2025/09/10 by Malte Mederacke, Mederacke, Malte, Cheng‐Rong Yu +6 · 1 voice
Mathematics · Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Mathematical Biology Tumor Growth #Cellular Mechanics and Interactions #Micro and Nano Robotics
paper · pdf · doi:10.48550/arxiv.2509.08930
We present a COMSOL Multiphysics implementation of a continuum model for directed cell migration, a key mechanism underlying tissue self-organization and morphogenesis. The model is formulated as a partial integro-differential equation (PIDE), combining random motility with non-local, density-dependent guidance cues to capture phenomena such as cell sorting and aggregation. Our framework supports simulations in one, two, and three dimensions, with both zero-flux and periodic boundary conditions, and can be reformulated in a Lagrangian setting to efficiently handle tissue growth and domain deformation. We demonstrate that COMSOL Multiphysics enables a flexible and accessible implementation of PIDEs, providing a generalizable platform for studying collective cell behavior and pattern formation in complex biological contexts.