Characterization of the Centroidal Geometry of Human Ribs

Abstract

While a number of studies have quantified overall ribcage morphology (breadth, depth, kyphosis/lordosis) and rib cross-sectional geometry in humans, few studies have characterized the centroidal geometry of individual ribs. In this study, a novel model is introduced to describe the centroidal path of a rib (i.e., the sequence of centroids connecting adjacent cross-sections) in terms of several physically-meaningful and intuitive geometric parameters. Surface reconstructions of rib levels 2-10 from 16 adult male cadavers (aged 31-75 years) were first extracted from CT scans, and the centroidal path was calculated in 3D for each rib using a custom numerical method. The projection of the centroidal path onto the plane of best fit (i.e., the "in-plane" centroidal path) was then modeled using two geometric primitives (a circle and a semiellipse) connected to give C1 continuity. Two additional parameters were used to describe the deviation of the centroidal path from this plane; further, the radius of curvature was calculated at various points along the rib length. This model was fit to each of the 144 extracted ribs, and average trends in rib size and shape with rib level were reported. In general, upper ribs (levels 2-5) had centroidal paths which were closer to circular, while lower ribs (levels 6-10) tended to be more elliptical; further the centroidal curvature at the posterior extremity was less pronounced for lower ribs. Lower ribs also tended to exhibit larger deviations from the best-fit plane. The rib dimensions and trends with subject stature were found to be consistent with findings previously reported in the literature. This model addresses a critical need in the biomechanics literature for the accurate characterization of rib geometry, and can be extended to a larger population as a simple and accurate way to represent the centroidal shape of human ribs.