Abstract
Traditionally, the complex mechanical behavior of planar soft biological tissues is characterized by (multi)axial tensile testing. While uniaxial tests do not provide sufficient information for a full characterization of the material anisotropy, biaxial tensile tests are difficult to perform and tethering effects limit the analyses to a small central portion of the test sample. In both cases, determination of local mechanical properties is not trivial. Local mechanical characterization may be performed by indentation testing. Conventional indentation tests, however, often assume linear elastic and isotropic material properties, and therefore these tests are of limited use in characterizing the nonlinear, anisotropic material behavior typical for planar soft biological tissues. In this study, a spherical indentation experiment assuming large deformations is proposed. A finite element model of the aortic valve leaflet demonstrates that combining force and deformation gradient data, one single indentation test provides sufficient information to characterize the local material behavior. Parameter estimation is used to fit the computational model to simulated experimental data. The aortic valve leaflet is chosen as a typical example. However, the proposed method is expected to apply for the mechanical characterization of planar soft biological materials in general.
References
1.
Clark
, R.
E.
, 1973,
“Stress-Strain Characteristics of Fresh and Frozen Human
Aortic and Mitral Leaflets and Chordae Tendinae
,” J.
Thorac. Cardiovasc. Surg.
0022-5223, 66
(2
), pp.
202
–208
.2.
Lanir
,
Y.
, and
Fung
, Y.
C.
, 1974,
“Two-Dimensional Mechanical Properties of Rabbit Skin—II.
Experimental Results
,” J. Biomech.
0021-9290,
7
(2
), pp.
171
–182
. 3.
Humphrey
, J.
D.
, 2002,
Cardiovascular Solid Mechanics: Cells, Tissues, and Organs
,
Springer
,
Berlin
.4.
Ghista
, D.
N.
, and Rao
, A.
P.
, 1973,
“Mitral-Valve Mechanics—Stress/Strain Characteristics of
Excised Leaflets, Analysis of Its Functional Mechanics and Its Medical
Application
,” Med. Biol. Eng.
0025-696X, 11
(6
), pp.
691
–702
.5.
Lanir
,
Y.
, and
Fung
, Y.
C.
, 1974,
“Two-Dimensional Mechanical Properties of Rabbit Skin—I.
Experimental System
,” J. Biomech.
0021-9290,
7
(1
), pp.
29
–34
. 6.
Vito
, R.
P.
, 1980,
“The Mechanical Properties of Soft Tissues—I: A Mechanical
System for Biaxial Testing
,” J. Biomech.
0021-9290, 13
(11
), pp.
947
–950
.7.
Billiar
, K.
L.
, and Sacks
, M.
S.
, 1997,
“A Method to Quantify the Fiber Kinematics of Planar Tissues
Under Biaxial stretch
,” J. Biomech.
0021-9290,
30
(7
), pp.
753
–756
. 8.
Sacks
, M.
S.
, 2000,
“Biaxial Mechanical Evaluation of Planar Biological
materials
,” J. Elast.
0374-3535, 61
, pp.
199
–244
. 9.
Sacks
, M.
S.
, and Sun
,
W.
,
2003, “Multiaxial
Mechanical Behavior of Biological Materials
,” Annu.
Rev. Biomed. Eng.
1523-9829, 5
, pp.
251
–284
.10.
Fung
, Y.
C.
, 1973,
“Biorheology of Soft Tissues
,”
Biorheology
0006-355X, 10
(2
), pp.
139
–155
.11.
Chew
, P.
H.
, Yin
, F. C.
P.
, and Zeger
, S.
L.
, 1986,
“Biaxial Stress-Strain Properties of Canine
Pericardium
,” J. Mol. Cell. Cardiol.
0022-2828, 18
(6
), pp.
567
–578
.12.
May-Newman
,
K.
, and
Yin
, F. C.
P.
, 1995,
“Biaxial Mechanical Behavior of Excised Porcine Mitral Valve
Leaflets
,” Am. J. Physiol.
0002-9513, 269
, pp.
H1319
–H1327
.13.
Billiar
, K.
L.
