  In several pathological conditions, such as coronavirus infections, multiple
sclerosis, Alzheimer's and Parkinson's diseases, the physiological shape of
axons is altered and a periodic sequence of bulges appears. Experimental
evidences suggest that such morphological changes are caused by the disruption
of the microtubules composing the cytoskeleton of the axon. In this paper, we
develop a mathematical model of damaged axons based on the theory of continuum
mechanics and nonlinear elasticity. The axon is described as a cylinder
composed of an inner passive part, called axoplasm, and an outer active cortex,
composed mainly of F-actin and able to contract thanks to myosin-II motors.
Through a linear stability analysis we show that, as the shear modulus of the
axoplasm diminishes due to the disruption of the cytoskeleton, the active
contraction of the cortex makes the cylindrical configuration unstable to
axisymmetric perturbations, leading to a beading pattern. Finally, the
non-linear evolution of the bifurcated branches is investigated through finite
element simulations.
