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.

Finite Element-Derived Surrogate Models of Locked Plate Fracture Fixation Biomechanics

“…Casha et al . 6 developed a quadratic mathematical model of the relationship between rib height and FEA-determined intercostal muscle force.…”

Microanatomical diversity of amniote ribs: an exploratory quantitative study

“…Indeed, the relative form (length, thickness, and curvature) and number, and, when present, the pattern of regional variation within the rib series (e.g. cervical, thoracic, lumbar, sacral, caudal ribs) are all diverse at both broad and fine taxonomic scales within tetrapods (Clack, ; Asher et al ., ; Casha et al ., ). We did not sample gastralia because their ontogenetic origin (as dermal elements) differs from that of true ribs (dorsal, endoskeletal elements); therefore, we standardized our sample by sectioning only dorsal and thoracic ribs (when this regional differentiation exists).…”

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.…”