A comparison of Cartesian-only vs. Cartesian-spherical hybrid coordinates for statistical shape modeling in the lumbar spine☆

Objective: The purpose of this study was to compare two methods for quantifying differences in geometric shapes of human lumbar vertebra using statistical shape modeling (SSM). Methods: A novel 3D implementation of a previously published 2D, nonlinear SSM was implemented and compared to a commonly used, Cartesian method of SSM. The nonlinear method, or Hybrid SSM, and Cartesian SSM were applied to lumbar vertebra shapes from a cohort of 18 full lumbar triangle meshes derived from CT scans. The comparison included traditional metrics for cumulative variance, generality, and specificity and results from application-based biomechanics using finite element simulation. Results: The Hybrid SSM has less compactness - likely due to the increased number of mathematical constraints in the SSM formulation. Similar results were found between methods for specificity and generality. Compared to the previously validated, manually-segmented FE model, both SSM methods produced similar and agreeable results. Conclusion: Visual, statistical, and biomechanical findings did not convincingly support the superiority of the Hybrid SSM over the simpler Cartesian SSM. Significance: This work suggests that, of the two methods compared, the Cartesian SSM is adequate to capture the variations in shape of the posterior spinal structures for biomechanical modeling applications. (c) 2021 Elsevier B.V. All rights reserved.