume conductors as a single lumped conductor. With these simulations, we examined the effects of the intramural rotation of the fiber axes on the timing and pattern of activation. To achieve practical solution times, we extended numerical techniques from previous reports and developed a range of new techniques applicable to this class of problems. Simulations of the depolarization wavefront used the nonlinear Ebihara and Johnson membrane equations for the fast sodium current as the membrane model. Simulations of the full action potential cycle combined the Ebihara and Johnson fast sodium current with the Beeler and Reuter membrane equations. Our results demonstrated that the individual volume conductors and the rotation of fiber axes have unique and identifiable consequences on the electrical activation in models of ventricular myocardium.

Action Potentials↗
PubMed1991

Examination of the choice of models for computing the extracellular potential of a single fibre in a restricted volume conductor.

The paper compares the rigorous and the conventional approximate line source solution of Laplace's equation used to evaluate the potential of a single cylindrical fibre. Particular attention is given to the solutions for a radially restricted circular cylindrical volume conductor. The effect of the extent of the volume conductor b on the difference between the potentials evaluated according to the different models is examined. For values of b larger than 10 times the fibre radius, the relative difference is less than 1 per cent and the values of b around 2 times the fibre radii, the error reaches as much as 17 per cent.

Action Potentials↗
PubMed1991

Modification of a cylindrical bidomain model for cardiac tissue.

Previous models based on a cylindrical bidomain assumed either that the ratio of intracellular and interstitial conductivities in the principal directions were the same or that there was no radial variation in potential (i.e., a planar front, delta Vm/delta rho = 0). This paper presents a formulation and the expressions for the intracellular, interstitial, extracellular, and transmembrane potentials arising from nonplanar propagation along a cylindrical bundle of cardiac tissue represented as a bidomain with arbitrary anisotropy. For unequal anisotropy, the transmembrane current depends not only on the local change of the transmembrane potential but also on the nature of the transmembrane potential throughout the volume.

Animals↗
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

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

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

Finite element analysis of bioelectric phenomena.

This article reviews the application of finite element methods to models of bioelectric phenomena. The models represent the electrical fields created in the body as a result of membrane current sources or external current applied for diagnostic or therapeutic purposes. We formulate the governing equations for these models and then derive the finite element equations for the generalized bioelectric problem. The 32 papers reviewed here, all those appearing in the literature to date, cover the areas of electrocardiology, therapeutic and functional electrical stimulation in the cerebellum, cochlea, spinal cord, and peripheral nerves, cardiac defibrillation, electrical impedance tomography, bidomain cardiac models, electroporation, and therapeutic electrical stimulation of bone. For each, we summarize the purpose of the study, the model details and assumptions, the major results, and the applicability of the study. The models are then considered as a group to critique the appropriateness of the finite element method, the means of implementation, and the factors affecting accuracy, thus providing an overview of the state of finite element modeling of bioelectric phenomena.

Central Nervous System Diseases↗
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↗