Articular cartilage is often characterized as an isotropic elastic material with no interstitial fluid flow during instantaneous and equilibrium conditions, and indentation testing commonly used to deduce material properties of Young’s modulus and Poisson’s ratio. Since only one elastic parameter can be deduced from a single indentation test, some other test method is often used to allow separate measurement of both parameters. In this study, a new method is introduced by which the two material parameters can be obtained using indentation tests alone, without requiring a secondary different type of test. This feature makes the method more suitable for testing small samples in situ. The method takes advantages of the finite layer effect. By indenting the sample twice with different-sized indenters, a nonlinear equation with the Poisson’s ratio as the only unknown can be formed and Poisson’s ratio obtained by solving the nonlinear equation. The method was validated by comparing the predicted Poisson’s ratio for urethane rubber with the manufacturer’s supplied value, and comparing the predicted Young’s modulus for urethane rubber and an elastic foam material with modulii measured by unconfined compression. Anisotropic and nonhomogeneous finite-element (FE) models of the indentation were developed to aid in data interpretation. Applying the method to bovine patellar cartilage, the tissue’s Young’s modulus was found to be 1.79±0.59MPa in instantaneous response and 0.45±0.26MPa in equilibrium, and the Poisson’s ratio 0.503±0.028 and 0.463±0.073 in instantaneous and equilibrium, respectively. The equilibrium Poisson’s ratio obtained in our work was substantially higher than those derived from biphasic indentation theory and those optically measured in an unconfined compression test. The finite element model results and examination of viscoelastic-biphasic models suggest this could be due to viscoelastic, inhomogeneity, and anisotropy effects.

1.
Hayes
,
W. C.
, and
Mockros
,
L. F.
,
1971
, “
Viscoelastic Properties of Human Articular Cartilage
,”
J. Appl. Physiol.
,
31
(
4
), pp.
562
568
.
2.
Hori
,
R. Y.
, and
Mockros
,
L. F.
,
1976
, “
Indentation Tests of Human Articular Cartilage
,”
J. Biomech.
,
9
, pp.
259
268
.
3.
Kempson
,
G. E.
,
Freeman
,
M. A. R.
, and
Swanson
,
S. A. V.
,
1971
, “
The Determination of a Creep Modulus for Articular Cartilage from Indentation Tests on the Human Femoral Head
,”
J. Biomech.
,
4
, pp.
239
250
.
4.
Jurvelin
,
J. S.
,
Buschmann
,
M. D.
, and
Hunziker
,
E. B.
,
1997
, “
Optical and Mechanical Determination of Poisson’s Ratio of Adult Bovine Humeral Articular Cartilage
,”
J. Biomech.
,
30
(
3
), pp.
235
241
.
5.
Wong
,
M.
,
Ponticiello
,
M.
,
Kovanen
,
V.
, and
Jurvelin
,
J. S.
,
2000
, “
Volumetric Changes of Articular Cartilage During Stress Relaxation in Unconfined Compression
,”
J. Biomech.
,
33
, pp.
1049
1054
.
6.
Korhonen
,
R. K.
,
Laasanen
,
M. S.
,
Toyras
,
J.
,
Rieppo
,
J.
,
Hirvonen
,
J.
,
Helminen
,
H. J.
, and
Jurvelin
,
J. S.
,
2002a
, “
Comparison of the Equilibrium Response of Articular Cartilage in Unconfined Compression, Confined Compression and Indentation
,”
J. Biomech.
,
35
, pp.
903
909
.
7.
Mak
,
A. F.
,
Lai
,
W. M.
, and
Mow
,
V. C.
,
1987
, “
Biphasic Indentation of Articular Cartilage—I. Theoretical Solution
,”
J. Biomech.
,
20
, pp.
703
714
.
8.
Mow
,
V. C.
,
Gibbs
,
M. C.
,
Lai
,
W. M.
,
Zhu
,
W. B.
, and
Athanasiou
,
K. A.
,
1989
, “
Biphasic Indentation of Articular Cartilage—II. A Numerical Algorithm and an Experimental Study
,”
J. Biomech.
,
22
(
8/9
), pp.
853
861
.
9.
Setton
,
L. A.
,
Mow
,
V. C.
,
Muller
,
F. J.
,
Pita
,
J. C.
, and
Howell
,
D. S.
,
1992
, “
Mechanical Properties of Canine Articular Cartilage are Significantly Altered Following Transection of the Anterior Cruciate Ligament
,”
J. Orthop. Res.
,
12
(
4
), pp.
451
463
.
10.
Schenck
,
R. C.
,
Athanasiou
,
K. A.
,
Constantinides
,
G.
, and
Gomez
,
E.
