In this paper, a quantitative interpretation for atomic force microscopy-based dynamic nanoindentation (AFM-DN) tests on the superficial layers of bovine articular cartilage (AC) is provided. The relevant constitutive parameters of the tissue are estimated by fitting experimental results with a finite element model in the frequency domain. Such model comprises a poroelastic stress–strain relationship for a fibril reinforced tissue constitution, assuming a continuous distribution of the collagen network orientations. The identification procedure was first validated using a simplified transversely isotropic constitutive relationship; then, the experimental data were manually fitted by using the continuous distribution fibril model. Tissue permeability is derived from the maximum value of the phase shift between the input harmonic loading and the harmonic tissue response. Tissue parameters related to the stiffness are obtained from the frequency response of the experimental storage modulus and phase shift. With this procedure, an axial to transverse stiffness ratio (anisotropy ratio) of about 0.15 is estimated.

References

References
1.
Pearle
,
A.
,
Warren
,
R.
, and
Rodeo
,
S.
,
2005
, “
Basic Science of Articular Cartilage and Osteoarthritis
,”
Clin. Sports Med.
,
24
(
1
), pp.
1
12
.10.1016/j.csm.2004.08.007
2.
Mankin
,
H.
,
Mow
,
V.
, and
Buckwalter
,
J.
,
1999
, “
Articular Cartilage Structure, Composition and Function
,”
Orthopaedic Basic Science: Biology and Biomechanics of the Musculoskeletal System
,
American Academy of Orthopaedic Surgeons
,
Rosemont, IL
, pp.
443
470
.
3.
Poole
,
A.
,
Kojima
,
T.
,
Yasuda
,
T.
,
Mwale
,
F.
,
Kobayashi
,
M.
, and
Laverty
,
S.
,
2001
, “
Composition and Structure of Articular Cartilage: A Template for Tissue Repair
,”
Clin. Orthop. Relat. Res.
,
391
(
Suppl.
), pp.
S26
S33
.10.1097/00003086-200110001-00004
4.
Schinagl
,
R.
,
Gurskis
,
D.
,
Chen
,
A.
, and
Sah
,
R.
,
1997
, “
Depth-Dependent Confined Compression Modulus of Full Thickness Bovine Articular Cartilage
,”
J. Orthop. Res.
,
15
(
4
), pp.
499
506
.10.1002/jor.1100150404
5.
Appleyard
,
R.
,
Burkhardt
,
D.
,
Ghosh
,
P.
,
Read
,
R.
,
Cake
,
M.
,
Swain
,
M.
, and
Murrel
,
G.
,
2003
, “
Topographical Analysis of the Structural, Biochemical and Dynamical Biomechanical Properties of Cartilage in an Ovine Model of Osteoarthritis
,”
Osteoarthritis Cartilage
,
11
(
1
), pp.
65
77
.10.1053/joca.2002.0867
6.
Huang
,
C.
,
Mow
,
V.
, and
Ateshian
,
G.
,
2001
, “
The Role of Flow Independent Viscoelasticity in the Biphasic Tensile and Compressive Responses of Articular Cartilage
,”
ASME J. Biomech. Eng.
,
123
(
5
), pp.
410
418
.10.1115/1.1392316
7.
Hu
,
Y.
,
Zhao
,
X.
,
Vlassak
,
J.
, and
Suo
,
Z.
,
2010
, “
Using Indentation to Characterize the Poroelasticity of Gels
,”
Appl. Phys. Lett.
,
96
(
12
), p.
121904
.10.1063/1.3370354
8.
Ebenstein
,
D.
, and
Pruitt
,
L.
,
2006
, “
Nanoindentation of Biological Materials
,”
Nano Today
,
1
(
3
), pp.
26
33
.10.1016/S1748-0132(06)70077-9
9.
Stolz
,
M.
,
Gottardi
,
R.
,
Raiteri
,
R.
,
Miot
,
S.
,
Martin
,
I.
,
Imer
,
R.
,
Staufer
,
U.
,
Raducanu
,
A.
,
Duggelin
,
M.
,
Baschong
,
W.
,
Daniels
,
A.
,
Friederich
,
N.
,
Aszodi
,
A.
, and
Aebi
,
U.
,
2009
, “
Early Detection of Aging Cartilage and Osteoarthritis in Mice and Patient Samples Using Atomic Force Microscopy
,”
Nat. Nanotechnol.
,
4
(3), pp.
186
192
.10.1038/nnano.2008.410
10.
Armstrong
,
C.
,
Lai
,
V.
, and
Mow
,
V.
,
1984
, “
An Analysis of the Unconfined Compression of Articular Cartilage
,”
ASME J. Biomed. Eng.
