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. Current research topics with selected publications:Multiscale methods Data-driven simulation Mathematical modeling in biology Multiscale numerical methods •T. G. Fai and C. Rycroft, Lubricated Immersed Boundary Method in Two Dimensions. J. Comput. Phys., 356, 319-339, 2018 (link, arxiv).  Data-driven simulation 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  Our cells contain extensive machinery to control division, but is it possible that cellular precursors replicated by a very simple mechanism? I have performed 3D simulations of a permeable, growing membrane to explore a model of prebiotic cells. These simulations show that a simple mechanical model can give rise to many modes of growth, including uniform expansion and the emergence of thin membrane ridges and deep recesses |
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