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Technical Brief

Polar Histograms of Curvature for Quantifying Skeletal Joint Shape and Congruence

[+] Author and Article Information
Eni Halilaj

Center for Biomedical Engineering
and School of Engineering,
Brown University,
Providence, RI 02912

David H. Laidlaw

Department of Computer Science,
Brown University,
Providence, RI 02912

Douglas C. Moore

Department of Orthopaedics,
The Warren Alpert Medical School
of Brown University and Rhode Island Hospital,
Providence, RI 02903

Joseph J. Crisco

Department of Orthopaedics,
The Warren Alpert Medical School
of Brown University and Rhode Island Hospital,
Providence, RI 02903
e-mail: joseph_crisco@brown.edu

1Corresponding author.

Manuscript received February 3, 2014; final manuscript received June 23, 2014; accepted manuscript posted July 2, 2014; published online July 21, 2014. Assoc. Editor: Kristen Billiar.

J Biomech Eng 136(9), 094503 (Jul 21, 2014) (6 pages) Paper No: BIO-14-1064; doi: 10.1115/1.4027938 History: Received February 03, 2014; Revised June 23, 2014; Accepted July 02, 2014

The effect of articular joint shape and congruence on kinematics, contact stress, and the natural progression of joint disease continues to be a topic of interest in the orthopedic biomechanics literature. Currently, the most widely used metrics of assessing skeletal joint shape and congruence are based on average principal curvatures across the articular surfaces. Here we propose a method for comparing articular joint shape and quantifying joint congruence based on three-dimensional (3D) histograms of curvature—shape descriptors that preserve spatial information. Illustrated by experimental results from the trapeziometacarpal joint, this method could help unveil the interrelations between joint shape and function and provide much needed insight for the high incidence of osteoarthritis (OA)—a mechanically mediated disease whose onset has been hypothesized to be precipitated by joint incongruity.

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Topics: Shapes
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Figures

Grahic Jump Location
Fig. 1

Polar coordinate systems on the mating articular surfaces of a joint, illustrating the dimensions of the 3D histograms: the radial coordinate or the distance from the pole (r), the angular coordinate or the angle from the polar axis (θ), and curvature (k)

Grahic Jump Location
Fig. 2

Illustration of arthritic progressions in the trapezium, with 3D bone models extracted from CT scans of volunteers (normal, early OA) and excised trapezia of patients who underwent trapeziectomy (late stage OA)

Grahic Jump Location
Fig. 3

(a) 3D bone models of a wrist and hand from a CT scan, (b) manually selected subchondral facets on the trapeziometacarpal joint, (c) the fifth order polynomial surfaces fitted to the facets, and (d) minimum curvature vector fields on the fitted surface ranging from 0 to 0.45 mm−1, represented here at lower resolution, for visual purposes

Grahic Jump Location
Fig. 4

The mean (±SD) position specific dissimilarity measure, pJC, in the normal and arthritic groups during (a) neutral, (b) key pinch, (c) jar grasp, (d) jar open, (e) extension, (f) flexion, (g) abduction, and (h) adduction position, as well as the previously used CI, where, for both pJC and CI, a higher value indicates lower congruence

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