, and Sacks
, M.
S.
, 2000,
“Biaxial Mechanical Properties of the Native and
Glutaraldehyde-Treated Aortic Valve Cusp: Part II—A Structural Constitutive
Model
,” ASME J. Biomech. Eng.
0148-0731,
122
(4
), pp.
327
–335
. 14.
Lanir
,
Y.
,
Lichtenstein
,
O.
, and
Immanuel
,
O.
,
1996, “Optimal Design of
Biaxial Tests for Structural Material Characterization of Flat
Tissues
,” ASME J. Biomech. Eng.
0148-0731, 118
(1
), pp.
41
–47
.15.
Nielsen
, P. M.
F.
, Hunter
, P.
J.
, and Smaill
, B.
H.
, 1991,
“Biaxial Testing of Membrane Biomaterials: Testing Equipment
and Procedures
,” ASME J. Biomech. Eng.
0148-0731, 113
(3
), pp.
295
–300
.16.
Nielsen
, P. M.
F.
, Malcolm
, D. T.
K.
, Hunter
, P.
J.
, and Charette
,
P. G.
, 2002,
“Instrumentation and Procedures for Estimating The
Constitutive Parameters of Inhomogeneous Elastic Membranes
,”
Biomechan. Model. Mechanobiol.
,
1
(3
), pp.
211
–218
.17.
Gow
, B.
S.
, and Vaishnav
,
R. N.
, 1975,
“A Microindentation Technique to Measure Rheological
Properties of the Vascular Intima
,” ASME J. Appl.
Mech.
0021-8936, 38
(2
), pp.
344
–350
.18.
Hori
, R.
Y.
, and Mockros
, L.
F.
, 1976,
“Indentation Tests of Human Articular
Cartilage
,” J. Biomech.
0021-9290,
9
(4
), pp.
259
–268
. 19.
Gow
, B.
S.
, Castle
, W.
D.
, and Legg
, M.
J.
, 1983,
“An Improved Microindentation Technique to Measure Changes in
Properties of Arterial Intima During Atherogenesis
,”
J. Biomech.
0021-9290, 16
(6
), pp.
451
–458
.20.
Zheng
, Y.
P.
, and Mak
, A.
F.
, 1996,
“An Ultrasound Indentation System for Biomechanical
Properties Assessment of Soft Tissues In-Vivo
,” IEEE
Trans. Biomed. Eng.
0018-9294,
43
(9
), pp.
912
–918
. 21.
Lundkvist
,
A.
,
Lilleodden
,
E.
,
Siekhaus
,
W.
,
Kinney
,
J.
,
Pruitt
,
L.
, and
Balooch
,
M.
,
1997, “Viscoelastic
Properties of Healthy Human Artery Measured in Saline Solution by AFM-Based
Indentation Technique
,” Thin Films: Stresses and
Mechanical Properties VI
, W. W.
Gerberich
,
H.
Gao
, J.
E.
Sundgren
, and
S. P.
Baker
, eds.,
Materials Research Society
,
Boston
, Vol. 436
, pp.
353
–358
.22.
Han
,
L.
,
Noble
, J.
A.
, and Burcher
,
M.
,
2003, “A Novel
Ultrasound Indentation System for Measuring Biomechanical Properties of in
Vivo Soft Tissue
,” Ultrasound Med. Biol.
0301-5629, 29
(6
), pp.
813
–823
.23.
Ebenstein
, D.
M.
, and Pruitt
, L.
A.
, 2004,
“Nanoindentation of Soft Hydrated Materials for Application
to Vascular Tissues
,” J. Biomed. Mater. A.
,
69
(2
), pp.
222
–232
.24.
Hertz
,
H.
,
1881, “Uber Die
Berührung Fester Elastischer Körper (On the Contact of Elastic
Solids)
,” J. Reine Angew. Math.
0075-4102, 92
, pp.
156
–171
.25.
Green
, A.
E.
, and Zerna
,
W.
,
1968, Theoretical
Elasticity
, Oxford University
Press
,
London
.26.
Humphrey
, J.
D.
