Global existence of weak solutions to a tissue regeneration model

2025/11/03 by Nishith Mohan, Mohan, Nishith, Christina Surulescu +1
Mathematics · Engineering · Biochemistry, Genetics and Molecular Biology · #Mathematical Biology Tumor Growth #3D Printing in Biomedical Research #Cellular Mechanics and Interactions

paper · pdf · doi:10.48550/arxiv.2511.01335

Abstract

We study a cross-diffusion model for tissue regeneration which involves the dynamics of human mesenchymal stem cells interacting with chondrocytes in a medium containing a differentiation factor. The latter acts as a chemoattractant for the chondrocytes and influences the (de)differentiation of both cell phenotypes. The stem cells perform haptotaxis towards extracellular matrix expressed by the chondrocytes and degraded by themselves. Cartilage production as part of the extracellular matrix is ensured by condrocytes. The growth factor is provided periodically, to maintain the cell dynamics. We provide a proof for the global existence of weak solutions to this model, which is a simplified version of a more complex setting deduced in \citesurulescu_AMM.

Citations

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Related

• Global existence of weak solutions to a cell migration and (de)differentiation model with double haptotaxis in the context of tissue regeneration
• On a mathematical model for tissue regeneration
• Cell seeding dynamics in a porous scaffold material designed for meniscus tissue regeneration
• An in-silico approach to meniscus tissue regeneration: Modeling, numerical simulation, and experimental analysis
• A mathematical model for meniscus cartilage regeneration