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F A Roberge

Publications and source records attributed to F A Roberge.

At least 19 recordsLinked to original sources
PubMed1992

Modeling the dynamic features of the electrogenic Na,K pump of cardiac cells.

The purpose of this paper is to examine the dynamic features of the electrogenic Na,K pump of cardiac cells, based on a comparative analysis of a mechanistic model and an ad hoc mathematical description of the Na,K pump. Both representations are incorporated into a modified version of the Beeler-Reuter model for the ventricular membrane, and the resulting action potential models are studied under conditions of repetitive stimulation at steady rates between 0 and 3 Hz. The two Na,K pump representations have nearly identical steady-state characteristics of sensitivity to internal Na+ concentration, external K+ concentration, and membrane potential. Rapid voltage-dependent transient pump currents are present in the mechanistic model, while they are absent in the ad hoc mathematical description we used. The stimulation results show that a sizable peak of pump current caused by the action potential upstroke in the mechanistic model affects phase 1 repolarization, and that this effect is relatively independent of the stimulation rate. The pump current generated by our ad hoc mathematical description is constant during the action potential and does not affect directly the repolarization time course. While the two Na,K pump models show similar pumping efficiency at low stimulation rates, the mechanistic pump is more efficient at high rates of activity. In essence, the distinctive features of the mechanistic model are due to an energy barrier expressing the voltage dependence of the translocation step of the mechanism, and to the redistribution of the intermediates of the biochemical reactions during activity. In comparison, the ad hoc mathematical description exhibits a fixed dependence of the pump current on voltage and ionic concentrations.

Action Potentials↗
PubMed1992

Propagation of activation in cardiac muscle.

The hypothesis of local circuit current flow underlying propagation of activation in cardiac muscle has been extensively documented by one-dimensional and two-dimensional simulation studies. The assumptions of spatially uniform membrane capacitance and membrane ionic properties yield simulation results that are in good agreement with experimental observations in healthy cardiac muscle, thereby indicating that differences in propagation velocity and action potential upstroke between longitudinal and transverse directions can be explained solely on the basis of anisotropic intercellular coupling. Two-dimensional model studies of anisotropic propagation have also stressed the more efficient charging of the membrane capacitance and higher safety factor of propagation in the transverse direction. These conditions favor the occurrence of longitudinal unidirectional block and the initiation of reentry via transverse propagation. The authors simulated rotating waves initiated by properly phased transverse and longitudinal plane waves in a two-dimensional sheet model. Sustained propagation requires a minimum anisotropy ratio, corresponding to a velocity ratio of about 4:1. It was found, for uniform anisotropy, that the central focus wandered slightly. A higher anisotropy ratio favors a more stable rotating pattern and a more restricted movement of the central focus.

Animals↗
PubMed1992

A model study of electric field interactions between cardiac myocytes.

The transmission of excitation via electric field coupling was studied in a model comprising two myocytes abutted end-to-end and placed in an unbounded volume conductor. Each myocyte was modeled as a small cylinder of membrane (10 microns in diameter and 100 microns in length) capped at both ends. A Beeler-Reuter model modified for the Na+ current dynamics served to simulate the membrane ionic current. There was no resistive coupling between the myocytes and the intercellular junction consisted of closely apposed pre- and post-junctional membranes, separated by a uniform cleft distance. The membrane current crossing the prejunctional membrane during the action potential upstroke tends to flow out of the cleft, but it is partly prevented from doing so by the shunt resistance constituted by the cleft volume conductor. The prejunctional upstroke gives rise to a pulse of positive potential within the cleft which induces a small capacitive current across the post-junctional membrane to yield a small positive change in the intracellular potential in the post-junctional cell. The net result is an hyperpolarization of the post-junctional cleft membrane and a slight depolarization of the rest of the cell membrane since the extracellular potential outside of the cell is zero. The magnitude of this depolarization is quite small for a flat junctional membrane and it can be increased by membrane folding and interdigitation, so as to increase the junctional membrane area by a factor of 10 or more. Even then the post-junctional depolarization does not reach threshold when the extracellular potential around the post-junctional cell is effectively zero. Threshold depolarization occurs in the presence of a large decrease of post-junctional load, by increasing the junctional membrane capacitance and/or decreasing the volume of the post-junctional cell. Assuming that the normal resistive coupling between two cardiac myocytes is 1-4 M omega, our model study indicates that electric field coupling would then be about two orders of magnitude smaller. However, substantial enhancement of the efficacy of electric field transmission was observed in the case of cells with substantial junctional membrane folding.

