# Mathematical model for pre-operative planning of linear and closing-wedge metatarsal osteotomies for the correction of hallux valgus

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## Abstract

First-metatarsal osteotomy is performed for an abnormal intermetatarsal angle and severe hallux valgus deformity. The metatarsal head is slid along the osteotomy and fixed with a Kirschner wire to achieve angular and linear realignment with respect to the other metatarsals. When reduction of joint subluxation is also sought, a bone wedge is removed. A mathematical model and a corresponding computer-based tool were developed for pre-operative planning of the optimum surgical solution. Standard intermetatarsal angle correction, head-to-sesamoids re-alignment, joint subluxation reduction and metatarsal length adjustment were all pursued. A standard pre-surgical dorso-plantar radiograph of the patient, with an additional metal ball for calculation of X-ray magnification, was necessary to analyse the original and final geometrical configurations. For the first time, expected bone loss and wire diameter were also considered. The angles of bone cuts and the amount of sliding along these cuts were calculated by the model according to the surgical goal. All the resulting geometrical parameters, both in the pre- and planned post- operative configuration, were provided in graphical and tabular form. In a change from former qualitative analysis of radiograms, the surgeon can now enter the operating theatre with a detailed plan of the goal to be achieved.

## Keywords

First metatarsophalangeal joint Hallux valgus Metatarsal osteotomy Preoperative planning Geometrical modelling Radiograph-based measurements## Preview

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