,
1994
, “
A Biomechanical Analysis of Articular Cartilage of the Human Elbow and a Potential Relationship to Osteochondritis Dissecans
,”
Clin. Orthop.
,
299
, pp.
305
312
.
11.
Hale
,
J. E.
,
Rudert
,
M. J.
, and
Brown
,
T. D.
,
1993
, “
Indentation Assessment of Biphasic Mechanical Property Deficits in Size-Dependent Osteochondral Deffect Repair
,”
J. Biomech.
,
26
(
11
), pp.
1319
1325
.
12.
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.
,
12
, pp.
340
349
.
13.
DiSilvestro
,
M. R.
,
Zhu
,
Q.
, and
Suh
,
J.-K. F.
,
2001a
, “
Biphasic Poroviscoelastic Simulation of the Unconfined Compression of Articular Cartilage: II Effect of Variable Strain Rates
,”
J. Biomech. Eng.
,
123
, pp.
198
200
.
14.
Mak
,
A. F.
,
1986
, “
The Apparent Viscoelastic Behavior of Articular Cartilage—The Contributions from the Intrinsic Matrix Viscoelasticity and Interstitial Fluid Flows
,”
J. Biomech. Eng.
,
108
, pp.
123
130
.
15.
Garcia
,
J. J.
,
Altiero
,
N. J.
, and
Haut
,
R. C.
,
2000
, “
Estimation of in situ Elastic Properties of Biphasic Cartilage Based on a Transversely Isotropic Hypo-Elastic Model
,”
J. Biomech. Eng.
,
122
, February, pp.
1
8
.
16.
Hayes
,
W. C.
,
Keer
,
L. M.
,
Herrmann
,
G.
, and
Mockros
,
L. F.
,
1972
, “
A Mathematical Analysis for Indentation Tests of Articular Cartilage
,”
J. Biomech.
,
5
, pp.
541
551
.
17.
Sakamoto, M., Hara, T., Shibuya, T., and Koizumi, T., 1991, “Indentation by a Circular Rigid Punch of a Transversely Isotropic Layer on a Rigid Foundation,” JSMA, International Journal, Series I, Vol. 34, No. 2, pp. 130–134. Sokoloff, L., Elasticity of Aging Cartilage. Proc. Fedn Am Socs exp. Biol. 25, pp. 1089–1095.
18.
ABAQUS/Standard User’s Manual, Vol. 1, Version 5.8, p. 10.2.1–4, Hibbitt, Karlsson & Sorensen, Inc., 1998.
19.
Korhonen
,
R. K.
,
Wong
,
M.
,
Arokoski
,
J.
,
Lindgern
,
R.
,
Helminen
,
H. J.
,
Hunziker
,
E. B.
, and
Jurvelin
,
J. S.
,
2002b
, “
Importance of the Superfical Tissue Layer for the Indentation Stiffness of Articular Cartilage
,”
Med. Eng. Phys.
,
24
, pp.
99
108
.
20.
Mow, V. C., Good, P. M., and Gardner, T. R., 2000, “A New Method to Determine the Tensile Properties of Articular Cartilage Using the Indentation Test,” Orthopaedic Research Society, 46th Annual Meeting, March 12–15, Orlando, Florida, 0103.
21.
Mow, V. C., and Ratcliffe, A., 1997, “Structure and Function of Articular Cartilage and Meniscus, Basic Orpthopaedic Biomechanics,” 2nd edition, Lippincott-Raven, 1997, edited by V. C. Mow and W. C. Hayes.
22.
Rieppo, J., Laasanen, M. S., Korhonen, R. K., Toyras, J., Hirvonen, J., Helminen, H. J., and Jurvelin, J. S., 2001, “Depth-Dependent Mechanical Properties of Bovine Patellar Cartilage,” Orthopaedic Research Society, Transactions Vol. 26, 0440, San Francisco, California.
23.
DiSilvestro
,
M. R.
, and
Suh
,
J-K. F.
,
2001b
, “
A Cross-Validation of the Biphasic Poroviscoelastic Model of Articular Cartilage in Unconfined Compression, Indentation and Confined Compression
,”
J. Biomech.
,
34
, pp.
519
5225
.
24.
Hayes
,
W. C.
,
Bodine
,
A. J.
,
1978
, “
Flow-Independent Viscoelastic Properties of Articular Cartilage Matrix
,”
J. Biomech.
,
11
, pp.
407
407
.
25.
Mow
,
V. C.
,
Mak
,
A. F.
,
Lai
,
W. M.
, and
Rosenberg
,
L. C.
,
Tang
,
L. H.
,
1984
, “
Viscoelastic Properties of Proteoglycan Subunits and Aggregates in Varying Solution Concentrations
,”
J. Biomech.
,
17
, pp.
325
338
.
You do not currently have access to this content.