The growth and development of solid tumours occurs in two distinct stages—the avascular
growth phase and the vascular growth phase. During the former growth phase the tumour …

In this paper we build on the mathematical model of Ward and King (1998) to study the
effects of high molecular mass mitotic inhibitors released at cell death. The model assumes …

We present a mathematical model of the growth of tumours. The cells in the tumour are
taken to proliferate and die at rates determined by the concentration of oxygen which …

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

We present a physiologically structured lattice model for vascular tumor growth which
accounts for blood flow and structural adaptation of the vasculature, transport of oxygen …

In this chapter we present a variety of reaction-diffusion-taxis (ie macroscopic) models of
several key stages of solid tumour growth–avascular growth, the immune response to solid …

In this paper, we carry out an examination of four mechanisms that can potentially lead to
changing morphologies in a growing tumor: variations in nutrient consumption rates, cellular …

Competition for available nutrients and the presence of anatomical barriers are major
determinants of tumor growth in vivo. We extend a model recently proposed to simulate the …

In this paper, we present and investigate a model for solid tumor growth that incorporates
features of the tumor microenvironment. Using analysis and nonlinear numerical …

In this paper we present a new model framework for studying vascular tumour growth, in
which the blood vessel density is explicitly considered. Our continuum model comprises …