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.

References

1.
Marzke
,
M. W.
,
Tocheri
,
M. W.
,
Steinberg
,
B.
,
Femiani
,
J. D.
,
Reece
,
S. P.
,
Linscheid
,
R. L.
,
Orr
,
C. M.
, and
Marzke
,
R. F.
,
2010
, “
Comparative 3D Quantitative Analyses of Trapeziometacarpal Joint Surface Curvatures Among Living Catarrhines and Fossil Hominins
,”
Am. J. Phys. Anthropol.
,
141
(
1
), pp.
38
51
.10.1002/ajpa.21112
2.
Tocheri
,
M. W.
,
Razdan
,
A.
,
Williams
,
R. C.
, and
Marzke
,
M. W.
,
2005
, “
A 3D Quantitative Comparison of Trapezium and Trapezoid Relative Articular and Nonarticular Surface Areas in Modern Humans and Great Apes
,”
J. Hum. Evol.
,
49
(
5
), pp.
570
586
.10.1016/j.jhevol.2005.06.005
3.
Williams
,
G. M.
,
Chan
,
E. F.
,
Temple-Wong
,
M. M.
,
Bae
,
W. C.
,
Masuda
,
K.
,
Bugbee
,
W. D.
, and
Sah
,
R. L.
,
2010
, “
Shape, Loading, and Motion in the Bioengineering Design, Fabrication, and Testing of Personalized Synovial Joints
,”
J. Biomech.
,
43
(
1
), pp.
156
165
.10.1016/j.jbiomech.2009.09.021
4.
Beck
,
M.
,
Kalhor
,
M.
,
Leunig
,
M.
, and
Ganz
,
R.
,
2005
, “
Hip Morphology Influences the Pattern of Damage to the Acetabular Cartilage Femoroacetabular Impingement as a Cause of Early Osteoarthritis of the Hip
,”
J. Bone Joint Surg. Br.
,
87-B
(
7
), pp.
1012
1018
.10.1302/0301-620X.87B7.15203
5.
Colombo
,
V.
,
Palla
,
S.
, and
Gallo
,
L. M.
,
2008
, “
Temporomandibular Joint Loading Patterns Related to Joint Morphology: A Theoretical Study
,”
Cells Tissues Organs
,
187
(
4
), pp.
295
306
.10.1159/000113408
6.
Daniel
,
M.
,
Iglic
,
A.
, and
Kralj-Iglic
,
V.
,
2005
, “
The Shape of Acetabular Cartilage Optimizes Hip Contact Stress Distribution
,”
J. Anat.
,
207
(
1
), pp.
85
91
.10.1111/j.1469-7580.2005.00425.x
7.
Noble
,
P. C.
,
Kamaric
,
E.
,
Sugano
,
N.
,
Matsubara
,
M.
,
Harada
,
Y.
,
Ohzono
,
K.
, and
Paravic
,
V.
,
2003
, “
Three-Dimensional Shape of the Dysplastic Femur: Implications for THR
,”
Clin. Orthop.
,
417
, pp.
27
40
.30.3097/01.blo.0000096819.67494.32
8.
Smith
,
R. W.
,
Egger
,
P.
,
Coggon
,
D.
,
Cawley
,
M. I.
, and
Cooper
,
C.
,
1995
, “
Osteoarthritis of the Hip Joint and Acetabular Dysplasia in Women
,”
Ann. Rheum. Dis.
,
54
(
3
), pp.
179
181
.10.1136/ard.54.3.179
9.
Felson
,
D. T.
,
Zhang
,
Y.
,
Hannan
,
M. T.
,
Naimark
,
A.
,
Weissman
,
B. N.
,
Aliabadi
,
P.
, and
Levy
,
D.
,
1995
, “
The Incidence and Natural History of Knee Osteoarthritis in the Elderly, the Framingham Osteoarthritis Study
,”
Arthritis Rheum.
,
38
(
10
), pp.
1500
1505
.10.1002/art.1780381017
10.
Felson
,
D. T.
, and
Zhang
,
Y.
,
1998
, “
An Update on the Epidemiology of Knee and Hip Osteoarthritis With a View to Prevention
,”
Arthritis Rheum.
,
41
(
8
), pp.
1343
1355
.10.1002/1529-0131(199808)41:8<1343::AID-ART3>3.0.CO;2-9
11.
Richette
,
P.
,
Corvol
,
M.
, and
Bardin
,
T.
