The Research On Apex Shift Phenomenon Of Red Blood Cells Using Variation Method

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.