In this paper we examine spatio-temporal pattern formation in reaction-diffusion systems on
the surface of the unit sphere in 3D. We first generalise the usual linear stability analysis for …

The early development of solid tumours has been extensively studied, both experimentally
via the multicellular spheroid assay, and theoretically using mathematical modelling. The …

In this paper a generalized model for the growth of avascular tumours is presented. The
formulation leads naturally to the incorporation of free boundaries which define the outer …

Interactions between tumor cells and their environment lead to the formation of microregions
containing nonhomogeneous subpopulations of cells and steep gradients in oxygen …

We address the problem of pattern formation on the surface of a sphere using Turing
equations. By considering a generic reaction-diffusion model, we numerically investigate the …

We study two-species reaction–diffusion systems on growing manifolds, including situations
where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear …

Tumor spheroids grown in vitro have been widely used as models of in vivo tumor growth
because they display many of the characteristics of in vivo growth, including the effects of …

Based on first principles, we derive a general model to describe the spatio-temporal
dynamics of two morphogens. The diffusive part of the model incorporates the dynamics …

Solid tumors, whether in vitro or in vivo, are not an undifferentiated mass of cells. They
include necrotic regions, regions of cells that are in a quiescent state (either slowly growing …

To what extent the growth dynamics of tumors is controlled by nutrients, biomechanical
forces and other factors at different stages and in different environments is still largely …