External rib structure can be predicted using mathematical models : an anatomical study with application to understanding fractures and intercostal muscle function

Abstract

As ribs adapt to stress like all bones, and the chest behaves as a pressure vessel, the effect of stress on the ribs can be determined by measuring rib height and thickness. Rib height and thickness (depth) were measured using CT scans of seven rib cages from anonymized cadavers. A Finite Element Analysis (FEA) model of a rib cage was constructed using a validated approach and used to calculate intramuscular forces as the vectors of both circumferential and axial chest wall forces at right angles to the ribs. Nonlinear quadratic models were used to relate rib height and rib thickness to rib level, and intercostal muscle force to vector stress. Intercostal muscle force was also related to vector stress using Pearson correlation. For comparison, rib height and thickness were measured on CT scans of children. Rib height increased with rib level, increasing by 13% between the 3rd and 7th rib levels, where the 7th/8th rib was the widest part or “equator” of the rib cage, P < 0.001 (t-test). Rib thickness showed a statistically significant 23% increase between the 3rd and 7th ribs, P = 0.004 (t-test). Intercostal muscle force was significantly related to vector stress, Pearson correlation r = 0.944, P = 0.005. The three nonlinear quadratic models developed all had statistically significant parameter estimates with P < 0.03. External rib morphology, in particular rib height and thickness, can be predicted using statistical mathematical models. Rib height is significantly related to the calculated intercostal muscle force, showing that environmental factors affect external rib morphology.