Our preliminary indentation experiments showed that the equilibrium elastic modulus of murine tibial cartilage increased with decreasing indenter size: flat-ended 60deg conical tips with end diameters of 15μm and 90μm gave 1.50±0.82MPa (mean±standard deviation) and 0.55±0.11MPa, respectively (p<0.01). The goal of this paper is to determine if the dependence on tip size is an inherent feature of the equilibrium elastic modulus of cartilage as measured by indentation. Since modulus values from nonindentation tests are not available for comparison for murine cartilage, bovine cartilage was used. Flat-ended conical or cylindrical tips with end diameters ranging from 5μmto4mm were used to measure the equilibrium elastic modulus of bovine patellar cartilage. The same tips were used to test urethane rubber for comparison. The equilibrium modulus of the bovine patellar cartilage increased monotonically with decreasing tip size. The modulus obtained from the 2mm and 4mm tips (0.63±0.21MPa) agreed with values reported in the literature; however, the modulus measured by the 90μm tip was over two and a half times larger than the value obtained from the 1000μm tip. In contrast, the elastic modulus of urethane rubber obtained using the same 5μm4mm tips was independent of tip size. The equilibrium elastic modulus of bovine patellar cartilage measured by indentation depends on tip size. This appears to be an inherent feature of indentation of cartilage, perhaps due to its inhomogeneous structure.

1.
Hori
,
R. Y.
, and
Mockros
,
L. F.
, 1976, “
Indentation Tests of Human Articular Cartilage
,”
J. Biomech.
0021-9290,
9
, pp.
259
268
.
2.
Hoch
,
D. H.
,
Grodzinsky
,
A. J.
,
Koob
,
T. J.
,
Albert
,
M. L.
, and
Eyre
,
D. R.
, 1983, “
Early Changes in Material Properties of Rabbit Articular Cartilage After Meniscectomy
,”
J. Orthop. Res.
0736-0266,
1
, pp.
4
12
.
3.
Athanasiou
,
K. A.
,
Zhu
,
C. F.
,
Wang
,
X.
, and
Agrawal
,
C. M.
, 2000, “
Effects of Aging and Dietary Restriction on the Structural Integrity of Rat Articular Cartilage
,”
Ann. Biomed. Eng.
0090-6964,
28
, pp.
143
149
.
4.
Athanasiou
,
K. A.
,
Agarwal
,
A.
, and
Dzida
,
F. J.
, 1994, “
Comparative Study of the Intrinsic Mechanical Properties of the Human Acetabular and Femoral Head Cartilage
,”
J. Orthop. Res.
0736-0266,
12
, pp.
340
349
.
5.
Mow
,
V. C.
,
Gibbs
,
M. C.
,
Lai
,
W. M.
,
Ahu
,
W. B.
, and
Athanasiou
,
K. A.
, 1989, “
Biphasic Indentation of Articular Cartilage-II. A Numerical Algorithm and an Experimental Study
,”
J. Biomech.
0021-9290,
22
, pp.
853
861
.
6.
Bae
,
W. C.
,
Temple
,
M. M.
,
Amiel
,
D.
,
Coutts
,
R. D.
,
Niederauer
,
G. G.
, and
Sah
,
R. L.
, 2003, “
Indentation Testing of Human Cartilage
,”
Arthritis Rheum.
0004-3591,
48
, pp.
3382
3394
.
7.
Kempson
,
B. E.
,
Tuke
,
M. A.
,
Dingle
,
J. T.
,
Barrett
,
A. J.
,
Horsfield
,
P. H.
, 1976, “
The Effects of Proteolytic Enzymes on the Mechanical Properties of Adult Human Articular Cartilage
,”
Biochim. Biophys. Acta
0006-3002,
428
, pp.
741
760
.
8.
Athanasiou
,
K. A.
,
Agarwal
,
A.
,
Muffoletto
,
A.
,
Dzida
,
F. J.
,
Constantinides
,
G.
, and
Clem
,
M.
, 1995, “
Biomechanical Properties of Hip Cartilage in Experimental Animal Models
,”
Clin. Orthop. Relat. Res.
