Complex problems in biomedicine often need to be modeled by multiscale couplings between partial differential equations (PDEs) and ordinary differential equations (ODEs), in order to combine the accurate three-dimensional (3D) description of a local region of interest with the global features of the problem represented by reduced lumped models. We focus on a PDE/ODE system stemming from the multiscale interface coupling between a local description of tissue perfusion via a 3D deformable porous medium and a 0D lumped hydraulic circuit accounting for the blood circulation to and from the tissue. We present solution methods of the multiscale problem described above, focusing on a detailed comparison between functional iterations and an energy-based operator splitting method and how they handle the nonlocal interface conditions.
Analysis of a Multiscale Model based on the Coupling of ODEs and PDEs for Tissue Perfusion
Lorena Bociu, NC State University
2023 AWM Research Symposium
Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]