Equations used to determine vertebral failure tolerances without the need for destructive testing are useful for scaling applied sub-maximal forces during in vitro repetitive loading studies. However, existing equations that use vertebral bone density and morphology for calculating compressive failure tolerance are unsuitable for calculating vertebral shear failure tolerance since the primary site of failure is the pars interarticularis and not the vertebral body. Therefore, this investigation developed new equations for non-destructively determining vertebral shear failure tolerance from morphological and/or bone density measures. Shear failure was induced in 40 porcine cervical vertebral joints (20 C3-C4 and 20 C5-C6) by applying a constant posterior displacement to the caudal vertebra at 0.15 mm/s. Prior to destructive testing, morphology and bone density of the posterior elements were made with digital calipers, X-rays, and peripheral quantitative computed tomography. Iterative linear regression identified mathematical relationships between shear failure tolerance, and morphological and bone density measurements. Along with vertebral level, pars interarticularis length and lamina height from the cranial vertebra, and inferior facet height from the caudal vertebra collectively explained 61.8% of shear failure tolerance variance. Accuracy for this relationship, estimated using the same group of specimens, was 211.9 N or 9.8% of the measured shear failure tolerance.
In vitro testing of vertebrae and vertebral joints is important for quantifying biomechanical failure tolerances, establishing ergonomic limits, and identifying tissue injury mechanisms 1, 2, 3, 4, 5, 6, 7 and 8. A recent review on occupational spine biomechanics emphasized the need for further in vitro investigations to identify acute tissue damage thresholds under modes of loading other than compression (e.g. shear), and to establish thresholds for cumulative spine loading [9]. In response to the second part of Potvin's [9] recommendation, the current study developed an equation that could be used to determine the shear failure tolerance of porcine cervical vertebral joints without the need for destructive testing. The equation developed from this study would provide a preliminary, but pivotal step for future in vitro studies using repetitive shear loading paradigms to establish the vertebral joint's cumulative shear tolerance, and the influence of sub-maximal shear force magnitude on the cumulative tolerance.
To investigate the influence of applied force magnitude on fatigue life in a repetitive loading protocol, it is often desirable to ensure that specimens can be grouped on the basis of acute injury potential imposed by repetitively applied sub-maximal forces [10]. As an example, these authors scaled repetitively applied sub-maximal compressive forces to a percentage of each specimen's estimated compressive failure tolerance to control the acute injury potential imposed by the applied force's magnitude. Normalizing the applied sub-maximal compressive force magnitude to a percentage of the predicted failure tolerance is also beneficial for enhancing comparisons of in vitro results between animal and human specimens. Specimen-specific estimates of acute compressive failure tolerance can be non-destructively obtained by using a linear regression model that mathematically relates measurements of the vertebral body's endplate area to acute vertebral joint compressive failure tolerances measured from in vitro tests [11]. This is a reasonable approach for predicting compressive failure tolerance since endplate fractures are commonly observed injuries resulting from compressive force during in vitro testing 12 and 13. Other equations have also used measurements of the vertebral body's bone mineral density, either by itself or in conjunction with morphological measurements such as endplate area, to predict compressive strength 11, 12, 14, 15 and 16. In fact, combining measurements of vertebral morphology and bone density has been shown to improve predictions of compressive strength in human and macaque vertebral bodies 14 and 17, but did not enhance prediction of compressive strength in porcine cervical FSUs [11].
Given that vertebral tissue damage following destructive testing differs according to the mode of applied loading 3, 5 and 13, it is unlikely that previously developed equations for determining the vertebral joint's compressive failure tolerance would also be suitable for determining failure tolerances in other modes of loading such as shear. Pars interarticularis (PI) fractures have been identified by in vivo and in vitro studies as the predominant injury associated with exposure to vertebral shear force 18 and 19. Furthermore, these fractures are initiated at the caudal and ventral aspect of the pars [20]. Since the primary vertebral bony structures that interact under shear forces are the facets, a bending moment generated about the PI by facet articulation has been hypothesized as a shear injury mechanism for the spine 5, 21 and 22. Therefore, any mathematical model that attempts to determine the vertebral joint's acute shear failure tolerance without mechanical testing should likely include morphological measurements from the PI and/or facets and/or measurements of bone density. Likewise, other bony structures located posterior to the vertebral body, such as the lamina and pedicles have also been shown to influence facet interaction and vertebral mechanics with exposure to shear force 23, 24 and 25. Thus, it is possible that morphology of these structures may also be related to vertebral acute shear failure tolerance. Recent evidence using human lumbar specimens has shown that bone density may explain up to 59% of the variance in peak shear force when a FSU's cranial vertebra is displaced in an anterior direction relative to the stationary caudal vertebra [26]. Regression models that relate bone morphology and density of the elements located posterior to the vertebral body to shear failure tolerances may also help to identify critical parameters linked to fracture risk from facet interaction induced by shear loading.
This investigation developed new equations using stepwise linear regression that mathematically related vertebral morphological and/or bone density measurements to acute shear failure tolerances measured from in vitro tests using porcine cervical FSUs as surrogates for the human lumbar spine. Based on similar work performed for compressive loading of vertebrae 14 and 17, it was hypothesized that combining morphological and bone density measurements into a single equation would explain the most variance in measured acute vertebral shear failure tolerance.
