Stiffness of occipital-cervical constructs: beam theory

The purpose of this study is to show that stiffness of an occipital-cervical construct can be predicted based on rod geometry and material.

Various rod-plate implants were tested as previously reported biomechanical studies of occipital-cervical fixation with the exception that no spine was used. A testing frame that holds paired contoured rods and plates to the same position as in the biomechanical testing protocol for occipital-cervical fixation was tested in the flexion-extension direction on a servo-hydraulic testing machine. Stiffness was determined from the plots of applied moment versus angular displacement. The occipital-cervical constructs were then modeled as a curved beam in pure bending in the sagittal plane to calculate the moment of inertia and theoretical stiffness. The Pearson correlation coefficient was used to assess the correlation of the experimental to the theoretical calculated stiffness. Product of inertia and material stiffness were determined for implants from previously published studies and the predicted rank order of this product was compared with the rank order of the observed biomechanical results in each study.

A strong correlation was observed between the experimental and theoretical stiffness (R = 0.85). A strong influence of the inertia was also found on the experimental construct stiffness (R = 0.77). In five of six previously published studies, the best experimental performance was predicted using simple mechanical calculations.

This study shows that both the theoretical stiffness and the calculated area moment of inertia are strongly correlated with the experimental stiffness of tested occipital-cervical fixation constructs.