Prediction of the 3D shape of the L1 vertebral body from adjacent vertebrae

The aim of treatments of vertebral fractures is the anatomical reduction to restore the physiological biome-chanics of the spine and the stabilization of the fracture to allow bone healing. However, the three-dimensional shape of the fractured vertebral body before the fracture is unknown in the clinical setting. Information about the pre-fracture vertebral body shape could help surgeons to select the optimal treatment. The goal of this study was to develop and validate a method based on Singular Value Decomposition (SVD) to predict the shape of the vertebral body of L1 from the shapes of T12 and L2.The geometry of the vertebral bodies of T12, L1 and L2 vertebrae of 40 patients were extracted from CT scans available from the VerSe2020 open-access dataset. Surface triangular meshes of each vertebra were morphed onto a template mesh. The set of vectors with the node coordinates of the morphed T12, L1 and L2 were compressed with SVD and used to build a system of linear equations. This system was used to solve a minimi-zation problem and to reconstruct the shape of L1. A leave-one-out cross-validation was performed. Moreover, the approach was tested against an independent dataset with large osteophytes.The results of the study show a good prediction of the shape of the vertebral body of L1 from the shapes of the two adjacent vertebrae (mean error equal to 0.51 +/- 0.11 mm on average, Hausdorff distance equal to 2.11 +/- 0.56 mm on average), compared to current CT resolution typically used in the operating room. The error was slightly higher for patients presenting large osteophytes or severe bone degeneration (mean error equal to 0.65 +/- 0.10 mm, Hausdorff distance equal to 3.54 +/- 1.03 mm). The accuracy of the prediction was significantly better than approximating the shape of the vertebral body of L1 by the shape of T12 or L2. This approach could be used in the future to improve the pre-planning of spine surgeries to treat vertebral fractures.