J Manipulative Physiol Ther. 1996 Jan; 19(1): 26-31.

Equations of motion for the "Flopping Doctor" model of spinal manipulative therapy.

Solinger AB.

Department of Research, Life Chiropractic College West, Hayward, CA, USA.

OBJECTIVE: To rigorously develop the physics and mathematics of the model of spinal manipulative therapy (SMT) consisting of a damped linear oscillator representing the vertebra impacted by a spring system representing the doctor, to interpret the results and to compare and contrast them with an earlier similar study originally developed in approximation. DESIGN: Mathematical physics analysis. RESULTS: Careful consideration of the exact equations and their meaning leads one to eliminate as unnecessary the picture of the doctor as a spring system, replacing it with the force function, which represents the applied SMT thrust as a function of time. Thus, with correct application of the principles of physics to the original model, one is led directly to a linear harmonic oscillator model for the vertebral system, with a forcing function for the SMT thrust and possible preload. The details of the application of such a model are developed elsewhere. CONCLUSIONS: The distraction resultant from an SMT thrust is shown to be a function of the momentum transfer, not, as asserted by the originator of the model, the velocity. The quickness of the application of the SMT thrust must be measured relative to normal mode frequencies of the spine. Further detailed examination of the physics of the model leads one to modify or contradict several other conclusions of the model's originator. Most importantly, the fact that the details of the physics of this model can be worked out analytically (as opposed to having to employ numerical methods) holds out the promise of additional insights to be gained by further development of this approach.