Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
Journal of Computational Physics
Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A phase field method for simulating morphological evolution of vesicles in electric fields
Journal of Computational Physics
Journal of Computational Physics
A phase field model for vesicle-substrate adhesion
Journal of Computational Physics
Modeling and computation of two phase geometric biomembranes using surface finite elements
Journal of Computational Physics
A fast algorithm for simulating vesicle flows in three dimensions
Journal of Computational Physics
A level set projection model of lipid vesicles in general flows
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.49 |
A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic model for these membranes employs a two-dimensional-fluid-like elastic constitutive law which is sensitive to curvature, and subjects vesicles to physically imposed constraints on surface area and volume. This model is implemented numerically via the use of C^1-conforming triangular Loop subdivision finite elements. The validity of the framework is tested by computing equilibrium shapes from previously-determined axisymmetric shape-phase diagram of lipid bilayer vesicles with homogeneous material properties. Some of the benefits and challenges of finite element modeling of lipid bilayer systems are discussed, and it is indicated how this framework is natural for future investigation of biologically realistic bilayer structures involving nonaxisymmetric geometries, binding and adhesive interactions, heterogeneous mechanical properties, cytoskeletal interactions, and complex loading arrangements. These biologically relevant features have important consequences for the shape mechanics of nonidealized vesicles and cells, and their study requires not simply advances in theory, but also advances in numerical simulation techniques, such as those presented here.