REU Site: IUPUI REU Program in Mathematics with Applications to Medicine, Neuroscience, and Engineering

Indiana University, Bloomington IN

Investigators

Abstract

The 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 applied to medicine, neuroscience, and engineering. The students will spend seven weeks during the summer in Indianapolis working with faculty mentors from the IUPUI Department of Mathematical Sciences and Department of Mechanical Engineering on one of four main projects: modeling treatment strategies for heart transplant patients, investigating the influence of addictive drugs on the brain, simulating cancer cell motion, and designing novel topology optimization methods for impact-protective structures. Research in mathematics provides students with important skills that they can use to analyze and solve problems in all disciplines and environments. This program is extremely beneficial to undergraduate students because it introduces students to interdisciplinary research, it connects students with professors who will become important mentors and role models in their lives, and it yields new results that will impact multiple scientific disciplines, including immunology, oncology, emergency medicine, and mechanical engineering. As the world continues to make technological advances at an incredibly rapid pace, there is an increased need for scientists and engineers. Exposing the IUPUI REU Program students to applied mathematics research will encourage many of these students to pursue careers in STEM-related fields and will ultimately provide the United States with individuals who possess a deep knowledge of modern science and who are well equipped to have an impact on science and technology in the public and private sectors. The REU projects address new and open problems in applied mathematics, and the progress that the students make on the respective projects will advance research in transplant immunology, fluid dynamics, neuroscience, and mechanical engineering. Students participating in the first REU project will work closely with a mathematician and immunologist to design, analyze, and validate a mathematical model of mouse heart transplantation and potential adoptive transfer therapeutic approaches. The second project involves the development of a mathematical model of cancer cell motion in microfluidic devices and vessels in order to determine possible methods for decreasing cancer cell metastasis. In the third project, the students will develop a mathematical model for mesocortical representations of choices and the influence of drugs of abuse (mainly alcohol) on them. Behavioral and in vivo electrophysiological approaches will be combined with computational modeling to integrate data obtained in different experimental setups to reveal mechanisms of alcohol influence and to make and test predictions in silico. A fourth project will focus on the analytical derivation and numerical implementation of novel topology optimization methods and their application to the design of impact-protective structures. Students will apply a numerical approach to determine the most effective material distribution for synthesizing complex, high-performance structures without any preconceived shape. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.