, Halperin
, H.
R.
, and Yin
, F. C.
P.
, 1991,
“Small Indentation Superimposed on a Finite Equibiaxial
Stretch: Implications for Cardiac Mechanics
,” ASME
J. Appl. Mech.
0021-8936, 58
, pp.
1108
–1111
.27.
Hayes
, W.
C.
, Keer
, L.
M.
, Hermann
,
G.
, and
Mockros
, L.
F.
, 1972,
“A Mathematical Analysis for Indentation Tests of Articular
Cartilage
,” J. Biomech.
0021-9290,
5
(5
), pp.
541
–551
. 28.
Matthewson
, M.
J.
, 1981,
“Axi-symmetric Contact on Thin Compliant
Coatings
,” J. Mech. Phys. Solids
0022-5096,
29
(2
), pp.
89
–113
. 29.
Costa
, K.
D.
, and Yin
, F. C.
P.
, 1999,
“Analysis of indentation: Implications for Measuring
Mechanical Properties With Atomic Force Microscopy
,”
ASME J. Biomech. Eng.
0148-0731, 121
(5
), pp.
462
–471
.30.
Aoki
,
T.
,
Ohashi
,
T.
,
Matsumoto
,
T.
, and
Sato
,
M.
,
1997, “The Pipette
Aspiration Applied to the Local Stiffness Measurement of Soft
Tissues
,” Ann. Biomed. Eng.
0090-6964, 25
(3
), pp.
581
–587
.31.
Ohashi
,
T.
,
Matsumoto
,
T.
,
Abe
,
H.
, and
Sato
,
M.
,
1997, “Intramural
Distribution of Local Elastic Moduli in Bovine Thoracic Aorta Measured by
Pipette Aspiration Method
,” Cell. Eng.
,
2
(1
), pp.
12
–18
.32.
Ohashi
,
T.
,
Abe
,
H.
,
Matsumoto
,
T.
, and
Sato
,
M.
,
2005, “Pipette
Aspiration Technique for the Measurement of Nonlinear and Anisotropic
Mechanical Properties of Blood Vessel Walls Under Biaxial
Stretch
,” J. Biomech.
0021-9290, 38
(11
), pp.
2248
–2256
.33.
Bischoff
, J.
E.
, 2004,
“Static Indentation of Anisotropic Biomaterials Using Axially
Asymmetric Indenters—A Computational Study
,” ASME J.
Biomech. Eng.
0148-0731,
126
(4
), pp.
498
–505
. 34.
Holzapfel
, G.
A.
, Gasser
, T.
C.
, and Ogden
, R.
W.
, 2000,
“A New Constitutive Framework for Arterial Wall Mechanics and
a Comparative Study Of Material Models
,” J.
Elast.
0374-3535, 61
(1–3
), pp.
1
–48
. 35.
van Oijen
,
C. H. G. A.
, 2003,
“Mechanics and Design of Fiber-Reinforced Vascular
Prostheses
,” Ph.D. thesis, Eindhoven University of
Technology, Eindhoven; 36.
Driessen
, N. J.
B.
, Bouten
, C. V.
C.
, and Baaijens
,
F. P. T.
, 2005,
“A Structural Constitutive Model for Collagenous
Cardiovascular Tissues Incorporating the Angular Fiber
Distribution
,” ASME J. Biomech. Eng.
0148-0731,
127
(3
), pp.
494
–503
. 37.
Billiar
, K.
L.
, and Sacks
, M.
S.
, 2000,
“Biaxial Mechanical Properties of the Natural and
Glutaraldehyde Treated Aortic Valve Cusp—Part I: Experimental
results
,” ASME J. Biomech. Eng.
0148-0731,
122
(1
), pp.
23
–30
. 38.
Sauren
,
A. A. H. J.
, 1981,
“The Mechanical Behavior of the Aortic
Valve
,” Ph.D. thesis, Technische Hogeschool Eindhoven,
Eindhoven; 39.
Sutton
,
M.
,
Wolters
,
W.
,
Peters
, III,
W.
,
Ranson
,
W.
, and
McNeill
,
S.