,
106
(
2
), pp.
165
173
.10.1115/1.3138475
11.
Li
,
C.
,
Pruitt
,
L.
, and
King
,
K.
,
2006
, “
Nanoindentation Differentiates Tissue-Scale Functional Properties of Native Articular Cartilage
,”
J. Biomed. Mater. Res., Part A
,
78
(
4
), pp.
729
758
.10.1002/jbm.a.30751
12.
Stolz
,
M.
,
Raiteri
,
R.
,
Daniels
,
A.
,
van Landingham
,
M.
,
Baschong
,
W.
, and
Aebi
,
U.
,
2004
, “
Dynamic Elastic Modulus of Porcine Articular Cartilage Determined at Two Different Levels of Tissue Organization by Indentation-Type Atomic Force Microscopy
,”
Biophys. J.
,
85
(
5
), pp.
3269
3683
.10.1016/S0006-3495(04)74375-1
13.
Loparic
,
M.
,
Wirtz
,
D.
,
Daniels
,
A.
,
Raiteri
,
R.
,
van Landingham
,
M.
,
Guex
,
G.
,
Martin
,
I.
,
Aebi
,
U.
, and
Stolz
,
M.
,
2010
, “
Micro- and Nanomechanical Analysis of Articular Cartilage by Indentation-Type Atomic Force Microscopy: Validation With a Gel–Microfiber Composite
,”
Biophys. J.
,
98
(
11
), pp.
2731
2740
.10.1016/j.bpj.2010.02.013
14.
Simha
,
N.
,
Jin
,
H.
,
Hall
,
M.
,
Chiravarambath
,
S.
, and
Lewis
,
J.
,
2007
, “
Effect of Indenter Size on Elastic Modulus of Cartilage Measured by Indentation
,”
ASME J. Biomech. Eng.
,
129
(
5
), pp.
767
775
.10.1115/1.2768110
15.
Franke
,
O.
,
Goken
,
M.
,
Meyers
,
M.
,
Durst
,
K.
, and
Hodge
,
A.
,
2011
, “
Dynamic Nanoindentation of Articular Porcine Cartilage
,”
Mater. Sci. Eng. C
,
31
(
4
), pp.
789
795
.10.1016/j.msec.2010.12.005
16.
Han
,
L.
,
Frank
,
E.
,
Greene
,
J.
,
Lee
,
H.
,
Hung
,
H.
,
Grodzinsky
,
A.
, and
Ortiz
,
C.
,
2011
, “
Time-Dependent Nanomechanics of Cartilage
,”
Biophys. J.
,
100
(
7
), pp.
1846
1854
.10.1016/j.bpj.2011.02.031
17.
Taffetani
,
M.
,
Bertarelli
,
E.
,
Gottardi
,
R.
,
Raiteri
,
R.
, and
Vena
,
P.
,
2012
, “
Modelling of the Frequency Response to Dynamic Nanoindentation of Soft Hydrated Anisotropic Materials: Application to Articular Cartilage
,”
Comput. Model. Eng. Sci.
,
87
(
5
), pp.
433
460
.10.3970/cmes.2012.087.433
18.
Taffetani
,
M.
,
Griebel
,
M.
,
Gastaldi
,
D.
,
Klisch
,
S.
, and
Vena
,
P.
,
2014
, “
Poroviscoelastic Finite Element Model Including Continuous Fiber Distribution for the Simulation of Nanoindentation Tests on Articular Cartilage
,”
J. Mech. Behav. Biomed. Mater.
,
32
(1), pp.
17
30
.10.1016/j.jmbbm.2013.12.003
19.
Hutter
,
J.
, and
Bechhoefer
,
J.
,
1993
, “
Calibration of Atomic Force Microscope Tips
,”
Rev. Sci. Instrum.
,
64
(
7
), pp.
1868
1876
.10.1063/1.1143970
20.
Raiteri
,
R.
,
Preuss
,
M.
,
Grattarola
,
M.
, and
Butt
,
H.
,
1998
, “
Preliminary Results on the Electrostatic Double Layer Force Between Two Surface With High Surface Potential
,”
Colloid Surf. A
,
136
(
1–2
), pp.
195
201
.10.1016/S0927-7757(97)00339-7
21.
Johnson
,
K.
,
1985
,
Contact Mechanics
,
Cambridge University
,
Cambridge, UK
.10.1017/CBO9781139171731
22.
Field
,
J.
, and
Swain
,
M.
,
1993
, “
A Simple Predictive Model for Spherical Indentation
,”
J. Mater. Res.
,
8
(
2
), pp.
297
306
.10.1557/JMR.1993.0297
23.
Cowin
,
S.
, and
Doty
,
S.
