My research is focused on the modeling and simulation of biological phenomena, including the fluid dynamics inside of cells and membrane growth and form in cellular precursors. To model these phenomena I use ideas from subjects such as partial differential equations, graph theory, and differential geometry. Computational approaches are needed because the resulting equations are often too complicated to solve by hand; I work on developing efficient numerical methods to simulate fluid-structure interaction and to incorporate experimental data into simulations. Research highlights with selected publications:Multiscale methods Data-driven simulation Mathematical modeling in biology Multiscale numerical methods ![]() The red blood cell cytoskeleton is an elastic network that may be modeled as a graph of actin-based junctional complexes (nodes) connected by spectrin polymers (edges). I have simulated the effect of cytoskeletal remodeling on the cell’s mechanical response to prescribed stress and strain, using images obtained by cryo-electron microscopy to generate a random graph with realistic statistical properties. This model may be useful for studying the fundamental question of how red blood cells age. • T. G. Fai, A. Leo-Macias, D. L. Stokes, and C. S. Peskin, Image-Based Model of the Spectrin Cytoskeleton for Red Blood Cell Simulation. PLOS Comput. Biol., 11(6), e1005790, 2017 (link, preprint).
Mathematical models of fluid-structure interaction at cellular and sub-cellular scales ![]() |