A Continuum Mathematical Model of Substrate-Mediated Tissue Growth.

ABSTRACT: We consider a continuum mathematical model of biological tissue formation inspired by recent experiments describing thin tissue growth in 3D-printed bioscaffolds. The continuum model, which we call the substrate model, involves a partial differential equation describing the density of tissue, [Formula: see text] that is coupled to the concentration of an immobile extracellular substrate, [Formula: see text]. Cell migration is modelled with a nonlinear diffusion term, where the diffusive flux is proportional to [Formula: see text], while a logistic growth term models cell proliferation. The extracellular substrate [Formula: see text] is produced by cells and undergoes linear decay. Preliminary numerical simulations show that this mathematical model is able to recapitulate key features of re

SUBMITTER: El-Hachem M 

PROVIDER: S-EPMC8891221 | biostudies-literature | 2022 Mar

REPOSITORIES: biostudies-literature