Geometric Evaluation of Mandibular Distraction

Abstract

In planning mandibular distraction, the deficiency of the vertical ramus and body is measured. The position of the pin placement is evaluated by the following formula:

180 - gomal angle × vertical deficiency/total deficiency

This is more accurately presented by the new formula

arctan (sin gonial angle)/(horizontal deficiency/vertical deficiency) - sin gonial angle

In one patient the original formula evaluated the pin placement angle to be 9.94, compared with 9.92, in the more accurate but more complex new formula. When the gonial angle is obtuse, the difference is small. When the gonial angle is more acute, as in a normal gonial angle for a 2-year-old child −134 degrees—the difference is still only 0.1 degrees. The original formula is simpler to use and is accurate enough for clinical use in mandibular distraction. The distraction distance is not the sum of the vertical ramal deficiency plus the body deficiency but is given by the following formula:

vertical deficiency sin gonial angle/sin pin placement angle

It would be accurate enough to plan the total distraction distance to be less than the sum of the two distances. The more acute the gonial angle is, the less the distraction distance will need to be.