The influence of tumour vasculature on fluid flow in solid tumours: a mathematical modelling study.

Tumour vasculature is known to be aberrant, tortuous and erratic which can have significant implications for fluid flow. Fluid dynamics in tumour tissue plays an important part in tumour growth, metastasis and the delivery of therapeutics. Mathematical models are increasingly employed to elucidate the complex interplay between various aspects of the tumour vasculature and fluid flow. Previous models usually assume a uniformly distributed vasculature without explicitly describing its architecture or incorporate the distribution of vasculature without accounting for real geometric features of the network. In this study, an integrated computational model is developed by resolving fluid flow at the single capillary level across the whole tumour vascular network. It consists of an angiogenesis model and a fluid flow model which resolves flow as a function of the explicit vasculature by coupling intravascular flow and interstitial flow in tumour tissue. The integrated model has been used to examine the influence of microvascular distribution, necrosis and vessel pruning on fluid flow, as well as the effect of heterogeneous vessel permeability. Our results reveal the level of nonuniformity in tumour interstitial fluid pressure (IFP), with large variations in IFP profile between necrotic and non-necrotic tumours. Changes in microscopic features of the vascular network can significantly influence fluid flow in the tumour where removal of vessel blind ends has been found to reduce IFP and promote interstitial fluid flow. Our results demonstrate the importance of incorporating microscopic properties of the tumour vasculature and intravascular flow when predicting fluid flow in tumour tissue.