Proximal shortening lesser metatarsal osteotomy: A mathematical-geometric basis

Abstract

Reconstruction and restoration of the lesser metatarsal parabola after an iatrogenic complication of a lesser metatarsal osteotomy provides a difficult surgical dilemma for the foot and ankle surgeon. This study's purpose was to determine if a formula could be developed, through a geometric and mathematical basis, for the proximal shortening lesser metatarsal osteotomy to aid the surgeon in determining the amount of bone needed to be resected to correct the deformity. This study was divided into three parts. In part I, 15 lesser metatarsals (metatarsals 2, 3, and 4) harvested from fresh frozen cadavers had shortening proximal osteotomies performed. This osteotomy removes a cylindrical piece of bone that is perpendicular to the metatarsal shaft from the proximal aspect of the lesser metatarsal to create axial shortening of the metatarsal and changes the relationship of the metatarsal head to the weightbearing surface. These metatarsals had five radio-opaque markers placed into them and were radiographed pre- and postosteotomy. These markers created a pre- and postgeometric graphic plotting for the changes in length, height, and dorsiflexion. Computer graphing was then utilized to analyze changes in height, length, and dorsiflexion of each metatarsal. Formulas were created from these plottings to determine the actual change in height, length, and dorsiflexion for a set amount of bone removed. The formulas created from these data were: Length: Actual change = Bone removed *0.95; Height: Actual change = Bone removed *0.54; and Dorsiflexion: Actual change = Bone removed *0.44 mm/deg. In part II of study, 15 identical saw bone lesser metatarsals were used to verify the formulas, by taking out the amount of bone needed for 0.5-mm increment change, starting at 1.0 mm and increasing to 8.0 mm. Techniques used were identical to part one. Part III was performed to demonstrate that the formula would be reproducible for height when there is a difference in the angulation of the metatarsal. Fifteen identical sawbones where plotted in plaster at declinations ranging from 8 degrees to 42 degrees. Then the osteotomy was performed removing 4.0 mm of sawbone from each specimen using the same technique as parts I and II. All parts and the formulas were statistically analyzed using a bivariate regression model, which showed that the formulas were valid for length, height, and dorsiflexion with a 95% confidence. With these experimental models, the authors found reproducible formulas that hopefully could aid the surgeon in determining the amount of bone they needed to resect to effect correction of this difficult reconstruction.