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Biomedical subjects

A V Holden

Publications and source records attributed to A V Holden.

At least 19 recordsLinked to original sources
PubMed2006

Computational evaluation of the roles of Na+ current, iNa, and cell death in cardiac pacemaking and driving.

Voltage-dependent sodium (Na(+)) channels are heterogeneously distributed through the pacemaker of the heart, the sinoatrial node (SA node). The measured sodium channel current (i(Na)) density is higher in the periphery but low or zero in the center of the SA node. The functional roles of i(Na) in initiation and conduction of cardiac pacemaker activity remain uncertain. We evaluated the functional roles of i(Na) by computer modeling. A gradient model of the intact SA node and atrium of the rabbit heart was developed that incorporates both heterogeneities of the SA node electrophysiology and histological structure. Our computations show that a large i(Na) in the periphery helps the SA node to drive the atrial muscle. Removal i(Na) from the SA node slows down the pacemaking rate and increases the sinoatrial node-atrium conduction time. In some cases, reduction of the SA node i(Na) results in impairment of impulse initiation and conduction that leads to the SA node-atrium conduction exit block. Decrease in active SA node cell population has similar effects. Combined actions of reduced cell population and removal of i(Na) from the SA node have greater impacts on weakening the ability of the SA node to pace and drive the atrium.

Action Potentials↗
PubMed2005

Dynamical and cellular electrophysiological mechanisms of ECG changes during ischaemia.

The interpretation of normal and pathological electrocardiographic (ECG) patterns in terms of the underlying cellular and tissue electrophysiology is rudimentary, as the existing theories rely on geometrical aspects. We relate effects of sub-endocardial ischaemia on the ST-segment depression in ECG to patterns of transmural action potential propagation in a one-dimensional virtual ventricular wall. Our computational study exposes two electrophysiological mechanisms of ST depression: dynamic-predominantly positive spatial gradients in the membrane potential during abnormal repolarization of the wall, produced by action potential duration changes in the ischaemic region; and static-a negative spatial gradient of the resting membrane potential between the normal and ischaemic regions. Hyperkalaemia is the major contributor to both these mechanisms at the cellular level. These results complement simulations of the effects of cardiac geometry on the ECG, and dissect spatio-temporal and cellular electrophysiological mechanisms of ST depression seen in sub-endocardial ischaemia.

Action Potentials↗
PubMed2004

Pursuit-evasion predator-prey waves in two spatial dimensions.

We consider a spatially distributed population dynamics model with excitable predator-prey kinetics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive spread. Earlier, we have described new phenomena in this model in one spatial dimension, not found in analogous systems without taxis: reflecting and self-splitting waves. Here we identify new phenomena in two spatial dimensions: unusual patterns of meander of spirals, partial reflection of waves, swelling wave tips, attachment of free wave ends to wave backs, and as a result, a novel mechanism of self-supporting complicated spatiotemporal activity, unknown in reaction-diffusion population models.

Adaptation, Physiological↗
PubMed2003

Quasisoliton interaction of pursuit-evasion waves in a predator-prey system.

We consider a system of partial differential equations describing two spatially distributed populations in a "predator-prey" interaction with each other. The spatial evolution is governed by three processes: positive taxis of predators up the gradient of prey (pursuit), negative taxis of prey down the gradient of predators (evasion), and diffusion resulting from random motion of both species. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially depends on the taxis and is entirely different from waves in a reaction-diffusion system. Unlike typical reaction-diffusion waves, which annihilate on collision, these "taxis" waves can often penetrate through each other and reflect from impermeable boundaries.

Animals↗
PubMed2001

Gradient model versus mosaic model of the sinoatrial node.

BACKGROUND: A radical reinterpretation (mosaic model) of the makeup of the sinoatrial (SA) node has been proposed to explain the characteristic regional differences in electrical activity between the periphery and center of the SA node. According to the mosaic model, the differences result from a change in the mix of atrial cells and uniform SA node cells from periphery to center, whereas according to the alternative gradient model, there are no atrial cells within the functional SA node, and the differences result from a change in the intrinsic properties of SA node cells from periphery to center. METHODS AND RESULTS: A mosaic model of peripheral and central tissue has been constructed computationally by use of a coupled ordinary differential equation network (CODE) in a 2D lattice (20x20), with each node of the lattice designated randomly as an atrial cell or SA node cell (in correct proportions for periphery and center). The mosaic model fails to predict the characteristic differences in action potential rate and shape between the periphery and center, whereas the existing gradient model can do so. CONCLUSIONS: The mosaic model of the SA node is untenable, and the SA node is adequately described by the gradient model.

Animals↗
PubMed2001

Re-entrant cardiac arrhythmias in computational models of long QT myocardium.

