Linear modelling and Fourier spectroscopy of stress-relaxation in the cervical spine

Abstract

Single joints of the cervical spine were subject to axial compressive loads and the load relaxation recorded for 15 minutes. Isochronal plots of stress against strain were plotted for each specimen and showed high linear correlation coefficients (>0.955). Accordingly, a linear model was chosen and fitted to data obtained from a fuller range (3 hours) of the complete relaxation curve. The relaxation times extracted from this model were approximately 10 minutes and 5 hours. Fourier transform of the relaxation curve allows the storage modulus and the loss modulus of the relaxation spectrum to be shown separately as functions of frequency. Fourier analysis shows that the cervical spine has a wide and smooth distribution of relaxation times. Examination of the higher frequency components of the relaxation in the region of 1 to 20 Hz show the loss modulus to be almost flat and tending towards zero. This work shows that while the disc is capable of dissipating a large proportion of the applied strain energy, it can only do this slowly, and the discs of the cervical spine are inefficient as `shock absorbers' of axial loads.