Vinet A, Roberge F A
Institute of Biomedical Engineering, Ecole Polytechnique, Université de Montéal, Canada.
J Theor Biol. 1994 Sep 21;170(2):201-14. doi: 10.1006/jtbi.1994.1179.
An iterative difference equation (DE) model based on a small set of functional characteristics derived from the modified Beeler-Reuter ionic model (MBR) of a space-clamped membrane of the ventricular myocyte was studied. These characteristics were expressed as functions of a common independent variable, the diastolic interval (DIA), to define threshold, Thr (DIA), latency, L (DIA), action potential duration, APD (DIA), and delayed excitability recovery, R(DIA), owing to a sub-threshold response. Memory effects, in the form of a dependence on the immediately proceeding action potential waveform, were not included in the current DE formulation. The entrainment bifurcation structure of the DE model was found to be very sensitive to the form of APD (DIA) but, with a suitable choice of parameter values, the model reproduced the successive stable rhythms of synchronization (1:1-->2:2-->2:1-->4:2) found in the MBR model with decreasing basic cycle lengths. The fine details of the transition between stable rhythms were seen to depend on the specific forms of APD (DIA) and R (DIA) chosen, and on the initial conditions at the onset of pacing. The minor deficiencies of the DE R (DIA) chosen, and on the initial conditions at the onset of pacing. The minor deficiencies of the DE model are attributable to the memory-free APD (DIA) used, and to uncertainties in the description of the MBR model behavior owing to the slow convergence toward a given stable rhythm. Overall, the iterative DE formulation based on the transient properties of an ionic model, as derived by premature stimulation, it is also adequate to describe the stable entrainment patterns of the ionic model.
研究了一种基于从心室肌细胞空间钳制膜的改良比勒-罗伊特离子模型（MBR）导出的一小组功能特性的迭代差分方程（DE）模型。这些特性被表示为一个共同自变量舒张期（DIA）的函数，以定义阈值Thr（DIA）、潜伏期L（DIA）、动作电位持续时间APD（DIA）以及由于阈下反应导致的延迟兴奋性恢复R（DIA）。当前的DE公式中不包括以对紧接在前的动作电位波形的依赖性形式存在的记忆效应。发现DE模型的夹带分岔结构对APD（DIA）的形式非常敏感，但通过适当选择参数值，该模型再现了在MBR模型中随着基本周期长度减小而发现的连续稳定同步节律（1:1→2:2→2:1→4:2）。稳定节律之间转变的精细细节被认为取决于所选择的APD（DIA）和R（DIA）的具体形式，以及起搏开始时的初始条件。DE模型的微小缺陷可归因于所使用的无记忆APD（DIA），以及由于向给定稳定节律的缓慢收敛而导致的MBR模型行为描述中的不确定性。总体而言，基于过早刺激导出的离子模型瞬态特性的迭代DE公式也足以描述离子模型的稳定夹带模式。
