REU Site: Mathematics with Applications to Medical Sciences, Biophysics, and Inverse Problems at IUPUI

Indiana University, Bloomington IN

Investigators

Abstract

This program of Research Experiences for Undergraduates (REU) at Indiana University-Purdue University Indianapolis (IUPUI) will provide eight undergraduate students from across the United States with the opportunity to conduct applied mathematics research in the medical sciences, biophysics, and inverse problems. The students will spend eight weeks during the summer working with faculty mentors from the IUPUI Department of Mathematical Sciences on one of four main projects: (i) modeling the redistribution of blood flow and pressure in the leg following a major arterial occlusion, (ii) investigating the influence of abused drugs on the human brain, (iii) analyzing the diffusion dynamics of biomolecules, and (iv) uncovering methods to solve inverse problems for phase retrieval, gravitational fields, and acoustic waves. Research in mathematics provides students with important skills that they can use to analyze and solve problems in all disciplines and environments. The projects in this program will also train students to answer specific questions in vascular surgery, emergency medicine, biophysics, and astronomy. As the world continues to make technological advances at an incredibly rapid pace, there is an increased need for scientists and engineers. Exposing the 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 award is supported by the Division of Mathematical Sciences (DMS) in the Directorate for Mathematical and Physical Sciences (MPS) and the Division of Biological Infrastructure (DBI) in the Directorate for Biological Sciences (BIO). The REU projects address new and open problems in applied mathematics, and the progress that the students make on the summer projects will advance these research areas. Students participating in the first REU project will work closely with a mathematician and vascular physiologist to develop a model, based on experiments conducted in the mouse hind limb, to simulate the effects of increased vascular number or diameter on blood flow following a major arterial occlusion to determine whether angiogenic or arteriogenic therapies provide the maximum benefit. The second project involves the development of a mathematical model for the response of the human brain to drugs. The model will be based on electrophysiological experiments, and the inputs, intrinsic properties, and release of dopamine will be modeled. In the third project, students will explore a framework for diffusion dynamics motivated by the observations that the heat released from a catalytic reaction enhances an enzyme's diffusion coefficient by causing a sudden center of mass translation of the enzyme, and that particles and biomolecules of various types and sizes diffuse faster inside cells with an active metabolism. The students will explore a novel framework based on the regular Fokker-Planck equation (which describes diffusion driven by forces and random Brownian motion) to determine the importance of inertial effects for a protein. Students working on the fourth project will be studying a variety of inverse problems and solutions based on algebraic and analytic algorithms. The students will tackle problems of phase retrieval that arise in the experimental use of diffraction to determine internal structure, as well as inverse problems for gravitational fields and acoustical waves.