Off-axis response due to mechanical coupling across all six degrees of freedom in the human disc

The kinematics of the intervertebral disc are defined by six degrees of freedom (DOF): three translations (Tz: axial compression, Tx: lateral shear, and Ty: anterior-posterior shear) and three rotations (Rz: torsion, Rx: flexion-extension, and Ry: lateral bending). There is some evidence that the six DOFs are mechanically coupled, such that loading in one DOF affects the mechanics of the other five "off-axis" DOFs, however, most studies have not controlled and/or measured all six DOFs simultaneously. Additionally, the relationships between disc geometry and disc mechanics are important for evaluation of data from different sized donor and patient discs. The objectives of this study were to quantify the mechanical behavior of the intervertebral disc in all six degrees of freedom (DOFs), measure the coupling between the applied motion in each DOF with the resulting off-axis motions, and test the hypothesis that disc geometry influences these mechanical behaviors. All off-axis displacements and rotations were significantly correlated with the applied DOF and were of similar magnitude as physiologically relevant motion, confirming that off-axis coupling is an important mechanical response. Interestingly, there were pairs of DOFs that were especially strongly coupled: lateral shear (Tx) and lateral bending (Ry), anterior-posterior shear (Ty) and flexion-extension (Rx), and compression (Tz) and torsion (Rz). Large off-axis shears may contribute to injury risk in bending and flexion. In addition, the disc responded to shear (Tx, Ty) and rotational loading (Rx, Ry, and Rz) by increasing in disc height in order to maintain the applied compressive load. Quantifying these mechanical behaviors across all six DOF are critical for designing and testing disc therapies, such as implants and tissue engineered constructs, and also for validating finite element models.