Global existence of weak solutions to a cell migration and (de)differentiation model with double haptotaxis in the context of tissue regeneration

TL;DR

This paper proves the global existence of weak solutions for a complex cross-diffusion system modeling cell migration and differentiation influenced by double haptotaxis, relevant to tissue regeneration.

Contribution

It introduces a novel mathematical proof establishing global weak solutions for a new cell migration model with double haptotaxis.

Findings

Proved global existence of weak solutions.

Established mathematical framework for cell migration models.

Enhanced understanding of tissue regeneration dynamics.

Abstract

We study a model for the spread and (de)differentiation of mesenchymal stem cells and chondrocytes in a scaffold whose fibers are coated with hyaluron. The chondrocytes produce new extracellular matrix, which, together with hyaluron, serves as haptotactic cue for the stem cell migration. We prove global existence of weak solutions of the corresponding cross-diffusion system with double haptotaxis.