Article

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

ABSTRACT

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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    • "Therefore, many models exist to describe the action potentials (AP) of single ventricular cells. For better comparison with experimental results, these models are often developed to represent dynamics of specific mammals: For example, the well-known Luo-Rudy model[4]can be used to model guinea pig ventricular cells, while the model used by Wang and Sobie[5]describes mouse ventricular action potentials, and the one used by Sato et al.[1](first AP model, in the following referred to as the Sato model) models ventricular rabbit myocytes. However, many of these models share the feature of consisting of a great number of equations and parameters. "
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    ABSTRACT: The dynamics of a detailed ionic cardiac cell model proposed by Sato et al. [Sato D, et al. Synchronization of chaotic early afterdepolarizations in the genesis of cardiac arrhytmias. PNAS 2009;106(9):2983–2988.] is investigated in terms of periodic and chaotic action potentials, bifurcation scenarios, and coexistence of attractors. Starting from the model’s standard parameter values bifurcation diagrams are computed to evaluate the model’s robustness with respect to (small) parameter changes. While for some parameters the dynamics turns out to be practically independent from their values, even minor changes of other parameters have a very strong impact and cause qualitative changes due to bifurcations or transitions to coexisting attractors. Implications of this lack of robustness are discussed.
    Full-text · Article · Jan 2016 · Communications in Nonlinear Science and Numerical Simulation
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    • "In most studies, SNC is quantified using the so-called standard S1S2 protocol under the conditions of reduced extracellular potassium concentration (Chialvo et al., 1990; Davidenko et al., 1990; Luo and Rudy, 1991; de Lange and Kucera, 2010). In the S1S2 protocol, the tissue is paced for N beats at constant cycle length (equal to S1) followed by a stimulus (S2) delivered at progressively shorter or longer intervals (i.e., the interval between the last S1 stimulus and S2 is varied and then the sequence of N stimuli at S1 interval is repeated). "
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    ABSTRACT: Spatially discordant alternans (DA) of action potential durations (APD) is thought to be more pro-arrhythmic than concordant alternans. Super normal conduction (SNC) has been reported to suppress formation of DA. An increase in conduction velocity (CV) as activation rate increases, i.e., a negative CV restitution, is widely considered as hallmark of SNC. Our aim in this study is to show that it is not an increase in CV for faster rates that prevents formation of DA, rather, it is the ratio of the CV for the short relative to the long activation that is critical in DA suppression. To illustrate this subtlety, we simulated this phenomenon using two approaches; (1) by using the standard, i.e., S1S2 protocol to quantify restitution and disabling the slow inactivation gate j of the sodium current (INa), and (2) by using the dynamic, i.e., S1S1 protocol for quantification of restitution and increasing INa at different cycle lengths (CL). Even though both approaches produced similar CV restitution curves, DA was suppressed only during the first approach, where the CV of the short of the long-short action potential (AP) pattern was selectively increased. These results show that negative CV restitution, which is considered characteristic of SNC, per se, is not causal in suppressing DA, rather, the critical factor is a change in the ratio of the velocities of the short and the long APs.
    Full-text · Article · Jan 2016 · Frontiers in Physiology
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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.
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