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IUPUI REU Program in Mathematics

Program details

The 2018 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. 

The students will spend eight 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 4, 2018 - July 27, 2018
  • Eligibility: any undergraduate student who is a United States citizen or permanent resident
  • Application deadline:  February 1, 2018

Student participants will receive:

  • $4000 research stipend
  • $400 for travel expenses
  • Apartment housing and meal allowance for 8 weeks 

Apply for the program

Project options

See descriptions for each project option below that describes the five applied mathematics research projects for the REU program.

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.  By adapting a mathematical model of transplant rejection to include the effects of adoptive transfer, students working on this project will theorize the best strategies for Treg adoptive transfer alone and in combination 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 cancer cell motion (REU Advisor: Dr. Jared Barber)

Students working on this REU project will compare the effectiveness of two different mathematical models of cancer cell motion, calibrate the models, and use the models to explore the effects of cancer cell properties on their transport through a microfluidic device (including experimental comparisons) and transport in capillaries.  Students will accomplish these research goals by running simulations using two pre-existing models, analyzing some pre-existing data from collaborators, and performing a guided literature search.

Project 3. Modeling the influence of addictive drugs on the brain (REU Advisor: Dr. Alexey Kuznetsov)

Students working on this REU project will develop a mathematical model that investigates the influence of addictive drugs on the brain. Addictions and several major psychiatric disorders are connected with abnormal levels of the neurotransmitter dopamine. In general, dopamine neurotransmission is involved in detecting salient events and learning rewarding behaviors. How dopamine levels are regulated is one of the most important and challenging problems in neuroscience. This project addresses the problem using mathematical modeling and electrophysiological experiments. The dopamine system is modeled at multiple levels: from intrinsic properties of the dopamine neurons to network dynamics. Dr. Kuznetsov's lab welcomes students who are interested in research at every level of this system.

Project 4. Computational modeling of cellular-level tissue dynamics (REU Mentor: Dr. Andres Tovar)

Tissue-engineered medical products present increasingly complex design considerations, particularly concerning the cellular-level processes associated with tissue dynamics during homeostasis, morphogenesis, and wound healing. Recently, a computational model of cellular-level activities has been proposed using a hybridized kinetic Monte Carlo method and agent-based modeling principles. While this model has already been shown to predict many relevant phenomena to morphogenesis in spheroid-based biofabrication methods, current work seeks to develop and validate mathematical models describing more advanced phenomena like complex migratory behavior and cell-fate processes. The student participating in this project will be exposed to the mathematical and physical principles of cellular-level tissue dynamics and its numerical implementation. The result of this research experience is the calibration of numerical model and the study of its potential applications. 

Project 5. Implementation of advanced topology optimization methods (REU Mentor: Dr. Andres Tovar)

In applied mathematics and engineering, topology optimization is known as the most effective material distribution numerical approach for synthesizing structures without any preconceived shape. Currently, a number of topology optimization algorithms is freely available in Matlab and other programming languages. Most of these algorithms use so-called density-based method, which can be used in 2D and 3D structures. The objective of this work is to implement more advanced topology optimization methods such as the level set-based and/or the phase field-based method. The student participating in this project will gain a complete understanding of the mathematics behind topology optimization and exposed to all related Matlab tools. The result of this research experience is the numerical implementation, analysis, and application of advanced topology optimization methods in structural optimization.