| Abstract: |
| We propose and analyze a haptotaxis model for mensicus tissue regeneration, obtained by parabolic upscaling from kinetic transport equations written for the mesoscopic densities of mesenchymal stem cells and chondrocytes, which evolve in an artificial scaffold impregnated with hyaluron. We establish global existence of classical solutions to the coupled macroscopic system and investigate the qualitative behavior of solutions through stability and bifurcation analysis. They reveal that haptotaxis mechanisms primarily drive the emergence of spatial patterns. Numerical simulations further illustrate the influence of varying tactic sensitivities and initial configurations on the spatio-temporal evolution of the system. |
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