| Summary: | Lack of objective guidelines in surgical metatarsal osteotomies, justify this study's purpose that is to compare the Weil osteotomy, the Weil osteotomy with a slice of bone removed from the proximal fragment, and the axial osteotomy, through a mathematical geometric analysis. The cervical shortening axial osteotomy (CSAO) is an extraarticular axial osteotomy; its high stability is provided by retention of a plantar bone block on the distal fragment. In a right triangle, the hypotenuse is the metatarsal axis, one side is the horizontal plane, and the angle in between is the declination angle. For a 15° initial declination angle, and for 5 mm and 10 mm shortening, we calculate the length, heigth, and angle modifications. An horizontal Weil osteotomy cause a 1° to 2.5° change in plantar flexion. In an oblique Weil osteotomy the head's plantar displacement average 0.8 to 3.4 mm and the declination angle increase to 5.8°. The effects of a slice of bone removed from the proximal frgament in the Weil osteotomy are not the same if it was made before or after the head's proximal translation. Made before the head's translation, the resection of a slice of bone above the cephalic fragment, cause a plantar displacement, a plantar flexion of the metatarsal, and a great increase in the shortening effect. To be effective, it has to be done after the head's proximal translation. The advantages of the axial shortening osteotomy are the declination angle preservation, the dorsal head's displacement, from 1.5 to 3 mm. The vertical vector of a force "F" passing trouhg the metatarsal, is greater in a Weil osteotomy with plantar and proximal translation than in a theorical pure plantar translation osteotomy. The metatarsal plantar flexion angle increases the vertical vector force more than the head's plantar displacement.
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