REU Program

REU Advisor: Dr. Julia Arciero, Mathematical Sciences

Solid organ transplantation is a life-saving procedure that requires lifelong immunosuppression to prevent transplant rejection. Students working on this project will adapt an existing ODE model of murine heart transplant rejection that includes immunosuppression and adoptive transfer treatment strategies to predict how the immune response will respond when a bacterial infection is introduced into the system. The presence of immunosuppression causes a higher risk of susceptibility to opportunistic infections, and the students will explore the impact of bacterial infection on a heart transplant patient undergoing a typical immunosuppression treatment regimen. Students will gain experience coding in MATLAB and building and analyzing mathematical models of the immune response.

REU Advisor: Dr. Jared Barber, Mathematical Sciences

Osteocytes are bone cells that are embedded deep in bone. As we perform common activities, the forces exerted on the bone at the macroscale are somehow amplified by the osteocyte’s microscale environment so that the osteocytes release bone growth-related signals. Exactly how this happens and what parts of the osteocyte are most responsible for sensing such forces is still up for debate. To better understand such issues, we’ve created macroscale and microscale models of the bone and the osteocyte, and this project will help knit together those two different models (in 2D) to better understand how macroscale dynamics may affect microscale forces. While most of the needed tools are already assembled, students will still learn about those tools so that the final step in the process can be performed more efficiently and reliably. Students will end up learning more about fluid and solid mechanics, bone biology, the lattice-Boltzmann method, the immersed boundary method, finite elements, and other topics.

REU Advisor: Dr. Horia Petrache, Physics

In order to survive and grow, biological cells need nutrients such as glucose. We will use the CompuCell3D platform to analyze the diffusion of glucose in cellular aggregates with the goal of finding optimum geometries and cell growth rates. Since uptake of glucose is through cellular membranes, we will also analyze membrane transport using Molecular Dynamics simulations of lipid bilayers.

REU Advisor: Dr. Luoding Zhu, Mathematical Sciences

Cell migration plays a critical role in various biological processes, including cancer cell metastasis. Despite extensive research, the mechanisms underlying cell migration remain poorly understood. This process is inherently complex, involving interactions among the deformable cell body, interstitial fluid, and extracellular matrix—a phenomenon known as fluid-structure interaction. To study this, we will employ a computational framework that incorporates fluid-structure interaction using the lattice-Boltzmann immersed boundary (LB-IB) method. However, due to the very small flow speeds and spatial scales associated with cell migration—resulting in a very low Reynolds number—the above traditional approach faces challenges. Specifically, the standard explicit lattice-Boltzmann method is very slow to converge to a steady state. To address this limitation, we propose using an implicit lattice-Boltzmann immersed boundary method, which is based on solving the stationary Stokes equations. This project will focus on modeling and simulating the relaxation of a perturbed cell to its equilibrium state within a viscous fluid in two dimensions. Students participating in this project will gain foundational knowledge of the lattice-Boltzmann and immersed boundary methods.