Internal rib structure can be predicted using mathematical models : an anatomic study comparing the chest to a shell dome with application to understanding fractures

Abstract

The human rib cage resembles a masonry dome in shape. Masonry domes have a particular construction that mimics stress distribution. Rib cortical thickness and bone density were analyzed to determine whether the morphology of the rib cage is sufficiently similar to a shell dome for internal rib structure to be predicted mathematically. A finite element analysis (FEA) simulation was used to measure stresses on the internal and external surfaces of a chest-shaped dome. Inner and outer rib cortical thickness and bone density were measured in the mid-axillary lines of seven cadaveric rib cages using computerized tomography scanning. Paired t tests and Pearson correlation were used to relate cortical thickness and bone density to stress. FEA modeling showed that the stress was 82% higher on the internal than the external surface, with a gradual decrease in internal and external wall stresses from the base to the apex. The inner cortex was more radio-dense, P < 0.001, and thicker, P < 0.001, than the outer cortex. Inner cortical thickness was related to internal stress, r = 0.94, P < 0.001, inner cortical bone density to internal stress, r = 0.87, P = 0.003, and outer cortical thickness to external stress, r = 0.65, P = 0.035. Mathematical models were developed relating internal and external cortical thicknesses and bone densities to rib level. The internal anatomical features of ribs, including the inner and outer cortical thicknesses and bone densities, are similar to the stress distribution in dome-shaped structures modeled using FEA computer simulations of a thick-walled dome pressure vessel. Fixation of rib fractures should include the stronger internal cortex.