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.

Microanatomical diversity of amniote ribs: an exploratory quantitative study

“…Previous studies have shown that the different ribs of the rib series are subject to contrasted mechanical stresses (e.g. as a result of locomotion or posture: Fujiwara et al ., ; Casha et al ., ), which is likely to affect their cortical thickness (Casha et al ., ). Lifestyle adaptations could also affect preferentially certain zones of the rib series depending on the taxa considered.…”

“…Within the rib series, the various elements usually show differences in morphologies and microstructures that may reflect their mechanical loads (Fujiwara et al ., ; Waskow & Sander, ; Casha et al ., , b). However, identifying the rib most affected by the mechanical load and the lifestyle is difficult because it depends on diverse factors such as locomotion mode and posture, and the identity of the optimal rib (for our purpose) may thus be variable between taxa (Bramble & Carrier, ; Fujiwara et al ., ).…”

“…However, identifying the rib most affected by the mechanical load and the lifestyle is difficult because it depends on diverse factors such as locomotion mode and posture, and the identity of the optimal rib (for our purpose) may thus be variable between taxa (Bramble & Carrier, ; Fujiwara et al ., ). Unfortunately, most of the literature related to intraspecific variability in rib architecture is medically‐driven and pertains to humans; it emphasizes assessments of the impact of ageing or traumatic events on the rib cage biomechanics (Yoganandan & Pintar, ; Li et al ., ; Mitton et al ., ; Casha et al ., ,b) or the effect of nutritional or physiological stresses (Heinrich, ).…”

Physiological rules for the heart, lungs and other pressure-based organs

“…Some physiological processes are more efficient when handled by a pressure based process e.g., ventilation is more efficient in mammals than insects where it is limited by diffusion, permitting an increase in maximum body size. The torso in effect becomes a pressure vessel with limbs, with the ribs undergoing morphological changes including external dimensions, cortical thickness and bone density typical of a pressure vessel (23,24). Figure 1 A set of seven physiological rules applied to pressure-based organs or organ systems showing isometry.…”