Multistability and switching dynamics in vascular networks

Thesis

The formation of regions of low oxygen concentration, or hypoxia, within tumours is a hallmark of many types of cancer. Oxygen starvation of cancerous cells within tumours creates an environment that causes tumours to become more aggressive and more resistant to treatment. Hypoxia within tumours is described as chronic or cycling. Chronic-hypoxia describes permanently hypoxic regions of tissue, and cycling-hypoxia describes short term fluctuations of hypoxia. Counterintuitively, the short term application of oxygen to hypoxic regions does not reverse the negative impact of hypoxia and in many cases exacerbates the negative health impacts associated with hypoxia. A recent hypothesis for the formation of chronic-hypoxia based on the equilibria of steady-state models of blood flow in vasculature networks has been computationally verified. Blood flow within the vasculature dictates the distribution of RBCs (Red Blood Cells) within a tumour, and if the distribution of RBCs for a blood flow equilibrium is asymmetric and uneven, then the tissue surrounding vessels with fewer RBCs suffers hypoxia.

Our goal for this thesis is to expand upon blood flow models to propose a possible mechanistic explanation for the formation of cycling-hypoxia. We propose a model of blood flow switching between multiple stable equilibria of vascular networks. In this thesis we link the existence of multiple equilibria with the change in the flow direction in network motifs. After demonstrating the importance of flow direction for the existence of multiple equilibria, we show that stochastic fluctuations of RBC partitioning at vessel junctions can force the blood flow in vasculature to change direction, resulting in the blood flow switching between stable equilibria. We hypothesise that this switching of the blood flow between at least two equilibria may result in part of a tumour being exposed to cycles of normoxic and hypoxic conditions.

Authors: Atkinson, GW

• DOI: 10.5287/ora-nzzkbxeoq
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: networks; rheology; multistability; Haematocrit; red blood cells; fluid mechanics; stochasticity; microcirculation
• Subjects: Biology--Mathematical models; Biology; Mathematics