Energetic Phase Field Methods and Modeling in Biological Microstructures

Florida State University, Tallahassee FL

Investigators

Abstract

Wang DMS-0807915 During recent years, the energetic phase field approach has emerged as a successful modeling and simulation method with many advantages in studying microstructure evolutions. The idea of phase field methods is to introduce a set of phase field variables to implicitly track the moving surfaces of microstructures, which can be very complex and nonlinear. In this project, the investigator and his collaborators apply phase field methods to study biological microstructures, especially cell membranes. The project is mainly concerned with further analysis on phase field methods, and the broadening of applications in studying the evolution of biological microstructures for which phase field methods and related concepts can be used as a basis for more convenient or efficient treatments. The project includes modeling, numerical methods, and theoretical analysis. The investigator studies some theoretic and algorithmic problems in phase field methods that still remain unsolved or partly unsolved today, such as asymptotic behavior of phase field variables (which is related to the De Giorgi conjecture), the consistency of the fluid coupled phase field model to the sharp interface model, topological information retrieval formulations, and convergence and acceleration of some popular algorithms. He also applies the theoretical results to the modeling and simulation of some complex microstructure systems, especially cellular adhesion and rolling in a shear flow, which can be used in the study of blood flows. Cell motility is another complex biological phenomenon that can be simulated using phase field models. Also considered is the simulation of acto-myosin driven cell oscillations, which can be applied to study cell division and migration, two of the most important functions of living cells. Besides simulating some observed phenomenon, phase field models can also be applied to predict details of some structures that are not yet fully known, such as highly folded membranes.