The long QT syndrome (LQTS) is an inherited disorder in which repolarization of cardiac ventricular cells is prolonged. Patients with the LQTS are at an increased risk of ventricular cardiac arrhythmias. Two phenotypes of the inherited LQTS are caused by defects in K(+)channels (LQT1 and LQT2) and one by defects in Na(+)channels (LQT3). Patients with LQT1 are more likely to have self-terminating arrhythmias than those with LQT3. The aim of this computational study was to propose an explanation for this finding by comparing the vulnerability of normal and LQT tissue to re-entry, and estimating the likelihood of self-termination by motion of re-entrant waves to an inexcitable boundary in simulated LQT1, LQT2 and LQT3 tissue. We modified a model of mammalian cardiac cells to simulate LQT1 by reducing maximal I(K(s))conductance, LQT2 by reducing maximal I(K(r))conductance, and LQT3 by preventing complete inactivation of I(Na)channels. Each simulated phenotype was incorporated into a computational model of action potential propagation in one- and two-dimensional homogeneous tissue. Simulated LQT tissue was no more vulnerable to re-entry than simulated normal tissue, but the motion of re-entrant waves in simulated LQT1 tissue was between 2 and 5 times greater than the motion of re-entrant waves in simulated LQT2 and LQT3 tissue. These findings suggest that LQT arrhythmias do not result from increased vulnerability to re-entry, and that re-entry once initiated is more likely to self-terminate by moving to an inexcitable tissue boundary in LQT1 than in LQT2 and LQT3. This finding is consistent with clinical observations.

Action Potentials↗
PubMed2001

Engineering virtual cardiac tissue.

The kinetics of proteins involved in ion transfer, sequestration and binding in cardiac cells can be modelled to construct a model of the electrical activity of isolated cardiac cells as a system of ordinary differential equations. These cell models may be incorporated into tissue models, which, when combined with histology and anatomy, form virtual tissues. The effects of changes in specific protein expression, or changes in protein kinetics, produced by mutations or pharmacological agents, can be simulated using these tissue models and used to account for the whole organ effects of changes in specific ion-transport protein activity.

Action Potentials↗
PubMed2000

Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node.

Mathematical models of the action potential in the periphery and center of the rabbit sinoatrial (SA) node have been developed on the basis of published experimental data. Simulated action potentials are consistent with those recorded experimentally: the model-generated peripheral action potential has a more negative takeoff potential, faster upstroke, more positive peak value, prominent phase 1 repolarization, greater amplitude, shorter duration, and more negative maximum diastolic potential than the model-generated central action potential. In addition, the model peripheral cell shows faster pacemaking. The models behave qualitatively the same as tissue from the periphery and center of the SA node in response to block of tetrodotoxin-sensitive Na(+) current, L- and T-type Ca(2+) currents, 4-aminopyridine-sensitive transient outward current, rapid and slow delayed rectifying K(+) currents, and hyperpolarization-activated current. A one-dimensional model of a string of SA node tissue, incorporating regional heterogeneity, coupled to a string of atrial tissue has been constructed to simulate the behavior of the intact SA node. In the one-dimensional model, the spontaneous action potential initiated in the center propagates to the periphery at approximately 0.06 m/s and then into the atrial muscle at 0.62 m/s.

Action Potentials↗
PubMed1999

Spatiotemporal irregularity in an excitable medium with shear flow.

We consider an excitable medium moving with relative shear, subjected to a localized disturbance that in a stationary medium would produce a pair of spiral waves. The spiral waves so created are distorted and then broken by the motion of the medium. Such breaks generate new spiral waves, and so a "chain reaction" of spiral wave births and deaths is observed. This leads to a complicated spatiotemporal pattern, the "frazzle gas" [term suggested by Markus et al., Nature (London) 371, 402 (1994)], which eventually fills the whole medium. In this paper, we display and interpret the main features of the pattern.

Journal Article↗
PubMed1999

Reentrant arrhythmias and their control in models of mammalian cardiac tissue.

We use detailed biophysical and simplified models of excitation propagation in heart muscle to study the properties of reentrant arrhythmias. Using a detailed model of excitation combined with a bidomain description of propagation and action of electric current, we have obtained a theoretical estimation for the defibrillation threshold consistent with experimental data. Reentry acts as a spiral wave, propagating around a region of block, the core. A series of properly timed low-voltage stimuli can cause directed "resonant" drift of this block and act as a low-voltage defibrillation strategy. Experimentally observed activation patterns in fibrillating tissue are more complicated than the simplest spiral wave patterns. This is due to complicated geometry, the 3-dimensional nature of the tissue, and its anisotropy and inhomogeneity. However, some fibrillation patterns can be produced by a single reentrant wave, modulated by inhomogeneous tissue properties and Wenckebach frequency division.

Animals↗
PubMed1998

Re-entrant excitation initiated in models of inhomogeneous atrial tissue.

