Abstract
Vascularisation is a key feature of cancer growth, invasion and metastasis. To better understand the governing biophysical processes and their relative importance, it is instructive to develop physiologically representative mathematical models with which to compare to experimental data. Previous studies have successfully applied this approach to test the effect of various biochemical factors on tumour growth and angiogenesis. However, these models do not account for the experimentally observed dependency of angiogenic network evolution on growth-induced solid stresses. This work introduces two novel features: the effects of hapto- and mechanotaxis on vessel sprouting, and mechano-sensitive dynamic vascular remodelling. The proposed three-dimensional, multiscale, in-silico model of dynamically coupled angiogenic tumour growth is specified to in-vivo and in-vitro data, chosen, where possible, to provide a physiologically consistent description. The model is then validated against in-vivo data from murine mammary carcinomas, with particular focus placed on identifying the influence of mechanical factors. Crucially, we find that it is necessary to include hapto- and mechanotaxis to recapitulate observed time-varying spatial distributions of angiogenic vasculature.
Highlights
The role of angiogenesis—the process whereby existing blood vessels produce new vasculature—in cancerous growth, invasion and metastasis has been extensively studied over the past five decades
In order to effectively describe the coupling between the time-varying extracellular matrix (ECM) density, due to the interaction of matrix metalloproteases (MMPs) with insoluble species, with the solid macromechanics of the host-tissue–we introduce a single factor describing the structural integrity of the ECM through isotropic damage to the matrix (c.f. the reduction factor defined in Holzapfel’s book [32], Chapter 6)
We focus on a single growth factor—referred here as the tumour-angiogenic factor (TAF)—as a homogenised chemical modulator of capillary sprouting and elongation
Summary
The role of angiogenesis—the process whereby existing blood vessels produce new vasculature—in cancerous growth, invasion and metastasis has been extensively studied over the past five decades. Starting with the assertion of Folkman [1] that angiogenesis is a necessary component for neoplasmic growth, the current paradigm is that tumours induce neo-vascularisation upon reaching an avascular limit [2] This limit represents a critical tumour size that can be supported by oxygen diffusion from the existing vasculature alone, beyond which substrate gradients produce internal regions of oxygen deprivation, i.e. hypoxia. Motile ECs migrate from the vessel lining up the TAF gradient field towards the TAF source, forming tubes with sprout-tips at the leading edge of a new vascular lumen These tubes can form networks in a process termed anastomosis and penetrate into the tumour, depending on how the ECs respond to mechano-chemical factors. Hypo-perfusion, in turn, has been shown to inhibit the delivery of chemotherapy, reducing drastically treatment efficacy [5, 6]
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