Marc Courtemanche

Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model

The mechanisms underlying many important properties of the human atrial action potential (AP) are poorly understood. Using specific formulations of the K+, Na+, and Ca2+ currents based on data recorded from human atrial myocytes, along with representations of pump, exchange, and background currents, we developed a mathematical model of the AP. The model AP resembles APs recorded from human atrial samples and responds to rate changes, L-type Ca2+ current blockade, Na+/Ca2+ exchanger inhibition, and variations in transient outward current amplitude in a fashion similar to experimental recordings. Rate-dependent adaptation of AP duration, an important determinant of susceptibility to atrial fibrillation, was attributable to incomplete L-type Ca2+ current recovery from inactivation and incomplete delayed rectifier current deactivation at rapid rates. Experimental observations of variable AP morphology could be accounted for by changes in transient outward current density, as suggested experimentally. We conclude that this mathematical model of the human atrial AP reproduces a variety of observed AP behaviors and provides insights into the mechanisms of clinically important AP properties.

Ionic targets for drug therapy and atrial fibrillation-induced electrical remodeling: insights from a mathematical model.

UNLABELLED Recent advances in molecular electrophysiology have made possible the development of more selective ion channel blockers for therapeutic use. However, more information is needed about the effects of blocking specific channels on repolarization in normal human atrium and in atrial cells of patients with atrial fibrillation (AF). AF-induced electrical remodeling is associated with reductions in transient outward current (Ito), ultrarapid delayed rectifier current (IKur), and L-type calcium current (ICa,L). Direct evaluation of the results of ion channel depression is limited by the nonspecificity of the available pharmacological probes. OBJECTIVES Using a mathematical model of the human atrial action potential (AP), we aimed to: (1) evaluate the role of ionic abnormalities in producing AP changes characteristic of AF in humans and (2) explore the effects of specific channel blockade on the normal and AF-modified AP (AFAP). METHODS We used our previously developed mathematical model of the normal human atrial AP (NAP) based on directly measured currents. We constructed a model of the AFAP by incorporating experimentally-measured reductions in Ito (50%), IKur (50%), and ICa,L (70%) current densities observed in AF. RESULTS The AFAP exhibits the reductions in AP duration (APD) and rate-adaption typical of AF. The reduction in ICa,L alone can account for most of the morphological features of the AFAP. Inhibition of Ito by 90% leads to a reduction in APD measured at -60 mV in both the NAP and AFAP. Inhibition of the rapid component of the delayed rectifier (IKr) by 90% slows terminal repolarization of the NAP and AFAP and increases APD by 38% and 34%, respectively. Inhibition of IKur by 90% slows early repolarization and increases plateau height, activating additional IK and causing no net change in APD at 1 Hz in the NAP. In the presence of AF-induced ionic modifications, IKur inhibition increases APD by 12%. Combining IKur and IKr inhibition under both normal and AF conditions synergistically increases APD. In the NAP, altering the model parameters to reproduce other typical measured AP morphologies can significantly alter the response to K(+)-channel inhibition. CONCLUSIONS (1) The described abnormalities in Ito, IKur and ICa,L in AF patients can account for the effects of AF on human AP properties; (2) AP prolongation by IKur block is limited by increases in plateau height that activate more IK; (3) Blockers of IKur may be more effective in prolonging APD in patients with AF; 4) Inhibition of both IKur and IKr produces supra-additive effects on APD. These observations illustrate the importance of secondary current alterations in the response of the AP to single channel blockade, and have potentially important implications for the development of improved antiarrhythmic drug therapy for AF.

Complex spiral wave dynamics in a spatially distributed ionic model of cardiac electrical activity.

This study presents computations and analysis of the dynamics of reentrant spiral waves in a realistic model of cardiac electrical activity, incorporating the Beeler-Reuter equations into a two-dimensional cable model. In this medium, spiral waves spontaneously break up, but may be stabilized by shortening the excitation pulse duration through an acceleration of the dynamics of the calcium current. We describe the breakup of reentrant waves based on the presence of slow recovery fronts within the medium. This concept is introduced using examples from pulse circulation around a ring and extended to two-dimensional propagation. We define properties of the restitution and dispersion relations that are associated with slow recovery fronts and promote spiral breakup. The role of slow recovery fronts is illustrated with concrete examples from numerical simulations. (c) 1996 American Institute of Physics.

Method for Simultaneous Epicardial and Endocardial Mapping of In Vivo Canine Heart: Application to Atrial Conduction Properties and Arrhythmia Mechanisms

Endocardial/Epicardial Mapping of AF. Introduction: It has been suggested that the three‐dimensional structure of the atria may be crucial in arrhythmogenesis; however, previous in vivo atrial activation mapping studies have been limited to either endocardial or epicardial approaches.

