So far, the elliptic shape parameters k and r have been determined. Based on the test data shown in Figure 2, we obtain k = 1.5134 and r = 0.8636. Finally, we can solve r and k by r = √A and k=√(B+1). The point which makes F minimum is the extremum of F. Solving above two equations, we can get the arrest point (A, B), then comparing the values of F near the point (A,B). The model equations suitable for viscoelastic solid that introduce single relaxation time for the volumetric strain relaxation are the Kelvin–Voigt model and the Zener model. The volumetric strain relaxation under constant stress condition points to viscoelastic solid. Interestingly, the osmotic stress of 5 kPa significantly reduced the growth of mouse CT26 cell lines tumor spheroid at the time scale of days. measured the cell–cell distances and pointed out their dependence on the local cell density and applied volumetric compression of the spheroid. This time scale corresponds to the relaxation of single-cell volumes and the state of cell–cell adhesion contacts under stress. The aggregate volume and volumetric strain relaxation time correspond to a few minutes and increases with stress. At the end of the experiment ( t = 10 minutes), the volumetric compression of cells in the outer region is ~ 5 %. This stress induces isotopic compression of cells that leads to the decrease of single-cell volumes at a time scale of minutes.
reported that osmotic stress of 5 kPa induces mechanical stress at aggregate surface equal to ~ 1.5 kPa while the residual mechanical stress in the core region of the spheroid is three to four times higher. Applied hyperosmotic stress induces (1) aggregate compression and (2) decrease of single-cell volumes, which leads to the accumulation of mechanical stress. considered cell aggregate volumetric strain relaxation under hyperosmotic stress in the range of 5–15 kPa for 10 minutes. Ivana Pajic-Lijakovic, in Viscoelasticity and Collective Cell Migration, 2021 2.5.2 Cell aggregate under hyperosmotic stress
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