Investigation of Vibration Characteristics of the Ligamentous Lumbar Spine Using the Finite Element Approach

A nonlinear, three-dimensional finite element model of the ligamentous L4-SI segment was developed to analyze the dynamic response of the spine in the absence of damping. The effects of the upper body mass were simulated by including a mass of 40 kg on the L4 vertebral body. The modal analyses of the model indicated a resonant frequency of 17.5 Hz in axial mode and 3.8 Hz in flexion-extension mode. Accordingly, the predicted responses for the cyclic load of −400 ± 40 N applied at four different frequencies (5, 11, 16.5, and 25 Hz) were compared with the corresponding results for axial compressive static loads (−360, and −440 N). As compared to the static load cases, the predicted responses were higher for the cyclic loading. For example, the effect of cyclic load at 11 Hz was to produce significant changes (9.7 – 19.0 percent) in stresses, loads transmitted through the facets, intradiscal pressure (IDP), disk bulge, as compared to the static load predictions. The responses were found to be frequency dependent as well; supporting the in vivo observations of other investigators that the human spine has a resonant frequency. For example, the 11 Hz model (DYN11) compared to the DYN5 model showed an increase in majority of the predicted parameters. The parameters showed an increase with frequency until 17.5 Hz (resonant frequency of the model); thereafter a decrease at 25 Hz. A chronic change in these parameters, especially at the resonant frequency, beyond the “base” values may trigger the bone remodeling process leading to spinal degeneration/disorders associated with chronic vibration exposure. Future directions for extending the present model as a complement to the experimental investigations are also discussed.