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.
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
.Copyright © 2006
by American Society of Mechanical Engineers
You do not currently have access to this content.
