The role of speed and technique in determining amplitude of vertebral response.

Lantz CA, Solinger AB. The role of speed and technique in determining amplitude of vertebral response. Chiropractic Research J. 1997; Spring 4:31.

Abstract: It has been previously shown that vertebra respond with oscillatory movements to the application of adjustive force. The various frequencies of oscillation are innate qualities of the individual; each vertebra’s frequency is determined by the stiffness of its ligaments and discs, its mass, and its dissipative interactions, largely determined by the resistive qualities of the surrounding tissues.

The amplitude or excursion, however, is directly controlled by the adjustive procedure. For a simple model of the thrust, the maximum excursion A has been calculated to be A=[Dp(mk)1/2(1-pi*lambda/2) where Dp is the net momentum transferred to the vertebra, m is the vertebral mass, k is the stiffness coefficient of the restraining disc and/or ligament in the direction of motion, and lambda is the ration of damping time constant to oscillation period.

Although the terms "speed" and "depth" have not been quantitatively defined, clearly they are related to the length of time (duration) and the amount of the force exerted. If we interpret them straight-forwardly we can deduce the relationship between amplitude, speed, and depth for a given amount of thrusting force: The net momentum transfer Dp is approximately given by (THRUST FORCE) x (DURATION OF THRUST), and the duration is simply the distance traveled in application of the force (depth) divided by the velocity of application (speed).

Assuming the thrust force to be proportional to the speed raised to the r-th power, one has (with a as the constant proportionality): Dp-a(SPEED)r-1x(DEPTH). Thus, the speed of thrust or recoil and the depth of the thrust are directly related to the amplitudes predicted from the previously developed one-degree-of-freedom elastic, dissipative model, for two different types of adjustive procedure, the Grostic and toggle recoil procedures, and for several different speeds of thrust and/or recoil.

If the duration of the thrust and/or recoil is short compared to the innate period of oscillation of the vertebra, the adjustment amplitude is maximized.