Development of an equation for calculating vertebral shear failure tolerance without destructive mechanical testing using iterative linear regression

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.