LEAPS-MPS: Mathematical Modeling of Targeted Drug Delivery: Unifying Lighthill and Taylor Theories

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。靶向给药技术的出现使纳米医学和患者护理取得了重大进展。在这个临床过程中，载体在特定部位运输和释放药物，从而最大限度地减少对健康细胞和组织的负面副作用。为了优化递送，通常使用各种方法来指导载体，包括模拟微生物推进的技术。这一跨学科项目将为综合靶向给药框架奠定基础。它结合了生物学、计算科学、数学和物理学来开发优化载体路径和释放的策略和条件。研究结果将为控制携带者安全用药的方法提供见解。该项目还将支持和帮助培训所有STEM领域的学生。该项目将利用该研究中的问题开发基于项目的课程，为陶森大学的学生提供研究实践经验。将积极招募代表性不足的学生，并鼓励他们在项目中担任领导角色。这些学生将受益于全年接触先进的数学方法和与其他研究人员的互动，帮助他们对自己的科学身份更有信心。因此，该项目将直接有助于增加研究生院和其他STEM职业中代表性不足的学生的代表性。该项目还将影响陶森大学，为有动力的学生提供更多应用研究的机会。这些机会将进一步提高陶森大学在巴尔的摩地区的知名度，并使其成为数学和物理科学前沿变革研究的有吸引力的目的地。该项目适合于一个复杂的、多部分的、多尺度的动态系统，该系统将捕捉靶向给药的基本原理。目标是利用偏微分方程、流体动力学和包括神经网络在内的数值方法，开发一个新的数学/计算框架，用于在直流电场中包裹在软颗粒中的微生物的游泳。作为第一步，在直流电场中，包裹在表面活性剂覆盖的液滴中的推进纤毛微生物的理想表示将用于描述带电介质中药物载体的定向运动。解析和数值工具将有助于探索和解决控制问题的偏微分方程，包括球面谐波、渐近分析和机器学习。具体来说，对于超出分析模型有效性范围的条件，将使用物理信息神经网络在数值上近似求解。在此开发的模型和技术具有内在的数学价值，源于当代跨学科的应用，如微机器人推进和微流体。它们还体现了广泛的研究活动，包括生物有机体的游泳动力学和软颗粒的电流体动力学。一旦完成，该项目还将为物理信息神经网络的超参数提供统一而有效的收敛理论。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。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). The advent of Targeted Drug Delivery has led to significant progress in nano-medicine and patients' care. In this clinical process, a carrier transports and releases drugs at a specific site, thus minimizing negative side effects on healthy cells and tissues. To optimize delivery, the carrier is often directed using various methods, including technologies that mimic the propulsion of microorganisms. This interdisciplinary project will lay the foundations for an integrated Targeted Drug Delivery framework. It combines biology, computational sciences, mathematics, and physics to develop strategies and conditions for optimizing the carrier's path and release. The research results will provide insights into the ways carriers can be controlled to safely administer drugs. The project will also support and help to train students in all STEM fields. The PI will use problems from this research to develop project-based courses that provide Towson University students with hands-on experience in research. Underrepresented students will actively be recruited and encouraged to take leading roles in the project. These students will benefit from year-round exposure to advanced mathematical methods and interactions with other researchers, helping them to grow more confident in their science identity. As a result, this project will directly contribute to increasing the representation of underrepresented students in graduate schools and other STEM careers. The project will also impact Towson University by providing more opportunities in applied research for motivated students. These opportunities will further raise Towson University's profile in the Baltimore region and turn it into an attractive destination for cutting-edge transformative research in the mathematical and physical sciences.The project fits into a complex, multipart, and multiscale dynamic system that will capture the fundamentals of Targeted Drug Delivery. The goal is to develop a new mathematical/computational framework for the swimming of microorganisms enclosed in a soft particle in dc electric field using partial differential equations, fluid dynamics, and numerical methods including neural networks. As a first step, an idealized representation of a propelling ciliated microorganism enclosed in a surfactant-covered drop in a dc electric field will be used to describe the directed motion of a drug carrier in an electrified medium. Analytical and numerical tools will help to probe and solve the partial differential equations that govern the problem, including spheroidal harmonics, asymptotic analyses, and machine learning. Specifically, for conditions beyond the analytical models' range of validity, solutions will be approximated numerically using physics-informed neural networks. The models and techniques developed herein have intrinsic mathematical merit, arising from contemporary interdisciplinary applications such as microrobots propulsion and microfluidics. They also embody a broad scope of research activities including swimming dynamics of biological organisms and electrohydrodynamics of soft particles. Once completed, this project will also result in a unified and efficient convergent theory for hyperparameters of physics-informed neural networks.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.