0009-921X,
316
, pp.
254
266
.
9.
Hyttinen
,
M. M.
,
Toyras
,
J.
,
Lapvetelainen
,
T.
,
Lindblom
,
J.
,
Prockop
,
D. J.
,
Li
,
S.-W.
,
Arita
,
M.
,
Jurvelin
,
J. S.
, and
Helminen
,
H. J.
, 2001, “
Inactivation of One Allele of the Type II Collagen Gene Alters the Collagen Network in Murine Articular Cartilage and Makes Cartilage Softer
,”
Ann. Rheum. Dis.
0003-4967,
60
, pp.
262
268
.
10.
Cao
,
L.
,
Youn
,
I.
,
Guilak
,
F.
, and
Setton
,
L. A.
, 2006, “
Compressive Properties of Mouse Articular Cartilage determined in a Novel Micro-indentation Test Method and Biphasic Finite Element Model
,”
J. Biomech. Eng.
0148-0731,
128
, pp.
766
774
.
11.
Ebenstein
,
D. M.
,
Kuo
,
A.
,
Rodrigo
,
J. J.
,
Reddi
,
A. H.
,
Ries
,
M.
, and
Pruitt
,
L.
, 2004, “
A Nanoindentation Technique for Functional Evaluation of Cartilage Repair Tissue
,”
J. Mater. Res.
0884-2914,
19
, pp.
273
281
.
12.
Oliver
,
W. C.
, and
Pharr
,
G. M.
, 1992, “
An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments
,”
J. Mater. Res.
0884-2914,
7
, pp.
1564
1583
.
13.
Stolz
,
M.
,
Raiteri
,
R.
,
Daniels
,
A. U.
,
Van Landingham
,
M. R.
, and
Baschong
,
W.
, 2004, “
Dynamic Elastic Modulus of Porcine Articular Cartilage Determined at Two Different Levels of Tissue Organization by Indentation-Type Atomic Force Microscopy
,”
Biophys. J.
0006-3495,
86
, pp.
3269
3283
.
14.
Armstrong
,
C. G.
,
Bahrani
,
A. S.
, and
Gardner
,
D. L.
, 1979, “
In Vitro Measurement of Articular Cartilage Deformations in the Intact Human Hip Joint Under Load
,”
J. Bone Joint Surg. Br.
0301-620X
61A
, pp.
744
755
.
15.
Dimitriadis
,
E. K.
,
Horkay
,
F.
,
Maresca
,
J.
,
Kachar
,
B.
, and
Chadwick
,
R. S.
, 2002, “
Determination of Elastic Moduli of Thin Layers of Soft Material Using the Atomic Force Microscope
,”
Biophys. J.
0006-3495,
82
, pp.
2798
2810
.
16.
Imetra Inc.
, 2003, private communication.
17.
Mak
,
A. F.
,
Lai
,
W. M.
, and
Mow
,
V. C.
, 1987, “
Biphasic Indentation of Articular Cartilage—I. Theoretical Analysis
,”
J. Biomech.
0021-9290,
20
, pp.
703
714
.
18.
Sneddon
,
I. N.
, 1965, “
The Relation Between Load and Penetration in the Axisymmetric Boussinesq Problem for a Punch of Arbitrary Profile
,”
Int. J. Eng. Sci.
0020-7225,
3
, pp.
47
57
.
19.
Briscoe
,
B. J.
,
Sebastian
,
K. S.
, and
Adams
,
M. J.
, 1994, “
The Effect of Indenter Geometry on the Elastic Response to Indentation
,”
J. Phys. D
0022-3727,
27
, pp.
1156
1162
.
20.
Hayes
,
W. C.
,
Keer
,
L. M.
,
Herrmann
,
G.
, and
Mockros
,
L. F.
, 1972, “
A Mathematical Analysis for Indentation Tests of Articular Cartilage
,”
J. Biomech.
0021-9290,
5
, pp.
541
551
.
21.
Korhonen
,
R. K.
,
Laasanen
,
M. S.
,
Toyras
,
J.
,
Rieppo
,
J.
,
Hirvonen
,
J.
