Biointerface dynamics – Multi scale modeling considerations

Mechanical Oscillations in 2D Collective Cell Migration: The Elastic Turbulence

“…Consequently, the modeling consideration accounts for the following steps: (1) the expression of cell velocity − → v c as the rate of change the cell displacement field, i.e., d − → u c dτ (where − → u c is the cell displacement field) [8,9]; (2) the formulation of local cell shear and volumetric strainsε cS andε cv , respectively, as a function of the cell displacement field [8,9]; (3) the introduction of a constitutive viscoelastic model for cellsσ c =σ c (ε c ) (wherẽ σ c is the cell stress andε c is the cell strain) [28,29]; (4) the formulation of the rate of change the matrix displacement field [29,30], (5) the formulation of local matrix shear and volumetric strainsε mS ,ε mv , respectively, as a function of the matrix displacement field [29,30]; (6) the discussion of the rheological behaviors of various matrix applied as a substrate for 2D collective cell migrationσ m =σ m ε m (whereσ m is the matrix stress andε m is the matrix strain) [2,3,30] as the viscoelastic force, the traction force, and the surface tension force based on modified model proposed by Murray et al [15]; and (10) the formulation of the interrelation between the cell velocity − → v c and the forces that influences generation of propagative waves and standing wave based on the corresponding momentum balance. Discussion of cell longtime rearrangement in the context of the elastic turbulence proposed by Groisman and Steinberg [23] is the main goal of this paper.…”

“…Murray et al [15] proposed the Kelvin-Voigt model for describing the viscoelasticity of fibrous extracellular matrices. Pajic-Lijakovic et al [29] described the long-time change of the matrix displacement field d − → u m dτ by cell action as follows:…”