A delay equation representation of pulse circulation on a ring in excitable media

This paper develops a theory for pulse circulation on a ring in a continuous excitable medium. Simulations of a partial differential equation (PDE) modeling propagation of electrical pulses on a one-dimensional ring of cardiac tissue are presented. The dynamics of the circulating pulse in this excitable medium are reduced to a single integral-delay equation. Stability conditions for steady circulation are obtained, and estimates are derived for the wavelength, growth rate, and asymptotic amplitude of oscillating solutions near the transition from steady rotation to oscillatory pulse dynamics. The analytical results agree with simulations of the delay equation and the PDE model and uncover previously uncharted solutions of the PDE equations.

Stable three-dimensional action potential circulation in the FitzHugh-Nagumo model

Abstract Excitable media generally support vortex rings of self-excitation. Depending on the exact nature of the medium, such a ring may expand or contract, possibly to a stable radius. We describe one such case encountered during numerical experiments on a simple model of electrophysiological excitability in nerve and cardiac muscle membrane. The rings rate of shrinkage depends parabolically on curvature and on proximity to other rings. The vortex period also depends on curvature, so rings of different sizes compete for territory. We associate the stability of the ring with repulsive forces which we show are present between two-dimensional rotors. The observed minimal distance for repulsion agrees with the stable radius of the vortex ring.

A circle map in a human heart

Abstract A circle is divided into two regions, a black one and a white one. Successive iterates of an invertible nonlinear circle map generate a symbolic string indicating whether each iterate is in the black or white region. A number of remarkable properties of the symbolic sequences are described. These properties were previously described for a linear circle map corresponding to a rigid rotation in the “gaps and steps” problem. These results have direct application to a cardiac arrhythmia, parasystole, that results from the competition between two pacemakers in the heart, one in the sinus mode and the other in the ventricles. The theoretical results are directly applicable to a clinical case of a young man who had frequent extra heartbeats.

State‐dependent barium block of wild‐type and inactivation‐deficient HERG channels in Xenopus oocytes

1 The effects of Ba2+ on current resulting from the heterologous expression of the human ether‐à‐go‐go related gene (HERG) (IHERG) was studied with two‐electrode voltage clamp techniques in Xenopus oocytes. 2 Ba2+ produced time‐ and voltage‐dependent block of IHERG. Significant inhibition was seen at concentrations as low as 1 μm. Inhibition was greatest at step potentials between ‐40 and 0 mV; at more positive potentials, inhibition decreased in association with time‐dependent unblocking of channels. 3 An inactivation‐attenuated mutant of HERG (S631A) was prepared and expressed in Xenopus oocytes. Ba2+ block of S631A differed from that of HERG in that extensive unblocking was no longer seen at positive potentials and the voltage dependence of step current block was greatly attenuated. 4 A mathematical model was applied to analyse quantitatively the inhibitory effects of Ba2+ on IHERG. The model suggested similar voltage‐dependent affinity of Ba2+ for the open and closed states, along with absence of binding to the inactivated state, and accounted well for Ba2+ effects on both wild‐type and S631A channels. 5 We conclude that Ba2+ potently inhibits IHERG in a characteristic state‐dependent fashion, with strong unblocking at positive potentials related to the presence of an intact C‐type inactivation mechanism.

A Clinical Study of the Dynamics of Parasystole

A mathematical model for pure parasystole ond modulated parasystole leads to a number of quantitative predictions. The predictive power of the model is examined by confronting it with data obtained from a 16‐year‐oId symptomatic male born with a ventricular septal defect that was surgically closed at 5 years of age. A diagnosis of ventricular parasystole and inducible ventricular tachycardia was made following a syncopal episode. The physiological variables required by the model to make specific predictions are the sinus and ectopic cycle lengths and the ventricular refractory period. From these three variables, a two‐dimensional parameter space is constructed consisting of the ratio of the refractory period to the sinus cycle length and the ratio of the ectopic to sinus cycle length. For any set of parameters, predictions are made concerning the number of sinus beats between ectopic beats. The different behaviors exhibited in the electrocardiographic (ECG) data agree with theoretical predictions.

Wave propagation and curvature effects in a model of excitable media

Abstract This paper presents a theory of planar and curved front propagation in a simple model of excitable media based on a diffusion mechanism. It uses the diffusion coefficient along with space and time constants to model propagation. The model allows for analytical computation of planar wave speed as well as curvature relations (speed c vs curvature K of front) in the continuum limit, including a determination of the critical curvature at which propagation fails, Kcr. It is shown that the model exhibits a lower bound for the propagation speed related to the space and time constants, and compute unstable solutions in the planar and curved wave cases. The theoretical results are compared with numerical simulations of a discrete-space/continuous-time version of the model and with similar results in reaction-diffusion equations.