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、神经科学和工程学的数学研究。暑假期间，这些学生将在印第安纳波利斯与IUPUI数学科学系和机械工程系的教师导师一起，就四个主要项目之一进行工作：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，以及为碰撞保护结构设计新的拓扑优化方法。数学研究为学生提供了重要的技能，他们可以使用这些技能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，它将学生与教授联系起来，他们将成为他们生活中的重要导师和榜样，它产生的新结果将影响多个科学学科，包括免疫学、肿瘤学、急救医学和机械工程。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越来越大。让IUPUI REU项目的学生接触应用数学研究将鼓励其中许多学生在STEM相关领域追求职业生涯，并最终为美国提供拥有深厚现代科学知识并具备在公共和私营部门对科学和技术产生影响的个人。REU项目解决了应用数学中新的和开放的问题，学生在各自项目上取得的进展将促进移植免疫学、流体动力学、神经科学和机械工程的研究。参与第一个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的数学模型和潜在的采用转移治疗方法。第二个项目涉及开发一个癌细胞在微流控装置和血管中运动的数学模型，以确定减少癌细胞转移的可能方法。在第三个项目中，学生们将开发一个数学模型，用来描述选择和滥用药物(主要是酒精)对它们的影响。行为和活体电生理学方法将与计算建模相结合，以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，并在硅胶中进行预测和测试。第四个项目将侧重于新的拓扑优化方法的解析推导和数值实现，以及它们在冲击防护结构设计中的应用。学生将应用数值方法来确定最有效的材料分布，以合成复杂、高性能的结构，而没有任何先入为主的形状。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.