Collaborative Research: Analysis of Nonsmooth Oscillatory Dynamical Systems with Applications to the Lower Urinary Tract

Lower urinary tract (LUT) dysfunction is a pervasive public health challenge across the U.S. It affects millions of Americans by severely altering their quality of life and introducing substantial economic costs to the healthcare system. Developing effective treatments for LUT dysfunction is challenging because in most cases the underlying causes of symptoms are poorly understood. Medical research in this area typically relies on animal studies to explore the causes of these symptoms, but this route is costly, invasive, and time-consuming. This project addresses this critical societal challenge by developing mathematical tools capable of determining the hidden factors behind LUT dysfunctions and their corresponding symptoms. Two integrated aims drive this project: 1) Develop advanced models that mimic the LUT cycle to identify how changes in bladder behavior affect how well the organ empties (a key marker of overall LUT health); and 2) Create reliable, easy-to-use methods to predict bladder function and health, and verify that these predictions are accurate using the team’s extensive library of animal study data. By building predictive models of biological behavior, this research establishes a foundational framework for advances in biotechnology that will allow researchers to rapidly and non-invasively evaluate potential treatments. Beyond its medical contributions, the project delivers broader societal impacts by advancing biotechnology workforce training and expanding local research capacity for mathematical innovations. Moreover, this project actively integrates research outcomes into higher education curricula and develops hands-on learning modules for K-12 classrooms, paving new pathways for the next generation of STEM leaders. Motivated by a poor understanding of dysfunctions of the lower urinary tract (LUT), which represents a pervasive public health challenge in the U.S., this project establishes a rigorous framework to analyze the physiological cycling of the LUT. Because the LUT functions as a piecewise system that transitions discontinuously between gradual filling and abrupt voiding, standard mathematical approaches fail to accurately capture its dynamics. To resolve this issue, the project team will make novel theoretical contributions in nonsmooth dynamical systems theory and generalized derivatives. The goal of the project is to address fundamental biological questions concerning the LUT, by creating tools that link switching dynamics to clinically relevant patterns of dysfunction. Accordingly, two interrelated aims drive this project: 1) Develop new practically implementable theory for nonsmooth oscillatory dynamical systems capable of characterizing parametric sensitivities, to determine how cycles impact bladder voiding efficiency; and 2) Create new tools for determining the existence and structural stability of cycles in nonsmooth oscillatory dynamical systems, to validate predictions using the team’s database of lower urinary tract animal studies. These contributions will help make it possible to computationally assess hypotheses about the causes of LUT symptoms and dysfunctions. Beyond this application, this work directly impacts the field of computational biology and biotechnology by providing a framework and toolkit suitable for large-scale, complex physiological systems. The mathematical techniques developed in this project for nonsmooth systems will provide predictive computational tools with broad applicability to other biological processes and bioengineering systems. 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.