Dokos S, Celler B G, Lovell N H
Biomedical Systems Laboratory, School of Electrical Engineering, University of New South Wales, Australia.
Ann Biomed Eng. 1993 Jul-Aug;21(4):321-35. doi: 10.1007/BF02368625.
We present a new mathematical model for vagal control of rabbit sinoatrial (SA) node electrical activity based on the DiFrancesco-Noble equations. The original equations were found to be unstable, resulting in progressive cycle by cycle depletion or accumulation of ions in intra- and extracellular compartments. This problem was overcome by modifying the maximum Na-K pump current and the time constant for uptake of intracellular calcium. We also included a formulation for the acetylcholine (ACh)-activated potassium current which was consistent with experimental data. This formulation was based on kinetics first proposed by Osterrieder and later modified by Yanagihara. The resulting model exhibits cycle-cycle ionic stability, and includes an ACh-activated potassium current which accurately reproduces experimentally observed effects of vagal stimulation on both the membrane potential and its time-derivative. Simulations were performed for both brief-burst and prolonged vagal stimulation using simplified square wave profiles for the concentration of ACh in the synaptic cleft space. This protocol permits the isolation of cardiac period dynamics caused by changes in membrane potential and intra- and extracellular ionic concentrations from those caused by other mechanisms including the dynamics of ACh release, diffusion, hydrolysis and washout. Simulation results for the effects of brief-burst single cycle stimulation on the cardiac period agree closely with experimental data reported in the literature, accurately reproducing changes in membrane potential and the phasic dependency of the response to the position of vagal stimulus bursts within the cycle. Simulation of the effects of prolonged vagal stimulation accurately reproduced the steady-state characteristics of heart period response, but did not yield the complex multimodal dynamics of the recovery phase, or the pronounced post vagal tachycardia observed experimentally at the termination of the stimulus. Our results show that the major chronotropic effects of vagal stimulation on the SA cell membrane can be explained in terms of the ACh-activated potassium current. The effects of this membrane current however are generally fast acting and cannot contribute to any long lasting dynamics of the cardiac period response. The modified DiFrancesco-Noble model presented in this article provides a valuable theoretical tool for further analysis of the dynamics of vagal control of the cardiac pacemaker.
我们基于迪弗朗切斯科 - 诺布尔方程提出了一种用于迷走神经控制家兔窦房（SA）结电活动的新数学模型。发现原始方程不稳定，导致细胞内和细胞外隔室中离子逐周期逐渐耗尽或积累。通过修改最大钠 - 钾泵电流和细胞内钙摄取的时间常数克服了这个问题。我们还纳入了一种与实验数据一致的乙酰胆碱（ACh）激活钾电流的公式。该公式基于奥斯特里德最初提出并由柳原后来修改的动力学。所得模型表现出逐周期离子稳定性，并包括一种ACh激活钾电流，该电流准确再现了迷走神经刺激对膜电位及其时间导数的实验观察到的影响。使用突触间隙空间中ACh浓度的简化方波轮廓对短暂爆发和长时间迷走神经刺激进行了模拟。该方案允许将由膜电位变化以及细胞内和细胞外离子浓度变化引起的心脏周期动力学与由其他机制（包括ACh释放、扩散、水解和清除的动力学）引起的动力学分离。短暂爆发单周期刺激对心脏周期影响的模拟结果与文献中报道的实验数据密切一致，准确再现了膜电位变化以及反应对周期内迷走神经刺激爆发位置的相位依赖性。长时间迷走神经刺激影响的模拟准确再现了心脏周期反应的稳态特征，但未产生恢复阶段复杂的多峰动力学，也未产生刺激终止时实验观察到的明显迷走神经后心动过速。我们的结果表明，迷走神经刺激对SA细胞膜的主要变时效应可以用ACh激活钾电流来解释。然而，这种膜电流的效应通常作用迅速，并且对心脏周期反应的任何持久动力学没有贡献。本文提出的修改后的迪弗朗切斯科 - 诺布尔模型为进一步分析心脏起搏器迷走神经控制的动力学提供了有价值的理论工具。
