A Computational Framework for Lymph Node Physiology

Lymph nodes are vital components of the immune and lymphatic systems, playing a key role in filtering lymphatic fluid, facilitating immune cell transfer, and regulating protein content in lymph. This project aims to develop a novel mathematical model and computational framework for lymph node dynamics, capturing both lymph flow and the elastic deformation of the node, which remains largely unexplored in current models. By quantifying key parameters and processes governing these dynamics under various physiological conditions, this project will provide deeper insights into the basic function of lymph nodes. The project also supports educational development by training students who will work in a multidisciplinary environment, gaining intensive training in mathematical modeling, numerical analysis, and scientific computing, as well as developing a deep understanding of biological concepts. An outreach activity at a local K-8 school is planned, where topics related to this research will be used in hands-on workshops designed to present mathematics, modeling, and coding as exciting and accessible topics. This project addresses a critical gap in lymph node modeling by developing a multiphysics, moving-domain computational framework that couples lymph flow with the elastic deformation of the node. The model captures the interaction between an incompressible viscous fluid (lymph), a thin elastic membrane (capsule), and a poroelastic structure (inner compartments), taking into account both linear and nonlinear formulations. A novel partitioned numerical scheme based on the Robin interface conditions will be developed and rigorously analyzed for stability, convergence, and second-order accuracy. The method will be implemented in the high-performance programming language Julia and validated against published experimental data under physiological and pathological conditions. A parameter sensitivity study will be performed to identify critical model parameters and to guide estimation of coefficients that are not directly measurable. The framework will be further applied to modeling lymphadenopathy, investigating how dynamic changes in porosity, elasticity, and fluid density during immune activation alter intranodal flow patterns and lymph-blood fluid exchange. From the standpoint of biotechnology, the project will integrate an advection-diffusion transport model to study macromolecule transport through the conduit network under normal and inflammatory conditions. This novel computational framework can be integrated with in vitro models as an alternative method to validate cell therapies and drug screening. 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. NSF Award ID: 2602215 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Martina Bukac | Institution: University of Notre Dame, NOTRE DAME, IN | Award Amount: $470,116 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2602215 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2602215.html