3D Multiscale Modelling of Angiogenesis and Vascular Tumour Growth - Bioanalysis Advanced Materials Methods and Devices - page 29

interact with tumour and healthy cells. We also demonstrate how our model may be
combined with experimental data, to predict the spatio-temporal evolution of a
vascular tumour.

3.1 Introduction

Angiogenesis marks an important turning point in the growth of solid tumours.
Avascular tumours rely on diffusive transport to supply them with the nutrients
they need to grow, and, as a result, they typically grow to a maximal size of
several millimetres in diameter. Growth stops when there is a balance between the
rate at which nutrient-starved cells in the tumour centre die and the rate at which
nutrient-rich cells on the tumour periphery proliferate. Under low oxygen, tumour
cells secrete angiogenic growth factors that stimulate the surrounding vasculature
to produce new capillary sprouts that migrate towards the tumour, forming new
vessels that increase the supply of nutrients to the tissue and enable the tumour to
continue growing and to invade adjacent healthy tissue. At a later stage, small
clusters of tumour cells may enter the vasculature and be transported to remote
locations in the body, where they may establish secondary tumours and
metastases [ 12 ].
In more detail, the process of angiogenesis involves degradation of the extracel-
lular matrix, endothelial cell migration and proliferation, capillary sprout anasto-
mosis, vessel maturation and adaptation of the vascular network in response to
blood flow [ 29 ]. Angiogenesis is initiated when hypoxic cells secrete tumour
angiogenic factors (TAFs), such as vascular endothelial growth factor (VEGF)
[ 27 , 13 ]. The TAFs are transported through the tissue by diffusion and stimulate
the existing vasculature to form new sprouts. The sprouts migrate through the
tissue, responding to spatial gradients in the TAFs by chemotaxis. When sprouts
connect to other sprouts or to the existing vascular network via anastomosis, new
vessels are created. Angiogenesis persists until the tissue segment is adequately
vascularised. The diameter of perfused vessels changes in response to a number of
biomechanical stimuli such as wall shear stress (WSS) and signalling cues such as
VEGF [ 31 , 26 ]. For example, vessels which do not sustain sufficient blood flow will
regress and be pruned from the network [ 10 , 28 ].
Tumour growth and angiogenesis can be modelled using a variety of
approaches (for reviews, see [ 18 , 35 ]). Spatially averaged models can be
formulated as systems of ordinary differential equations (ODEs) (see [ 8 , 7 ]).
Alternatively, a multiphase approach can be used to develop a spatially structured
continuum model that describes interactions between tumour growth and angio-
genesis and is formulated as a mixed system of partial differential equations
(PDEs) [ 9 ]. Alternatively, a 2D stochastic model that tracks the movement of
individual endothelial cells to regions of high VEGF concentration is introduced
in [ 6 ]. Following [ 6 ], McDougall and co-workers [ 19 ] have developed a model for
angiogenesis and vascular adaptation in which the tissue composition is static and