,
Helminen
,
H. J.
, and
Jurvelin
,
J. S.
, 2002, “
Comparison of the Equilibrium Response of Articular Cartilage in Unconfined Compression, Confined Compression and Indentation
,”
J. Biomech.
0021-9290,
35
, pp.
903
909
.
22.
DiSilvestro
,
M. R.
,
Zhu
,
Q.
, and
Suh
,
J.-K. F.
, 2001, “
Biphasic Poroviscoelastic Simulation of the Unconfined Compression of Articular Cartilage: II—Effect of Variable Strain Rates
,”
ASME J. Biomech. Eng.
0148-0731,
123
, pp.
198
200
.
23.
Manufacturer specifications, private communication.
24.
DiSilvestro
,
M. R.
, and
Suh
,
J.-K. F.
, 2001, “
A Cross-Validation of the Biphasic Poroviscoelastic Model of Articular Cartilage in Unconfined Compression, Indentation, and Confined Compression
,”
J. Biomech.
0021-9290,
34
, pp.
519
525
.
25.
Schinagl
,
R. M.
,
Gurskis
,
D.
,
Chen
,
A. C.
, and
Sah
,
R. L.
, 1997, “
Depth-Dependent Confined Compression Modulus of Full-Thickness Bovine Articular Cartilage
,”
J. Orthop. Res.
0736-0266,
15
, pp.
499
506
.
26.
Krishnan
,
K.
,
Park
,
S.
,
Eckstein
,
F.
, and
Ateshian
,
G. A.
, 2003, “
Inhomogeneous Cartilage Properties Enhance Superficial Interstitial Fluid Support and Frictional Properties, But Do Not Provide a Homogeneous State of Stress
,”
ASME J. Biomech. Eng.
0148-0731,
125
, pp.
569
577
.
27.
Soltz
,
M. A.
, and
Ateshian
,
G. A.
, 2000, “
A Conewise Linear Elasticity Mixture Model for the Analysis of Tension-Compression Nonlinearity in Articular Cartilage
,”
ASME J. Biomech. Eng.
0148-0731,
122
, pp.
576
586
.
28.
Nix
,
W. D.
, and
Gao
,
H.
, 1998, “
Indentation Size Effects in Crystalline Materials: A Law for Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
46
, pp.
411
425
.
29.
McClintock
,
F. A.
, and
Argon
,
A. S.
, 1966,
Mechanical Behavior of Materials
,
Addison-Wesley
,
Reading, MA
.
30.
Liang
,
L. H.
,
Li
,
J. C.
, and
Jiang
,
Q.
, 2002, “
Size-Dependent Elastic Modulus of Cu and Au Thin Films
,”
Solid State Commun.
0038-1098,
121
, pp.
453
455
.
31.
Cuenot
,
S.
,
Demoustier-Champagne
,
S.
, and
Nysten
,
B.
, 2000, “
Elastic Modulus of Polypyrrole Nanotubes
,”
Phys. Rev. Lett.
0031-9007,
85
, pp.
1690
1693
.
32.
Baalbaki
,
W.
,
Baalbaki
,
M.
,
Benmokrane
,
B.
, and
Aitcin
,
P.-C.
, 1992, “
Influence of Specimen Size on Compressive Strength and Elastic Modulus of High-Performance Concrete
,”
Cem. Concr. Aggr. (ASTM)
,
14
, pp.
113
117
.
33.
Lakes
,
R. S.
, 1983, “
Size Effects and Micromechanics of a Porous Solid
,”
J. Mater. Sci.
0022-2461,
18
, pp.
2572
2580
.
34.
Briscoe
,
B. J.
,
Fiori
,
L.
, and
Pelillo
,
E.
, 1998, “
Nano-Indentation of Polymeric Surfaces
,”
J. Phys. D
0022-3727,
31
, pp.
2395
2405
.
35.
Jin
,
H.
, and
Lewis
,
J. L.
, 2004, “
Determination of Poisson’S Ratio of Articular Cartilage by Indentation Using Different Sized Indenters
,”
ASME J. Biomech. Eng.
0148-0731,
126
, pp.
138
145
.
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