2020/09/23 by Chiara Villa, Villa, Chiara, Mark A. J. Chaplain +5 · 1 citation
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · Engineering · #35Q74 #35Q92 #3D Printing in Biomedical Research #74D99 #92-08 #92-10 #92C10 #92C15 #Biocrusts and Microbial Ecology #Cellular Mechanics and Interactions #FOS: Biological sciences #Tissues and Organs (q-bio.TO)
paper · pdf · doi:10.48550/arxiv.2009.10953
openalex publication_date 2020/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mechanochemical models of pattern formation in biological tissues have been\nused to study a variety of biomedical systems and describe the physical\ninteractions between cells and their local surroundings. These models generally\nconsist of a balance equation for the cell density, one for the density of the\nextracellular matrix (ECM), and a force-balance equation describing the\nmechanical equilibrium of the cell-ECM system. Assuming this system can be\nregarded as an isotropic linear viscoelastic material, the force-balance\nequation is often defined using the Kelvin-Voigt model of linear\nviscoelasticity to represent the stress-strain relation of the ECM. However,\ndue to the multifaceted bio-physical nature of the ECM constituents, there are\nrheological aspects that cannot be effectively captured by this model and,\ntherefore, depending on the type of biological tissue considered, other\nconstitutive models of linear viscoelasticity may be better suited. In this\nwork, we systematically assess the pattern formation potential of different\nstress-strain constitutive equations for the ECM within a mechanical model of\npattern formation in biological tissues. The results obtained through linear\nstability analysis support the idea that constitutive equations capturing\nviscous flow and permanent set (Maxwell model, Jeffrey model) have a pattern\nformation potential much higher than the others (Kelvin-Voigt model, standard\nlinear solid model), further confirmed by the results of our numerical\nsimulations. Our findings suggest that further empirical work is required to\nacquire detailed quantitative information on the mechanical properties of\ncomponents of the ECM in different biological tissues in order to furnish\nmechanochemical models of pattern formation with stress-strain constitutive\nequations for the ECM that provide a more faithful representation of the\nunderlying tissue rheology.\n