  Mechanochemical models of pattern formation in biological tissues have been
used to study a variety of biomedical systems and describe the physical
interactions between cells and their local surroundings. These models generally
consist of a balance equation for the cell density, one for the density of the
extracellular matrix (ECM), and a force-balance equation describing the
mechanical equilibrium of the cell-ECM system. Assuming this system can be
regarded as an isotropic linear viscoelastic material, the force-balance
equation is often defined using the Kelvin-Voigt model of linear
viscoelasticity to represent the stress-strain relation of the ECM. However,
due to the multifaceted bio-physical nature of the ECM constituents, there are
rheological aspects that cannot be effectively captured by this model and,
therefore, depending on the type of biological tissue considered, other
constitutive models of linear viscoelasticity may be better suited. In this
work, we systematically assess the pattern formation potential of different
stress-strain constitutive equations for the ECM within a mechanical model of
pattern formation in biological tissues. The results obtained through linear
stability analysis support the idea that constitutive equations capturing
viscous flow and permanent set (Maxwell model, Jeffrey model) have a pattern
formation potential much higher than the others (Kelvin-Voigt model, standard
linear solid model), further confirmed by the results of our numerical
simulations. Our findings suggest that further empirical work is required to
acquire detailed quantitative information on the mechanical properties of
components of the ECM in different biological tissues in order to furnish
mechanochemical models of pattern formation with stress-strain constitutive
equations for the ECM that provide a more faithful representation of the
underlying tissue rheology.
