Predicting the Effect of Bilateral Pelvic Osteotomy onSagittal Alignment Correction and Surrounding Muscles:A Mathematical Model

Mathematical Model.Objectives.To investigate the relationship between pelvic osteotomy opening angle (OA) andits effect on spinopelvic sagittal parameters as well as the resting length of surrounding muscles.Methods.Predictive equationscorrelating OA with spinopelvic parameters were derived using geometric relationships. A geometric model calculated spinopelvicparameters (SVA, pelvic incidence [PI], PT, and T1 pelvic angle [TPA]) produced by progressively increasing the OA. These valueswere compared to optimal balance criteria in the literature. Four muscles crossing the osteotomy site were evaluated: GluteusMedius (GMED), Gluteus Maximus (GMAX), Piriformis (P), and Tensor Fascia Lata (TFL). Insertion points were obtained froman OpenSim software model. GMAX and GMED were subdivided into 3 (anterior, middle, and posterior).Results.OA correlatednegatively with PI, TPA, and SVA and positively with PT. From baseline SVA of 22 cm, OA 21∘reduced SVA to 5cm. OA 23∘reducedTPA to 14∘.OA30∘increasedPTto20∘.OA26∘decreased PI-LL to 10∘.OArangeof26∘-30∘resulted in optimal sagittal deformitycorrection. OA correlated with SR positively for TFL and anterior GMED and negatively for the rest of muscles. For this OA, theSR approximately decreased 6%, 5%, 6%, 8%, and 5% for posterior GMED, anterior GMAX, middle GMAX, posterior GMAX,and P, respectively. It increased 8% and 4% for anterior GMED and TFL, respectively.Conclusion.Predictive relationships betweenosteotomy OA and spinopelvic parameters were shown, providing proof of concept that sagittal balance may be achieved via pelvicosteotomy.