Dipartimento di Biologia Evolutiva e Funzionale - Sezione Fisiologia, Università degli Studi di Parma, V.le G.P. Usberti 11 A, 43124 Parma, Italy.
Math Biosci. 2011 Oct;233(2):98-110. doi: 10.1016/j.mbs.2011.06.008. Epub 2011 Jul 12.
The number of mathematical models of cardiac cellular excitability is rapidly growing, and compact graphical representations of their properties can make new acquisitions available for a broader range of scientists in cardiac field. Particularly, the intrinsic over-determination of the model equations systems when fitted only to action potential (AP) waveform and the fact that they are frequently tuned on data covering only a relatively narrow range of dynamic conditions, often lead modellers to compare very similar AP profiles, which underlie though quite different excitable properties. In this study I discuss a novel compact 3D representation of the cardiac cellular AP, where the third dimension represents the instantaneous current-voltage profile of the membrane, measured as repolarization proceeds. Measurements of this type have been used previously for in vivo experiments, and are adopted here iteratively at a very high time, voltage, current-resolution on (i) the same human ventricular model, endowed with two different parameters sets which generate the same AP waveform, and on (ii) three different models of the same human ventricular cell type. In these 3D representations, the AP waveforms lie at the intersection between instantaneous time-voltage-current surfaces and the zero-current plane. Different surfaces can share the same intersection and therefore the same AP; in these cases, the morphology of the current surface provides a compact view of important differences within corresponding repolarization dynamics. Refractory period, supernormal excitability window, and extent of repolarization reserve can be visualized at once. Two pivotal dynamical properties can be precisely assessed, i.e. all-or-nothing repolarization window and membrane resistance during recovery. I discuss differences in these properties among the membranes under study, and show relevant implications for cardiac cellular repolarization.
心脏细胞兴奋的数学模型数量正在迅速增加，而这些模型特性的紧凑图形表示可以使更多的心脏领域的科学家能够获得新的信息。特别是，当仅根据动作电位（AP）波形拟合模型方程系统时，会出现内在的过度决定，并且这些模型经常根据仅涵盖相对较窄动态条件范围的数据进行调整，这通常导致建模者比较非常相似的 AP 轮廓，尽管这些 AP 轮廓具有截然不同的兴奋特性。在本研究中，我讨论了一种新颖的心脏细胞 AP 的紧凑 3D 表示形式，其中第三维表示膜的瞬时电流-电压曲线，在复极过程中进行测量。这种类型的测量以前曾用于体内实验，并在这里以非常高的时间、电压、电流分辨率在（i）同一个具有两个不同参数集的人类心室模型上进行迭代，这两个参数集生成相同的 AP 波形，以及在（ii）三个不同的相同人类心室细胞类型的模型上进行迭代。在这些 3D 表示中，AP 波形位于瞬时时-电压-电流曲面和零电流平面的交点处。不同的曲面可以共享相同的交点，因此具有相同的 AP；在这些情况下，电流曲面的形态提供了对应复极动力学中重要差异的紧凑视图。可以同时可视化不应期、超常兴奋性窗口和复极储备程度。可以精确评估两个关键的动力学特性，即全或无复极窗口和恢复期间的膜电阻。我讨论了研究中这些膜之间这些特性的差异，并展示了它们对心脏细胞复极的相关影响。
