Multiscale Multiphysics Modeling of Blood Clotting and Thrombus Biochemomechanics in the Vasculature

The process of clot formation and growth at the site of injury on a blood vessel wall involves a number of multiscale simultaneous processes including: multiple chemical reactions in the coagulation cascade, species transport, platelet adhesion as well as the haemodynamics and blood rheology. We model these processes at different levels of description (e.g. macro- vs. microscales). At continuum level, we solve Navier-Stokes equations for blood flow as well as the PDEs associated with advection-diffusion-reaction (ADR) of multiple species in the coagulation cascade using a spectral element solver. Depending on the required degrees of fidelity, platelets could be modeled either as a continuum concentration field or their transport and adhesion could be addressed by looking at individual platelets in a Lagrangian way. At cellular and sub-cellular levels, however, particle-based methods such as Dissipative Particle Dynamics (DPD) have proven themselves to be more effective in addressing complex biological systems. I will present the recent developments in DPD framework that extends its applicability to transport problems, and discrete models of soft biological tissues. The major drawback of modeling such fully-resolved systems at the cellular scale, however, is the long-term computation of their whole course of evolutions. There are numerous biological and materials systems that evolve at slow rates (e.g. clotting), which make the simulations prohibitively long. I propose a multifidelity technique based on co-krigging information fusion approach in statistical learning in order to facilitate acceleration in time. The multiscale framework's implications and future directions will also be discussed.

Research Interests:

• Soft Biological Systems, Multiphase and Complex Fluids (e.g., Blood)

• High-order Spectral Element and Coarse-grained Particle-based Methods for Multiphysics

• Fluid-structure Interactions and Immersed Boundary Method for Cardiovascular Mechanics

• Applied Mathematics and High-performance Scientific Computing

and Multiscale Problems

Teaching Interests:

• Fluid Mechanics (undergraduate and graduate)

• Numerical Methods and Computational Fluid Mechanics

• Heat Transfer

• Selected Topics in Multiscale Modeling

• Biomechanics