Rheology of growing axons

The growth of axons is a key process in neural system development, which relies upon a subtle balance between external mechanical forces and remodeling of cellular constituents. A key problem in the biophysics of axons is therefore to understand the overall response of the axon under stretch, which is often modeled phenomenologically using morphoelastic or viscoelastic models. Here, we develop a microscopic mixture model of growth and remodeling based on protein turnover and damage to obtain the macroscopic rheology of axonal shafts. First, we provide an estimate for the instantaneous elastic response of axons. Second, we predict that under moderate traction velocities, the axonal core behaves like a viscoelastic Maxwell material whose rheological parameters can be expressed in terms of the microscopic properties. Third, for larger velocities, we show that failure takes place due to extensive damage