Action Potentials↗
PubMed1991

Structural complexity effects on transverse propagation in a two-dimensional model of myocardium.

A thin sheet of cardiac tissue was modeled as a set of resistively coupled excitable cables with membrane dynamics described by the modified Beeler Reuter model. Transverse connections have a resistance Rn and are regularly distributed with a spacing delta on any given cable, to provide alternating input and output junctions. Flat wave longitudinal propagation corresponds to propagation along a single continuous cable since all units of the network are functionally isolated due to the absence of transverse current flow. Events on a given cable during flat transverse propagation include electrotonic spread of potential from input to output junctions, action potential initiation at input junctions, and collision at output junctions. The propagating two-dimensional transverse wavefront is an undulating transmembrane potential surface with highs at the input junctions and lows at the output junctions. The action potential upstroke is also modulated in a periodic manner with minimum and maximum Vmax at the input and output junctions respectively. Thus, the network is capable of a diversity of dynamic behavior spatially distributed in relation to the specific pattern of transverse connections chosen. Overall, the behavior of the network model is in good agreement with available structural and electrophysiological data on myocardium. In addition, this network topology allows to handle more easily parameters governing propagation and to avoid very large matrices which are costly in computational effort and overall computer time.

Computer Simulation↗
PubMed1991

Directional characteristics of action potential propagation in cardiac muscle. A model study.

Propagation of an elliptic excitation wave front was studied in a two-dimensional model of a thin sheet of cardiac muscle. The sheet model of 2.5 x 10 mm consisted of a set of 100 parallel cables coupled through a regular array of identical transverse resistors. The membrane dynamics was represented by a modified Beeler-Reuter model. We defined the charging factor (CF) to represent by a single number the proportion of input current used to charge the membrane locally below threshold and showed that CF is inversely correlated with the time constant of the foot of the action potential (tau foot) during propagation on a cable. A safety factor of propagation (SF) was also defined for the upstroke of the action potential, with SF directly correlated with the maximum rate of depolarization (Vmax) and, for cablelike propagation, with propagation velocity. Propagation along the principal longitudinal axis of the elliptic wave front is cablelike but, in comparison with a flat wave front, transverse current flow provides a drag effect that somewhat reduces the propagation velocity, Vmax, SF, and CF. With a longitudinal-to-transverse velocity ratio of 3:1 or more, the wave front propagating along the principal transverse axis is essentially flat and is characterized by multiple collisions between successive pairs of input junctions on a given cable; Vmax, SF, and CF are larger than for longitudinal propagation, but CF is no longer correlated with tau foot. There are transient increases in propagation velocity and Vmax with distance from the stimulation site along both principal axes until stablized values are achieved, and a similar transient decrease in tau foot. Away from the principal axes, the action potential characteristics change progressively along the elliptic wave front.(ABSTRACT TRUNCATED AT 250 WORDS)

Action Potentials↗
PubMed1990

A model study of stability and oscillations in the myocardial cell membrane.

As a step towards an improved understanding of cardiac arrhythmias caused by abnormal automaticity, we perform a stability analysis of a Hodgkin-Huxley model of the myocardial cell membrane (modified Beeler-Reuter, MBR). The bifurcation structure of the model is obtained as a function of three parameters: the intensity of an applied constant current; the potassium equilibrium potential representing the accumulation of K+ ions in the external medium; and the maximum conductance of the slow inward current mimicking the local application of catecholamines on the membrane. For a range of parameter values, the model exhibits either stable automaticity or bistability between two quiescent states or between a quiescent state and an oscillatory state. These transformations of the bifurcation structure are shown to depend on the interrelationship between three elements: the activation of the slow inward current, the region of high slope conductance of the time-independent potassium current functions, and the slow variables controlling the activation of the potassium current and the inactivation of the slow inward current. Reduced two- and three-dimensional models are shown to reproduce the main stability properties of the full MBR model and to facilitate the understanding of its dynamic behavior. The onset of instability and the oscillatory features of the MBR model are in good agreement with relevant experimental results, and possible sources of disagreement on certain points are discussed.

Arrhythmias, Cardiac↗
PubMed1990

A model study of the contribution of active Na-K transport to membrane repolarization in cardiac cells.

