Leon H Charney Division of Cardiology, New York University School of Medicine, New York, NY 10016, USA.
Proc Natl Acad Sci U S A. 2010 Aug 17;107(33):14603-8. doi: 10.1073/pnas.1008443107. Epub 2010 Jul 29.
We present a multiscale model and an adaptive numerical scheme for simulating cardiac action potential propagation along a linear strand of heart muscle cells. This model couples macroscale partial differential equations posed over the tissue to microscale equations posed over discrete cellular geometry. The microscopic equations are used only near action potential wave fronts, and the macroscopic equations are used everywhere else. We study the effects of gap-junctional and ephaptic coupling on conduction in the multiscale model and its fully macroscale and fully microscale analogues. Our simulations reveal that the adaptive multiscale model accurately reproduces the action potential wave forms and wave speeds of the fully microscale model. They also demonstrate that, at low gap-junctional conductivities, the accuracy of fully macroscale simulations is sensitive to numerical grid spacing. Moreover, adaptive multiscale simulations capture the effect of ephaptic coupling, whereas fully macroscale simulations do not. We propose two ways of generalizing our multiscale model to higher dimensions, and we argue that such generalizations may be necessary to obtain accurate three-dimensional simulations of cardiac conduction in certain pathophysiological parameter regimes.
我们提出了一种多尺度模型和自适应数值方案，用于模拟线性心肌细胞链上的心脏动作电位传播。该模型将组织上的宏观偏微分方程与离散细胞几何结构上的微观方程耦合在一起。微观方程仅在动作电位波前附近使用，而宏观方程则在其他所有地方使用。我们研究了缝隙连接和电突触耦合对多尺度模型及其完全宏观和完全微观类似物中的传导的影响。我们的模拟表明，自适应多尺度模型准确地再现了完全微观模型的动作电位波形和波速。它们还表明，在低缝隙连接导率下，完全宏观模拟的准确性对数值网格间距敏感。此外，自适应多尺度模拟捕捉到了电突触耦合的影响，而完全宏观模拟则没有。我们提出了两种将我们的多尺度模型推广到更高维度的方法，并认为在某些病理生理参数范围内获得准确的三维心脏传导模拟可能需要这样的推广。
