A simple adaptation of a handheld ECG recorder to obtain chest lead equivalents.

Hand held ECG recorders are transforming the way we detect and diagnose heart rhythm disorders. The Kardia 6 L was launched in 2019 to detect and diagnose heart rhythm disorders recording a six lead (limb lead) ECG. Recording and analysis of precordial leads are currently not supported by the Kardia 6 L. In this study we aim to assess if reliable chest lead data can be obtained using a simple modification to the recording system.

Towards a computational reconstruction of the electrodynamics of premature and full term human labour.

We apply virtual tissue engineering to the full term human uterus with a view to reconstruction of the spatiotemporal patterns of electrical activity of the myometrium that control mechanical activity via intracellular calcium. The three-dimensional geometry of the gravid uterus has been reconstructed from segmented in vivo magnetic resonance imaging as well as ex vivo diffusion tensor magnetic resonance imaging to resolve fine scale tissue architecture. A late-pregnancy uterine smooth muscle cell model is constructed and bursting analysed using continuation algorithms. These cell models are incorporated into partial differential equation models for tissue synchronisation and propagation. The ultimate objective is to develop a quantitative and predictive understanding of the mechanisms that initiate and regulate labour.

Stochastic vagal modulation of cardiac pacemaking may lead to erroneous identification of cardiac "chaos".

Fluctuations in the time interval between two consecutive R-waves of electrocardiogram during normal sinus rhythm may result from irregularities in the autonomic drive of the pacemaking sinoatrial node (SAN). We use a biophysically detailed mathematical model of the action potentials of rabbit SAN to quantify the effects of fluctuations in acetylcholine (ACh) on the pacemaker activity of the SAN and its variability. Fluctuations in ACh concentration model the effect of stochastic activity in the vagal parasympathetic fibers that innervate the SAN and produce varying rates of depolarization during the pacemaker potential, leading to fluctuations in cycle length (CL). Both the estimated maximal Lyapunov exponent and the noise limit of the resultant sequence of fluctuating CLs suggest chaotic dynamics. Apparently chaotic heart rate variability (HRV) seen in sinus rhythm can be produced by stochastic modulation of the SAN. The identification of HRV data as chaotic by use of time series measures such as a positive maximal Lyapunov exponent or positive noise limit requires both caution and a quantitative, predictive mechanistic model that is fully deterministic.

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.

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.

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.

Defibrillation threshold computed from normal and supernormal excitable cardiac tissue.

The applicability of the 'upper limit of vulnerability' defibrillation theory was evaluated in models of cardiac tissue in which spatial changes within cells are retained. Defibrillation thresholds were computed from two models of cardiac tissue: one with, and one without, a supernormal period, and compared with those predicted by the theory. In the cardiac virtual tissue with a monotonic recovery of excitation - a normal refractory period, the computed defibrillation threshold is consistent with the prediction of the 'upper limit of vulnerability' defibrillation theory. However, in cardiac tissue with non-monotonic recovery of excitation - a supernormal period, the computed defibrillation threshold is significantly less than the theory prediction.

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.

Enhanced self-termination of re-entrant arrhythmias as a pharmacological strategy for antiarrhythmic action.

Ventricular tachycardia and fibrillation are potentially lethal cardiac arrhythmias generated by high frequency, irregular spatio-temporal electrical activity. Re-entrant propagation has been demonstrated as a mechanism generating these arrhythmias in computational and in vitro animal models of these arrhythmias. Re-entry can be idealised in homogenous isotropic virtual cardiac tissues as spiral and scroll wave solutions of reaction-diffusion equations. A spiral wave in a bounded medium can be terminated if its core reaches a boundary. Ventricular tachyarrhythmias in patients are sometimes observed to spontaneously self-terminate. One possible mechanism for self-termination of a spiral wave is meander of its core to an inexcitable boundary. We have previously proposed the hypothesis that the spatial extent of meander of a re-entrant wave in the heart can be directly related to its probability of self-termination, and so inversely related to its lethality. Meander in two-dimensional virtual ventricular tissues based on the Oxsoft family of cell models, with membrane excitation parameters simulating the inherited long Q-T syndromes has been shown to be consistent with this hypothesis: the largest meander is seen in the syndrome with the lowest probability of death per arrhythmic episode. Here we extend our previous results to virtual tissues based on the Luo-Rudy family of models. Consistent with our hypothesis, for both families of models, whose different ionic mechanisms produce different patterns of meander, the LQT virtual tissue with the larger meander simulates the syndrome with the lower probability of death per episode. Further, we search the parameter space of the repolarizing currents to find their conductance parameter values that give increased meander of spiral waves. These parameters may provide targets for antiarrhythmic drugs designed to act by increasing the likelihood of self-termination of re-entrant arrhythmias. (c) 2002 American Institute of Physics.

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.

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.

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.

Characterization of patterned irregularity in locally interacting, spatially extended systems: Ventricular fibrillation.

The re-entrant ventricular arrhythmias of monomorphic ventricular tachycardia and fibrillation are produced by abnormal spatio-temporal patterns of propagation in the ventricular myocardium. These behaviors can be described by solutions of reaction-diffusion equation excitable medium models. The direct comparison of such solutions with existing experimental observations is virtually impossible as there are too many factors to be taken into account, including not only the complicated dynamics of the re-entrant waves of excitation in the tissue, but also the way the appearance of these waves on the surface is modified by the inhomogeneity, anisotropy and three-dimensional nature of heart tissue. One way of indirect comparison is to compare characteristics of the complexity of the model and the real data, that are invariant under these modifications of the signal. Karhunen-Loeve decomposition is a standard tool for evaluating the complexity of multidimensional signals. A comparison of the separate and conjoint complexities of the signals on the opposite sides of the preparation can be considered as an indicator how much three-dimensional effects are essential in the preparation behavior. (c) 2001 American Institute of Physics.

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.

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.

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.

Velocity and stability of solitary planar travelling wave solutions of intracellular [Ca]2+.

Normal cardiac muscle contraction occurs in response to a rapid rise followed by a slower decay in intracellular calcium concentration. When cardiac muscle cells are loaded with calcium, an intracellular store releases calcium into the cytosol by the process of calcium-induced calcium release (CICR). This release contributes to the rise in intracellular calcium which in turn triggers contraction. We use two qualitative piecewise linear reaction-diffusion models of this behaviour to investigate the speed, stability and waveform of plane waves using singular perturbation techniques.

Effects of shear flows on nonlinear waves in excitable media.

If an excitable medium is moving with relative shear, the waves of excitation may be broken by the motion. We consider such breaks for the case of a constant linear shear flow. The mechanisms and conditions for the breaking of solitary waves and wavetrains are essentially different: the solitary waves require the velocity gradient to exceed a certain threshold, whilst the breaking of repetitive wavetrains happens for arbitrarily small velocity gradients. Since broken waves evolve into new spiral wave sources, this leads to spatio-temporal irregularity.

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.