A biochemical model of active Na-K transport in cardiac cells was studied in conjunction with a representation of the passive membrane currents and ion concentration changes. The active transport model is based on the thermodynamic and kinetic properties of a six-step reaction scheme for the Na,K-ATPase. It has a fixed Na:K stoechiometry of 3:2, and its activation is governed by three parameters: membrane potential intracellular Na+ concentration, and interstitial K+ concentration. The Na-K pump current is directly proportional to the density of Na,K-ATPase molecules. The passive membrane currents and ion concentration changes involve only Na+ and K+ ions, and no attempt was made to provide a precise representation of Ca2+ currents or Ca2+ concentration changes. The surface-to-volume ratio of the interstitial compartment is 55 times larger than that of the intracellular compartment. The flux balance conditions are such that the original equilibrium concentration values are re-established at each stimulation cycle. The underlying assumptions of the model were checked against experimental measurements on Na-K pump activity in a variety of preparations. In addition, the qualitative validation of the model was carried out by comparing its behavior following sudden frequency shifts to corresponding experimental observations. The overall behavior of the model is quite satisfactory and it is used to provide the following indications: (1) when the intracellular and interstitial volumes are relatively large, the ion concentration transients are small and the pumping rate depends essentially on average concentration levels. (2) An increase in internal Na+ concentration potentiates the response of the Na-K pump to rapid membrane depolarizations. (3) When the internal Na+ concentration is large enough, the Na-K pump current transient plays an important role in shaping the plateau and repolarization phase of the action potential. (4) A rapid increase in external K+ concentration during voltage clamp in multicellular preparations could saturate the Na-K pump response and lead to a fairly linear dependence of the pump activity on the internal Na+ concentration.

Action Potentials↗
PubMed1990

A new cable model formulation based on Green's theorem.

We describe an alternative formulation of the cable equation to model excitation in a cylinder of cardiac fiber. The formulation uses Green's theorem to develop equations for the extracellular and intracellular potential on either side of the excitable membrane, the dynamics of which are described by a Hodgkin-Huxley type model, without assuming that the radial current is zero. These equations are discretized to yield a system of linear equations which are solved at each instant in time. We found no qualitative differences between this approach and the standard cable model for parameters within accepted physiological limits. When the cable diameter is of the same order as the length constant the new formulation takes into account the intracellular potential change in the radial direction and gives an accurate expression of the conduction velocity.

Action Potentials↗
PubMed1990

Simulation and experimental studies of the factors influencing the frequency spectrum of cardiac extracellular waveforms.

Spectral analysis of electrocardiographic signals has been proposed as a tool to detect features reflecting cardiac diseases, such as ventricular hypertrophy, myocardial infarction, and a predisposition to sustained ventricular tachycardia. The lack of a theoretical basis to address this question prompted the authors to undertake a simulation study using a bidomain volume conductor model of a strip of cardiac tissue, combined with Fourier analysis, and electrograms recorded from an isolated right atrial canine preparation. In the crista terminalis, the bandwidth of the normal electrogram was 840 +/- 200 Hz (mean +/- SD) during longitudinal propagation and 660 +/- 370 Hz during transverse propagation. During premature stimulation, signal bandwidth and propagation velocity increase with the coupling interval. In the model, a linear combination of Vmax and propagation velocity values allows simulation of the various features of premature excitation. Vmax is the major determinant of the high-frequency content of the signal. An important decrease in the high-frequency content of electrograms occurs when the recording electrode is moved away from the preparation or the simulation model; at distances larger than 1-5 mm, the bandwidth levels off to a value of 50-120 Hz. Partial blockade of axial current flow in the direction of propagation due to microscopic discontinuities and variable activation delays at these discontinuities may be the cause of fragmented activity in necrotic myocardium, which is associated with a reduced bandwidth. Thus, short- and long-term effects of ischemia followed by infarction, such as decreased propagation velocity, decreased action potential upstroke, and fragmentation, tend to decrease the electrocardiographic bandwidth.

Action Potentials↗
PubMed1990

Estimation of fractional changes in peak gNa, -gNa, ENa, and h infinity (V) of cardiac cells from Vmax of the propagating action potential.

