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

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.