ABSTRACT

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.

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