Biomedical subjects

L J Leon

Publications and source records attributed to L J Leon.

At least 19 recordsLinked to original sources

PubMed2005

Atrial cell action potential parameter fitting using genetic algorithms.

Understanding of the considerable variation in action potential (AP) shape throughout the heart is necessary to explain normal and pathological cardiac function. Existing mathematical models reproduce typical APs, but not all measured APs, as fitting the sets of non-linear equations is a tedious process. The study describes the integration of a pre-existing mathematical model of an atrial cell AP with a genetic algorithm to provide an automated tool to generate APs for arbitrary cells by fitting ionic channel conductances. Using the Nygren model as the base, the technique was first verified by starting with random values and fitting the Nygren model to itself with an error of only 0.03%. The Courtemanche model, which has a different morphology from that of the Nygren model, was successfully fitted. The AP duration restitution curve generated by the fit matched that of the target model very well. Finally, experimentally recorded APs were reproduced. To match AP duration restitution behaviour properly, it was necessary simultaneously to fit over several stimulation frequencies. Also, fitting of the upstroke was better if the stimulating current pulse replicated that found in situ as opposed to a rectangular pulse. In conclusion, the modelled parameters were successfully able to reproduce any given atrial AP. This tool can be useful for determining parameters in new AP models, reproducing specific APs, as well as determining the locus of drug action by examining changes in conductance values.

Action Potentials↗

PubMed2003

Cardiac near-field morphology during conduction around a microscopic obstacle--a computer simulation study.

In a recent paper, we described the behavior of the cardiac electric near-field, E, parallel to the tissue surface during continuous conduction. We found that the tip of E describes a vector-loop during depolarization with the peak field, E, pointing opposite to the direction of propagation, phiI(m). Experimentally recorded loop morphologies of E, however, frequently showed significant deviations from the theoretically predicted behavior. We hypothesized that this variety of morphologies might be caused by conduction obstacles at a microscopic size scale. This study examines the influence of obstacles on the morphology of vector loops of E and whether the peak of distorted loops remains a reliable indicator for the direction of propagation. We used a computer model of a sheet of cardiac tissue with a central conduction obstacle immersed in an unbounded volume conductor. We studied the loop morphologies of E and the differences between the intracellularly determined direction of propagation, phiI(m), and the direction of E, phiE. Distortions of the vector loop were morphologically similar to those observed experimentally. Differences between phiI(m) and phiE were less than 18 degrees at all observation sites. The obstacle led to deformations of the loop morphology, particularly during the initial and terminal phases, and to a lesser degree near the instant of E. We concluded that E is a reliable indicator of phiI(m).

Animals↗

PubMed2001

Effect of fibre rotation on the initiation of re-entry in cardiac tissue.

Transmural rotation of cardiac fibres can have a big influence on the initiation of re-entry in the heart. However, owing to computational demands, this has not been fully explored in a three-dimensional model of cardiac tissue that has a microscopic description of membrane currents, such as the Luo-Rudy model. Using a previously described model that is computationally fast, re-entry in three-dimensional blocks of cardiac tissue is induced by a cross-shock protocol, and the activity is examined. In the study, the effect of the transmural fibre rotation is ascertained by examining differences between a tissue block with no rotation and ones with 1, 2 and 3 degrees of rotation per fibre layer. The direction of the re-entry is significant in establishing whether or not re-entry can be induced, with clockwise re-entry being easier to initiate. Owing to the rotating anisotropy that results in preferential propagation along the fibre axis, the timing of the second stimulus in the cross-shock protocol has to be changed for different rates of fibre rotation. The fibre rotation either increases or decreases the window of opportunity for re-entry, depending on whether the activation front is perpendicular or parallel to the fibre direction. By varying the transmural extent of the S2, it is found that a deeper stimulus has to be applied to the blocks with fibre rotation to create re-entry. Increasing the transmural resistance also tends to reduce the extent of the S2 required to induce re-entry. Results suggest that increasing fibre rotation reduces the susceptibility of the tissue to re-entry, but that more complex spatiotemporal patterns are possible, e.g. stable figure-of-eight re-entries and transient rotors. Three mechanisms of re-entry annihilation are identified: front catchup, filling of the excitable gap and core wander.

Anisotropy↗

PubMed1999

Electrophysiological basis of mono-phasic action potential recordings.

Monophasic action potentials (MAPs) have been recorded for over a century, however, the exact mechanism responsible for their genesis has yet to be elucidated fully. The goal of the paper is to examine the physical basis of MAP recordings. MAP recordings are simulated by modelling a three-dimensional block of cardiac tissue. The effect of the MAP electrode is modelled by introducing a large, non-specific leakage conductance to the small region under the electrode. From the spread of the electrical activity, the equivalent extracellular current flow can be efficiently determined. These computed current sources are then input into a boundary element model of the tissue to determine the surface potentials. Finally, differences in surface potentials are used to compute waveforms that closely resemble MAP recordings. By varying model parameters, the mechanisms responsible for the MAP are determined, and a theory is put forward that can account for all observations. It is hypothesised that the leakage current causes the formation of a double-layer potential with a strength equal to the difference in transmembrane voltage between the regions under the electrode and those outside the electrode, leading to a recorded potential that mimics the transmembrane voltage outside the electrode region, although offset. Based on experimental MAP recordings, an equivalent leakage channel with a conductance of 0.1 mS cm-2 and a reversal potential of -43 mV is introduced by the electrode.

