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首页> 外文期刊>Journal of Mathematical Biology >A two layers monodomain model of cardiac electrophysiology of the atria
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A two layers monodomain model of cardiac electrophysiology of the atria

机译：心房心脏电生理的两层单域模型

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摘要

Numerical simulations of the cardiac electrophysiology in the atria are often based on the standard bidomain or monodomain equations stated on a two-dimensional manifold. These simulations take advantage of the thinness of the atrial tissue, and their computational cost is reduced, as compared to three-dimensional simulations. However, these models do not take into account the heterogeneities located in the thickness of the tissue, like discontinuities of the fiber direction, although they can be a substrate for atrial arrhythmia (Hocini et al., Circulation 105(20):2442-2448, 2002; Ho et al., Cardiovasc Res 54(2):325-336, 2002; Nattel, Nature 415(6868):219-226, 2002). We investigate a two-dimensional model with two coupled, superimposed layers that allows to introduce three-dimensional heterogeneities, but retains a reasonable computational cost. We introduce the mathematical derivation of this model and error estimates with respect to the three-dimensional model. We give some numerical illustrations of its interest: we numerically show its convergence for vanishing thickness, introduce an optimization process of the coupling coefficient and assess its validity on physiologically relevant geometries. Our model would be an efficient tool to test the influence of three-dimensional fiber direction heterogeneities in reentries or atrial arrhythmia without using three-dimensional models.
机译：心房中心脏电生理的数值模拟通常基于二维流形上规定的标准双域或单域方程。与三维模拟相比，这些模拟利用了心房组织的薄度，并降低了计算成本。然而，尽管这些模型可能是房性心律失常的基质，但这些模型并未考虑到位于组织厚度中的异质性，例如纤维方向的不连续性（Hocini等人，Circulation 105（20）：2442-2448 ，2002; Ho等，Cardiovasc Res 54（2）：325-336，2002; Nattel，Nature 415（6868）：219-226，2002）。我们研究了具有两个耦合的叠加层的二维模型，该模型允许引入三维异质性，但保留了合理的计算成本。我们介绍了该模型的数学推导以及相对于三维模型的误差估计。我们给出了一些其感兴趣的数值图示：我们以数字方式显示了其消失厚度的收敛性，介绍了耦合系数的优化过程，并评估了其在生理相关几何形状上的有效性。我们的模型将是不使用三维模型来测试三维纤维方向异质性对折返或房性心律不齐的影响的有效工具。

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