Does 3D orientation account for variation in osteon morphology assessed by 2D histology?

The primary microstructural unit of cortical bone, the secondary osteon or Haversian system, is widely assumed to have a cylindrical shape. It is generally accepted that osteons are roughly circular in cross-section and deviations from circularity have been attributed to deviations from longitudinal orientation. To our knowledge this idealized geometric relationship, which assumes osteons are perfect cylinders, has not been rigorously explored. As such, we sought to explore two research questions: (i) Does the orientation of osteons in 3D explain variation in shapes visualized in 2D? (ii) Can differences in osteon 3D orientation explain previously reported age-related differences observed in their 2D cross-sectional shape (e.g. more circular shape and decreased area with age)? To address these questions we utilized a combination of 2D histology to identify osteon shape and superimposed micro-computed tomography data to assess osteon orientation in 3D based upon the osteonal canal. Shape was assessed by the inverse of Aspect Ratio (On.AspR(-1), based on a fitted ellipse) - which ranged from 0 (infinitely elongated shape) to 1 (perfectly circular). A sample (n = 27) of human female anterior femoral cortical bone samples from across the human lifespan (20-87 years) were included in the analysis, which involved 1418 osteons. The overall mean measure of On.AspR(-1) was 0.703 (1.42 Aspect Ratio). Mean osteon orientation was 79.1° (90° being longitudinal). While we anticipated a positive relation between orientation and On.AspR(-1), we found the opposite - a weak negative correlation (with more oblique 3D osteon alignment, the 2D shape became more circular as reflected by increased On.AspR(-1)). When analysis of covariance was performed with age and orientation as covariates, the negative relation with orientation was replaced by a significant relation with age alone. This relation with age accounted for 41% of the variation of On.AspR(-1). The results revealed that osteons, on average, are not circular in cross-section and that 3D orientation cannot account for deviation from circular shape. Osteons thus are strictly speaking not cylinders, as they tend to have elliptical cross-sections. We observed that osteons did become less elliptical in cross-section with age independent of orientation - suggesting this is a real change in morphology.

Brief communication: the relation between standard error of the estimate and sample size of histomorphometric aging methods.

Histomorphometric aging methods report varying degrees of precision, measured through Standard Error of the Estimate (SEE). These techniques have been developed from variable samples sizes (n) and the impact of n on reported aging precision has not been rigorously examined in the anthropological literature. This brief communication explores the relation between n and SEE through a review of the literature (abstracts, articles, book chapters, theses, and dissertations), predictions based upon sampling theory and a simulation. Published SEE values for age prediction, derived from 40 studies, range from 1.51 to 16.48 years (mean 8.63; sd: 3.81 years). In general, these values are widely distributed for smaller samples and the distribution narrows as n increases--a pattern expected from sampling theory. For the two studies that have samples in excess of 200 individuals, the SEE values are very similar (10.08 and 11.10 years) with a mean of 10.59 years. Assuming this mean value is a 'true' characterization of the error at the population level, the 95% confidence intervals for SEE values from samples of 10, 50, and 150 individuals are on the order of ± 4.2, 1.7, and 1.0 years, respectively. While numerous sources of variation potentially affect the precision of different methods, the impact of sample size cannot be overlooked. The uncertainty associated with SEE values derived from smaller samples complicates the comparison of approaches based upon different methodology and/or skeletal elements. Meaningful comparisons require larger samples than have frequently been used and should ideally be based upon standardized samples.