Action Potentials↗

PubMed1998

Spatiotemporal evolution of ventricular fibrillation.

Sudden cardiac death is the leading cause of death in the industrialized world, with the majority of such tragedies being due to ventricular fibrillation. Ventricular fibrillation is a frenzied and irregular disturbance of the heart rhythm that quickly renders the heart incapable of sustaining life. Rotors, electrophysiological structures that emit rotating spiral waves, occur in several systems that all share with the heart the functional properties of excitability and refractoriness. These re-entrant waves, seen in numerical solutions of simplified models of cardiac tissue, may occur during ventricular tachycardias. It has been difficult to detect such forms of re-entry in fibrillating mammalian ventricles. Here we show that, in isolated perfused dog hearts, high spatial and temporal resolution mapping of optical transmembrane potentials can easily detect transiently erupting rotors during the early phase of ventricular fibrillation. This activity is characterized by a relatively high spatiotemporal cross-correlation. During this early fibrillatory interval, frequent wavefront collisions and wavebreak generation are also dominant features. Interestingly, this spatiotemporal pattern undergoes an evolution to a less highly spatially correlated mechanism that lacks the epicardial manifestations of rotors despite continued myocardial perfusion.

Electric Stimulation↗

PubMed1995

Calculation of transmembrane current from extracellular potential recordings: a model study.

INTRODUCTION: A mathematical/computer model of cardiac tissue was used to study the estimation of transmembrane current (EIm) from extracellular potential recordings. METHODS AND RESULTS: The simulated EIm of transmembrane current was compared with the simulated transmembrane current (Im), and both simulated values were compared with experimentally derived EIm obtained during sinus rhythm and ventricular fibrillation in dogs. We found that although EIm measurements slightly overestimate the duration of the Im waveform, they provide a reasonable approximation of Im during normal conduction and during decremental conduction and conduction block. CONCLUSIONS: There is a very clear linear correlation between the time spent at or below 25% of the peak inward transmembrane current (Im25), its corresponding estimate (EIm25), the peak inward Im and EIm, and the peak ionic current, providing some evidence that EIm25 may be a suitable in vivo measure of peak ionic current.

Algorithms↗

PubMed1993

On the interpretation of voltage-clamp data using the Hodgkin-Huxley model.

This paper describes a method to extract membrane model parameters from experimental voltage-clamp records. The underlying theory is based on two premises: (1) the membrane dynamics can be described by a Hodgkin-Huxley (HH) model, and (2) the most reliable data provided by voltage clamp experiments are peak current (Ip) measurements. First, the steady-state characteristics of activation (x infinity) and inactivation (z infinity) must be estimated, and it is shown that Ip data provided by standard voltage-clamp stimulation protocols are sufficient for this purpose for the case of well-separated activation (tau x) and inactivation (tau z) time constants, tau x << tau z. Next, we propose a test (R test) to establish the suitability of the HH model to represent the data. When the HH model is applicable (successful R test), the procedure yields the degree of the gating variables, a range of maximum membrane conductance (g) values, and a tau x/tau z ratio that relates x infinity and z infinity to the Ip data. When additional information is available, such as the time of occurrence of Ip or an estimate of tau z from the late portion of the ionic current response, one can narrow down the value of g and estimate all the HH parameters and functions. Otherwise, when the R test is not successful, one can conclude that x infinity and z infinity have been incorrectly estimated because tau x and tau z are not sufficiently separated or that the HH model is not applicable to the data.

Algorithms↗

PubMed1993

A model study of extracellular stimulation of cardiac cells.

Point source extracellular stimulation of a myocyte model was used to study the efficacy of excitation of cardiac cells, taking into account the shape of the pulse stimulus and its time of application in the cardiac cycle. The myocyte was modeled as a small cylinder of membrane (10 microns in diameter and 100 microns in length) capped at both ends and placed in an unbounded volume conductor. A Beeler-Reuter model modified for the Na+ dynamics served to simulate the membrane ionic current. The stimulus source was located on the cylinder axis, close to the myocyte (50 microns) in order to generate a nonlinear extracellular field (phi e). The low membrane impedance associated with the high frequency component of the make and break of the rectangular current pulse leads to a current flow across the membrane and an abrupt change in intracellular potential (phi i). Because the intracellular space is very small, phi i is nearly uniform over the length of the myocyte and the membrane potential (V = phi i-phi e) is governed by the applied field phi e. There is then a longitudinal gradient of membrane polarization which is the inverse of the gradient of extracellular potential. With an anodal (positive) pulse, for instance, the proximal portion of the myocyte is hyperpolarized and the distal portion is depolarized. Based on this principle and considering the voltage-dependent activation/inactivation dynamics of the membrane, it is shown that a cathodal (negative) pulse is the most efficacious stimulus at diastolic potentials, an anodal current is preferable during the plateau phase of the action potential, and a biphasic pulse is optimal during the relative refractory phase. Thus a biphasic pulse would constitute the best choice for maximum efficacy at all phases of the action potential.

