Mathematical modeling of regenerative processes in axolotl spinal cord

CALIARO VALERIA; PEURICHARD DIANE; CHARA OSVALDO

Marsella

Conferencia; Mathematics of Complex Systems in Biology and Medicine; 2020

CIRM - Centre International de Rencontres Mathématiques

Tissue response after amputation induces either scar formation or regeneration and, in particular, regeneration has been observed and described in axolotl. However, what are the mechanisms implicated in the regulation of regenerative processes and what is their role remains poorly understood. Our goal is to develop a numerical model for tissue regeneration and to use it toexplore the main mechanisms influencing spinal cord regeneration in axolotl. In particular, we are currently developing a 2D hybrid model where individual 2D spheres interact via mechanical repulsion with their close neighbours (agent-based model) and divide randomly with a division rate depending on a chemical signal diffusing through the tissue (continuous field). We developed a Fortran90 code to numerically explore the behaviour of solutions as function of the parameters, and the simulations will be confronted to experimental data in order to identify the main mechanisms in tissue regeneration. The next step will consist in exploring the limit of large number of individuals to derive the macroscopic (PDE) model from the agent-based formulation, in order to perform the mathematical analysis of the corresponding macroscopic equation.