﻿ 高压输电线路对细胞膜一侧离子浓度影响分析 Modulation of Ion Concentration of Isolate Cell Exposed to the Electric Field of High-Voltage Transmission Line

Biophysics
Vol.06 No.03(2018), Article ID:26553,7 pages
10.12677/BIPHY.2018.63004

Modulation of Ion Concentration of Isolate Cell Exposed to the Electric Field of High-Voltage Transmission Line

Xiaodi Zhang, Qing Ma, Yongjun Zhou, Hui Zhang*

College of Physics & Electronic Engineering, Xianyang Normal University, Xianyang Shaanxi

Received: Jul. 26th, 2018; accepted: Aug. 16th, 2018; published: Aug. 23rd, 2018

ABSTRACT

The bio-effect of the high-voltage transmission line is one of the hot issues in the study of biological electromagnetics. In this paper, the single cell model and the calculation of the electric field of the high-voltage transmission line with charge simulation method are given. And based on the Nernst formula and the Boltzmann formula, the relative change rate of the ion concentration on the cell surface and its numerical solution are analyzed. The result shows that the higher of the high-voltage transmission line to ground, the smaller the electric field near by the transmission line. The positions of the maximum value and the minimum of the relative change rate of the ion concentration change with the distance change to the under the transmission line. The high-voltage transmission line will produce the bio-effect.

Keywords:High-Voltage Transmission Line, Electric Field Intensity, Ion Concentration, Cell Membrane

1. 引言

2. 理论模型

2.1. 单细胞模型

2.2. 高压输电线产生的电场

$\left[\begin{array}{c}{U}_{1}\\ {U}_{2}\\ ⋮\\ {U}_{n}\end{array}\right]=\left[\begin{array}{cccc}{\lambda }_{11}& {\lambda }_{12}& \cdots & {\lambda }_{1n}\\ {\lambda }_{21}& {\lambda }_{22}& \cdots & {\lambda }_{2n}\\ ⋮& ⋮& & ⋮\\ {\lambda }_{n1}& {\lambda }_{n2}& \cdots & {\lambda }_{nn}\end{array}\right]\left[\begin{array}{c}{Q}_{1}\\ {Q}_{2}\\ ⋮\\ {Q}_{n}\end{array}\right]$ (1)

${\lambda }_{ii}=\frac{1}{2\text{π}{\epsilon }_{0}}\mathrm{ln}\frac{2{h}_{i}}{{R}_{i}}$${\lambda }_{ij}=\frac{1}{2\text{π}{\epsilon }_{0}}\mathrm{ln}\frac{2{{l}^{\prime }}_{ij}}{{l}_{ij}}$ (2)

Figure 1. Single cell model

Figure 2. Sketch map of calculating potential coefficient

${E}_{x}=\frac{1}{2\text{π}{\epsilon }_{0}}\underset{i=1}{\overset{n}{\sum }}{Q}_{i}\left(\frac{x-{x}_{i}}{{L}_{i}^{2}}-\frac{x-{x}_{i}}{{\left({{L}^{\prime }}_{i}\right)}^{2}}\right)$${E}_{y}=\frac{1}{2\text{π}{\epsilon }_{0}}\underset{i=1}{\overset{n}{\sum }}{Q}_{i}\left(\frac{y-{y}_{i}}{{L}_{i}^{2}}-\frac{y+{y}_{i}}{{\left({{L}^{\prime }}_{i}\right)}^{2}}\right)$ (3)

2.3. 电场对细胞跨膜电位的影响

$V={V}_{0}+\Delta \varphi$ (4)

${C}_{1}={C}_{2}{\text{e}}^{\frac{{V}_{0}}{\varsigma {V}_{T}}}$ (5)

${C}_{1n}={C}_{2}{\text{e}}^{\frac{V}{\varsigma {V}_{T}}}={C}_{2}{\text{e}}^{\frac{{V}_{0}}{\varsigma {V}_{T}}}{\text{e}}^{\frac{\Delta \varphi }{\varsigma {V}_{T}}}$ (6)

$\left({C}_{1n}-{C}_{1}\right)/{C}_{1}={\text{e}}^{\frac{\Delta \varphi }{\varsigma {V}_{T}}}-1$ (7)

3. 数值分析与讨论

3.1. 下相导线离地高度、离地不同高度处高压输电线产生的电场分布

3.2. 高压输电线路引起的跨膜离子迁移量变化

Figure 3. Schematic diagram of electric field intensity with the distance

Figure 4. Schematic diagram of the relative change of electric field intensity varies with distance

(a)(b)

Figure 5. Schematic diagram of (C1n – C1)/C1 with the direction angle

4. 结论

Modulation of Ion Concentration of Isolate Cell Exposed to the Electric Field of High-Voltage Transmission Line[J]. 生物物理学, 2018, 06(03): 43-49. https://doi.org/10.12677/BIPHY.2018.63004

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