Simula Research Laboratory, Center for Biomedical Computing, Lysaker 1325, Norway.
Math Biosci. 2011 Apr;230(2):79-86. doi: 10.1016/j.mbs.2011.01.004. Epub 2011 Feb 4.
We consider mathematical models of a collection of cardiomyocytes (myocardial tissue) coupled to a varying number of fibroblasts. Our aim is to understand how conductivity (δ) and fibroblast density (η) affect the stability of the collection. We provide mathematical and computational arguments indicating that there is a region of instability in the η-δ space. Mathematical arguments, based on a simplified model of the coupled myocyte-fibroblast system, show that for certain parameter choices, a stationary solution cannot exist. Numerical experiments (1D,2D) are based on a recently developed model of electro-chemical coupling between a human atrial myocyte and a number of associated atrial fibroblasts. The numerical experiments demonstrate that there is a region of instability of the form observed in the simplified model analysis.
我们考虑了与数量不定的成纤维细胞偶联的心肌细胞（心肌组织）的数学模型。我们的目的是了解电导率（δ）和成纤维细胞密度（η）如何影响集合的稳定性。我们提供了数学和计算上的论据，表明在η-δ空间中有一个不稳定区域。基于偶联心肌细胞-成纤维细胞系统的简化模型的数学论证表明，对于某些参数选择，不存在稳定解。数值实验（1D，2D）基于最近开发的人类心房肌细胞与多个相关的心房成纤维细胞之间的电化学反应耦合模型。数值实验表明，存在一种形式的不稳定性区域，与简化模型分析中观察到的形式相同。
