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


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Structural and chiropractic

J Manipulative Physiol Ther.2002 Oct;25(8):485-96.


T S Keller, C J Colloca


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. Conclusions: The simple analytical model presented in this study can be used to predict the static, cyclic, and impulsive force PA displacement response of the lumbar spine. The model provides data on lumbar segmental and intersegmental motion patterns that are otherwise difficult to obtain experimentally. Modeling of the PA motion response of the lumbar spine to PA forces assists in the understanding the biomechanics of therapeutic PA forces applied to the lumbar spine and may ultimately be used to validate chiropractic technique procedures and minimize risk to patients receiving spinal manipulative therapy.

Publication Date: 

2002 Oct



Keller, ST., Colloca, JC. (2002) 'A rigid body model of the dynamic posteroanterior motion response of the human lumbar spine', J Manipulative Physiol Ther.2002 Oct;25(8):485-96.

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