IUPUI REU Program in Mathematics
The 2020 REU Program at Indiana University-Purdue University Indianapolis (IUPUI) will provide eight undergraduate students from across the United States with the opportunity to conduct mathematics research with applications in the medical sciences and bioengineering. Program details.
The students will spend seven weeks during the summer in Indianapolis, Indiana working with faculty mentors from the IUPUI Department of Mathematical Sciences and IUPUI Department of Mechanical and Energy Engineering. The REU program is supported by the National Science Foundation.
- Program dates: June 15, 2020 - July 31, 2020
- Eligibility: any undergraduate student who is a United States citizen or permanent resident
- Application deadline: February 7, 2020
Student participants will receive:
- $4000 research stipend
- $450 for travel expenses
- Apartment housing and meal allowance for 7 weeks
Applied Math Projects:
- Modeling treatment strategies for heart transplant patients (Advisor: Dr. Julia Arciero)
- Modeling slow cell motion (Advisor: Dr. Jared Barber)
- Synchronization of brain rhythms in health and disease: the function of temporal patterning of synchrony (Advisor: Dr. Leonid Rubchinsky & Dr. Anh Nguyen)
- Multimaterial topology optimization through models of biological pattern formation (Advisor: Dr. Andres Tovar)
ADDITIONAL PROJECT INFORMATION:
Project 1. Modeling treatment strategies for heart transplant patients
(REU Advisor: Dr. Julia Arciero)
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.
Project 2. Modeling slow cell migration
(REU Advisor: Dr. Jared Barber)
While several models of cell migration exist, recent research by our collaborators has yielded new information regarding some of the subcellular components and their roles during cell migration. This information includes nano-level force measurements on contracting and relaxing filaments and connectors. To fully utilize these novel measurements, we are developing models of migrating cells that specifically include these nano-level components alongside other larger micron-level components. By combining our models with these experiments, we hope to gain fresh insight into the emerging roles of these nano-level components. Students working on us in this project will help us develop static versions of these models for use when the flow near/in the cells is very slow. This will consist of extending a past similar REU project involving 2d cancer cell models in slow flow to include both three dimensions and active contracting filaments. Depending on progress, this may also include calibration of the model to our collaborators' experimental data. This model will help serve as a building block and benchmark test for future models of cell migration in low and normal flow regimes.
Project 3. Synchronization of brain rhythms in health and disease: the function of temporal patterning of synchrony
(REU Advisor: Dr. Leonid Rubchinsky; Co-advisor: Dr. Anh Nguyen)
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.
Project 4. Multimaterial topology optimization through models of biological pattern formation
(REU Advisor: Dr. Andres Tovar)
In applied mathematics and engineering, topology optimization is recognized as the most effective numerical method to design high-performance structures without any preconceived shape. The resulting structures commonly depict organic, complex, and non-intuitive layouts, which makes topology optimization appealing to designers in various disciplines (architecture, automotive, aerospace). Recently, topology optimization has been extended to handle multiple materials, increasing the performance of the optimized structures. However, existing multimaterial topology optimization methods are still limited to problems involving linear, elastic (ordinal) material models and cannot be used with real, engineering (categorical) materials. This work introduces a new approach to multimaterial topology optimization based on models of biological pattern formation and self-organization. With this approach, the optimal multimaterial structure emerges as a synthetic pattern from the interaction of materials clusters modeled as cells, which are provided with motility, adhesion, and differentiation capabilities. Students participating in this project will gain experience with Matlab-based multimaterial topology optimization algorithms and be exposed to the mathematical and physical principles of cellular dynamics, formalization of self-organization, and spatial-temporal pattern formation models (lattice-gas cellular automata). The result of this research experience is the numerical implementation of a pattern formation model and its evaluation as a multimaterial topology optimization method. Please note that "topology optimization" refers a numerical method used in engineering to generate structures and it does not study the properties of invariant spaces under continuous deformation as typically understood in pure mathematics.