# Angiogenesis and vascular remodelling in normal and cancerous tissues

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## Abstract

Vascular development and homeostasis are underpinned by two fundamental features: the generation of new vessels to meet the metabolic demands of under-perfused regions and the elimination of vessels that do not sustain flow. In this paper we develop the first multiscale model of vascular tissue growth that combines blood flow, angiogenesis, vascular remodelling and the subcellular and tissue scale dynamics of multiple cell populations. Simulations show that vessel pruning, due to low wall shear stress, is highly sensitive to the pressure drop across a vascular network, the degree of pruning increasing as the pressure drop increases. In the model, low tissue oxygen levels alter the internal dynamics of normal cells, causing them to release vascular endothelial growth factor (VEGF), which stimulates angiogenic sprouting. Consequently, the level of blood oxygenation regulates the extent of angiogenesis, with higher oxygenation leading to fewer vessels. Simulations show that network remodelling (and de novo network formation) is best achieved via an appropriate balance between pruning and angiogenesis. An important factor is the strength of endothelial tip cell chemotaxis in response to VEGF. When a cluster of tumour cells is introduced into normal tissue, as the tumour grows hypoxic regions form, producing high levels of VEGF that stimulate angiogenesis and cause the vascular density to exceed that for normal tissue. If the original vessel network is sufficiently sparse then the tumour may remain localised near its parent vessel until new vessels bridge the gap to an adjacent vessel. This can lead to metastable periods, during which the tumour burden is approximately constant, followed by periods of rapid growth.

## Keywords

Blood flow Multiscale modelling Tumour angiogenesis Vascular adaptation Vascularisation VEGF## Mathematics Subject Classification (2000)

9208 92C15 92C17 92C35 62P10## Supplementary material

Movie corresponding to Fig. 3: Evolution, from an initial pair of straight vessels (both with inflow at the left and outflow at the right), of an irregular vascular network via angiogenesis. Note that the normal cells most distant from the original two parent vessels initially die, until angiogenesis provides sufficient oxygen to sustain them. Parameter values are as in Tables 1-4 in the manuscript. ESM (mov 997 kb)

Movie corresponding to Fig. 5A: Pruning followed by angiogenesis. The chemotactic sensitivity gamma=8x10^{4}, and the new vessels are poorly directed and hence lead to poorer vascularisation. ESM (mov 1,204 kb)

Movie corresponding to Fig. 5B: Increasing the chemotaxis coefficient to gamma=8x10^{5} gives more rapid and better directed sprout growth, hence effectively remodelling the vasculature and oxygenating the whole tissue region. ESM (mov 990 kb)

Movie corresponding to Fig. 7B: Angiogenesis from a single initial vessel. Parameters as for Figure 5B, including an inflow pressure Pin=22 mmHg. From a single initial vessel the whole tissue region is fully oxygenated after 800 time units. At first, normal cells far from the parent vessel die, and then the whole region is repopulated in a wave-like manner as new vessels and normal cells grow together. ESM (mov 1,887 kb)

Movie corresponding to Fig. 7C: For a lower inflow pressure, Pin=19 mmHg, the balance between angiogenesis and vessel regression is altered, so that the vessel network cannot extend across the whole region, and hypoxia induced VEGF production is not eliminated. ESM (mov 2,994 kb)

Movie corresponding to Fig. 10: A simulation with tumour cells implanted in a tissue with normal cells and two linear initial vessels (as in Figure 3). Notice how the tumour remains confined close to the upper vessel until connections are made that allow it to spread fully into the lower half of the domain. Also worth noting is that tumour cells' increased oxygen consumption triggers VEGF expression by more normal cells as well, since they also experience resultant low oxygen levels. The final vascular density is significantly higher than with normal cells only (see Figure 12). Parameter values are as in Tables 1-4 in the manuscript. ESM (mov 882 kb)

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