Modelització matemàtica i computacional de l'homeòstasi dinàmica de organoides de l'intestí prim

Homeostasis is a process by which biological systems maintain stability in an evolving environment. However, homeostasis is far from being a static state. In rapidly self-renewing tissues such as the small intestine epithelium, most cells are replaced every few days, and during their lifespan undergo differentiation and migrate over long distances along gradients of cell shape and density. We model mathematically and computationally intestinal organoids, a simpler in-vitro system which captures the essential features of intestinal homeostasis. To model this system, we adopt a continuum hydrodynamic model where the system is described in terms of the cell number density and the concentration of morphogen Wnt. We provide a systematic derivation of the model, its numerical discretization, and examine its ability to self-organize into dynamical steady-states, which closely mimic the experimental observations in terms of cell density fields, velocity fields and division/extrusion patterns