Statistical shape modeling (SSM) and statistical density modeling (SDM) are tools capable of describing the main modes of deviation in the shape and density distribution of the shoulder using a set of uncorrelated variables called principal components (PCs). We hypothesize that the first PC of the SDM, which scales overall density up/down, will be inversely correlated with age and will, on average, be greater for males than females. We also hypothesize that there is a correlation between some PCs of shape and density.

SSM and SDM were developed for scapulae and humeri by segmenting surface meshes from computed tomographic images of 75 cadaveric shoulders. Bones were co-registered and defined by the same surface mesh. Volumetric tetrahedral meshes were defined for one of the specimens serving as base meshes for SDM. Base meshes were morphed to each individual bone's surface and superimposed upon the corresponding CT data to determine image intensity in Hounsfield units at each node. Principal component analysis was performed on the exterior shape and internal density distribution of bones. T-tests were performed to find any differences in PC scores between males and females, and Pearson correlation coefficients were calculated for age and PC scores. Finally, correlation coefficients between each of the PCs of the shape and density models were calculated.

For the humerus, the first three PCs of the SDM were significantly correlated with age (ρ = 0.40, −0.46, and 0.36, all p ≤ 0.007). For the scapula, the first and ninth PCs showed such correlation (ρ = −0.31, and −0.32, all p ≤ 0.02). Statistically significant differences due to sex were found for the second to sixth SDM PCs of the humerus, with differences in average PC scores of 1, 1, −0.7, −0.8, and −0.6 standard deviations, respectively, for males relative to females. For the scapula, the second, fifth and seventh SDM PCs were significantly different between males and females, with average PC scores differing by 1.1, 0.7, and −0.6 standard deviations. Finally, for both bones, the first PC of SSM showed a weak but significant correlation with the second PC of the SDM (ρ = 0.47, p < 0.001 for the humerus, and ρ = 0.39, p < 0.001 for the scapula).

The results of this study suggest that age has a significant influence on the first PC of the SDM, associated with scaling the density in the cortical boundary. Moreover, the negative correlation of age with the second PC of the humerus in SDM which mostly influences the thickness of the cortical boundary implies cortical thinning with age. The second PC of both bones differed significantly between males and females, implying that cortical thickness differs between sexes. Also, there was a significant correlation between the size of the bones and the thickness of the cortical boundary. These findings can help guide the designs of population-based prosthesis components.

Introduction

Stress shielding of bone around the stem components of total shoulder replacement (TSR) implants can result in bone resorption, leading to loosening and failure. Titanium is an ideal biomaterial for implant stems; however, it is much stiffer than bone. Recent advances in additive manufacturing (AM) have enabled the production of parts with complex geometries from titanium alloys, such as hollow or porous stems. The objective of this computational study is to determine if hollow titanium stems can reduce stress shielding at the proximal humerus. We hypothesize that hollow TSR implant stems will reduce stress shielding in comparison with solid stems and the inner wall thickness of the hollow stem will be a design parameter with a direct effect on bone stresses.