David Williams and Dr. Anton Bowden, Mechanical Engineering Departmenet, with Holly Woods
This ORCA research project has focused on the determination of the effects of the order of the mechanical tests on the response of an intervertebral disc. We hypothesized that the order of the mechanical tests may influence the rate of diffusion of the Trypsin throughout the disc, affecting the biomechanical response. We have planned to determine the magnitude of this influence by using statistical techniques to analyze the data acquired. Virtually all of us (80 to 90 percent) will experience back pain in our lives. Low back pain is the leading cause of missed work days. The estimated economic impact is over $100 billion dollars annually in the US. Research on how to adequately treat spinal injuries is an ongoing endeavor. Back pain is associated with intervertebral disc degeneration, although the exact relationship is still under investigation. The degeneration was accomplished by the injection of Trypsin into the annulus fibrosus (AF) of an intervertebral disc from bovine tail. Some intervertebral discs were injected with fetal bovine serum (FBS) as the control. Injected intervertebral discs were exposed to two mechanical tests: flexion/extension and axial rotation. The proposed third mechanical test of compression was not performed. This research was completed in order to develop a viable model of intervertebral disc degeneration in vitro that could be used for future research and testing of prosthetic intervertebral disc implantable devices. Similar research is now being performed on human intervertebral discs. Since the data for human intervertebral discs have not been obtain, a statistical analysis of the bovine tail test data has been performed for this research. It has been found that a variation in the data due to the order of the tests is not significant.
Test data of the mechanical response of bovine tail intervertebral discs that had been injected with Trypsin and fetal bovine serum (FBS) were collected. Data was collected at four points in the test. Intervertebral discs that had been injected with Trypsin were tested after 30 minutes, 60 minutes, and 180 minutes. Intervertebral discs that had been injected with the control (FBS) were tests after 180 minutes. Data was collected for the angle deflected or rotated and the resulting torque of the intervertebral discs. Typically two flexion and two rotation tests were performed on the intervertebral discs. The order of the flexion and rotation tests varied randomly for the 30 minute and 60 minute Trypsin and the 180 minute FBS test points. The order for the 180 minute Trypsin test point has been lost, so this data was not included in the analysis.
The resulting test data were sorted and organized. The number of data sets at the three test points is shown in Figure 1. The column titled “first” refers to the number of flexion tests that were performed before the rotation tests, and vice versa for the “second” column.
The data sets were statistically analyzed to determine if the flexion or rotation test produced significantly different results when performed before or after the other test. Due to the limitations of this report, only a summary of the calculated values is provided here. The average and standard deviation of the torque readings from the data sets were calculated. It was found that the average values were close to zero for most data sets, which is due to the post-test conditioning of the data. However the standard deviations of each data set varied greatly. Therefore the standard deviation values of the data sets were analyzed more in depth. The standard deviation values of the torque readings for each data set were analyzed for significance. An average and standard deviation of the standard deviations were found for each test method, as subdivided into test points (see Figure 2, refer to AVG and STD DEV rows). In addition to this, the upper and lower confidence intervals for each group of data were found, as calculated from the uncertainty (UCL or LCL = AVG + uncertainty). The uncertainty is calculated from the equation Uncertainty – STD ERR X T – Value.
To clarify whether or not there is a significant difference in standard deviations for flexion and rotation tests completed first or second, a matched-pairs two-tailed t-test was performed. A confidence interval of 95% is used, or alpha is equal 0.05 for these t-tests. The resulting p-values of four sets of data are shown in Figure 3. None of the p-values are below the alpha (0.05), and therefore it is shown that there is not a significant difference between the standard deviation and average of the standard deviations of the first and second tests.
In conclusion, it has been statistically shown that there is no bias created from the order of the mechanical testing of the intervertebral discs. An analysis of the average values and standard deviations of the torque readings has resulted in this conclusion. Matched-pairs two-tailed t-tests performed to show statistical significant difference in the data resulted in p-values within the 95% confidence interval. However it should be noted that the p-value of the standard deviation of the standard deviations of the flexion tests (0.1126) is nearing the alpha of 0.05. This low pvalue could suggest that further testing and data analysis should be considered to ensure that there is no bias from the order of the mechanical tests.