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

长期以来，人们一直假设，肿瘤血管网络的异常和异质结构促进了血流速度、红细胞压积分布和随后的氧气输送的不规则时空变化。这些不规则性会导致周期性缺氧区的形成--经历短暂的缺氧和复氧的区域。暴露在这种波动的氧气水平下，被认为是选择和促进转移扩散和对放化疗的抵抗。因此，了解促进宏观氧合振荡的微观结构和流体动力学机制以及如何在临床上改变它们是非常重要的。本项目的目标是建立一个多尺度的数学框架来模拟血管肿瘤内的血液流动和氧气运输，以阐明微观血流动力学机制与宏观上循环性缺氧的出现之间的联系。该方法将基于多尺度均质化，这是一种正式的数学方法，用于通过将对传输现象的描述从单个毛细血管尺度提升到肿瘤的宏观尺度来推导连续统方程系统。使用这种方法，我将确定微结构血管的不均一性，以及由依赖于红细胞压积的血液粘度和血管分支点的偏向红细胞压积分配所引起的流动非线性，如何导致宏观的血流振荡和随后的不稳定的组织氧合。从长远来看，这样开发的数学框架可以用来识别将从瞬时血管正常化治疗中受益的肿瘤结构，预测这种方案在减少缺氧方面的后续效果，从而改善和个性化肿瘤对现有治疗的反应。

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.