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

 lube_page1_newSimulations on uniform fluid grids can break down when objects come close to touching. I have developed a numerical method for fluid-structure interaction that uses a subgrid model based on lubrication theory to accurately resolve near-contact.This method allows for the efficient simulation of phenomena such as the migration of deformable red blood cells away from blood vessel walls. 

•T. G. Fai and C. Rycroft, Lubricated Immersed Boundary Method in Two Dimensions. J. Comput. Phys., 356, 319-339, 2018 (link, arxiv).

rbc_page1Data-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

protocells_page1 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

• T. Ruiz-Herrero, T. G. Fai, and L. Mahadevan. Dynamics of growth and form in prebiotic vesicles. Phys. Rev. Lett., 123, 038102, 2019 (linkarxiv). Featured in Nature Reviews Physics. (highlight