The quasi-linear viscoelastic (QLV) model was applied to incremental stress-relaxation tests and an expression for the stress was derived for each step. This expression was used to compare two methods for normalizing stress data prior to estimating QLV parameters. The first and commonly used normalization method was shown to be strain-dependent. Thus, a second normalization method was proposed and shown to be strain-independent and more sensitive to QLV time constants. These analytical results agreed with representative tendon data. Therefore, this method for normalizing stress data was proposed for future studies of incremental stress-relaxation, or whenever comparing stress-relaxation at different strains.
Issue Section:
Soft Tissues
1.
Fung, Y., 1993, “Bioviscoelastic Solids,” In: Biomechanics: Mechanical Properties of Living Tissues, pp. 242–320, Springer-Verlag, New York, NY.
2.
Funk
, J. R.
, Hall
, G. W.
, Crandall
, J. R.
, and Pilkey
, W. D.
, 2000
, “Linear and Quasi-Linear Viscoelastic Characterization of Ankle Ligaments
,” J. Biomech. Eng.
, 122
(1
), pp. 15
–22
.3.
Lam
, T. C.
, Frank
, C. B.
, and Shrive
, N. G.
, 1993
, “Changes in the Cyclic and Static Relaxations of the Rabbit Medial Collateral Ligament Complex During Maturation
,” J. Biomech.
, 26
, pp. 9
–17
.4.
Lynch
, H. A.
, Johannessen
, W.
, Wu
, J. P.
, Jawa
, A.
, and Elliott
, D. M.
, “Effect of Fiber Orientation and Strain-Rate on the Nonlinear Uniaxial Tensile Material Properties of Tendon
,” J. Biomech. Eng.
, 125
(5
), pp. 628
–638
.5.
Provenzano
, P.
, Lakes
, R.
, Keenan
, T.
, and Vanderby
, R.
, 2001
, “Nonlinear Ligament Viscoelasticity
,” Ann. Biomed. Eng.
, 29
, pp. 908
–914
.6.
Robinson, P. S., Lin, T. W., Reynolds, P. R., Derwin, K. A., Iozzo, R. V., and Soslowsky, L. J., “Strain Rate Sensitive Mechanical Properties of Tendon Fascicles From Mice With Genetically Engineered Alterations in Collgen and Decorin,” J. Biomech. Eng., in review.
7.
Woo
, S. L.
, Gomez
, M. A.
, and Akeson
, W. H.
, 1981
, “The Time and History-Dependent Viscoelastic Properties of the Canine Medical Collateral Ligament
,” J. Biomech. Eng.
, 103
(4
), pp. 293
–298
.8.
Wren
, T. A.
, Yerby
, S. A.
, Beaupre
, G. S.
, and Carter
, D. R.
, 2001
, “Mechanical Properties of the Human Achilles Tendon
,” Clin. Biomech. (Bristol, Avon)
, 16
(3
), pp. 245
–51
.9.
Akizuki
, S.
, Mow
, V. C.
, Muller
, F.
, Pita
, J. C.
, Howell
, D.
, and Manicourt
, D. H.
, 1986
, “Tensile Properties of Human Knee Joint Cartilage: I. Influence of Ionic Conditions, Weight Bearing, and Fibrillation on the Tensile Modulus
,” J. Orthop. Res.
, 4
, pp. 379
–392
.10.
Elliott
, D. M.
, Guilak
, F.
, Vail
, T. P.
, Wang
, J. Y.
, and Setton
, L. A.
, 1999
, “Tensile Properties of Articular Cartilage are Altered by Meniscectomy in a Canine Model of Osteoarthritis
,” J. Orthop. Res.
, 17
(4
), pp. 503
–508
.11.
Elliott
, D. M.
, and Setton
, L. A.
, 2001
, “Anisotropic and Inhomogeneous Tensile Behavior of the Human Anulus Fibrosus: Experimental Measurement and Material Model Predictions
,” J. Biomech. Eng.