,
2003
, “
Estrogens, Cartilage, and Osteoarthritis
,”
Jt., Bone, Spine
,
70
(
4
), pp.
257
262
.10.1016/S1297-319X(03)00067-8
12.
Wilson
,
D. R.
,
McWalter
,
E. J.
, and
Johnston
,
J. D.
,
2008
, “
The Measurement of Joint Mechanics and Their Role in Osteoarthritis Genesis and Progression
,”
Rheum. Clin. North Am.
,
34
(3), pp.
605
622
.10.1016/j.rdc.2008.05.002
13.
Hunter
,
D. J.
, and
Wilson
,
D. R.
,
2009
, “
Imaging the Role of Biomechanics in Osteoarthritis
,”
Rheum. Clin. North Am.
,
35
(3), pp.
465
483
.10.1016/j.rdc.2009.08.002
14.
Hunter
,
D. J.
, and
Wilson
,
D. R.
,
2009
, “
Role of Alignment and Biomechanics in Osteoarthritis and Implications for Imaging
,”
Radiol. Clin. North Am.
,
47
(4), pp.
553
566
.10.1016/j.rcl.2009.04.006
15.
Ateshian
,
G. A.
,
Rosenwasser
,
M. P.
, and
Mow
,
V. C.
,
1992
, “
Curvature Characteristics and Congruence of the Thumb Carpometacarpal Joint: Differences Between Female and Male Joints
,”
J. Biomech.
,
25
(
6
), pp.
591
607
.10.1016/0021-9290(92)90102-7
16.
Hohe
,
J.
,
Faber
,
S.
,
Muehlbauer
,
R.
,
Reiser
,
M.
,
Englmeier
,
K. H.
, and
Eckstein
,
F.
,
2002
, “
Three-Dimensional Analysis and Visualization of Regional MR Signal Intensity Distribution of Articular Cartilage
,”
Med. Eng. Phys.
,
24
(3), pp.
219
227
.10.1016/S1350-4533(02)00006-1
17.
Kwak
,
S. D.
,
Colman
,
W. W.
,
Ateshian
,
G. A.
,
Grelsamer
,
R. P.
,
Henry
,
J. H.
, and
Mow
,
V. C.
,
1997
, “
Anatomy of the Human Patellofemoral Joint Articular Cartilage: Surface Curvature Analysis
,”
J. Orthop. Res.
,
15
(
3
), pp.
468
472
.10.1002/jor.1100150322
18.
Allaire
,
S.
,
Jacq
,
J. J.
,
Burdin
,
V.
, and
Roux
,
C.
,
2007
, “
Ellipsoid-Constrained Robust Fitting of Quadrics With Application to the 3D Morphological Characterization of Articular Surfaces
,”
Conf. Proc. IEEE Eng. Med. Biol. Soc.
,
2007
, pp.
5087
5090
.10.1109/ICCV.2007.4409163
19.
Kozic
,
N.
,
Weber
,
S.
,
Büchler
,
P.
,
Lutz
,
C.
,
Reimers
,
N.
,
González Ballester
,
M. A.
, and
Reyes
,
M.
,
2010
, “
Optimisation of Orthopaedic Implant Design Using Statistical Shape Space Analysis Based on Level Sets
,”
Med. Image Anal.
,
14
(
3
), pp.
265
275
.10.1016/j.media.2010.02.008
20.
Heimann
,
T.
, and
Meinzer
,
H.-P.
,
2009
, “
Statistical Shape Models for 3D Medical Image Segmentation: A Review
,”
Med. Image Anal.
,
13
(
4
), pp.
543
563
.10.1016/j.media.2009.05.004
21.
Bredbenner
,
T. L.
,
Eliason
,
T. D.
,
Potter
,
R. S.
,
Mason
,
R. L.
,
Havill
,
L. M.
, and
Nicolella
,
D. P.
,
2010
, “
Statistical Shape Modeling Describes Variation in Tibia and Femur Surface Geometry Between Control and Incidence Groups From the Osteoarthritis Initiative Database
,”
J. Biomech.
,
43
(
9
), pp.
1780
1786
.10.1016/j.jbiomech.2010.02.015
22.
Giessen
,
M.
,
Raedt
,
S.
,
Stilling
,
M.
,
Hansen
,
T. B.
,
Maas
,
M.
