Sex differences in proximal humeral outline shape: elliptical Fourier functions

A method is presented for the numerical analysis of sex differences in size and shape of the proximal humeral outlines using elliptical Fourier functions (EFFs). A skeletal sample consisting of right and left humeri pairs of 69 individuals, 36 males and 33 females, was used. The proximal superior view in the plane of the proximo-distal axis of each humerus was photographed and then 54 boundary points were located on the two-dimensional outline tracings. These points were digitized and used to compute EFFs with 27 harmonics. From the EFFs, a set of expected points on the proximal humeral outline was generated using the centroid as an origin. Superimposition of the male and female outlines on this centroid provided a detailed picture of the relative sex differences in size and shape with respect to that center. The bounded area of the proximal humeral outline showed statistically significant sex differences. Additionally, statistical results of the amplitudes derived from the "area-standardized" EFFs and visual assessments of the mean outline plots indicated significant sex differences in shape of the proximal humeral outlines. Focusing on localized regional differences, the greater tubercle was located more postero-medially and the lesser tubercle was located more anteriorly in the males compared to the females. Sex determinations from the proximal humeri were also examined with discriminant functions based on the amplitudes, which represent shape characteristics of the outline, and the hounded area. Using a cross-validation method, predictions of the percentages of cases correctly classified with the discriminant functions were ranged from 92.8% to 95.7% for the right and left humeral data. These results suggest that differences in size and shape of the proximal humeral outlines may be better predictors of sex when compared with conventional measurements of the humerus.