, 123
, pp. 256
–263
.12.
Fortin
, M.
, Soulhat
, J.
, Shirazi-Adl
, A.
, Hunziker
, E. B.
, and Buschmann
, M. D.
, 2000
, “Unconfined Compression of Articular Cartilage: Nonlinear Behavior and Comparison With a Fibril-Reinforced Biphasic Model
,” J. Biomed. Eng.
, 122
, pp. 189
–195
.13.
Schinagl
, R. M.
, Gurskis
, D.
, Chen
, A.
, and Sah
, R. L.
, 1997
, “Depth-Dependent Confined Compression Modulus of Full-Thickness Bovine Articular Cartilage
,” J. Orthop. Res.
, 15
, pp. 499
–506
.14.
Elliott, D. M., Robinson, P. S., Gimbel, J. A., Sarver, J., Abboud, J. A., Iozzo, R. V., and Soslowsky, L. J., “Effect of Altered Matrix Proteins on Quasi-Linear Viscoelastic Properties in Transgenic Mouse Tail Tendons,” Ann. Biomed. Eng., in review.
15.
Hansen
, K. A.
, Weiss
, J. A.
, and Barton
, J. K.
, 2002
, “Recruitment of Tendon Crimp With Applied Tensile Strain
,” J. Biomech. Eng.
, 124
(1
), pp. 72
–77
.16.
Weiss
, J. A.
, and Gardiner
, J. C.
, 2001
, “Computational Modeling of Ligament Mechanics
,” Crit. Rev. Biomed. Eng.
, 29
(3
), pp. 303
–371
.17.
Woo
, S. L. Y.
, Johnson
, G. A.
, and Smith
, B. A.
, 1993
, “Mathematical Modeling of Ligaments and Tendons
,” J. Biomech. Eng.
, 115
, pp. 468
–473
.18.
Fung
, Y.
, 1967
, “Elasticity of Soft Tissues in Simple Elongation
,” Am. J. Physiol.
, 213
(6
), pp. 1532
–1544
.19.
Haut
, R. C.
, and Little
, R. W.
, 1972
, “A Constitutive Equation for Collagen Fibers
,” J. Biomech.
, 5
, pp. 423
–430
.20.
Puso
, M. A.
, and Weiss
, J. A.
, 1998
, “Finite-Element Implementation of Anisotropic Quasi-Linear Viscoelasticity Using a Discrete Spectrum Approximation
,” J. Biomech. Eng.
, 120
, pp. 62
–70
.21.
Johnson
, G. A.
, Tramaglini
, D. M.
, Levine
, R. E.
, Ohno
, K.
, Choi
, N.-Y.
, and Woo
, S. L.-Y.
, 1994
, “Tensile and Viscoelastic Properties of Human Patellar Tendon
,” J. Orthop. Res.
, 12
, pp. 796
–803
.22.
Kwan
, M. K.
, Lin
, T. H.
, and Woo
, S. L.
, 1993
, “On the Viscoelastic Properties of the Anteromedial Bundle of the Anterior Cruciate Ligament
,” J. Biomech.
, 26
(4–5
), pp. 447
–452
.23.
Pradas
, M. M.
, and Calleja
, R. D.
, 1990
, “Nonlinear Viscoelastic Behavior of the Flexor Tendon of the Human Hand
,” J. Biomech.
, 23
, pp. 773
–781
.24.
Thomopoulos, S., Williams, G. R., Gimbel, J. A., Favata, M., and Soslowsky, L. J., “Variation of Biomechanical, Structural, and Compositional Properties Along the Tendon to Bone Insertion Site,” J. Orthop. Res., 32767.
25.
Bonifasi-Lista
, C.
, Lake
, S.
, Ellis
, B.
, Rosenberg
, T.
, and Weiss
, J. A.
, 2002
, “Strain- and Rate-Dependent Viscoleastic Properties of Human MCL in Tension
,” Transactions of the Orthopaedic Research Society
, 27
, p. 609
609
.26.
