Angiogenesis is the growth of new vasculature from existing blood vessels and is widely acknowledged to be a fundamental process that underpins cancer growth, invasion and metastasis. A growing, avascular tumour receives the nutrients it requires for growth via diffusion from the existing vasculature. Beyond a critical tumour size, nutrient gradients produce internal regions of hypoxia that induce tumour cells to secrete tumour angiogenic growth factors (TAFs), stimulating growth of endothelial sprouts towards the TAF-gradient field and forming new vascular networks. In order to study the effect of a given component in tumour-induced angiogenesis and characterize its physical origins, it is instructive to construct physiologically-representative in silico models. Whereas previous studies have explored the chemical i.e. solute-driven underpinning of both tumour growth and angiogenesis, here we extend these frameworks significantly to focus on the interplay between angiogenic network evolution and growth-induced solid stresses through (a) a hapto- and mechanotactic stimulus for vessel sprouting, and (b) a mechanics-based capillary wall remodelling.

A discrete three-dimensional model of vascular sprouting describes angiogenic response to TAF secretion, where the sprout-tips are represented as point masses in a continuum substratum. The secretion of TAFs and matrix metalloproteases (MMPs) by the tumour and vasculature, respectively, are described by coupled reaction-diffusion equations, and tumour growth is modelled according to a Gompertz-type relation, with the biomechanical response of the tumour-host at the macroscopic tissue scale modelled as a Green-elastic material. Capillary elongation, branching and remodelling are dependent upon mechanical factors, such as traction and magnitude of wall shear stress in a blood flow model that couples Poiseuille flow in the vasculature to Darcy's law in the interstitium, via Starling's law to describe the transvascular fluid flux. The developed three-dimensional finite element model is capable of simulating tumour-induced angiogenesis, and is validated against novel in vivo data on vascular density and structure, interstitial fluid pressure and mean solid stress from murine mammary carcinomas, specifically focusing on the role of mechanical signals in recapitulating in vivo measurements.