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

Qingshan Chen; Bela Suki; Kai-Nan An

doi:10.1115/1.1797991

Journal of Biomechanical Engineering | Volume 126 | Issue 5 | TECHNICAL PAPERS

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

Qingshan Chen, Bela Suki and Kai-Nan An

[+] 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

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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.

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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.

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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=2.0331C^2.1748(R²=0.918).

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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).

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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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Chen Q, Suki B, An K. Dynamic Mechanical Properties of Agarose Gels Modeled by a Fractional Derivative Model. ASME. J Biomech Eng. 2004;126(5):666-671. doi:10.1115/1.1797991.

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

References

Figures

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.

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=2.0331C^2.1748(R²=0.918).

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).

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

References

Figures

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.

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).

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).

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.

Tables

Errata

Discussions

Related Content

Journals

Conference Proceedings

eBooks

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.

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=2.0331C^2.1748(R²=0.918).

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).