论文摘要
外电场作用下的生物细胞会发生一系列的生物物理和生物化学变化。基于上述变化的应用大体分为两类。第一类是利用电场改变细胞的某些属性，比如由电场作用引起细胞穿透性程度的提高，从而可以实现将各种分子引入到细胞中，或引入到细胞膜中，以及细胞的融合。第二类是利用电场和电流来表征悬浮液中和组织中生物细胞和细胞各种成分的生物特性。研究细胞在电场中不同频率下的各种反应是第二类应用中重要方法之一。所以一些很难通过直接方法测定生物细胞的物理量可以得到确定（比如细胞膜和细胞质的电导率和电容）。上述两大类应用中的大部分方法的基本原理在于外电场作用下细胞膜内外不同电势，即跨膜电压（TMP）和细胞膜局部电场。细胞膜电压是反映细胞生命活力和功能的一个良好指标。在外加电场作用下，细胞膜电压的改变导致了胞内外离子的穿膜运动，打破了维持细胞正常生命活动的离子分布的平衡状态，从而引起细胞产生有利于或不利于其存活的生理和生化状态的改变。因此，建立外电场作用下细胞膜电压计算模型，掌握细胞膜电压变化规律，对更好研究细胞电磁生物效应及其在生物、医学领域的应用具有重要指导意义。外电场中单细胞膜电压计算模型早为人们熟知。然而对于属于多细胞系统的细胞悬液，细胞分布的不均匀性、以及细胞间相互作用的复杂性，使得精确建立悬液中细胞膜电压计算模型非常困难。为此，论文用场近似等效方法，初步解决了该建模难题。首先根据有效介质理论，计算不同外加电场作用下的细胞悬液的有效电导率。然后根据Laplace方程确定细胞悬液中的平均场。再次用场近似等效方法，确定悬液中一个细胞局部的实际场分布和独立处于外加场中单细胞场分布近似等效的条件。最后借助于单细胞膜电压计算公式，建立了外电场作用下悬液细胞膜电压近似计算模型。针对悬浮液中不同细胞占有率，对跨膜电压计算模型进行了讨论。通过比较数值解与解析解的一致性，证实了模型的可行性。论文对外电场作用下单细胞膜损耗功率计算模型进行分析。结果表明，细胞膜的损耗功率和细胞排列方式有关，以及证明了对称性和最值。细胞膜损耗功率计算模型的建立，为细胞电磁生物效应的机理研究提供了理论基础。针对正常细胞和癌细胞的物理参数的不同，讨论了正常细胞和癌细胞在不同频率下的跨膜电压。最后对细胞膜电导率为零时跨膜电压进行了分析：球细胞在恒定直流电场中极化，对称轴和电场方向平行时跨膜电压分析和对称轴与电场方向垂直时跨膜电压分析。论证了直流电场中单细胞跨膜电压的Schwan公式。对于假定具有简单属性的细胞膜电压的分析较为直接和容易，而且从理论上来说，研究的结论可以在学术界存在很长时间。但是从物理学角度来说，这些公式描述了电介质球体细胞表面的电压分布。其缺陷是没有考虑到细胞的生理特性。本论文中所推导的公式对以后研究更复杂生理条件和外电场作用下在跨膜电压的分析有指导意义。Exposure of biological cells to electric fields can lead to a variety of biophysical and biochemical responses. Applications based on these responses can roughly be divided into two groups. The first group uses electric fields as a tool to modify various properties of the cells. Herein are the applications that utilize the increase in membrane permeability caused by electric fields for introduction of various molecules into cells, insertion of molecules into cell membranes, and fusion of cells. The second group of applications uses electric fields and currents as tools to characterize various properties of biological cells or their constituents, both in suspensions and in tissues. Among the most important approaches in such characterization is the evaluation of cell’s response to electric fields at different frequencies.Consequently, various physical quantities of biological cell can be determined that are difficult to assess by direct measurement （e.g., conductivity and capacitance of the membrane and the cytoplasm）. The basic mechanism underlying majority of these methods is the inducement of potential difference across the membrane by the external electric field, which results in the trans-membrane potential （TMP） and membrane electric field.The trans-membrane potential of the cells is a suitable parameter reflecting the life activity and function of cells. During the exposure to an electric field, the change of the trans-membrane potential can cause the remotion of the ions through the membrane. Then, the balance state of the ions which is necessary to keep the normal life activity is broken, and the physiological and biochemical state of the cells will be changed. Therefore, it is very important to build the analytical models for trans-membrane potential induced on cells in biological and medical fields. The analytical model for trans-membrane potential on a single cell exposed to an external electrical field has been well known for a long time. However, due to the asymmetrical distribution of conductivity and the interactions among the cells exposed to an external electric field, the analytical model for trans-membrane potential on suspension cells is too complicated to obtain. Thus, in this paper, the approximate equivalence method is used to resolve this problem. Firstly, the average field inside the suspensions is calculated according to the effective medium theory. Secondly, the average strength of electric field inside the suspensions is analyzed by using Laplace formula, and the condition under which the local electric field of an unit cell in suspensions is approximately similar to that of a single cell exposed to external field was investigated. Finally, based on the analytical solution of a single cell, some analytical models for the trans-membrane potential on the cells in suspensions are built.The model of trans-membrane potential proves feasible by discussing the consistency of numerical and analytical results with different cell volume fractions. The distributed power dissipation in membrane of the single cell is discussed. The results show that the power