,
2006
,
Tissue Mechanics
,
Springer Verlag
,
New York
.10.1007/978-0-387-49985-7
24.
Ateshian
,
G.
,
Rajan
,
V.
,
Chahine
,
N.
,
Canal
,
C.
, and
Hung
,
C.
,
2009
, “
Modeling the Matrix of Articular Cartilage Using a Continuous Fiber Angular Distribution Predicts Many Observed Phenomena
,”
ASME J. Biomech. Eng.
,
131
(
6
), p.
061003
.10.1115/1.3118773
25.
Stender
,
M. E.
,
Raub
,
C. B.
,
Yamauchi
,
K. A.
,
Shirazi
,
R.
,
Vena
,
P.
,
Sah
,
R. L.
,
Hazelwood
,
S. J.
, and
Klisch
,
S. M.
,
2013
, “
Integrating qPLM and Biomechanical Test Data With an Anisotropic Fiber Distribution Model and Predictions of TGF-β 1 and IGF-1 Regulation of Articular Cartilage Fiber Modulus
,”
Biomech. Model. Mechanobiol.
,
12
(
6
), pp.
1073
1088
.10.1007/s10237-012-0463-y
26.
Cheng
,
Y.
,
Ni
,
W.
, and
Cheng
,
C.
,
2006
, “
Nonlinear Analysis of Oscillatory Indentation in Elastic and Viscoelastic Solids
,”
Phys. Rev. Lett.
,
97
(
7
), p.
075506
.10.1103/PhysRevLett.97.075506
27.
Buschmann
,
M.
, and
Grodzinsky
,
A.
,
1995
, “
A Molecular Model of Proteoglycan-Associated Electrostatic Forces in Cartilage Mechanics
,”
ASME J. Biomech. Eng.
,
117
(
2
), pp.
179
192
.10.1115/1.2796000
28.
Korhonen
,
R.
,
Wong
,
M.
,
Arokoski
,
J.
,
Lindgern
,
R.
,
Helminen
,
H.
,
Hunziker
,
E.
, and
Jurvelin
,
J.
,
2002
, “
Importance of the Superficial Tissue Layer for the Indentation Stiffness of Articular Cartilage
,”
Med. Eng. Phys.
,
24
(
2
), pp.
99
108
.10.1016/S1350-4533(01)00123-0
29.
Buckwalter
,
J.
,
2002
, “
Articular Cartilage Injuries
,”
Clin. Orthop. Relat. Res.
,
402
(1), pp.
21
37
.10.1097/00003086-200209000-00004
30.
Nia
,
H.
,
Han
,
L.
,
Li
,
Y.
,
Ortiz
,
C.
, and
Grodzinsky
,
A.
,
2011
, “
Poroelasticity of Cartilage at the Nanoscale
,”
Biophys. J.
,
101
(
9
), pp.
2304
2313
.10.1016/j.bpj.2011.09.011
31.
Lu
,
X.
,
Wan
,
L.
,
Guo
,
X.
, and
Mow
,
V.
,
2010
, “
A Linearized Formulation of Triphasic Mixture Theory for Articular Cartilage and Its Application to Indentation Analysis
,”
J. Biomech.
,
43
(
4
), pp.
673
679
.10.1016/j.jbiomech.2009.10.026
32.
Chen
,
A.
,
Bae
,
W.
,
Schinagl
,
R.
, and
Sah
,
R.
,
2001
, “
Depth- and Strain-Dependent Mechanical and Electromechanical Properties of Full-Thickness Bovine Articular Cartilage in Confined Compression
,”
J. Biomech.
,
34
(
1
), pp.
1
12
.10.1016/S0021-9290(00)00170-6
33.
Williamson
,
A.
,
Chen
,
A.
, and
Sah
,
R.
,
2001
, “
Compressive Properties and Function-Composition Relationships of Developing Bovine Articular Cartilage
,”
J. Orthop. Res.
,
19
(
6
), pp.
1113
1121
.10.1016/S0736-0266(01)00052-3
34.
Lu
,
X.
, and
Mow
,
V.
,
2008
, “
Biomechanics of Articular Cartilage and Determination of Material Properties
,”
Med. Sci. Sports Exercises
,
40
(
2
), pp.
193
199
.10.1249/mss.0b013e31815cb1fc
35.
Chahine
,
N.
,
Chen
,
F.
,
Hung
,
C.
, and
Ateshian
,
G.
,
2005
, “
Direct Measurement of Osmotic Pressure of Glycosaminoglycan Solutions by Membrane Osmometry at Room Temperature
,”
Biophys. J.
,
89
(
3
), pp.
1543
1550
.10.1529/biophysj.104.057315
You do not currently have access to this content.