REU Program

Research Experience for Undergraduates (REU) Program 2022

The NSF Research Experience for Undergraduates (REU) program in applied mathematics at IUPUI offers students an opportunity to conduct mathematical research with applications in the medical sciences, fluid mechanics, and neuroscience. Each year, we invite about ten undergraduate students from across the United States to participate in this competitive, eight-week summer program. Students will work in pairs under the guidance of a faculty research mentor from the IUPUI Department of Mathematical Sciences. Students will make specific research contributions that often lead to publications and/or conference presentations.

The program will be held in-person (pandemic permitting) in Summer 2022, although accommodations can be made for participants who prefer to participate virtually.  Each participant will receive a $4,000 research stipend; all in-person participants will also receive funding support for travel expenses and housing accommodations.

The 2022 REU Program will run June 6 - July 29, 2022. Complete applications are due January 31, 2022. Please see project descriptions and application below.

For additional information about the 2022 REU Program, please contact Dr. Julia Arciero at jarciero@iupui.edu.

Applied math projects for the 2022 REU Program

  1. Modeling treatment strategies for transplant patients (Advisor: Dr. Julia Arciero)
  2. Visualization and digitization of osteocyte images and simulations (Advisor: Dr. Jared Barber)
  3. Synchronization of brain rhythms in health and disease: the function of temporal patterning of synchrony (Advisor: Dr. Leonid Rubchinsky)
  4. Interaction of two osteocytes in lacuna-canalicular network (Advisor: Dr. Luoding Zhu)
  5. Modeling the impact of alcohol on neural mechanisms (Advisor: Dr. Alexey Kuznetsov)

Additional project details

REU Advisor: Dr. Julia Arciero, Mathematics

Organ transplantation is a life-saving surgical procedure, but the necessary life-long use of immunosuppressive drugs compromises the quality of life and survival of these patients. The development of a treatment that minimizes or eliminates the use of immunosuppression while preserving the graft is a great medical need. The adoptive transfer of regulatory T cells (Treg) offers a potential alternative to immunosuppressive drugs by down-regulating the body’s inflammatory response against the transplant. Students working on this project will adapt an ODE model of Treg adoptive transfer to determine the most effective combination treatment strategies of Tregs with low doses of immunosuppression or IL-2. Students taking part in this project will develop a mathematical model that accurately captures this physiological system, code and simulate model equations using Matlab, analyze the stability of model solutions, and interpret model results from a biological and clinical perspective.

This project will be in-person (but can accommodate remote participation, if desired.)

REU Advisor: Dr. Jared Barber, Mathematics

In bone, experiments suggest stresses at the macroscale level get multiplied at least ten-fold by the time they reach cellular scales where they cause osteocytes (bone cells) to react in ways that can promote or reverse bone growth. To model this multiscale phenomenon, we have developed a finite element macroscale model of the bone and a lattice Boltzmann microscale model of the osteocyte and its surrounding microenvironment. Integration of these two models requires interpolation tools that can be used to estimate quantities on the microscale rectilinear mesh given quantities on the macroscale tetrahedral finite element mesh and vice versa. In addition to learning about osteocytes and basic fluid and solid dynamics, the major goal for students will be to develop and learn about multi-dimensional interpolation methods including using cubic finite element functions, radial basis functions, and cell-based search algorithms.

This project will be in-person (but can accommodate remote participation, if desired.)

REU Advisors: Dr. Leonid Rubchinsky, Mathematics

Synchronization of neural activity in the brain is involved in a variety of brain functions including perception, cognition, memory, and motor behavior. Excessively strong, weak, or otherwise improperly organized patterns of synchronous oscillatory activity may contribute to the generation of symptoms of different neurological and psychiatric diseases (e.g., Parkinson's disease, addiction, schizophrenia, and autism spectrum disorders). However, neuronal synchrony is frequently not perfect, but rather exhibits intermittent dynamics. The same synchrony strength may be achieved with markedly different temporal patterns of activity. This project is aimed at the exploration of the functional role of the temporal patterns of synchronous activity and will include time-series analysis and dynamical systems theory and simulation.

This project will feature primarily remote meetings with the faculty mentor, but in-person participation in the REU is encouraged.

REU Advisor: Dr. Luoding Zhu, Mathematics

Students will work with Dr. Zhu on modeling and simulating the interaction of two deformable osteocytes in the lacunocanalicular network in two dimensions. Most computational models investigate only an isolated osteocyte. In reality osteocytes are interconnected as their processes extend through the bone matrix (via canals/canaliculi) to connect with each other. Modeling viscous fluid flow over two neighboring deformable osteocytes with connected processes and canaliculi can help yield insight into osteocyte interactions via interstitial fluid flow.

This project will be in-person (but can accommodate remote participation, if desired.)

REU Advisors: Dr. Alexey Kuznetsov, Mathematics

The project works to identify the neural mechanisms that underlie aberrant decision-making typical for alcoholic subjects. Interaction between two brain regions, the prefrontal cortex (PFC) and the basal ganglia (BG), is shown to be involved in guiding behavioral choices. How this interaction is altered by repeated alcohol use needs to be understood to design more effective treatment strategies. The objective of this project is to create a reduced predictive model of the PFC-BG circuitry in control and chronic alcohol conditions. The firing rate modeling formalism will be used, which allows for a highly simplified description of neural population activity. The models will be calibrated using local field potential (LFP) and single units recordings from collaborators (Prof. Lapish, IUPUI Department of Psychology). Two directions will be explored: First, the students will model how prior repeated alcohol changes value encoding in the BG. Second, the students will analyze how repeated alcohol use impairs the neural processes that underlie deliberation in the PFC. The research team will make modeling predictions on the mechanisms by which prior repeated alcohol use alters computation of value and deliberation performed by the interaction of the PFC and BG circuits.

This project will feature remote meetings with the faculty mentor, but in-person participation in the REU is encouraged.