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Explanation of the Plane Line Factor
By Roderic P. Rochester, D.C.
Orthospinologists use four factors to determine the line of drive for vectored adjustments that will best correct various upper cervical misalignments. These factors are components of the Grostic Model for upper cervical adjusting. The four factors are:
Plane Line
C/A Factor
Angles
Atlas/Odontoid
As we have learned the C/A Factor is the "Great Equalizer," and supplies us with a vectored line of drive that will equally reduce the central skull line and the lower angle line. In order for this equal correction to take place the adjustment has to be delivered not only at the C/A Factor, but has to be parallel to the plane line of the atlas vertebra. Therefore, the vector that will create an equal reduction has to be at the angle of the C/A vector plus the Plane Line vector. It is interesting to know that based on a recent study (available on request) that 89.4% of the Height Factor is made from the Plane Line and C/A Factors:
Plane Line Average 0.77 in. 1.8 degrees 19.8% (of Height Factor)
C/A Factor Average 2.69 in. 6.4 degrees 69.6%
At/Od Factor Average 0.20 in. 0.5 degrees 5.3%
Angles Factor Average 0.20 in. 0.5 degrees 5.3%
Height Factor Average 3.87 in. 9.2 degrees*
* (does not consider atlas rotation at this point)
The Plane Line Factor is relatively easy to calculate. The Plane Line Factor is simply the angle of the Atlas Plane Line on the nasium film compared to a horizontal. In mathematical terms it is the slope of the atlas plane line. The slope is then converted to either inches of height factor (for hand adjusting) or degrees of instrument tilt. Since hand adjusting preceded instrument adjusting, let's start here.
This factor posed a slight problem for John F. Grostic, D.C. when he designed it for the practicing chiropractor. In that day, no one had heard of a calculator much less a computer, so a quick way of determining the Plane Line Factor was devised.
Figure A
First let us understand that:
Atlas Plane Line Slope = H / X (rise/run)
Angle S = Tan-1 (H / X)
If H = 1 inch (of Height Factor) and X = 24 inches (Pisiform to shoulders center) then:
S = Tan-1 (1/24) = 2.39 degrees
So we add 1 inch to our height factor when the atlas is tilted at 2.39 degrees.
Dr. Grostic observed that the distance across the mandible is very consistent from person to person at about 4.5 inches. He then used basic trigonometry to solve for H.
Tan (2.39) = H / 4.5 inches (distance across mandible)
.0417 = H / 4.5
.0417 * 4.5 = H
.1878in. = H
Since most chiropractors had a ruler in inches he converted the decimal to 16ths of an inch:
.1878 = P / 16
.1878 * 16 = P
P = 3
Thus for every 3/16 inches the plane line is above the horizontal at the edge of the mandible we add 1 " to the Height Factor.
A second method is also available which eliminates the variable of the width of the jaw. This method is more reliable. We place the protractor along the edge of the film and measure the angle of the atlas plane line and multiply by .42 inches/degree. Some are curious why .42 degrees/inch. It is derived as follows:
(Refer to Fig. A)
If angle S = 1 then tan (1) = H / 24 so H = .4189
As we can see, each of the factors designed for this work has a specific reason. To leave out or alter this formula is not advised.
Please e-mail any questions or comments to Dr. Rochester at drbo33@aol.com.
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