【作者】 赵双良；

【导师】 刘全慧；

【作者基本信息】 湖南大学 ， 理论物理， 2004， 硕士

【摘要】 红血球是自然界比较简单的细胞之一，自从它被人们认识以来，对它的观察、研究比较多。在过去的许多物理学的理论研究中，一般把红血球作为封闭的流体膜来处理。在此基础上，1973年，Helfrich提出了著名的自发曲率弹性自由能模型。运用这一模型，近来人们解释了双面凹扁椭球特殊形状、闪烁现象、玻璃效应等红血球的一系列现象的物理机制。 1999年，欧阳等从大量的观测资料中发现，红血球双面凹扁椭球形状的脊峰在某种不同浓度的溶液中会发生位置的变化，这就是所谓的红血球的脊峰移动现象。随即，刘全慧等用微分法巧妙的在Helfrich自发曲率弹性自由能模型基础上对此进行了解释，认为这是由于渗透压和细胞膜表面弹性系数的变化引起了红血球峰值半径的改变。但他们的研究结论只适用于这两个参数的微小变化，当渗透压和弹性系数发生较大改变时，他们并不能给出相应的结论。 本文用U数曲线来描述红血球的形状，从Helfrich弹性自由能模型出发，运用变分法研究了渗透压和弹性系数在合理的大范围内变化时，红血球的脊峰移动的情况，并与实验进行了比较。发现当表面弹性系数在（-0.15～0.3）×10^-8N／m中取值时，随着渗透压的增加，红血球的峰值位置朝细胞中心移动，反之亦然。这一结论与实验观察资料吻合的非常好。 由于本研究是从闭合流体膜理论出发的，因此本文预测这一结论也同样适用于囊泡的情况，并进一步从理论上分析了表面弹性系数在更大范围内取值时的峰值移动的情况。更多还原

【Abstract】 Human red blood cells (RBC) are the simplest in nature. Large quantities of observations and researches on them have been done since they were discovered. In the past theoretical physical study, the RBC was generally dealed as closed fluid membrane. Then in 1973 Helfrich brought forward the famous spontaneous curvature Frank energy model and with the model, the RBC circular biconcave special shape, flicker phenomenon and the glass rod effect etc have been explained recently.In 1999, from many observation data Ou-Yang Zhong-Can with his copartners found that the apex of RBC could shift when they were exposed in the different concentrations of certain chemical agents namely the so-called apex shift phenomenon. Then Liu Quan-Hui et al skillfully explained it based on the Helfrich spontaneous curvature Frank energy model by differential coefficient method. They pointed out that the radius of the apex changed depending on the change of the osmotic pressure between the ambient and the internal environments and the surface tension coefficient. But there existed a problem in their theory that the two parameters only can take tiny variation corresponding to their research result. And when the two parameters vary in a long range, they haven’t given out the result that we expected.In this paper by variation method the apex shift phenomenon is studied when the osmotic pressure and the surface tension coefficient vary in a physically long range based on the Helfrich Frank energy model while using U curve to describe the RBC shape and compare last result with the experiments. It is demonstrated that when the surface tension coefficient varies between (-0.15- 0.3) 10-8N/m the radius of the apex of the biconcave shape can shift toward to the center depending on the increase of the osmotic pressure, and vice verse. It fits the experiments result very well.Since the research bases on the fluid membrane theory, so in the paper we forecast our result can be applied to all the fluid vesicles, and some further theoretically analysis on the details of the apex shift also are made when the surface tension coefficient takethe values out of the above range.更多还原