An anthropometric analysis to derive formulae for calculating the dimensions of anatomically shaped humeral heads

Background The elliptical shape of the humeral head has been vaguely described, but a more detailed mathematical description is lacking. The primary goal of this study was to create formulae to describe the mathematical relationships between the various dimensions of anatomically shaped humeral heads. Methods Three-dimensional computer models of 79 proximal humeri derived from computed tomography scans (white subjects, 47 male and 32 female; ages, 17-87 years) were studied. Linear regression analysis of the obtained humeral measurements was performed, and Pearson correlation coefficient ( R ) values were calculated. To substantiate the results of the linear regression analysis, Welch t -test was used to compare various parameters of small, medium, and large humeral heads. Results Formulae for calculating humeral head height, diameters of the base of the humeral head in the frontal and sagittal planes, and radii of curvature in the frontal and sagittal planes were derived from the linear regression plots that were found to have strong (1 ≥ R ≥ 0.50) correlations. By Welch t -test, differences between the 3 head sizes were statistically significant in each case ( P ≤ .022). The elliptical shape of the base of the humeral head was found to elongate with increasing humeral head size. Conclusions Mathematical formulae relating various humeral head dimensional measurements are presented. The formulae derived in this study may be useful for the design of future prosthetic shoulder systems in which the goal is to replicate normal anatomy. This is the first study to describe that the elliptical shape of the base of the humeral head elongates as head size increases.