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液流速、红细胞压积分布和随之而来的氧气输送的不规则时空变化。这些不规则性会导致循环缺氧区域的形成，即经历短暂缺氧和再氧合的区域。暴露于这种波动的氧水平被认为是选择和促进转移性扩散和对放疗和化疗的耐药性。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它们如何在临床上改变是非常重要的。该项目的目标是建立一个多尺度数学框架来模拟血管肿瘤内的血流和氧运输，以揭示微观血流动力学机制与宏观循环缺氧出现之间的联系。该方法将基于多尺度均质化——一种用于推导连续统方程系统的正式数学方法，通过将传输现象的描述从单个毛细管尺度提升到肿瘤的宏观尺度。使用这种方法，我将建立微结构血管的异质性，以及由红细胞压积依赖的血液粘度和血管分支点的红细胞压积偏倚分配引起的流动非线性，如何导致宏观的流动振荡和随之而来的不稳定的组织氧合。从长远来看，由此开发的数学框架可用于识别将受益于短暂血管正常化治疗的肿瘤结构，预测此类方案对减少缺氧的后续影响，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.