Theory of small vertebral motions: an analytical model compared to data
Related Experiment Video
Updated: Oct 18, 2026

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
Published on: April 11, 2018
1Research Department, Life Chiropractic College West, 22336 Main St., Hayward, CA 94541, USA. Asolinge@lifewest.edu
Object:
Develop an analytical theory describing the dynamics of small impulses applied to vertebrae, such as in chiropractic adjustments or spinal manipulative therapy.
Design:
Data were compared with damped harmonic oscillator models of vertebrae.
Background:
Evidence accumulates that chiropractic adjustments are effective in addressing a variety of health problems. However, the biomechanics characterizing spinal manipulation is largely unknown. Recently, relative separations of the L2-L3 vertebrae subsequent to activator adjusting instrument thrusts were measured in vivo at 2048 Hz.
Results:
Nine-parameter models for axial, shear and angular motions were fit to sets of 350 data points. They required frequencies of 5, 8 and 11 Hz, corresponding to well-known spinal resonances. The fits are excellent, with 0.75 < corrected R(2) < 0.96. Stiffnesses are calculated to be less than 10% of elastic zone values. Viscosities of the paravertebral medium are predicted to be between 6 and 30 poise, comparable to synovial fluids.
Conclusions:
This model ties together vertebral responses to small impulses with spinal resonances and other spinal/vertebral characteristics. Stiffness dominates damping resistance except in angular motions. Coupling appears unimportant in adjacent vertebral responses to small impulses. Further research is needed to clarify this issue.
Relevance:
This study indicates how both force (determining amplitude) and thrust speed or duration (determining frequencies excited) may enter in terms of optimizing the efficacy of chiropractic adjustments. If stimulation of specific spinal frequencies, say as central nervous input, were most essential, then many chiropractic thrusts could be clinically similar. This may explain how over 90 chiropractic techniques can co-exist.
Related Concept Videos
Relative Motion Analysis - Velocity
When an external force is exerted, it sets the crank into a rotational movement. This, in turn, instigates the motion of the connecting rod, leading to what is referred to as a general plane motion. This process involves two key points - point A on the connecting rod...
Relative Motion Analysis - Acceleration
Typical Model Studies
Relative Motion Analysis using Rotating Axes
However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x'y', is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it instrumental in...
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Absolute Motion Analysis- General Plane Motion
As the drone's propellers rotate, an upward force is generated that counteracts the force of gravity, enabling the drone to lift off from the ground. This initial movement of the drone is along a straight path, representing a form of translational motion. In this phase, every point on the drone...