Modelling tumour cell proliferation from vascular structure using tissue decomposition into avascular elements.

Computer models allow the mechanistically detailed study of tumour proliferation and its dependency on nutrients. However, the computational study of large vascular tumours requires detailed information on the 3-dimensional vessel network and rather high computation times due to complex geometries. This study puts forward the idea of partitioning vascularised tissue into connected avascular elements that can exchange cells and nutrients between each other. Our method is able to rapidly calculate the evolution of proliferating as well as dead and quiescent cells, and hence a proliferative index, from a given amount and distribution of vascularisation of arbitrary complexity. Applying our model, we found that a heterogeneous vessel distribution provoked a higher proliferative index, suggesting increased malignancy, and increased the amount of dead cells compared to a more static tumour environment when a homogenous vessel distribution was assumed. We subsequently demonstrated that under certain amounts of vascularisation, cell proliferation may even increase when vessel density decreases, followed by a subsequent decrease of proliferation. This effect was due to a trade-off between an increase in compensatory proliferation for replacing dead cells and a decrease of cell population due to lack of oxygen supply in lowly vascularised tumours. Findings were illustrated by an ectopic colorectal cancer mouse xenograft model. Our presented approach can be in the future applied to study the effect of cytostatic, cytotoxic and anti-angiogenic chemotherapy and is ideally suited for translational systems biology, where rapid interaction between theory and experiment is essential.