Thornton
, G. M.
, Oliynyk
, A.
, Frank
, C. B.
, and Shrive
, N. G.
, 1997
, “Ligament Creep Cannot Be Predicted From Stress Relaxation at Low Stress: A Biomechanical Study of the Rabbit Medial Collateral Ligament
,” J. Orthop. Res.
, 15
(5
), pp. 652
–656
.27.
Dortmans
, L. J.
, Sauren
, A. A.
, and Rousseau
, E. P.
, 1984
, “Parameter Estimation Using the Quasi-Linear Viscoelastic Model Proposed by Fung
,” J. Biomech. Eng.
, 106
(3
), pp. 198
–203
.28.
Myers
, B.
, McElhaney
, J.
, Nightingale
, R.
, and Doherty
, B.
, 1991
, “Experimental Limitations of Quasi-Linear Theory, and a Method for Reducing These Effects
,” ASME Advances in Bioengineering
, BED-20
, pp. 139
–142
.29.
Nigul
, I.
, and Nigul
, U.
, 1987
, “On Algorithms of Evaluation of Fung’s Relaxation Function Parameters
,” J. Biomech.
, 20
(4
), pp. 343
–352
.30.
Sauren
, A. A.
, and Rousseau
, E. P.
, 1983
, “A Concise Sensitivity Analysis of the Quasi-Linear Viscoelastic Model Proposed by Fung
,” J. Biomech. Eng.
, 105
(1
), pp. 92
–95
.31.
Hewitt
, J.
, Guilak
, F.
, Glisson
, R.
, and Vail
, T. P.
, 2001
, “Regional Material Properties of the Human Hip-Joint Capsule Ligaments
,” J. Orthop. Res.
, 19
(3
), pp. 359
–64
.32.
Elliott
, D. M.
, Narmoneva
, D. A.
, and Setton
, L. A.
, 2002
, “Direct Measurement of the Poisson’s Ratio of Human Patella Cartilage in Tension
,” J. Biomech. Eng.
, 124
(2
), pp. 223
–228
.33.
Roth
, V.
, and Mow
, V. C.
, 1980
, “Intrinsic Tensile Behavior of the Matrix of Bovine Articular Cartilage and Its Variation With Age
,” J. Bone Jt. Surg.
, 62A
(7
), pp. 1102
–1117
.34.
Woo
, S. L. Y.
, Akeson
, W. H.
, and Jemmott
, G. F.
, 1976
, “Measurements of Nonhomogeneous Directional Mechanical Properties of Articular Cartilage in Tension
,” J. Biomech.
, 9
, pp. 785
–791
.35.
Fithian
, D. C.
, Zhu
, W. B.
, Ratcliffe
, A.
, Kelly
, M. A.
, Mow
, B. C.
, and Malinin
, T. I.
, 1989
, “Exponential Law Representation of Tensile Properties of Human Mensicus
,” Proc. Inst. Mech. Eng.
, pp.
85
–90
.36.
Beck, J. V., and Arnold, K. J., 1977, Parameter Estimation in Engineering and Science, John Wiley & Sons, New York, NY.
37.
Scott
, E. P.
, and Saad
, Z.
, 1993
, “Estimation of Kinetic Parameters Associated With the Curing of Thermoset Resins; Theoretical Investigation
,” Polym. Eng. Sci.
, 33
(18
), pp. 1157
–1164
.38.
Pioletti
, D. P.
, and Rakotomanana
, L. R.
, 2000
, “On the Independence of Time and Strain Effects in the Stress Relaxation of Ligaments and Tendons
,” J. Biomech.
, 33
, pp. 1729
–1732
.39.
Provenzano
, P.
, Lakes
, R.
, DT
, C.
, and Vanderby
, R.
, 2002
, “Application of Nonlinear Viscoelastic Models to Describe Ligament Behavior
,” Biomechan Model Mechanobiol
, 1
, pp. 45
–57
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