A Multiphase Model Describing Vascular Tumour Growth

A multiphase model describing vascular tumour growth.

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 conservation of mass and momentum equations for the volume fractions of tumour cells, extracellular material and blood vessels. We include the physical mechanisms that we believe to be dominant, namely birth and death of tu...

“Cell Adhesion and Re-organisation in a Multiphase Model Describing Tumour and Tissue Growth”

Multiphase Models of Tumour Growth

A Mathematical Model of Vascular Tumour Growth and Invasion

In this paper, we develop a model of the vascularization and subsequent growth of a solid spherical tumour. The key elements that are encapsulated in this model are the development of a central necrotic core due to the collapse of blood vessels at the centre of the tumour and a peak of tumour cells advancing towards the main blood vessels together with the regression of newly{formed capillaries...

A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis

We derive a Cahn–Hilliard–Darcy model to describe multiphase tumour growth taking interactions with multiple chemical species into account as well as the simultaneous occurrence of proliferating, quiescent and necrotic regions. Via a coupling of the Cahn–Hilliard–Darcy equations to a system of reaction-diffusion equations a multitude of phenomena such as nutrient diffusion and consumption, angi...