Numerical simulation of stable structures of fluid membranes and vesicles

Authors:
Hassan Ugail;Raja Noshad Jamil;Razvan Satnoianu
Affiliations:
School of Informatics, University of Bradford, Bradford, UK;School of Informatics, University of Bradford, Bradford, UK;Cass Business School, City University, London, UK
Venue:
ICCOMP'06 Proceedings of the 10th WSEAS international conference on Computers
Year:
2006

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Abstract

We study the numerical simulation of stable structures of fluid membranes and vesicles in biological organisms. In particular, we discuss the effects of spontaneous curvature on vesicle cell membranes under the bending energy for given volume and surface area. The geometric modeling of the vesicle shapes are undertaken by means of surfaces generated as Partial Differential Equations (PDEs). We combine PDE based geometric modeling with numerical optimization in order to study the stable shapes adopted by the vesicle membranes. Thus, through the PDE method we generate a generic template of a vesicle membrane which is then efficiently parameterized. The parameterization is taken as a basis to set up a numerical optimization procedure which enables us to predict a series of vesicle shapes subject to given surface area and volume.