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

Computer model of excitation and recovery in the anisotropic myocardium. I. Rectangular and cubic arrays of excitable elements.

A computer model of propagated excitation and recovery in anisotropic cardiac tissue is presented that consists of a large number of excitable elements whose subthreshold interactions are governed by the anisotropic bidomain theory but whose suprathreshold behavior (action potential) is largely preassigned. The model's performance was first tested in a two-dimensional configuration with uniform anisotropy; this method allowed comparison of simulated isochrones of excitation and extracellular electrograms with the results of experimental in vitro studies of cardiac tissue. Next the model was used to study propagated excitation in a three-dimensional region representing the anisotropic properties of the ventricular wall, with attention to the effects produced by variable fiber direction from "endocardium" to "epicardium."

Action Potentials↗

PubMed1991

Computer model of excitation and recovery in the anisotropic myocardium. II. Excitation in the simplified left ventricle.

A computer model of propagated excitation and recovery in anisotropic cardiac tissue was described in the first report of this series. The model consists of a large number of excitable elements whose subthreshold interactions are governed by the anisotropic bidomain theory but whose suprathreshold behavior (action potential) is largely preassigned. As described in the first report, the model's performance was tested in rectangular and cubic arrays of excitable elements. This second report deals with three-dimensional simulations in a simplified left ventricle with anisotropy; specifically, the activation process in the "normal" ventricle is described (exemplified by the activation sequences started from various endocardial, intramural, and epicardial sites). To further substantiate our model's validity, we compare simulated epicardial and body-surface potential distributions with experimental findings in isolated canine hearts and with clinical evidence provided by electrocardiographic body-surface mapping.

Action Potentials↗

PubMed1991

Computer model of excitation and recovery in the anisotropic myocardium. III. Arrhythmogenic conditions in the simplified left ventricle.

A computer model of propagated excitation and recovery in anisotropic cardiac tissue has been described in the first two reports of this series. The model consists of a large number of excitable elements whose subthreshold interactions are governed by the anisotropic bidomain theory but whose suprathreshold behavior (action potential) is largely preassigned. As described in the previous two reports, the model's performance was tested in rectangular and cubic arrays of excitable elements and in the "normal" three-dimensional simplified left ventricle with anisotropy. The present report deals with arrhythmogenic conditions in the simplified left ventricle with anisotropy and ventricular-gradient properties; specifically, we studied activation and recovery in the presence of an ischemic region and under various stimulation protocols. The aim of these simulations was to elucidate the role of reentry in the genesis of ventricular tachycardia. Our simulations produced reentrant activation as a result of appropriate endocardial stimulation.

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 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↗

PubMed1987

The effect of torso geometry on magnetocardiographic isofield maps.

Using a computer model of a realistically shaped human torso with lungs and intraventricular blood masses, we have assessed how torso geometry and composition affect the extracorporal magnetic field produced by a current dipole in the centre of the ventricular mass. The magnetic induction vector B arising from the dipole has been calculated at points of a precordial measuring grid and the influence of boundaries has been assessed qualitatively, by comparing contour maps of the B component normal to the torso's frontal plane. We found that the maps reflected relatively faithfully the underlying dipolar source for the homogeneous torso and even for the torso with lungs. However, the intraventricular blood masses caused a noticeable rotation of the maps' extrema. Both lungs and blood masses tended to swing the distribution towards the distribution that would have been caused by a dipole oriented along the anatomical axis of the heart.

Computer Simulation↗

PubMedDate not supplied

Simulation of two-dimensional anisotropic cardiac reentry: effects of the wavelength on the reentry characteristics.

A two-dimensional sheet model was used to study the dynamics of reentry around a zone of functional block. The sheet is a set of parallel, continuous, and uniform cables, transversely interconnected by a brick-wall arrangement of fixed resistors. In accord with experimental observations on cardiac tissue, longitudinal propagation is continuous, whereas transverse propagation exhibits discontinuous features. The width and length of the sheet are 1.5 and 5 cm, respectively, and the anisotropy ratio is fixed at approximately 4:1. The membrane model is a modified Beeler-Reuter formulation incorporating faster sodium current dynamics. We fixed the basic wavelength and action potential duration of the propagating impulse by dividing the time constants of the secondary inward current by an integer K. Reentry was initiated by a standard cross-shock protocol, and the rotating activity appeared as curling patterns around the point of junction (the q-point) of the activation (A) and recovery (R) fronts. The curling R front always precedes the A front and is separated from it by the excitable gap. In addition, the R front is occasionally shifted abruptly through a merging with a slow-moving triggered secondary recovery front that is dissociated from the A front and q-point. Sustained irregular reentry associated with substantial excitable gap variations was simulated with short wavelengths (K = 8 and K = 4). Unsustained reentry was obtained with a longer wavelength (K = 2), leading to a breakup of the q-point locus and the triggering of new activation fronts.

Action Potentials↗