Mathematical methods for assessing the accuracy of pre-planned and guided surgical osteotomies.

[PURPOSE] The fibula-free flap (FFF) is a valuable reconstructive technique in maxillofacial surgery; however, the assessment of osteotomy accuracy remains challenging. We devised two novel methodologies to compare planned and postoperative osteotomies in FFF reconstructions that minimized user input but would still generalize to other operations involving the analysis of osteotomies.

[METHODS] Our approaches leverage basic mathematics to derive both quantitative and qualitative insights about the relationship of the postoperative osteotomy to the planned model. We have coined our methods 'analysis by a shared reference angle' and 'Euler angle analysis.'

[RESULTS] In addition to describing our algorithm and the clinical utility, we present a thorough validation of both methods. Our algorithm is highly repeatable in an intraobserver repeatability test and provides information about the overall accuracy as well as geometric specifics of the deviation from the planned reconstruction.

[CONCLUSION] Our algorithm is a novel and robust method for assessing the osteotomy accuracy of FFF reconstructions. This approach has no reliance on the overall position of the reconstruction, which is valuable due to the multiple factors that may influence the outcome of FFF reconstructions. Additionally, while our approach relies on anatomical features for landmark selections, the flexibility in our approach makes it applicable to evaluate any operation involving osteotomies.