Smooth Finite Element Modeling of Shape Evolution and Poration of Lipid Membranes
Open AccessA continuum model and a numerical scheme for simulating the topology changes of lipid membranes and the formation and evolution of pores in lipid membranes are introduced. This model is based on a variational approach that accounts for the competition of the edge and the bending energies during the evolution of lipid membranes. The classical model of lipid membranes is expressed in terms of curvature-dependent energy involving the mean and the Gaussian curvatures of membranes. It is customary to ignore the Gaussian energy as it takes a constant value for topologically equivalent closed membranes. In this work, the effect of the Gaussian energy on configurations of closed membranes is studied by using a phase-field model. Moreover, the pore evolution of open membranes and their transformation to closed membranes are investigated by considering Gaussian energy and changing the value of the line tension energy. The weak form of the governing equations for the model includes second-order derivatives of a phase-field function. Therefore, a C^1-conforming Argyris triangle is used for the finite element approximations. The numerical results of this research suggest the necessity of including Gaussian energy in the classical models for accurately capturing the topology changes of closed membranes. The results also indicate that considering the Gaussian energy improves the accuracy of models for open membranes, especially in capturing the formation and closing of a pore in biomembranes.
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Ebrahimi_gwu_0075A_15612.pdf | 2022-03-06 | Open Access |
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