Mechanical oscillations in biological tissues as a result of delayed rest-length changes

Author (s): Muñoz, J.J.; Dingle, M.; Wenzel, M.
Journal: Physical Review E

Volume: 98
Date: 2018

Oscillatory behaviour in tissue biology is ubiquitous and may be observed in the form of either chemical or mechanical signals. We here present and solve a mechanical cell model which exhibits oscillations emerging from delayed viscoelastic rheological laws. These include a time delay between the mechanical response and the rest-length changes, which evolve proportionally to the delayed cell deformation and use a remodelling rate parameter. We show that different regimes (no oscillatory response, sustained oscillations, and unstable oscillations) are obtained for different values of the delay or the remodelling rate.

The results are analytically demonstrated in a one-dimensional problem with one and two cells which are represented by simple line elements. Oscillations of the cell deformations are obtained whenever different delays co-exist, or the delay is size-dependent. We also extend our results to a multicellular two-dimensional vertex model that includes the same rheological law, and which inherits the presence of critical values of the delay or remodelling rate. We numerically show that indeed the size-dependent rest-length changes induce oscillations in the cell shapes and areas.



   author = "J.J. Mu{\~n}oz and M. Dingle and M. Wenzel",
   title = "Mechanical oscillations in biological tissues as a result of delayed rest-length changes",
   journal = "PHYSICAL REVIEW E",
   volume = "98",
   number = "",
   pages = "052409",
   month = "",
   year = "2018",
   note = "",