  Working in the framework of morphoelasticity, we develop a model of neurite
growth in response to elastic deformation. We decompose the applied stretch
into an elastic component and a growth component, and adopt an
observationally-motivated model for the growth law. We then compute the
best-fit model parameters by fitting to force-extension curves from
measurements of constant-speed uniaxial deformations of mechanically-induced
neurites of rat hippocampal neurons. We find a time constant for the growth law
of 0.009~s$^{-1}$, similar to the diffusion rate of actin in a cell. Our
results characterize the kinematics of neurite growth and establish new limits
on the growth rate of neurites.
