Linear Modelling and Fourier Spectroscopy of Stress- Relaxation in the Cervical Spine

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 fiom a fuller range (3 hours) of the complete relaxation curve. The relaxation times extracted fiom 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. Introduction: The intervertebral discs show marked viscoelastic behavior, and the more rapidly they are loaded then the greater the resistance they will show to the applied load (Smeathers, 1989). This has significant implications in liderstanding how the spinal joints work both individually and within the system of the spinal column. Work on the lumbar spine (Smeathers and Joanes, 1988) has shown that the 5 Hz resonance observed by other experimenters in vivo (e.g., Panjabi et al., 1986) is not reproduced in experiments performed in vitro under axial compression, and that the shortest time scales over which the lumbar spine shows any appreciable dissipation of strain energy is somewhere in the region of tens of minutes (Holmes, 1991). The cervical spine is another part of the spine where the time dependent mechanical properties of the structure is likely to be an important feature, whether the source of loading be from external oscillators (vibration of vehicles, pneumatic tools, etc.) or fiom impact loading on the cranium. Compression is likely to be a main loading mode, and the suggested second stiffest buckling axis in the cervical spine (King-Liu and Guo Dai, 1989) also would indicate that the compressive forces in the cervical spine may still be greatest even if the loading is not a true axial compression. Methods: 10 spinal segments were used from young male subjects(25 to 39 years old). Two adjacent vertebrae and the intervertebral disc connecting them were attached to a pair of loading plates using short bone screws, and mounted in a material tesling machine. Care was taken at all times during the preparation and mounting of the specimen to keep it thouroughly moistened with physiological saline. The experiments were separated into two parts: firstly to examine several relaxation curves fiom different strain values for the same segment to plot isochronal curves, and secondly to examine the long term relaxation of cervical motion segments. The relaxation curves for the isochronal plots were recorded over 15 minutes on a x-y plotter, and the 5 specimens used for this part of the experiments allowed to recover (in an unstressed state) for 45 minutes between each loading session. The data for long term relaxation was digitised through a 12 bit converter at 20 Hz and logged automatically on a microprocessor over three hours or longer. A preliminary test performed on an additional single motion segment loaded three times to the same initial stress showed that this resting time of 45 minutes allowed the segment to show reproducible relaxation curves indicating the segment had essentially 'forgotten' its past loading experience (Dorrington, 1980). Results dk Discussion: A typical isochronal plot for a single specimen at times of 0, 1 ,and 10 minutes is shown in figure 1. The lines marked on this figure are those obtained by linear regression analysis, and the lowest value obtained for the linear correlation coefficient was found to be 0.955 for all of the specimens tested (average ~0 .983) . Although the origin of the regression lines from these isochronal plots do not coincide with that of the x-y axis, this is to be expected as the isochronal plot is simply a reflection of the quasi-static stressstrain properties of the segment. A material that exhibits non-linear stress-strain properties may still exhibit linear stress relaxation, providing that (a) the shape of the isochronal plot for t=O is similar to that seen in quasi-static loading and (b) that the shape of the isochronal plot remains constant with increasing time (Holmes, 1991). 0-7803-5 164-9/98/$10.00