A rigid body model of the dynamic posteroanterior motion response of the human lumbar spine

Background: Clinicians apply posteroanterior (PA) forces to the spine for both mobility assessment and certain spinal mobilization and manipulation treatments. Commonly applied forces include low-frequency sinusoidal oscillations (<2 Hz) as used in mobilization, single haversine thrusts (<0.5 seconds) as imparted in high-velocity, low-amplitude (HVLA) manipulation, or very rapid impulsive thrusts (<5 ms) such as those delivered in mechanical-force, manually-assisted (MFMA) manipulation. Little is known about the mechanics of these procedures. Reliable methods are sought to obtain an adequate understanding of the force-induced displacement response of the lumbar spine to PA forces. Objective: The objective of this study was to investigate the kinematic response of the lumbar spine to static and dynamic PA forces. Design: A 2-dimensional modal analysis was performed to predict the dynamic motion response of the lumbar spine. Methods: A 5-degree-of-freedom, lumped equivalent model was developed to predict the PA motion of the lumbar spine. Lumbar vertebrae were modeled as masses, massless-spring, and dampers, and the resulting equations of motion were solved by using a modal analysis approach. The sensitivity of the model to variations in the spring stiffness and damping coefficients was examined, and the model validity was determined by comparing the results to oscillatory and impulsive force measurements of vertebral motion associated with spine mobilization and 2 forms of spinal manipulation. Results: Model predictions, based on a damping ratio of 0.15 (moderate damping) and PA spring stiffness coefficient ranging from 25 to 60 kN/m, showed good agreement with in vivo human studies. Quasi-static and low-frequency (<2.0 Hz) forces at L3 produced L3 segmental and L3-L4 intersegmental displacements up to 8.1 mm and 3.0 mm, respectively. PA oscillatory motions were over 2.5-fold greater for oscillatory forces applied at the natural frequency. Impulsive forces produced much lower segmental displacements in comparison to static and oscillatory forces. Differences in intersegmental displacements resulting from impulsive, static, and oscillatory forces were much less remarkable. The latter suggests that intersegmental motions produced by spinal manipulation may play a prominent role in eliciting therapeutic responses.