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An evaluation of some assumptions underpinning the bidomain equations of electrophysiology.
Mathematical Medicine and Biology ( IF 0.8 ) Pub Date : 2019-11-01 , DOI: 10.1093/imammb/dqz014
Jonathan P Whiteley 1
Affiliation  

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.

中文翻译:

对电生理双域方程基础的一些假设的评估。

组织水平的心脏电生理学通常通过双畴方程或双畴方程的单畴简化来建模。推导双畴方程时做出的一种假设是细胞内和细胞外空间都处于电平衡。该假设忽略了在靠近细胞膜的较薄区域(称为德拜层)中这种平衡的干扰。我们首先证明,在细胞或微米级的控制方程式可以适用于考虑这些Debye层,而几乎没有额外的复杂性,只要Debye层内的介电常数满足某些被认为对生物细胞满足的条件即可。然后,我们使用为几乎周期性的微观结构开发的技术对微观方程组进行均化。心脏组织通常被建模为彼此堆叠的心脏纤维片。一个常见的假设是,可以在心脏组织的每个点定义正交坐标系,其中第一轴在纤维方向上,第二轴与第一轴正交,但在心脏纤维片中,第三轴位于与心脏片正交。进一步假设细胞内和细胞外电导率张量相对于这些轴是对角线的,并且这些张量的对角线入口在整个组织中是恒定的。使用均质化技术,我们发现此假设通常对心脏组织有效,但突出显示了该假设可能无效的情况。一个常见的假设是,可以在心脏组织的每个点定义正交坐标系,其中第一轴在纤维方向上,第二轴与第一轴正交,但在心脏纤维片中,第三轴位于与心脏片正交。进一步假设细胞内和细胞外电导率张量相对于这些轴是对角线的,并且这些张量的对角线入口在整个组织中是恒定的。使用均质化技术,我们发现此假设通常对心脏组织有效,但突出显示了该假设可能无效的情况。一个常见的假设是,可以在心脏组织的每个点定义正交坐标系,其中第一轴在纤维方向上,第二轴与第一轴正交,但在心脏纤维片中,第三轴位于与心脏片正交。进一步假设细胞内和细胞外电导率张量相对于这些轴是对角线的,并且这些张量的对角线入口在整个组织中是恒定的。使用均质化技术,我们发现此假设通常对心脏组织有效,但突出显示了该假设可能无效的情况。第二轴线正交于第一轴线但位于心脏纤维片中,而第三轴线正交于心脏片。进一步假设细胞内和细胞外电导率张量相对于这些轴是对角线的,并且这些张量的对角线入口在整个组织中是恒定的。使用均质化技术,我们发现此假设通常对心脏组织有效,但突出显示了该假设可能无效的情况。第二轴线正交于第一轴线但位于心脏纤维片中,而第三轴线正交于心脏片。进一步假设细胞内和细胞外电导率张量相对于这些轴是对角线的,并且这些张量的对角线入口在整个组织中是恒定的。使用均质化技术,我们发现此假设通常对心脏组织有效,但突出显示了该假设可能无效的情况。
更新日期:2019-11-01
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