An evaluation of some assumptions underpinning the bidomain equations of electrophysiology.

IF 0.8 4区 数学 Q4 BIOLOGY
J. Whiteley
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引用次数: 2

Abstract

Tissue level cardiac electrophysiology is usually modelled by the bidomain equations, or the monodomain simplification of the bidomain equations. One assumption made when deriving the bidomain equations is that both the intracellular and extracellular spaces are in electrical equilibrium. This assumption neglects the disturbance of this equilibrium in thin regions close to the cell membrane known as Debye layers. We first demonstrate that the governing equations at the cell, or microscale, level may be adapted to take account of these Debye layers with little additional complexity, provided the permittivity within the Debye layers satisfies certain conditions that are believed to be satisfied for biological cells. We then homogenize the microscale equations using a technique developed for an almost periodic microstructure. Cardiac tissue is usually modelled as sheets of cardiac fibres stacked on top of one another. A common assumption is that an orthogonal coordinate system can be defined at each point of cardiac tissue, where the first axis is in the fibre direction, the second axis is orthogonal to the first axis but lies in the sheet of cardiac fibres and the third axis is orthogonal to the cardiac sheet. It is assumed further that both the intracellular and extracellular conductivity tensors are diagonal with respect to these axes and that the diagonal entries of these tensors are constant across the whole tissue. Using the homogenization technique we find that this assumption is usually valid for cardiac tissue, but highlight situations where the assumption may not be valid.
对支持电生理学双域方程的一些假设的评价。
组织水平的心脏电生理通常由比都域方程或比都域方程的单域简化来建模。推导双域方程时的一个假设是细胞内和细胞外空间都处于电平衡状态。这种假设忽略了在靠近细胞膜的称为德拜层的薄区域中这种平衡的干扰。我们首先证明,如果德拜层内的介电常数满足生物细胞所满足的某些条件,那么在细胞或微尺度水平上的控制方程可以适应于考虑这些德拜层,而没有额外的复杂性。然后,我们使用为几乎周期性微观结构开发的技术使微尺度方程均匀化。心脏组织通常被建模为一层一层堆叠在一起的心脏纤维。一个常见的假设是,在心脏组织的每个点上都可以定义一个正交坐标系,其中第一个轴在纤维方向上,第二个轴与第一个轴正交,但位于心脏纤维片上,第三个轴与心脏片正交。进一步假设细胞内和细胞外的导电性张量相对于这些轴是对角线的,并且这些张量的对角线分量在整个组织中是恒定的。使用均质化技术,我们发现这个假设通常是有效的心脏组织,但突出的情况下,假设可能是无效的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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