The future of cancer treatment optimization will depend on the seamless integration of experimental research and theoretical modeling. A significant challenge in oncology is the limited understanding of how therapeutic interventions influence the tumor microenvironment and how immune responses contribute to tumor regression. This knowledge gap is particularly pronounced in aggressive cancers such as triple-negative breast cancer (TNBC), which lacks standard biomarkers and remains difficult to treat. Our collaborative research focuses on developing a quantitative framework to investigate coupled immune and chemotherapeutic interventions. Specifically, we employ novel radiolabeled T-cell tracking to gain detailed insights into immunomodulation over time and use these data to inform optimal therapy scheduling strategies. In this talk, we will present ordinary differential equation (ODE) models that describe the dynamics of combined therapy, comparing scenarios with and without T-cell observations. Additionally, we will discuss the broader implications of this modeling approach, including its potential extension to organ-level analyses and the application of optimal control techniques to refine treatment strategies. Through this integrated approach, we aim to improve the predictive power of cancer treatment models and contribute to more effective, personalized therapeutic protocols.

Interfacial instabilities in volatile liquid thin films on a hydrophobic substrate can lead to complex droplet dynamics, such as droplet merging, splitting, and transport. Controlling these fundamental droplet behaviors is essential for digital microfluidics in biomedical and electric applications. In this talk, I will present our recent work on mean-field control of thin film droplets. We design an optimal control problem by formulating droplet dynamics as gradient flows of free energies in modified optimal transport metrics with nonlinear mobilities. As an example, we consider a thin volatile liquid film laden with an active suspension, where control is achieved through its activity field. Numerical examples, including droplet transport, bead-up/spreading, and merging/splitting, demonstrate the effectiveness of the proposed control mechanism.  

Over the summer, I attended the Early Graduate Research in Applied Mathematics Conference at Caltech in Pasadena, CA. This week-long event brought together graduate students from across the country to connect, share research interests, and build community. Through professional development sessions and hands-on activities, participants explored a wide range of applied mathematics topics, with special focus on using neural ordinary differential equations (ODEs) to model biological processes. In this talk, I will detail my experience investigating these topics and highlight the many professional development opportunities offered at this event.

I will then discuss my current research, which involves the development of an ordinary differential equation model to examine the dynamic relationship between inflammation, pain, and sleep in patients with sickle cell disease (SCD). The model consists of four compartments including pro-inflammation, anti-inflammation, pain, and sleep, with feedback mechanisms that capture clinically observed interactions. Specifically, pain disrupts sleep, poor sleep promotes inflammation, and elevated inflammation amplifies pain. The overall goal of this work is to identify interventions that could mitigate the impact of key feedback loops, which would provide insight into potential strategies for reducing pain crises in SCD.