College of Computer Science and Technology, Harbin Engineering University, Harbin 150001, China.
School of Computer Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia.
Biomed Res Int. 2020 Jun 25;2020:3608015. doi: 10.1155/2020/3608015. eCollection 2020.
The purpose of the paper is to derive a formula to describe the quantitative relationship among the number of the pacing cells required (NPR), the dimension , and the diffusion coefficient (electrical coupling or gap junction ). The relationship between NPR and has been investigated in different dimensions, respectively. That is, for each fixed , there is a formula to describe the relationship between NPR and ; and three formulas are required for the three dimensions. However, there is not a universal expression to describe the relationship among NPR, , and together. In the manuscript, surveying and investigating the basic law among the existed data, we speculate the preliminary formula of the relationship among the NPR, , and ; and then, employing the cftool in MATLAB, the explicit formulas are derived for different cases. In addition, the goodness of fit ( ) is computed to evaluate the fitting of the formulas. Moreover, the 1D and 2D ventricular tissue models containing biological pacemakers are developed to derive more data to validate the formula. The results suggest that the relationship among the NPR, , and the () could be described by a universal formula, where the NPR scales with the (the dimension) power of the product of the square root of () and a constant which is dependent on the strength of the pacing cells and so on.
本文旨在推导出一个公式，以描述所需起搏细胞数量 (NPR)、维度 和扩散系数 (电耦合或缝隙连接) 之间的定量关系。已经分别在不同的维度上研究了 NPR 和 之间的关系。也就是说，对于每个固定的 ，都有一个公式来描述 NPR 和 之间的关系；而对于三个维度，则需要三个公式。然而，没有一个通用的表达式可以描述 NPR、和 之间的关系。在本文中，通过对现有数据的调查和研究，我们推测了 NPR、和 之间关系的初步公式；然后，使用 MATLAB 中的 cftool，推导出了不同情况下的显式公式。此外，还计算了拟合优度 ( ) 来评估公式的拟合程度。此外，还开发了包含生物起搏器的 1D 和 2D 心室组织模型，以得出更多数据来验证公式。结果表明，NPR、和 之间的关系可以用一个通用公式来描述，其中 NPR 与 的乘积的平方根的 次方成正比，而常数 则取决于起搏细胞的强度等因素。
