Experimental and computational investigations of thoracic injury require an understanding of both the structural behavior and the fracture properties of ribs. To quantify the fracture tolerance, the present study sought to identify an appropriate failure predictor for individual ribs under anterior loading. Eighty-nine human ribs, extracted from levels 2 through 10 from nine cadaveric subjects, were loaded in anterior-posterior planar bending. The linear stiffness of each specimen was calculated, and several predictors of fracture tolerance—force, displacement, moment, and work—were defined. Additionally a series of matched tests at different rates examined the effect of loading rate on the stiffness and fracture characteristics.
It was found that the second rib was significantly stiffer (p < 0.001) compared to all other rib levels (3-10), while ribs 3 through 5 were less stiff than ribs 6 through 10. No trend in subject age or BMI was observed; however, female subjects were found to be more compliant than males. Comparing quasi-static (~2 mm/sec) and dynamic (~1 m/sec) tests, no significant difference in stiffness (p = 0.22) or failure parameters (p > 0.05 for all) was observed. Survival analysis was used to develop cumulative failure distributions for the various fracture predictors, and the distribution kurtosis was used to rank the predictors in terms of discriminatory power. The moment at the location of fracture and the normalized displacement between the rib extremities exhibited the highest values of kurtosis and thus were considered the most discriminatory predictors. Due to difficulties in measuring fracture moment, the end-to-end displacement was chosen as the most appropriate failure predictor in this study. A displacement of 25% of the initial depth of the rib was found to represent a 50% risk of injury under these boundary conditions.
The structural behavior of a human rib, and therefore its ability to withstand fracture, has been shown to be strongly affected by its geometric characteristics. To elucidate this relationship, the second component of this study quantified the influence of two aspects of the rib’s geometry—the centroidal axis description and the cross-sectional geometry—on its stiffness (defined as the ratio of the resultant force to the displacement). A novel seven-parameter model, defined in terms of elements of planar geometry, was developed and fit to each of the tested ribs in order to provide a mathematical description of the centroidal axis. Additionally, the rib’s cross-sectional properties (overall dimensions, cortical thickness, longitudinal twist, principal moments of inertia) were determined at five discrete locations along the centroidal axis. Trends with rib level in each of the centroidal and cross-sectional properties were reported.
A combination of beam theory and finite element techniques was then used to quantify the influence of each of these centroidal parameters on the stiffness of the rib. It was observed that changes in the geometry in the antero-lateral region of the rib had a greater effect on the rib stiffness than changes posteriorly. To examine the sensitivity of the stiffness to changes in cross-sectional geometry, four models of each rib’s cross-section—each incorporating various simplifications to the cross-sectional dimensions and cortical thickness distribution—were defined relative to a more complete description of the cross-sectional geometry. Modeling the rib with a variable cross-section and a uniform cortical thickness provided the best approximation to the actual cross-sectional geometry, over-predicting the stiffness of the rib by about 3%. The work presented here can be used by injury researchers to develop fracture injury criteria for ribs and to better understand the role of geometric variation on the structural behavior of the rib.