Speaker
Description
The Plateau--Rayleigh instability shows that a cylindrical fluid flow can be destabilized by surface tension. Similarly, capillary forces can make an elastic cylinder unstable when the elastocapillary length is comparable to the cylinder's radius. This is the case of axons: in the presence of several neurological pathologies, such as multiple sclerosis, Alzheimer's, and Parkinson's diseases, axons exhibit the formation of non-physiological, periodic bulges along their whole length. Experimental evidence suggests that the mutual interaction between the microtubule disassembly and the active contractility of the axonal cortex could represent the cause of this abnormal morphological deformation. While existing models, hypothesizing that surface tension is independent of the deformation of the solid and neglecting variations due to surface stretch, predict a single isolated bulge as the result of an instability, experiments reveal a periodic sequence of bulges spaced out by thinned regions, a phenomenon known as beading instability.
In this talk, we model axons as cylindrical bodies and assume that surface tension arises from the deformation of material particles near the free surface, treating it as a pre-stretched elastic surface. Using the theoretical framework proposed by Gurtin and Murdoch, we show that a cylindrical solid can undergo a mechanical instability with a finite critical wavelength if the body is sufficiently soft or axially stretched, explaining in mechanical terms the axonal beading phenomenon. Post-buckling numerical simulations reveal a morphology in qualitative agreement with experimental observations. Period-halving secondary bifurcations are also observed.