An anisotropic model of vascular tumour growth: implications for vascular collapse

摘要

It has been demonstrated recently that stress relaxation may be accommodated in a linear-elastic model of tissue growth without recourse to a viscoelastic constitutive law by considering growth as an anisotropic process. This paper incorporates the concept of anisotropic growth in a model which examines the evolution of stresses in a growing vascular tumour, attempting to elucidate the observed phenomenon of vascular collapse. This new model allows the growing tumour to develop two distinct regions: a rapidly growing, well-vascularised outer region, and a central region where the growth-induced stresses cause vascular collapse. The Lax-Wendroff method is modified to accommodate a growing two-region domain, so that stresses are calculated at a fixed number of evenly-distributed moving grid points.The two-region model is characterised by a nutrient concentration distribution which causes stresses to increase with distance from the tumour boundary up to a maximum value close to the boundary between the two regions. Beyond this point, stresses reduce, reaching a minimum at the tumour core. Hence, the model provides interesting insight into experiments which have demonstrated that in many tumours, an open connection with the systemic circulation exists only in the peripheral layer due to vascular collapse, with the inner region containing patent vessels with intact red blood cells.