A numerical method for simulation dynamics of incompressible lipid membranes in viscous fluid

A numerical scheme is presented for modeling dynamics of incompressible elastic lipid membranes imbedded into viscous fluid. A new elliptic equation for tension in the membrane implying its local incompressibility is derived. The membranes dynamics is approximated in a semi implicit way. The Lattice Boltzmann method is used to approximate the fluid flow. Forces acting on the fluid from the lipid membrane are implemented using the immersed boundary method by Peskin. The method is illustrated by examples of axisymmetric membranes with deformations and flows typical for experiments with lipid vesicles and nanotubes where deformations and flows can be modulated by external forces applied to the membrane.