Mathematical Methods for Assessing the Accuracy of Pre-Planned and Guided Surgical Osteotomies

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. 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'. In addition to describing our algorithm and the clinical utility, we present a thorough validation of both methods. Code is available at https://github.com/monkeygobah/osteoplane.