,
Streekstra
,
G. J.
,
Vliet
,
L. J.
, and
Vos
,
F. M.
,
2011
, “
Localized Component Analysis for Arthritis Detection in the Trapeziometacarpal Joint
,”
Medical Image Computing and Computer-Assisted Intervention—MICCAI 2011
,
G.
Fichtinger
,
A.
Martel
, and
T.
Peters
, eds.,
Springer
,
Berlin, Heidelberg
, pp.
360
367
.
23.
Lurie
,
A. I.
,
1964
,
Three-Dimensional Problems of the Theory of Elasticity
,
J. R. M.
Radok
, ed.,
Interscience
,
New York
.
24.
Connolly
,
K. D.
,
Ronsky
,
J. L.
,
Westover
,
L. M.
,
Küpper
,
J. C.
, and
Frayne
,
R.
,
2009
, “
Analysis Techniques for Congruence of the Patellofemoral Joint
,”
ASME J. Biomech. Eng.
,
131
(
12
), p.
124503
.10.1115/1.3212111
25.
Ankerst
,
M.
,
Kastenmüller
,
G.
,
Kriegel
,
H.-P.
, and
Seidl
,
T.
, “
3D Shape Histograms for Similarity Search and Classification in Spatial Databases
,”
Advances in Spatial Databases
,
R. H.
Güting
,
D.
Papadias
, and
F.
Lochovsky
, eds.,
Springer Berlin
,
Heidelberg, Berlin, Heidelberg
, pp.
207
226
.
26.
Taubin
,
G.
,
1995
, “
Estimating the Tensor of Curvature of a Surface From a Polyhedral Approximation
,”
Proceedings of Fifth International Conference on Computer Vision
, pp.
902
907
.
27.
Maciejewski
,
R.
,
2011
, “
Data Representations, Transformations, and Statistics for Visual Reasoning
,”
Synth. Lect. Vis.
,
2
(
1
), pp.
1
85
.10.2200/S00357ED1V01Y201105VIS002
28.
Vapnik
,
V. N.
,
1999
, “
An Overview of Statistical Learning Theory
,”
IEEE Trans. Neural Network
,
10
(
5
), pp.
988
999
.10.1109/72.788640
29.
Bhattacharyya
,
A.
,
1943
, “
On a Measure of Divergence Between Two Statistical Populations Defined by Their Probability Distributions
,”
Bull. Calcutta Math. Soc.
,
35
, pp.
99
109
.
30.
Cha
,
S.-H.
,
2007
, “Comprehensive Survey on Distance/Similarity Measures Between Probability Density Functions,”
Int. J. Math. Model. Meth. Appl. Sci.
,
1
(4), pp.
300
307
.
31.
Eaton
,
R. G.
, and
Glickel
,
S. Z.
,
1987
, “
Trapeziometacarpal Osteoarthritis. Staging as a Rationale for Treatment
,”
Hand Clin.
,
3
(
4
), pp.
455
471
.
32.
Marai
,
G. E.
,
Laidlaw
,
D. H.
, and
Crisco
,
J. J.
,
2006
, “
Super-Resolution Registration Using Tissue-Classified Distance Fields
,”
IEEE Trans. Med. Imaging
,
25
(
2
), pp.
177
187
.10.1109/TMI.2005.862151
33.
Xu
,
L.
,
Strauch
,
R. J.
,
Ateshian
,
G. A.
,
Pawluk
,
R. J.
,
Mow
,
V. C.
, and
Rosenwasser
,
M. P.
,
1998
, “
Topography of the Osteoarthritic Thumb Carpometacarpal Joint and Its Variations With Regard to Gender, Age, Site, and Osteoarthritic Stage
,”
J. Hand Surg.
,
23
(
3
), pp.
454
464
.10.1016/S0363-5023(05)80463-0
34.
Bronstein
,
A. M.
,
Bronstein
,
M. M.
, and
Ovsjanikov
,
M.
,
2012
, “
Feature-Based Methods in 3D Shape Analysis
,”
3D Imaging, Analysis and Applications
,
N.
Pears
,
Y.
Liu
, and
P.
Bunting
, eds.,
Springer
,
London
, pp.
185
219
.
35.
Banchoff
,
T. F.
, and
Lovett
,
S. T.
,
2010
,
Differential Geometry of Curves and Surfaces
,
CRC Press
, Boca Raton, FL.
36.
Stewart
,
J.
,
2011
,
Multivariable Calculus
,
Cengage Learning
, Belmont, CA.
You do not currently have access to this content.