,
1983, “Determination of
Displacements Using an Improved Digital Correlation Method
,”
Image Vis. Comput.
0262-8856,
1
(3
), pp.
133
–139
. 40.
Segal
,
A.
,
1984, SEPRAN User Manual,
Standard Problems and Programmer’s Guide
,
Ingenieursbureau SEPRA
,
Leidschendam, the
Netherlands
.41.
Hendriks
, M. A.
N.
, Oomens
, C. W.
J.
, Jans
, H. W.
J.
, Janssen
, J.
D.
, and Kok
, J.
J.
, 1990,
“A Numerical Experimental Approach for the Mechanical
Characterisation of Composites and Biological Tissues by Means of Non-Linear
Filtering
,” Proceedings of the 9th International
Conference on Experimental Mechanics
, V.
Askegaard
, ed., pp.
552
–561
.42.
Oomens
, C. W.
J.
, Hendriks
, M. A.
N.
, van Ratingen
,
M. R.
, Janssen
, J.
D.
, and Kok
, J.
J.
, 1993,
“A Numerical-Experimental Method for a Mechanical
Characterization of Biological Materials
,” J.
Biomech.
0021-9290,
26
(4/5
), pp.
617
–621
. 43.
Meuwissen
,
M. H. H.
, 1998,
“An Inverse Method for the Mechanical Characterisation of
Metals
,” Ph.D. thesis, Eindhoven University of Technology,
Eindhoven; 44.
Meuwissen
, M. H.
H.
, Oomens
, C. W.
J.
, Baaijens
, F. P.
T.
, Petterson
,
R.
, and
Janssen
, J.
D.
, 1998,
“Determination of Elasto-plastic Properties of Aluminium
Using a Mixed Numerical-Experimental Method
,” J.
Mater. Process. Technol.
0924-0136, 75
(1–3
), pp.
204
–211
.45.
Bard
,
Y.
,
1974, Nonlinear Parameter
Estimation
, Academic Press
,
London
.46.
Li
,
J.
,
Luo
, X.
Y.
, and Kuang
, Z.
B.
, 2001,
“A Nonlinear Anisotropic Model for Porcine Heart
Valves
,” J. Biomech.
0021-9290,
34
(10
), pp.
1279
–1289
. 47.
Lanir
,
Y.
,
1983, “Constitutive
Equations for Fibrous Connective Tissues
,” J.
Biomech.
0021-9290,
16
(1
), pp.
1
–12
. 48.
Vesely
,
I.
, and
Noseworthy
,
R.
,
1992, “Micromechanics of
the Fibrosa and the Ventricularis in Aortic Leaflets
,”
J. Biomech.
0021-9290,
25
(1
), pp.
101
–113
. 49.
Humphrey
, J.
D.
, Strumpf
, R.
K.
, and Yin
, F. C.
P.
, 1990,
“Determination of a Constitutive Relation for Passive
Myocardium: I. A New Functional Form
,” ASME J.
Biomech. Eng.
0148-0731, 112
(3
), pp.
333
–339
.50.
Sacks
, M.
S.
, 2003,
“Incorporation of Experimentally-Derived Fiber Orientation
Into a Constitutive Model for Planar Collagenous Tissues
,”
ASME J. Biomech. Eng.
0148-0731,
125
(2
), pp.
280
–287
. 51.
Mooney
,
M.
,
1940, “A Theory of Large
Elastic Deformation
,” J. Appl. Phys.
0021-8979,
11
, pp.
582
–592
. 52.
Zulliger
, M.
A.
, Fridez
,
P.
,
Hayashi
,
K.
, and
Stergiopulos
,
N.
,
2004, “A Strain Energy
Function for Arteries Accounting for Wall Composition and
Structure
,” J. Biomech.
0021-9290,
37
(7
), pp.
989
–1000
. 53.
Zioupos
,
P.
, and
Barbenel
, J.
C.
, 1994,
“II. A Structure Based Model for the Anisotropic Material
Behavior of the Tissue
,” Biomaterials
0142-9612,
15
(5
), pp.
374
–382
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