Xiangrong Li

TL;DR: In this paper, the authors provide an overview of multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis, and limit the scope further by considering models of tumor progression that do not distinguish tumour cells by their age and do not consider immune system interactions nor do they describe models of therapy.

TL;DR: This work shows that taxis may play a role in tumor invasion and that when nutrient plays the role of a chemoattractant, the diffusional instability is exacerbated by nutrient gradients, as predicted by linear stability theory.

TL;DR: A general approach for solving partial differential equations in complex, stationary, or moving geometries with Dirichlet, Neumann, and Robin boundary conditions with matched asymptotic expansions is presented.

TL;DR: A method is presented to solve two-phase problems involving a material quantity on an interface that can be advected, stretched, and change topology, and material can be adsorbed to or desorbed from it.

TL;DR: A simple go-or-grow model is formulated to investigate the dynamics of a population of glioma cells for which the switch from a migratory to a proliferating phenotype (and vice versa) depends on the local cell density.