Modeling female and male rib geometry with logarithmic spirals.

In this study we present a novel six-parameter shape model of the human rib centroidal path using logarithmic spirals. It provides a reduction in parameter space from previous models of overall rib shape, while simultaneously reducing fitting error by 34% and increasing curvature continuity. Furthermore, the model directly utilizes geometric properties such as rib end-to-end span, aspect ratio, rib "skewness", and inner angle with the spine in its parameterization, making the effects of each parameter on overall shape intuitive and easy to visualize. The model was tested against 2197 rib geometries extracted from CT scans from a population of 100 adult females and males of uniformly distributed ages between 20 and 70. Significant size and shape differences between genders were identified, and shape model utility is demonstrated by the production of statistically average male and female rib shapes for all rib levels. Simulated mechanical loading of the resulting model rib shapes showed that the stiffness of statistically average male and female ribs matched well with the average rib stiffness from each separate population. This in-plane rib shape model can be used to characterize variation in human rib geometry seen throughout the population, including investigation of the overall changes in shape and resultant mechanical properties that ribs undergo during aging or disease progression.