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

印第安纳大学-普渡大学印第安纳波利斯分校（IUPUI）的REU项目将为来自美国各地的8名本科生提供机会，进行应用于医学、神经科学和工程的数学研究。学生们将在印第安纳波利斯度过七个星期的暑假，与来自IUPUI数学科学系和机械工程系的教师导师一起进行四个主要项目中的一个：心脏移植患者的治疗策略建模，调查成瘾药物对大脑的影响，模拟癌细胞运动，设计新的拓扑优化方法保护结构。数学研究为学生提供了重要的技能，他们可以用来分析和解决所有学科和环境中的问题。这个项目对本科生非常有益，因为它向学生介绍跨学科研究，它将学生与将成为他们生活中重要导师和榜样的教授联系起来，它产生的新成果将影响多个科学学科，包括免疫学、肿瘤学、急诊医学和机械工程。随着世界继续以令人难以置信的速度取得技术进步，对科学家和工程师的需求也在增加。让IUPUI REU项目的学生接触应用数学研究将鼓励这些学生中的许多人在stem相关领域从事职业，并最终为美国提供拥有现代科学深厚知识的个人，并为公共和私营部门的科学和技术产生影响做好准备。REU项目解决应用数学中的新问题和开放问题，学生在各自项目上取得的进展将推动移植免疫学、流体动力学、神经科学和机械工程的研究。参加第一个REU项目的学生将与数学家和免疫学家密切合作，设计，分析和验证小鼠心脏移植和潜在的过继性转移治疗方法的数学模型。第二个项目涉及发展微流体装置和血管中癌细胞运动的数学模型，以确定减少癌细胞转移的可能方法。在第三个项目中，学生们将为选择的中脑皮层表征和滥用药物（主要是酒精）对他们的影响建立一个数学模型。行为和体内电生理方法将与计算建模相结合，整合在不同实验设置中获得的数据，以揭示酒精影响的机制，并在计算机上做出和测试预测。第四个项目将侧重于新型拓扑优化方法的解析推导和数值实现及其在防冲击结构设计中的应用。学生将运用数值方法来确定最有效的材料分布，以合成复杂的高性能结构，而不需要任何先入为主的形状。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.