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TECHNICAL PAPERS: Other

Dynamic Mechanical Properties of Agarose Gels Modeled by a Fractional Derivative Model

[+] Author and Article Information
Qingshan Chen, Kai-Nan An

Biomechanics Laboratory, Division of Orthopedic Research, Mayo Clinic, 200 First Street SW, Rochester, Minnesota USA

Bela Suki

Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, Massachusetts USA

J Biomech Eng 126(5), 666-671 (Nov 23, 2004) (6 pages) doi:10.1115/1.1797991 History: Received March 23, 2003; Revised May 07, 2004; Online November 23, 2004
Copyright © 2004 by ASME
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References

Normand,  V., Lootens,  D. L., Amici,  E., Plucknett,  K. P., and Aymard,  P., 2000, “New Insight into Agarose Gel Mechanical Properties,” Biomacromolecules, 1(4), pp. 730–738.
Aymard,  P., Martin,  D. R., Plucknett,  K., Foster,  T. J., Clark,  A. H., and Norton,  I. T., 2001, “Influence of Thermal History on the Structural and Mechanical Properties of Agarose Gels,” Biopolymers, 59(3), pp. 131–144.
Saris,  D. B., Mukherjee,  N., Berglund,  L. J., Schultz,  F. M., An,  K. N., and O’Driscoll,  S. W., 2000, “Dynamic Pressure Transmission through Agarose Gels,” Tissue Eng., 6(5), pp. 531–537.
Muthupillai,  R., Lomas,  D. J., Rossman,  P. J., Greenleaf,  J. F., Manduca,  A., and Ehman,  R. L., 1995, “Magnetic Resonance Elastography by Direct Visualization of Propagating Acoustic Strain Waves,” Science, 269(5232), pp. 1854–1857.
Ross-Murphy,  S. B., and Shatwell,  K. P., 1993, “Polysaccharide Strong and Weak Gels,” Biorheology, 30(3–4), pp. 217–227.
Benkherourou,  M., Rochas,  C., Tracqui,  P., Tranqui,  T., and Gumėry,  P. Y., 1999, “Standardization of a Method for Characterizing Low-concentration Biogels: Elastic Properties of Low-concentration Agarose Gels,” J. Biomech. Eng., 47(11), pp. 184–187.
Ziemann,  F., Radler,  J., and Sackmann,  E., 1994, “Local Measurements of Viscoelastic Moduli of Entangled Actin Networks Using an Oscillating Magnetic Bead Micro-rheometer,” Biophys. J., 66(6), pp. 2210–2216.
Benkherourou,  M., Gumery,  P. Y., Tranqui,  L., and Tracqui,  P., 2000, “Quantification and Macroscopic Modeling of the Nonlinear Viscoelastic Behavior of Strained Gels with Varying Fibrin Concentrations,” IEEE Trans. Biomed. Eng., 47(11), pp. 1465–75.
Kasapis,  S., and Sablani,  S. S., 2000, “First- and Second-approximation Calculations in the Relaxation Function of High-sugar/polysaccaride Systems,” Int. J. Biol. Macromol., 27(4), pp. 301–305.
Bagley,  R. L., 1983, “A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity,” J. Rheol., 27(3), pp. 201–210.
Suki,  B., Barabasi,  A. L., and Lutchen,  K. R., 1994, “Lung Tissue Viscoelasticity: A Mathematical Framework and Its Molecular Basis,” J. Appl. Physiol., 76(6), pp. 2749–2759.
Yuan,  H., Kononov,  S., Cavalcante,  F. S., Lutchen,  K. R., Ingenito,  E. P., and Suki,  B., 2000, “Effects of Collagenase and Elastase on the Mechanical Properties of Lung Tissue Strips,” J. Appl. Physiol., 89(1), pp. 3–14.
Yuan,  H., Ingenito,  E. P., and Suki,  B., 1997, “Dynamic Properties of Lung Parenchyma: Mechanical Contributions of Fiber Network and Interstitial Cells,” J. Appl. Physiol., 83, pp. 1420–1431.
Djordjevic,  V. D., Jaric,  J., Fabry,  B., Fredberg,  J. J., and Stamenovic,  D., 2003, “Fractional Derivatives Embody Essential Features of Cell Rheological Behavior,” Ann. Biomed. Eng., 31, pp. 692–699.
