Multiscale Dynamics of Blood Flow and Associated Cycling Hypoxia in Vascular Tumours

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It has long been hypothesised that the abnormal and heterogeneous architecture of tumour vascular networks promotes irregular spatio-temporal variations in blood flow rates, haematocrit distribution, and consequent oxygen delivery. These irregularities can cause the formation of cyclic hypoxic areas - regions experiencing transient periods of oxygen deprivation and reoxygenation. Exposure to such fluctuating oxygen levels is assumed to select and promote metastatic spread and resistance to radio- and chemo-therapy. Consequently, understanding the microstructural and fluid-dynamic mechanisms that promote macroscopic oxygenation oscillations and how they may be clinically altered is of great importance.The goal of this project is to develop a multiscale mathematical framework to model blood flow and oxygen transport within vascular tumours, in order to shed light on the links between microscopic haemodynamic mechanisms and the emergence of cycling hypoxia at the macroscale. The methodology will be based on multiple-scale homogenisation - a formal mathematical approach used to derive systems of continuum equations, by upscaling descriptions of transport phenomena from the single capillary scale to the macroscopic scale of the tumour. Using this method, I will establish how microstructural vascular heterogeneities, together with flow-nonlinearities induced by haematocrit-dependent blood viscosity and biased haematocrit partitioning at vessel branch-points, can lead to macroscopic flow-oscillations and consequent unsteady tissue oxygenation. The mathematical framework thus developed could be used, in the longer term, to identify tumour structures that will benefit from transient vascular normalisation treatments, to predict the consequent effect of such protocols on diminishing hypoxia, and thereby improve and personalise tumour responses to existing treatments.