  We propose a continuum model for pattern formation, based on the multiphase
model framework, to explore in vitro cell patterning within an extracellular
matrix. We demonstrate that, within this framework, chemotaxis-driven cell
migration can lead to formation of cell clusters and vascular-like structures
in 1D and 2D respectively. The influence on pattern formation of additional
mechanisms commonly included in multiphase tissue models, including cell-matrix
traction, contact inhibition, and cell-cell aggregation, are also investigated.
Using sensitivity analysis, the relative impact of each model parameter on the
simulation outcomes is assessed to identify the key parameters involved.
Chemoattractant-matrix binding is further included, motivated by previous
experimental studies, and to augment the spatial scale of patterning to within
a biologically plausible range. Key findings from the in-depth parameter
analysis of the 1D models, both with and without chemoattractant-matrix
binding, are demonstrated to translate well to the 2D model, obtaining
vascular-like cell patterning for multiple parameter regimes. Overall, we
demonstrate a biologically-motivated multiphase model capable of generating
long-term pattern formation on a biologically plausible spatial scale both in
1D and 2D, with applications for modelling in vitro vascular network formation.