We demonstrate that a shift of the vulnerable window caused by tissue inhomogeneity can play a role in the generation of re-entrant excitation. The Earm-Hilgemann-Noble equations were incorporated into one- and two-dimensional inhomogeneous partial differential equation models of atrial tissue. Inhomogeneity was produced by a reduction of gNa over part of the medium and the vulnerable window for initiating re-entrant activity in homogeneous models determined from numerical integrations. Forty percent reduction of gNa produced little effect on the width of the vulnerable window, but the onset of the vulnerable window was delayed. The delay of the vulnerable window facilitates the initiation of re-entry at junctions between tissue with normal and reduced excitability, even though there is hardly any change in action potential duration.

Animals↗
PubMed1998

Reentrant waves and their elimination in a model of mammalian ventricular tissue.

The vulnerability to reentrant wave propagation, its characteristics (period, meander, and stability), the effects of rotational transmural anisotropy, and the control of reentrant waves by small amplitude perturbations and large amplitude defibrillating shocks are investigated theoretically and numerically for models based on high order, stiff biophysically derived excitation equations.

Journal Article↗
PubMed1997

One-dimensional modelling of the vulnerability to re-entry of homogeneous atrial tissue.

A one-dimensional excitable medium model of atrial tissue derived from the Earm-Hilgemann-Noble excitation equations for atrial excitation is used to investigate (1) the rate dependence of the conduction velocity of travelling wave solutions and (2) vulnerability to unidirectional conduction block and hence re-entry. The effects of changes in the ACh activated K+ current and Na+/K+ pump inhibition on these properties are computed.

Acetylcholine↗
PubMed1997

Qualitative modeling of mechanoelectrical feedback in a ventricular cell.

Mechanical changes in the heart muscle can influence its electrical properties through a process called mechanoelectrical feedback (MEF). This feedback can operate via changes in calcium dynamics during the cross-bridge cycle or via mechanosensitive (stretch-activated) channels. We present a four-variable ordinary differential equation (ODE) system that caricatures the electrical and mechanical activity of a ventricular cell and their mutual interactions. A three-variable excitable system with restitution properties of the FitzHugh-Nagumo type is coupled to a fourth equation which describes changes in cell length during a lightly loaded contraction. The resulting four-variable system models MEF in a cell and can be incorporated into spatially distributed models for mechanoelectric behavior during wave propagation in the cardiac tissue.

Animals↗
PubMed1996

Re-entrant activity and its control in a model of mammalian ventricular tissue.

We characterize the meander of re-entrant excitation in a model of a sheet of mammalian ventricular tissue, and its control by resonant drift under feedback driven stimulation. The Oxsoft equations for excitability in a guinea pig single ventricular cell were incorporated in a two dimensional reaction-diffusion system to model homogeneous, isotropic tissue with a plane wave conduction velocity of 0.35 m s-1. Re-entrant spiral wave solutions have a spatially extended transient motion (linear core) that settles down into rotation with an irregular period of 100-110 ms around an irregular, multi-lobed spiky core. In anisotropic tissue this would appear as a linear conduction block. The typical velocity of drift of the spiral wave induced by low amplitude resonant forcing is 0.4 cm s-1.

Animals↗
PubMed1995

Characteristics of atrial re-entry and meander computed from a model of a rabbit single atrial cell.

A two-dimensional excitable medium model of atrial tissue has been constructed by incorporating the Earm-Hilgemann-Noble excitation equations for membrane voltage-dependent ionic currents and pump exchanger currents, time-dependent changes in intracellular and extracellular ionic concentrations, and storage and release of Ca2+, for an atrial cell in an homogeneous partial differential equation. A diffusion coefficient of 1.25 cm2 sec-1 gives the conduction velocity of a solitary planar wave as 0.6 m sec-1. A spiral wave with a period of 78 msec develops from a broken wavefront, and initially rotates around a circular core of 2 mm diameter. After 1.5 sec of rotation, a biperiodic meander, with 6 epicycles/cycle, develops. This simple meander pattern is reflected in a period-6 modulation of the intervals between successive wavefronts.

Action Potentials↗
PubMed1995

Control of re-entrant activity in a model of mammalian atrial tissue.

We evaluate the feasibility of using resonant drift under feedback driven stimulation to control re-entrant excitation in atrial muscle. We simulate a two-dimensional sheet of atrial tissue, where the local kinetics are described by the Earm-Hilgemann-Noble equations for a rabbit atrial cell, and the effects of small amplitude spatially uniform forcing of the whole sheet are computed. Repetitive forcing can induce a drift of a spiral wave in the two-dimensional model, with a drift velocity of up to 10 cm s-1. For a 4 cm x 4 cm atrial surface this resonant drift can move the re-entrant spiral to the inexcitable boundaries, eliminating re-entry in less than 10 s when the amplitude of the repetitive stimulation is 10% that of the single shock defibrillation threshold.

Animals↗