A Tissue Mineral Density-Weighted Polar Moment for microCT Cortical Bone Analysis

MicroCT cortical bone analysis routinely reports a polar moment of area (pMOA), but inconsistent terminology has led to this quantity being referred to as a polar moment of inertia (pMOI). This is inaccurate because pMOA is a purely geometric moment of area. pMOI would be inherently density-weighted, incorporating voxel-level tissue mineral density (TMD) values, and thereby reflect bone’s inhomogeneity. <div> We developed an open-source slice-by-slice framework, validated on test images and implemented in BoneJ, to compute both pMOA- and TMD-weighted pMOI from microCT datasets. We applied it to three rodent models in which cortical geometry and/or TMD vary. </div> <div> Across multiple rodent models, pMOA and pMOI responded equivalently when TMD was spatially uniform. However, in a BCL3 deletion model, pMOI detected significant differences in the TMD-weighted distribution of cortical bone that were not detected by pMOA, highlighting the sensitivity of TMD-weighted polar moments to biologically relevant mineral heterogeneity. </div> <div> These results demonstrate that pMOI captures density-weighted aspects of cortical bone that pMOA is inherently unable to detect. Thus, resolving the ambiguity surrounding “polar moment” terminology in microCT morphometry. We recommend reserving pMOA for the geometric polar moment of area and defining pMOI as a TMD-weighted polar moment. Incorporating one or both measures into microCT analysis enables more transparent interpretation of geometry- and density-driven changes in cortical bone. It may improve the consistency and sensitivity of preclinical bone phenotyping. This distinction may be particularly relevant in models where mineralisation and geometry are decoupled. </div>