Luo CH, Rudy Y. A model of the ventricular cardiac action potential. Depolarization,repolarization, and their interaction. Circ Res 1991;68(6):1501-1526

Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio 44106.
Circulation Research (Impact Factor: 11.02). 07/1991; 68(6):1501-26. DOI: 10.1161/01.RES.68.6.1501
Source: PubMed


A mathematical model of the membrane action potential of the mammalian ventricular cell is introduced. The model is based, whenever possible, on recent single-cell and single-channel data and incorporates the possibility of changing extracellular potassium concentration [K]o. The fast sodium current, INa, is characterized by fast upstroke velocity (Vmax = 400 V/sec) and slow recovery from inactivation. The time-independent potassium current, IK1, includes a negative-slope phase and displays significant crossover phenomenon as [K]o is varied. The time-dependent potassium current, IK, shows only a minimal degree of crossover. A novel potassium current that activates at plateau potentials is included in the model. The simulated action potential duplicates the experimentally observed effects of changes in [K]o on action potential duration and rest potential. Physiological simulations focus on the interaction between depolarization and repolarization (i.e., premature stimulation). Results demonstrate the importance of the slow recovery of INa in determining the response of the cell. Simulated responses to periodic stimulation include monotonic Wenckebach patterns and alternans at normal [K]o, whereas at low [K]o nonmonotonic Wenckebach periodicities, aperiodic patterns, and enhanced supernormal excitability that results in unstable responses ("chaotic activity") are observed. The results are consistent with recent experimental observations, and the model simulations relate these phenomena to the underlying ionic channel kinetics.

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    • "The dependency of these AP changes on fibroblast membrane properties were further explored by Xie et al. [26] who described such changes as a function of the two components of the F-M gap junctional current: (1) an early transient outward (í µí°¼ to )-like component and (2) a late background current component. They performed simulations using a modified version of the Luo and Rudy (LR1) model [27] and the passive fibroblast model (Section 2.1.1) and systematically modified the fibroblast membrane conductance, í µí°º f , and resting membrane potential, í µí°¸f , and observed its effects on the two components of the gap junctional current and on AP morphology during F-M coupling. "
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    ABSTRACT: The adult heart is composed of a dense network of cardiomyocytes surrounded by nonmyocytes, the most abundant of which are cardiac fibroblasts. Several cardiac diseases, such as myocardial infarction or dilated cardiomyopathy, are associated with an increased density of fibroblasts, that is, fibrosis. Fibroblasts play a significant role in the development of electrical and mechanical dysfunction of the heart; however the underlying mechanisms are only partially understood. One widely studied mechanism suggests that fibroblasts produce excess extracellular matrix, resulting in collagenous septa. These collagenous septa slow propagation, cause zig-zag conduction paths, and decouple cardiomyocytes resulting in a substrate for arrhythmia. Another emerging mechanism suggests that fibroblasts promote arrhythmogenesis through direct electrical interactions with cardiomyocytes via gap junctions. Due to the challenges of investigating fibroblast-myocyte coupling in native cardiac tissue, computational modeling and in vitro experiments have facilitated the investigation into the mechanisms underlying fibroblast-mediated changes in cardiomyocyte action potential morphology, conduction velocity, spontaneous excitability, and vulnerability to reentry. In this paper, we summarize the major findings of the existing computational studies investigating the implications of fibroblast-myocyte interactions in the normal and diseased heart. We then present investigations from our group into the potential role of voltage-dependent gap junctions in fibroblast-myocyte interactions.
    BioMed Research International 05/2015; 2015(5). DOI:10.1155/2015/465714 · 3.17 Impact Factor
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    • "For a classic example of a cardiac myocyte model and the accompanying equations see [11] or [12], a good example of the complexity of modern models is found in the detailed appendix to [3]. An example of a reduced cell model is given in this paper as Table I. "
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    ABSTRACT: Numerical simulation of muscle cells and tissue is an established tool in cardiac electrophysiology, where the electrical behavior of excitable heart muscle cells is commonly modeled as a stiff, non-linear system of ordinary differential equations. A common feature of this system’s right-hand side is the heavy use of computationally expensive univariate functions of the membrane potential. In this article, we investigate the performance benefits of replacing these functions with cubic spline approximations in an automated model simplification process. Clear performance gains were found when evaluating the right-hand side in isolation and when performing multi-cellular simulations using a simple forward Euler method. Single cell simulations run with an adaptive method saw smaller gains due to a higher overhead from the solver. A parallel multi-cellular simulation was also investigated, but the overhead of the implementation overshadowed the evaluation time of the right-hand side.
    21st International Symposium on Mathematical Theory of Networks and Systems, Groningen, The Netherlands; 07/2014
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    • "[16] [56] for recent reviews. Here we will consider the Luo−Rudy I (LR1) membrane model [21]. The conductivity tensors D i (x) and D e (x) at any point x ∈ Ω are assumed orthotropic, thus defined as "
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    ABSTRACT: The aim of this work is to compare a new uncoupled solver for the cardiac Bidomain model with a usual coupled solver. The Bidomain model describes the bioelectric activity of the cardiac tissue and consists of a system of a non-linear parabolic reaction-diffusion partial differential equation (PDE) and an elliptic linear PDE. This system models at macroscopic level the evolution of the transmembrane and extracellular electric potentials of the anisotropic cardiac tissue. The evolution equation is coupled through the non-linear reaction term with a stiff system of ordinary differential equations (ODEs), the so-called membrane model, describing the ionic currents through the cellular membrane. A novel uncoupled solver for the Bidomain system is here introduced, based on solving twice the parabolic PDE and once the elliptic PDE at each time step, and it is compared with a usual coupled solver. Three-dimensional numerical tests have been performed in order to show that the proposed uncoupled method has the same accuracy of the coupled strategy. Parallel numerical tests on structured meshes have also shown that the uncoupled technique is as scalable as the coupled one. Moreover, the conjugate gradient method preconditioned by Multilevel Hybrid Schwarz preconditioners converges faster for the linear systems deriving from the uncoupled method than from the coupled one. Finally, in all parallel numerical tests considered, the uncoupled technique proposed is always about two or three times faster than the coupled approach.
    ESAIM Mathematical Modelling and Numerical Analysis 07/2013; 47(4). DOI:10.1051/m2an/2012055 · 1.64 Impact Factor
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