Understanding how axons fail is critical to preventing brain injury. From stretch experiments, we know how axons respond to forces on the time scales of milliseconds and days. Yet, there is no mechanical model that explains the behavior of the axon at both short and long time scales. Here we propose a constitutive model to study the limits of stretch-mediated axonal disconnection at different time scales. Our model combines viscoelasticity using a neo-Hookean standard linear solid and growth using stress-mediated accelerated elongation. By limiting peak and average membrane tensions, our model predicts critical elongations and elongation rates. Interestingly, the critical elongation rate is not constant, but increases after an acclimation period. Combining viscoelasticity and growth is essential to simulate axonal disconnection in stretch-mediated growth at both short and long time scales. Our model can help optimize axonal stretch experiments and provides insight into the interacting time scales within the axon.
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This work was supported by the National Science Foundation Graduate Research Fellowship DGE 1656518 and the Stanford School of Engineering Fellowship to Lucy M. Wang and by the National Science Foundation Grant CMMI 1727268 and the Stanford Bio-X IIP seed Grant to Ellen Kuhl.
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Wang, L.M., Kuhl, E. Viscoelasticity of the axon limits stretch-mediated growth. Comput Mech 65, 587–595 (2020). https://doi.org/10.1007/s00466-019-01784-2