Free boundary-based multiscale/multiphyics modeling, simulation, and analysis of complicated biological systems
Mathematical Biosciences Institute, The Ohio State University
(September 13, 2012 10:20 AM - 11:15 AM)
In this talk I will be presenting two topics: (1) studying conducting and selectivity functions of ion channels and (2) exploring tumor growth under cancer-immune system interactions and therapeutic treatments. These complicated biological systems usually consists of composite materials and involve intensive interactions among components. The former is at molecular level: multiscale treatments (atomic and continuum) and multiphysics (classical and quantum) are applied to different components (water molecules, channel proteins, membranes, and mobile ions, etc) according to biological importances of objects and computational efficiency. The solute-solvent surface serves as a free boundary to couple the discrete and continuum scales. The cancer research is macroscopic: interactions pathways of a large amounts of cells and cytokines are outlined from experimental observations and modeled by a systems of governing equations; the tumor is described as a moving domain with free boundary and has obviously different phase-field from normal tissues.
Both of the two topics require advanced numerical techniques for solving partial differential equations and simulations are validated by experimental data. Analysis, such as existence and uniqueness of the solutions are performed to these free boundary problems.