Abstract
A methodology to identify tissue level axonal stress and strain from macroscopic parameters is outlined. A non-linear, viscoelastic, structural relationship is proposed to describe the in vivo response of the guinea pig optic nerve to uniaxial elongation. The optic nerve is modeled as a bundle of parallely aligned axons undulated to varying degrees. When straightened, each axon displays non-linear, viscoelastic behavior that contributes to the overall behavior of the optic nerve. Optic nerves were examined microscopically to calculate the undulation of individual axons. Axonal undulation was found to follow a gamma distribution, with a mean undulation of 1.070 and a standard deviation of 0.053. A reduced relaxation function, consisting of two exponential terms, was approximated from in vivo, dynamic elongation of the guinea pig optic nerve. Results from the in vivo relaxation tests indicated that the relaxation behavior was independent of displacement, a requirement for linear, viscoelastic theory based on hereditary integrals. The instantaneous elastic function was expressed as an integral of the undulation distribution and a function of the stretch ratio. Initially, a linear stretch ratio function was assumed to analyze the effects of the undulation distribution on the instantaneous elastic response. These results were compared with those obtained by increasing the order of the stretch ratio function to a third order polynomial. The computed results of the proposed structural relationship compared well to the experimental data from in vivo optic nerve tests, indicating that this model could provide a framework for identifying axonal thresholds for traumatic injury.