Asymptotic model of electroporation
Asymptotic model of electroporation
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DOI：
10.1103/physreve.59.3471
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发表时间：
1999-03-01
影响因子：
2.4
通讯作者：
Krassowska, W
中科院分区：
文献类型：
--
作者：
Neu, JC;Krassowska, W
电穿孔由偏微分方程式(PDE)数学描述，该方程控制作为其半径和时间的函数的孔的分布。这种偏微分方程没有解析解，而且由于存在不同的空间和时间尺度，数值解很难获得。这些困难限制了PDE的应用仅限于具有均匀极化的膜的实验装置。这项研究严格地、渐近地将偏微分方程简化为描述孔隙密度N(T)动态的常微分方程式(ODE)。给定N(T)，气孔在其半径空间中的精确分布可以通过渐近近似来确定。因此，渐近颂歌代表了偏微分方程中包含的大部分现象学。它很容易数值求解，这使得它成为研究具有显著空间依赖性的实验装置中的电穿孔的有力工具，例如外部电场中的小泡或细胞。[S1063-651X(99)10603-2]。
Electroporation is described mathematically by a partial differential equation (PDE) that governs the distribution of pores as a function of their radius and time. This PDE does not have an analytical solution and, because of the presence of disparate spatial and temporal scales, numerical solutions are hard to obtain. These difficulties limit the application of the PDE only to experimental setups with a uniformly polarized membrane. This study performs a rigorous, asymptotic reduction of the PDE to an ordinary differential equation (ODE) that describes the dynamics of the pore density N(t). Given N(t), the precise distribution of the pores in the space of their radii can be determined by an asymptotic approximation. Thus, the asymptotic ODE represents most of the phenomenology contained in the PDE. It is easy to solve numerically, which makes it a powerful tool to study electroporation in experimental setups with significant spatial dependence, such vesicles or cells in an external field. [S1063-651X(99)10603-2].