Fractional changes in the peak sodium conductances of the cardiac cell membrane during the action potential are often estimated from fractional changes in Vmax. The present model study shows, in reasonable accord with experimental evidence, that this approach is valid for propagating action potentials provided that the membrane capacitance does not change and that the nonsodium current is small at the time of Vmax. When the maximum conductance of the sodium channel (gNa) and the sodium equilibrium potential (ENa) are varied independently of one another, fractional changes in either of them can be predicted from fractional changes in Vmax if a reasonable estimate of the initial value of ENa is available. Manipulations which modify the resting membrane potential without changing gNa allow to calculate fractional changes in the steady-state Na+ inactivation [h infinity (V)] when ENa is known. Simulation runs were carried out for a continuous cable and a discontinuous cable with either a low (1 omega.cm2) or a high (10 omega.cm2) junctional resistance. The predictions of the model are valid in the discontinuous cable provided that the recording point remains strictly the same throughout the series of measurements. Because the high-resistance discontinuous cable provides conditions which reduce further the nonsodium current at the time of Vmax, the accuracy of the predictions are better in this case. It is concluded that properly designed experimental approaches based on Vmax measurements can yield important information on manipulations affecting gNa, ENa, and h infinity (V) during propagation, and that a better accuracy is possible in cardiac muscle when measurements are made during transverse propagation.

Action Potentials↗
PubMed1989

Model study of the spread of electrotonic potential in cardiac tissue.

This model study describes the electrotonic response of a cable model of cardiac tissue stimulated at one point. The stimulus is applied intracellularly in the form of a 2 ms pulse of current of near threshold amplitude. The attenuation of the electrotonic potential with distance and its mode of propagation along the cable are compared for equivalent passive, continuous and discontinuous cables. The three structures have the same basic physical and electrical characteristic and they differ either with respect to being active or passive or to the presence or absence of intercellular gap junctions. In the continuous cable a just subthreshold stimulus produces a local active response which propagates more slowly and is attenuated less rapidly with distance than in a passive cable. The spatial decrement of the local response in a discontinuous cable is faster than in a continuous cable of equal average resistivity. It is suggested that the larger time constant of the foot of the action potential observed in the longitudinal direction in cardiac muscle could be due in part to the electrotonic spread of the local response from the site of stimulation.

Action Potentials↗
PubMed1989

Using structural and visual information in physiological systems modeling.

This paper emphasizes the growing importance of precise models of biological structures to be used in conjunction with dynamic models of physiological events for improved physiological systems modeling. Medical imaging developments, represented mainly by computerized tomography, have been oriented principally towards medical diagnostic applications, that is towards the obtention of semi-quantitative information using sophisticated three-dimensional image display and manipulation capabilities. On the other hand, three-dimensional reconstruction of objects for modeling purposes presents rather more stringent requirements. The most important are the precise and independent representation and manipulation of the structures involved, the possibility of modifying the model parameters, the access to geometric data for specific measurements and transformation, and the compatibility with CAD/CAM software. Methods to obtain and manipulate such information are becoming available and a particular system used for the geometric modeling of the vertebral spine and knee is outlined.

Biomechanical Phenomena↗
PubMed1988

The inverse problem in electrocardiography: solutions in terms of equivalent sources.

This paper reviews those inverse electrocardiographic solutions that compute the electrical activity of the heart in terms of equivalent sources such as multipoles or multiple dipoles, as opposed to more realistic source formulations such as epicardial potentials. It treats, in succession, inverse solutions in terms of a single fixed-location dipole, a multipole series, moving dipoles, and, finally, multiple fixed-location dipoles. For each category of solution, simulation studies, animal experiments, and work involving human subjects are reviewed. Finally, more recent work that seeks to compute the cardiac activation isochrones, from the time integrals of the torso potentials during the QRS complex of the electrocardiogram, is described. The paper concludes with a discussion on the future of inverse electrocardiographic solutions in terms of equivalent sources.

Animals↗
PubMed1987

Revised formulation of the Hodgkin-Huxley representation of the sodium current in cardiac cells.

The purpose of this paper is to revise the parameters of the Hodgkin-Huxley formulation for the Na+ current in ventricular myocardial cells. To this end we have assembled much of the recent voltage clamp data on cardiac preparations obtained with modern voltage clamp and patch clamp techniques. The selected activation and inactivation characteristics of the Na+ channel and other membrane parameters represent a good compromise between available experimental measurements and lead to a reasonable average representation of the cardiac Na+ membrane current. The resulting Na+ conductance changes during the action potential upstroke are much larger than in earlier models, so that the upstroke is much faster and the peak depolarization is close to the Na+ equilibrium potential. The firing threshold level is nearly constant for resting potentials in the range of -70 and -90 mV. The maximum rate of rise of the action potential displayed by the new model is quite comparable to experimental observations.

