Research Papers

Characterization of the Centroidal Geometry of Human Ribs

[+] Author and Article Information
Matthew W. Kindig

Research Assistant
University of Virginia Center
for Applied Biomechanics,
4040 Lewis N. Clark Drive,
Charlottesville, VA 22911
e-mail: mwk5v@virginia.edu

Richard W. Kent

Deputy Director
University of Virginia,
Department of Mechanical and
Aerospace Engineering,
122 Engineer's Way,
Charlottesville, VA 22904;
University of Virginia Center
for Applied Biomechanics,
4040 Lewis N. Clark Drive,
Charlottesville, VA 22911
e-mail: rwk3c@virginia.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received February 25, 2013; final manuscript received August 13, 2013; accepted manuscript posted September 6, 2013; published online October 1, 2013. Assoc. Editor: Barclay Morrison.

J Biomech Eng 135(11), 111007 (Oct 01, 2013) (9 pages) Paper No: BIO-13-1102; doi: 10.1115/1.4025329 History: Received February 25, 2013; Revised August 13, 2013; Accepted September 06, 2013

While a number of studies have quantified overall ribcage morphology (breadth, depth, kyphosis/lordosis) and rib cross-sectional geometry in humans, few studies have characterized the centroidal geometry of individual ribs. In this study, a novel model is introduced to describe the centroidal path of a rib (i.e., the sequence of centroids connecting adjacent cross-sections) in terms of several physically-meaningful and intuitive geometric parameters. Surface reconstructions of rib levels 2–10 from 16 adult male cadavers (aged 31–75 years) were first extracted from CT scans, and the centroidal path was calculated in 3D for each rib using a custom numerical method. The projection of the centroidal path onto the plane of best fit (i.e., the “in-plane” centroidal path) was then modeled using two geometric primitives (a circle and a semiellipse) connected to give C1 continuity. Two additional parameters were used to describe the deviation of the centroidal path from this plane; further, the radius of curvature was calculated at various points along the rib length. This model was fit to each of the 144 extracted ribs, and average trends in rib size and shape with rib level were reported. In general, upper ribs (levels 2–5) had centroidal paths which were closer to circular, while lower ribs (levels 6–10) tended to be more elliptical; further the centroidal curvature at the posterior extremity was less pronounced for lower ribs. Lower ribs also tended to exhibit larger deviations from the best-fit plane. The rib dimensions and trends with subject stature were found to be consistent with findings previously reported in the literature. This model addresses a critical need in the biomechanics literature for the accurate characterization of rib geometry, and can be extended to a larger population as a simple and accurate way to represent the centroidal shape of human ribs.

Copyright © 2013 by ASME
Topics: Geometry , Shapes , Dimensions
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Grahic Jump Location
Fig. 1

Definition of rib local coordinate system and major plane

Grahic Jump Location
Fig. 2

(a) Initial centroidal axis calculation, with a representative node i (with cylindrical coordinates ri and θi) and a typical bin at θ = 45 deg shown. Note that, for clarity, the mesh is shown as coarser than that used in the study; similarly, the bin is not shown to scale. (b) Sweeping cylinders method applied along rib surface. (c) Isolation of rib cross-section perimeter and calculation of centroid using alpha shape technique.

Grahic Jump Location
Fig. 3

In-plane centroidal model, overlaid on rib. The portions of the geometric primitives (semiellipse and circle) that are part of the model are shown in solid lines. The connecting lines connecting the shapes to the x-axis (straight lines) and to each other (parabola) are shown in black. The endpoints of these connecting lines are numbered 1-4; point 1 is (x1, y1), point 2 is (x2, y2), etc.

Grahic Jump Location
Fig. 4

Definition of out-of-plane characteristics of the rib

Grahic Jump Location
Fig. 5

Variation in rib length (L) and depth (x0) with rib level. Mean ± standard deviation is shown.

Grahic Jump Location
Fig. 6

Variation in semielliptical parameters (a) and circular parameters (b) with rib level, normalized by x0. Mean ± standard deviation is shown.

Grahic Jump Location
Fig. 7

Variation in out-of-plane parameters with rib level. Mean ± standard deviation is shown.



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