Csendes,  T., 1988, “Nonlinear Parameter Estimation by a Global Optimization—Efficiency and Reliability,” Acta Cybern., 8, pp. 361–370.
Rouse,  P. E., 1953, “A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers,” J. Chem. Phys., 21(7), pp. 1272–1280.
De Gennes,  P. G., 1971, “Reptation of a Polymer Chain in the Presence of Fixed Obstacles,” J. Chem. Phys., 55, pp. 572–579.
Doi, M., and Edwards, S. F., 1986, The Theory of Polymer Dynamics, Clarendon Press, Oxford, UK, Chap. 10.
Cates,  M. E., 1987, “Reptation of Living Polymers: Dynamics of Entangled Polymers in the Presence of Reversible Chain-scission Reactions,” Macromolecules, 20, pp. 2289–2296.
Gu,  W. Y., Yao,  H., Huang,  C. Y., and Cheung,  H. S., 2003, “New Insight into Deformation-dependent Hydraulic Permeability of Gels and Cartilage, and Dynamic Behavior of Agarose Gels in Confined Compression,” J. Biomech., 36(4), pp. 593–598.
Arbogast,  K. B., Thibault,  K. L., Pinheiro,  S. B., Winey,  K. I., and Margulies,  S. S., 1997, “A High-Frequency Shear Device for Testing Soft Biological Tissues,” J. Biomech., 30(7), pp. 757–759.
Balgude,  A. P., Yu,  X., Szymanski,  A., and Bellamkonda,  R. V., 2001, “Agarose Gel Stiffness Determines Rate of DRG Neurite Extension in 3D Cultures,” Biomaterials, 22, pp. 1077–1084.
Kruse,  S. A., Smith,  J. A., Lawrence,  A. J., Dresner,  M. A., Manduca,  A., Greenleaf,  J. F., and Ehman,  R. L., 2000, “Tissue Characterization Using Magnetic Resonance Elastography: Preliminary Results,” Phys. Med. Biol., 45(6), pp. 579–1590.
Hamhaber,  U., Grieshaber,  F. A., Nagel,  J. H., and Klose,  U., 2003, “Comparison of Quantitative Shear Wave MR-Elastography with Mechanical Compression Test,” Magn. Reson. Med., 49, pp. 71–77.
Menard, K. P., 1999, Dynamic Mechanical Analysis: A Practical Introduction, CRC Press, Boca Raton, FL, Chap. 7.
Fung, Y. C., 1993, Biomechanics: Mechanical Properties of Living Tissues, 2nd ed., Springer, New York.

Figures

Grahic Jump Location
Double logarithm graph of the magnitude of complex modulus E* versus frequency for agarose gels of different concentrations. Dots symbol the values of E* measured with DMA 2980. Lines symbol the fitted values of E* from the global optimization. Error bars represent the standard deviation of the measured E* at each specific frequency.
Grahic Jump Location
Double logarithm graph of the storage modulus E as a function of frequency for 3% agarose gel. Error bars represent the standard deviation of E and E at each specific frequency.
Grahic Jump Location
H as a function of gel concentration C. Values of H are estimated from the global optimization of the complex modulus E* for each gel concentration. Estimated values of H are then curved fitted as the function of C (%) based on Eq. (11), which shows a power law of H=2.0331C2.1748(R2=0.918).
Grahic Jump Location
β as a function of gel concentration C. Values of β are calculated from the estimated H and G based on Eq. (5) for each gel concentration, and is then curve fitted as the function of C (%) based on Eq. (12), which showed β=0.0143 ln C+0.0136(R2=0.918).
Grahic Jump Location
DMA 2980 in shear sandwich mode with the gel samples housed in a chamber in connection to a humidifier to keep the samples from dehydration. One pair of gel samples of equal size is mounted into the shear fixture.

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