Predicting Allograft Volume in Orthopedic Oncology: Hemielipsoid Formula vs Intraoperative Fluid-Fill 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.

**Outcome Assessment:** The primary outcome is the agreement between preoperative hemielipsoid-estimated volume and intraoperative fluid displacement-measured volume, assessed by Bland-Altman analysis and intraclass correlation coefficient (ICC). The secondary outcome is the correlation between preoperative volume estimation and actual allograft volume used, to evaluate the utility of the hemielipsoid formula in reducing intraoperative allograft waste.

**Sample Size:** A priori power analysis was performed based on intraclass correlation coefficient (ICC) estimation (H0: ICC = 0.70; H1: ICC = 0.90; two-tailed alpha = 0.05; power = 0.80) using the Fisher z-transformation method, indicating a minimum required sample size of 25 patients. Target enrollment was set at 40 patients to account for a 10% dropout rate and to allow for potential subgroup analyses.

Inclusion criteria

• Patients diagnosed with a primary musculoskeletal tumor requiring surgical resection
• Structural allograft reconstruction planned following resection
• Routine preoperative CT imaging available for hemielipsoid measurements
• Age ≥ 18 years
• Written informed consent obtained

Exclusion criteria

• Metastatic bone tumors
• Pathological fracture at the resection site precluding accurate volume estimation
• Prior surgery at the same anatomical site
• Unavailability of adequate preoperative CT imaging
• Reconstruction planned with implant or autograft only (no structural allograft)