Preoperative Bone Defect Volume Estimation Using the Hemielipsoid Formula for Allograft Planning in Musculoskeletal Tumor Surgery: A Prospective Validation Study Against Intraoperative Fluid Displacement Measurement

**Background:** In orthopedic oncology, structural allograft reconstruction following primary musculoskeletal tumor resection requires precise preoperative planning. Currently, allograft selection at our institution relies on the surgeon's intraoperative visual estimation, with no standardized preoperative volumetric assessment protocol in place. This approach may result in allograft waste due to oversized graft selection, which is particularly problematic given the limited availability of allograft bank resources.

**Rationale:** The hemielipsoid formula (V = 4/3 × π × a × b × c / 2) offers a simple, reproducible method for estimating irregular bone defect volumes from standard cross-sectional imaging. If validated against an intraoperative reference standard, this formula could serve as a practical preoperative planning tool to guide allograft selection and minimize unnecessary graft use.

**Study Design:** This is a single-center prospective observational study conducted at Sakarya University Training and Research Hospital, Department of Orthopedics and Traumatology.

**Preoperative Assessment:** Defect volume will be estimated by the operating surgeon using the hemielipsoid formula applied to routine preoperative CT imaging. The three principal dimensions of the anticipated resection defect (length, width, and depth) will be measured on axial, coronal, and sagittal CT reconstructions, and volume will be calculated accordingly.

**Intraoperative Assessment:** Following tumor resection, the actual bone defect volume will be measured by direct cavity fluid displacement as the intraoperative reference standard. The resection cavity will be filled with a measured volume of saline to determine the true defect volume.