REU Program

Research Experience for Undergraduates (REU) Program 2021

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 engineering. Each year, we invite eight to twelve undergraduate students from across the United States to participate in this competitive, seven-week summer program. Students will work in pairs under the guidance of a faculty research mentor from the IUPUI Department of Mathematical Sciences or Department of Mechanical and Energy Engineering. Students will make specific research contributions that often lead to publications and/or conference presentations.

Due to the current uncertainty surrounding the COVID-19 pandemic, it is not yet known if this program will be held in-person or virtually in Summer 2021. Regardless, each participant will receive a $4,000 research stipend (as well as travel expenses and room/board, if held in-person).

The 2021 REU Program will run June 14 - July 30, 2021. Complete applications are due February 1, 2021. Please see project descriptions and application below.

For additional information about the 2021 REU Program, please contact Dr. Julia Arciero at jarciero@iupui.edu.

Applied math projects for the 2021 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 (Advisors: Dr. Leonid Rubchinsky and Dr. Anh Nguyen)
  4. Modeling the hierarchical patterns of natural materials (Advisor: Dr. Andres Tovar)
  5. Modeling and simulation of fluid flow over a cellular process in a canaliculus (Advisor: Dr. Luoding Zhu)
  6. Modeling fluid flow over an osteocyte (Advisors: Dr. Luoding Zhu and Dr. Jared Barber)

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.

REU Advisor: Dr. Jared Barber, Mathematics

In bone, force densities at the macroscale level get multiplied at least ten-fold by the time they reach cellular scales where these magnified forces cause osteocytes to react in ways that can promote or reverse bone growth. The mechanisms that cause this force magnification to take place and the force localization on the osteocyte are still not well characterized. We have begun developing multiscale computational models that will be calibrated with experiment in order to better understand osteocyte dynamics. Some of these models approximate three-dimensional space using collections of rectangular prisms (rectilinear grids/lattices) while other models use tetrahedrons (finite element grids). Increasing osteocyte insight relies on proper visualization of the solutions found on these grids. In addition, proper calibration relies on taking experimental images and converting them into a format comparable with the computational simulations, which take place on the grids. Using Mimics, Matlab, Gmsh, and other visualization software, the student will assist in these efforts by helping to develop tools that can be easily used to visualize simulations and convert experimental images into a format compatible with simulations. This project's mathematical (the project is highly geometric in nature), biological, and computational aspects makes it a worthwhile project for anyone interested in computational and mathematical modeling of biological systems.

REU Advisors: Dr. Leonid Rubchinsky and Dr. Anh Nguyen, 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.

REU Advisor: Dr. Andres Tovar, Mechanical and Energy Engineering

The complex, hierarchical structure of natural materials (e.g., culm, cuticle, bone) provides mechanical properties that can be superior to the ones of engineering materials (e.g., plastics, metals, ceramics). For example, the specific strength of bamboo (~114 MPa/(g/cm3)) is three to four times higher than the specific-yield strength of structural steel (~32 MPa/(g/cm3)). Also, the energy required to produce bamboo (below 1 MJ/kg) is many times smaller than the one utilized to produce steel (25 MJ/kg). To understand the formation of the architectural patterns in natural materials, our research implements mathematical and computational models that explain cellular dynamic behaviors and self-organization processes at different length scales. In these models, the emerging patterns are driven by physical principles such as energy minimization subject to entropic constraints. Students of this project will gain experience with cellular modeling software such as CompuCell3D and the numerical implementation of the Cellular Potts Model (CPM) and reaction-diffusion equations in Matlab and Python. Results of this research are of relevance in the design and additive manufacturing of engineering structures as well as in the design and fabrication of tissue using 3D bioprinting methods.

REU Advisor: Dr. Luoding Zhu, Mathematics

Osteocytes residing in the mineralized bone matrix are responsible for mechanotransduction: the conversion of mechanical stimuli into biochemical signals, leading to either bone formation or degradation. Despite intensive studies, it remains a mystery as to how mechanical forces at tissue level are amplified and sensed by which part of the osteocyte. To date, the relevant principles/mechanisms have yet to be identified. Our project aims to introduce physiologically realistic integrative computational models taking into account most physiological factors. Cellular processes are important component of an osteocyte and were proposed to be responsible for force amplification and mechanotransduction in literature. Students taking part on this project will perform modeling and simulation of a viscous fluid flow over a cellular process within a canaliculus, including model development, programming, running simulations, data processing and analysis, and interpretation of computational results from a biological perspective. Students will learn fundamentals of osteocytes, fluid mechanics, lattice Boltzmann and immersed boundary frameworks.

REU Advisors: Dr. Luoding Zhu and Dr. Jared Barber, Mathematics

Osteocytes residing in the mineralized bone matrix are responsible for mechanotransduction: the conversion of mechanical stimuli into biochemical signals, leading to either bone formation or degradation. Despite intensive studies, it remains a mystery as to how mechanical forces at tissue level are amplified and sensed by which part of the osteocyte. To date, the relevant principles/mechanisms have yet to be identified. Our project aims to introduce physiologically realistic integrative computational models taking into account most physiological factors. Students taking part on this project will perform modeling and simulation of a viscous fluid flow over an osteocyte, including model development, programming, running simulations, data processing and analysis, and interpretation of computational results from a biological perspective. Students will learn fundamentals of osteocytes, fluid mechanics, and various numerical techniques.