Population trends in human rib cross-sectional shapes

Abstract

Rib fractures remain the most frequent thoracic injury in motor vehicle crashes. Computational human body models (HBMs) can be used to simulate these injuries and design mitigation strategies, but they require adequately detailed geometry to replicate such fractures. Due to a lack of rib cross-sectional shape data availability, most commercial HBMs use highly simplified rib sections extracted from a single individual during original HBM development. This study provides human rib shape data collected from chest CT scans of 240 females and males across the full adult age range. A cortical bone mapping algorithm extracted cross-sectional geometry from scans in terms of local periosteal position with respect to the central rib axis and local cortex thickness. Principal component analysis was used to reduce the dimensionality of these cross-sectional shape data. Linear regression found significant associations between principal component scores and subject demographics (sex, age, height, and weight) at all rib levels, and predicted scores were used to explore the expected rib cross-sectional shapes across a wide range of subject demographics. The resulting detailed rib cross-sectional shapes were quantified in terms of their total cross-sectional area and their cortical bone cross-sectional area. Average-sized female ribs were smaller in total cross-sectional area than average-sized male ribs by between 20% and 36% across the rib cage, with the greatest differences seen in the central portions of rib 6. This trend persisted although to smaller differences of 14%-29% when comparing females and males of equal intermediate weight and stature. Cortical bone cross-sectional areas were up to 18% smaller in females than males of equivalent height and weight but also reached parity in certain regions of the rib cage. Increased age from 25 to 80 years was associated with reductions in cortical bone cross-sectional area (up to 37% in females and 26% in males at mid-rib levels). Total cross-sectional area was also seen to reduce with age in females but to a lesser degree (of up to 17% in mid-rib regions). Similar regions saw marginal increases in total cross-sectional area for male ribs, indicating age affects rib cortex thickness moreso than overall rib cross-sectional size. Increased subject height was associated with increased rib total and cortical bone cross-sectional areas by approximately 25% and 15% increases, respectively, in mid-rib sections for a given 30 cm increase in height, although the magnitudes of these associations varied by sex and rib location. Increased weight was associated with approximately equal changes in both cortical bone and total cross-sectional areas in males. These effects were most prominent (around 25% increases for an addition of 50 kg) toward lower ribs in the rib cage and had only modest effects (less than 12% change) in ribs 2-4. Females saw greater increases with weight in total rib area compared to cortical bone area, of up to 21% at the eighth rib level. Results from this study show the expected shapes of rib cross-sections across the adult rib cage and across a broad range of demographics. This detailed geometry can be used to produce accurate rib models representing widely varying populations.

Keywords: computational models; cortical bone; cross‐section; population; ribs; shape.

FIGURE 1

Percent of underlying rib shape data variance captured by each additional PC (left) and ability of demographics‐based regression models to explain PC score data (right).

FIGURE 2

Effects of the first 5 PCs for rib 6 on rib periosteal shape (cortex thicknesses not shown). Each PC modulates different aspects of overall rib 6 shape. The explanatory power (adjusted R ²) and significance (*, **, *** for p < 0.05, p < 0.01, p < 0.001, respectively) of the noninteraction demographic terms (age, sex, height, weight) for each PC's regression model are indicated on right.

FIGURE 3

Rib sectional differences between males and females for average statures and weights (above) and for equal statures and weights (below). Values indicated within each section show the percentage change in total area or cortical bone area from male to female subjects.

FIGURE 4

Expected rib sectional changes by age for males and females.

FIGURE 5

Expected rib sectional changes by height for males and females.

FIGURE 6

Rib sectional changes by weight for males and females.