Technical Briefs

An Experimental and Modeling Study of the Viscoelastic Behavior of Collagen Gel

[+] Author and Article Information
Haiyue Li

Department of Mechanical Engineering,
Boston University,
110 Cummington Mall,
Boston, MA 02215

Yanhang Zhang

Associate Professor
Department of Mechanical Engineering,
Department of Biomedical Engineering,
Boston University,
110 Cummington Mall,
Boston, MA 02215
e-mail: yanhang@bu.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received April 16, 2012; final manuscript received March 25, 2013; accepted manuscript posted April 4, 2013; published online April 24, 2013. Assoc. Editor: Stephen Klisch.

J Biomech Eng 135(5), 054501 (Apr 24, 2013) (4 pages) Paper No: BIO-12-1145; doi: 10.1115/1.4024131 History: Received April 16, 2012; Revised March 25, 2013; Accepted April 04, 2013

The macroscopic viscoelastic behavior of collagen gel was studied through relaxation time distribution spectrum obtained from stress relaxation tests and viscoelastic constitutive modeling. Biaxial stress relaxation tests were performed to characterize the viscoelastic behavior of collagen gel crosslinked with Genipin solution. Relaxation time distribution spectrum was obtained from the stress relaxation data by inverse Laplace transform. Peaks at the short (0.3 s–1 s), medium (3 s–90 s), and long relaxation time (>200 s) were observed in the continuous spectrum, which likely correspond to relaxation mechanisms involve fiber, inter-fibril, and fibril sliding. The intensity of the long-term peaks increases with higher initial stress levels indicating the engagement of collagen fibrils at higher levels of tissue strain. We have shown that the stress relaxation behavior can be well simulated using a viscoelastic model with viscous material parameters obtained directly from the relaxation time spectrum. Results from the current study suggest that the relaxation time distribution spectrum is useful in connecting the macro-level viscoelastic behavior of collagen matrices with micro-level structure changes.

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Kastelic, J.Galeski, A., and Baer, E., 1978, “The Multicomposite Structure of Tendon.” Connect. Tissue Res., 6, pp. 11–23. [CrossRef] [PubMed]
Fratzl, P., 2008, Collagen: Structure and Mechanics, Springer, New York.
Sherman, P., 1970, Industrial Rheology, Academic, New York.
Ferry, J. D., 1980, Viscoelastic Properties of Polymers, Wiley, New York.
Fung, Y. C., 1993, Biomechanics: Mechanical Properties of Living Tissues, Springer, New York.
Peleg, M., and Pollak, N., 1982, “The Problem of Equilibrium Conditions in Stress Relaxation Analyses of Solid Foods,” J. Texture Studies, 13, pp. 1–11. [CrossRef]
Malkin, Y. A., 2006, “The Use of a Continuous Relaxation Spectrum for Describing the Viscoelastic Properties of Polymers,” J. Polym. Sci. A, 48, pp. 39–45. [CrossRef]
Sodhi, N. S., Sasaki, T., Lu, Zh., and Kohyama, K., 2010, “Phenomenological Viscoelasticity of Some Rice Starch Gels,” Food Hydrocolloids, 24, pp. 512–517. [CrossRef]
Mao, R., Tang, J., and Swanson, B. G., 2000, “Relaxation Time Spectrum of Hydrogels by CONTIN Analysis,” J. Food Sci., 65, pp. 374–381. [CrossRef]
Li, W., Dobraszczyk, B. J., and Schofield, J. D., 2003, “Stress Relaxation Behavior of Wheat Dough, Gluten and Gluten Protein Fractions,” Cereal Chemistry, 80, pp. 333–338. [CrossRef]
Xu, B., Chow, M. J., and Zhang, Y., 2011, “Experimental and Modeling Study of Collagen Scaffolds With the Effects of Crosslinking and Fiber Alignment,” Int. J. Biomater., Vol. 2011. [CrossRef]
Sacks, M. S., 2000, “Biaxial Mechanical Evaluation of Planar Biological Materials,” J. Elasticity, 61, pp. 199–246. [CrossRef]
Zou, Y., and Zhang, Y., 2010, “The Orthotropic Viscoelastic Behavior of Aortic Elastin.” Biomech. Model. Mechanobiol., 10, pp. 613–625. [CrossRef] [PubMed]
Gasser, T. C., Ogden, R. W., and Holzapfel, G. A., 2006, “Hyperelastic Modeling of Arterial Layers With Distributed Collagen Fibre Orientations,” J. R. Soc., Interface, 3, pp. 15–35. [CrossRef]
Provencher, S. W., 1982, “CONTIN: A General Purpose Constrained Regularization Program for Inverting Noisy Linear Algebraic and Integral Equations,” Comput. Phys. Commun., 27, pp. 229–242. [CrossRef]
Komatsu, K., 2010, “Mechanical Strength and Viscoelastic Response of the Periodontal Ligament in Relation to Structure,” J. Dental Biomech., 1(1), pp. 1–18. [CrossRef]
Wagenseil, J. E., Wakatsuki, T., Okamoto, R. J., Zahalak, G. I., and Elson, E.L, 2003, “One-Dimensional Viscoelastic Behavior of Fibroblast Populated Collagen Matrices,” J. Biomech. Eng., 125, pp. 719–725. [CrossRef] [PubMed]
Toms, S. R., Dakin, G. J., Lemons, J. E., and Eberhardt, A. W., 2002, “Quasi-Linear Vicoelastic Behavior of the Human Periodontal Ligament,” J. Biomech., 35, pp. 1411–1415. [CrossRef] [PubMed]
Sundararaghavan, H. G., Monteiro, G. A., Firestein, B. L., and Shreiber, D. J., 2009, “Neurite Growth in 3D Collagen Gels With Gradients of Mechanical Properties,” Biotechnol. Bioeng., 102, 632–643. [CrossRef] [PubMed]
Bailey, A. J., 2001, “Molecular Mechanisms of Ageing in Connective Tissues,” Mech. Ageing Dev., 122, pp. 735–755. [CrossRef] [PubMed]
Gupta, H. S., Seto, J., Krauss, S., Boesecke, P., and Screen, H. R. C., 2010, “In situ Multi-Level Analysis of Viscoelastic Deformation Mechanisms in Tendon Collagen,” J. Struct. Biol., 169, pp. 183–191. [CrossRef] [PubMed]
Rigozzi, S., Stemmer, A., Muller, R., and Snedeker, J. G., 2001, “Mechanical Response of Individual Collagen Fibrils in Loaded Tendon as Measured by Atomic Force Microscopy,” J. Struct. Biol., 176, pp. 9–15. [CrossRef]


Grahic Jump Location
Fig. 1

Stress relaxation results of a collagen gel sample at different initial stress levels

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Fig. 2

Relaxation time distribution spectra obtained from biaxial stress relaxation tests of collagen gel under different initial stress levels

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Fig. 3

Effect of relaxation time on relaxation time distribution spectrum for collagen gel at the initial stress level of 25 kPa

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Fig. 4

Simulation results of biaxial tensile—stress relaxation tests of collagen gel at different initial stress levels. Solid lines represent the simulation results. Experiment results were shown in symbols for comparison. Material parameters in the hyperelastic model are C10 = 20 kPa, k1 = 30 MPa, k2 = 1150, γ = 45 deg and κ = 0.333; material parameters in the viscous model are listed in Table 1.



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