I am currently working on a three-dimensional computer simulation of red blood cells traveling through blood vessels. Realistic computer simulations of red blood cells hold much promise for medical applications. For example, they could be used to inexpensively test artificial red blood cells in order to develop treatments for diseases such as sickle cell anemia, in which the native red blood cells are defective.
A red blood cell may be thought of as a sac containing a highly viscous fluid relative to the surrounding plasma. To travel through capillaries, which may be as small as 4 microns in diameter, red blood cells, which are approximately 8 microns in diameter, must deform significantly and travel near the vessel walls. Realistic simulation of red blood cell dynamics must therefore incorporate variable viscosities, cell-cell interactions, and interactions with the vessel wall. Because it was formulated precisely to deal with fluid-structure interaction, the Immersed Boundary (IB) method lends itself well to interactions between elastic structures. Three-dimensional IB method simulations of red blood cells have been developed previously, but they have significant limitations. One important feature of the simulation I am developing is that it includes adaptive mesh refinement. This will make it possible for the thin fluid layers between red blood cells and the vessel wall or between multiple red blood cells to be simulated accurately and efficiently.
F. Balboa, J.B. Bell, R. Delgado-Buscalioni, A. Donev, T. G. Fai, B.E. Griffith, and C.S. Peskin. Staggered schemes for fluctuating hydrodynamics. SIAM J. Multiscale Modeling and Simulation, 10(4):1369-1408, 2012.
T.G. Fai, B.E. Griffith, Y. Mori, and C.S. Peskin. Immersed Boundary Method for Variable Viscosity and Variable Density Problems using Fast Constant-Coefficient Linear Solvers I: Numerical Method and Results. Submitted, 2012.
T.G. Fai, B.E. Griffith, Y. Mori, and C.S. Peskin. Immersed Boundary Method for Variable Viscosity and Variable Density Problems using Fast Constant-Coefficient Linear Solvers II: Theory. Submitted, 2012.
A. Donev and A. J. Nonaka and Y. Sun and T. G. Fai and A. L. Garcia and J. B. Bell. Low Mach number fluctuating hydrodynamics of diffusively mixing fluids. Submitted, 2013.
Moses A. Greenfield Research Award, 2012
Thomas Bringley Fellowship, 2011
Henry M. MacCracken Fellowship, 2008-2010
NSF Graduate Research Fellowship Honorable Mention, 2008
B.S. with Highest Distinction and High Honors in Mathematics, Univ. of Michigan, 2008
Phi Beta Kappa, 2008
Rogel Scholar, Univ. of Michigan, 2004-2008
Joseph Silber Fellowship, American Cancer Society, 2005