Action Potentials↗
PubMed1987

Using Vmax to estimate changes in the sodium membrane conductance in cardiac cells.

Relative changes in the sodium conductance of the resting cardiac cell membrane are often estimated from relative changes in the maximum rate of rise of the action potential (Vmax). This approach has given rise to some controversy and it has not been possible so far to test it directly on an experimental basis. We have examined here the validity of this estimation using three different Hodgkin-Huxley representations of the cardiac membrane sodium current. The two basic requirements are a constant membrane capacitance and a negligible relative value of the nonsodium membrane currents at the time of Vmax. It is shown further that the approach leads to a satisfactory estimation only when the latency of Vmax is kept constant and a correction factor for the sodium driving force is applied to Vmax measurements. This conclusion applies either to a nonpropagated action or to an action potential propagated at constant velocity, provided that the membrane is not too strongly depolarized. It is valid for a wide range of sodium equilibrium potentials and a range of maximum sodium conductances limited to about 50% of the nominal value.

Action Potentials↗
PubMed1986

Reconstruction of propagated electrical activity with a two-dimensional model of anisotropic heart muscle.

The propagated electrical activity in normal anisotropic cardiac muscle is characterized by directionally dependent variations in the rising phase of the action potential. An important question concerns the relation between such variations and the propagation velocity and extracellular potentials. This problem was studied here in a sheet of cells, under conditions of uniform intracellular anisotropic resistivity and constant electrical membrane properties, through a numerical solution of the two-dimensional propagation equation. The numerical solution implies a lumping of the cytoplasmic and intercellular resistances into an equivalent junctional resistance to form a distributed resistive network representing the intracellular domain. The interstitial space is assumed isotropic and unbounded, with a resistivity of 100 omega X cm. The electrical properties of the cell membrane are represented by a Beeler-Reuter model. The stimulus current is applied to a small area of the sheet, and attention is focussed on the stable propagated events occurring some 5 or 6 length constants away from the stimulation site. The numerical solution is a good approximation of a continuous uniform structure when the cell size is less than 10% of the length constant along both major axes. Conditions of non-uniform propagation, with directionally dependent variations in the maximum rate of rise and time constant of the foot of the action potential were simulated by increasing the cell size to 30% of the length constant in the transverse direction of the sheet. Our results indicate that the directional changes in the maximum rate of rise correspond to small modifications of the extracellular potentials, while the directional changes in time constant of the foot are associated with the propagation velocity. The maximum effects are observed along the transverse direction as follows: a 19% increase in maximum rate of rise corresponds to a decrease of about 6% in the peak-to-peak amplitude of the extracellular potential, and a 24% increase in time constant of the foot is associated with a decrease of about 7% in the propagation velocity. Under the conditions of the present study, however, the simulated directional changes in maximum rate of rise are smaller than those experimentally observed so the corresponding changes in the extracellular potentials are probably underestimated.

Action Potentials↗
PubMed1985

Numerical integration in the reconstruction of cardiac action potentials using Hodgkin-Huxley-type models.

A comparison between traditional numerical integration methods and a new hybrid integration method for the reconstruction of action potential activity is presented, using a mathematical model of the cardiac Purkinje fiber (MNT model). It is shown that the hybrid integration method reduces importantly the overall computation time required for solving the Hodgkin-Huxley differential equations describing membrane electrical events. To accomplish this, the particular form of the gating variable equations is exploited to reformulate the step-by-step computation. In this way, the time increment can be made much larger compared with traditional methods when the membrane potential changes slowly. A mathematical analysis of the hybrid integration method is presented also, together with a numerical verification of its performance both for the propagated and nonpropagated membrane action potential. It is shown that the local error, that is the error arising at each integration step, and the cumulative integration error are strictly controlled by the membrane potential offset. Using the MNT model, the nonpropagated cardiac Purkinje action potential can be reconstructed in real time with an accuracy of 1% for the potential and 5% for the time of occurrence of its main features. In reconstructing propagated events, the hybrid integration method allows computation time savings by a factor of 10 or more compared to accurate Runge-Kutta schemes.

Action Potentials↗