The complex modulus and elastic modulus of agarose gels (2% to 4%) are measured with a dynamic mechanical analyzer in frequency sweep shear sandwich mode between 0.1 and 20 Hz. The data showed that and increase with frequency according to a power law which can be described by a fractional derivative model to characterize the dynamic viscoelasticity of the gel. The functions between the model parameters including storage modulus coefficient and the power law exponent (β) and the agarose concentration are established. A molecular basis for the application of the fractional derivative model to gel polymers is also discussed. Such an approach can be useful in tissue culture studies employing dynamic pressurization or for validation of magnetic resonance elastography.
Issue Section:
Other
1.
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
.2.
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
.3.
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
.4.
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
.5.
Ross-Murphy
, S. B.
, and Shatwell
, K. P.
, 1993
, “Polysaccharide Strong and Weak Gels
,” Biorheology
, 30
(3–4), pp. 217
–227
.6.
Benkherourou
, M.
, Rochas
, C.
, Tracqui
, P.
, Tranqui
, T.
, and Gume˙ry
, 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
.7.
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
.8.
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
.9.
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
.10.
Bagley
, R. L.
, 1983
, “A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
,” J. Rheol.
, 27
(3
), pp. 201
–210
.11.
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
.12.
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
.13.
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
.14.
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
.15.
Csendes
, T.
, 1988
, “Nonlinear Parameter Estimation by a Global Optimization—Efficiency and Reliability
,” Acta Cybern.
, 8
, pp. 361
–370
.16.
Rouse
, Jr., P. E.
, 1953
, “A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers
,” J. Chem. Phys.
, 21
(7
), pp. 1272
–1280
.17.
De Gennes
, P. G.
, 1971
, “Reptation of a Polymer Chain in the Presence of Fixed Obstacles
,” J. Chem. Phys.
, 55
, pp. 572
–579
.18.
Doi, M., and Edwards, S. F., 1986, The Theory of Polymer Dynamics, Clarendon Press, Oxford, UK, Chap. 10.
19.
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
.20.
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
.21.
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
.22.
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
.23.
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
.24.
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
.25.
Menard, K. P., 1999, Dynamic Mechanical Analysis: A Practical Introduction, CRC Press, Boca Raton, FL, Chap. 7.
26.
Fung, Y. C., 1993, Biomechanics: Mechanical Properties of Living Tissues, 2nd ed., Springer, New York.
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