title: Nonlinear dynamics of the human lumbar intervertebral disc.
abstract: Systems with a quasi-static response similar to the axial response of the intervertebral disc (i.e. progressive stiffening) often present complex dynamics, characterized by peculiar nonlinearities in the frequency response. However, such characteristics have not been reported for the dynamic response of the disc. The accurate understanding of disc dynamics is essential to investigate the unclear correlation between whole body vibration and low back pain. The present study investigated the dynamic response of the disc, including its potential nonlinear response, over a range of loading conditions. Human lumbar discs were tested by applying a static preload to the top and a sinusoidal displacement at the bottom of the disc. The frequency of the stimuli was set to increase linearly from a low frequency to a high frequency limit and back down. In general, the response showed nonlinear and asymmetric characteristics. For each test, the disc had different response in the frequency-increasing compared to the frequency-decreasing sweep. In particular, the system presented abrupt changes of the oscillation amplitude at specific frequencies, which differed between the two sweeps. This behaviour indicates that the system oscillation has a different equilibrium condition depending on the path followed by the stimuli. Preload and amplitude of the oscillation directly influenced the disc response by changing the nonlinear dynamics and frequency of the jump-phenomenon. These results show that the characterization of the dynamic response of physiological systems should be readdressed to determine potential nonlinearities. Their direct effect on the system function should be further investigated.
authors.affiliation: Institute for Biomechanics, ETH Zurich, Hönggerbergring 64, HPP-O14, 8093 Zurich, Switzerland. Electronic address: gmarini@ethz.ch.
authors.forename: Giacomo
authors.initials: G
authors.lastname: Marini
authors.affiliation: Institute of Biomechanics, TUHH Hamburg University of Technology, Denickestraße 15, K, 21073 Hamburg, Germany.
authors.forename: Gerd
authors.initials: G
authors.lastname: Huber
authors.affiliation: Institute for Forensic Medicine, University Medical Center Hamburg-Eppendorf, Butenfeld 34, D-22529 Hamburg, Germany.
authors.forename: Klaus
authors.initials: K
authors.lastname: Püschel
authors.affiliation: Institute for Biomechanics, ETH Zurich, Hönggerbergring 64, HPP-O14, 8093 Zurich, Switzerland.
authors.forename: Stephen J
authors.initials: SJ
authors.lastname: Ferguson
mesh_terms: D000328:Adult; D000368:Aged; D001696:Biomechanical Phenomena; D002102:Cadaver; D006801:Humans; D007403:Intervertebral Disc / Q000502:physiology*; D008159:Lumbar Vertebrae / Q000502:physiology*; D008297:Male; D008875:Middle Aged; D017711:Nonlinear Dynamics; D016059:Range of Motion, Articular; D013314:Stress, Mechanical; D014732:Vibration; D016474:Weight-Bearing
keywords: Hardening; Intervertebral disc; Jump-phenomenon; Nonlinear dynamic; Softening