Rigorous Mathematical Derivation of Inclination Angle for Single Cut Rotational Osteotomy for Tibia Deformity Correction

Abstract

Background To rigorously derive easy to use formulae for the inclination angle for single cut rotation osteotomy that can be used for tibia deformity correction. Method Three theorems were proven using trigonometric identities and concepts of linear algebra. These were rigorously shown. The three concepts were how to convert deformities in an AP/Lateral plane to an oblique plane deformity with a true angular magnitude of deformity; how to project an angular quantity from one plane to another; and the calculation of the inclination angle for the oblique osteotomy plane. All figures in this article were created by the authors of this paper. Results From the formula derived, a statistical t-test was performed that showed no significant difference between the formula derived in this paper and the original Sangeorzan paper charts (p=0.8782). Conclusions The formulae described in this article are a method to accurately calculate the inclination angle of the osteotomy for a single cut rotational osteotomy for tibial deformity correction. Clinical Relevance The article gives a deeper understanding of fundamental concepts behind deformity correction and provides an easy-to-use mathematical formula to calculate the osteotomy inclination for single cut rotational osteotomies.