  Neovascularisation is essential for tissue development and regeneration, in
addition to playing a key role in pathological settings such as ischemia and
tumour development. Experimental findings in the past two decades have led to
the identification of a new mechanism of neovascularisation, cluster-based
vasculogenesis, during which endothelial progenitor cells (EPCs) mobilised from
the bone marrow are capable of bridging distant vascular beds in a variety of
hypoxic settings in vivo. This process is characterised by the formation of EPC
clusters during its early stages and, while much progress has been made in
identifying various mechanisms underlying cluster formation, we are still far
from a comprehensive description of such spatio-temporal dynamics. In order to
achieve this, we propose a novel mathematical model of the early stages of
cluster-based vasculogenesis, comprising of a system of nonlocal partial
differential equations including key mechanisms such as endogenous chemotaxis,
matrix degradation, cell proliferation and cell-to-cell adhesion. We conduct a
linear stability analysis on the system, solve the equations numerically,
conduct a parametric analysis of the numerical solutions of the 1D problem to
investigate the role of underlying dynamics on the speed of cluster formation
and the size of clusters, and verify the key results of the parametric analysis
with simulations of the 2D problem. Our results, which qualitatively compare
with data from in vitro experiments, elucidate the complementary role played by
endogenous chemotaxis and matrix degradation in the formation of clusters, and
they indicate that previous approaches to the nonlocal modelling of
cell-to-cell adhesion, while they capture the aggregating effect of
cell-to-cell adhesion, are not sufficient to capture its stabilising effect on
clusters, and new continuum cell-adhesion modelling strategies are required.
