Fractional order viscoelasticity of the aortic valve cusp: An alternative to quasilinear viscoelasticity

Journal of Biomechanical Engineering

Volumn 127, Issue 4, 2005, Pages 700-708

  Doehring, Todd C ^a   Freed, Alan D ^a,b   Carew, Evelyn O ^a   Vesely, Ivan ^a,c  

^a LERNER RESEARCH INSTITUTE   (United States)

^b NASA GLENN RESEARCH CENTER   (United States)

^c CHILDREN S HOSPITAL LOS ANGELES   (United States)

Author keywords

Aortic Valve; Fractals; Fractional Calculus; Nonlinear Elasticity; Soft Tissue; Viscoelasticity

Indexed keywords

BLOOD VESSELS; COLLAGEN; FRACTALS; OPTIMIZATION; PARAMETER ESTIMATION; TISSUE;

AORTIC VALVES; FRACTIONAL CALCULUS; NONLINEAR ELASTICITY; SOFT TISSUES;

VISCOELASTICITY;

ACCURACY; ANIMAL TISSUE; AORTA VALVE; ARTICLE; FRACTIONATION; MATERIALS TESTING; MATHEMATICAL ANALYSIS; MODEL; NONHUMAN; PARAMETER; RELAXATION TIME; SENSITIVITY ANALYSIS; STRESS; SWINE; THEORY; VISCOELASTICITY;

ANIMALS; AORTIC VALVE; ELASTICITY; HUMANS; LINEAR MODELS; MODELS, CARDIOVASCULAR; NONLINEAR DYNAMICS; STRESS, MECHANICAL; SWINE; TENSILE STRENGTH; VISCOSITY;

EID: 23644445170     PISSN: 01480731     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1933900     Document Type: Article

References (27)

1. Fung, Y. C., 1973, "Biorheology of soft tissues," Biorheology, 10, pp. 139-155.
2. Pinto, J. G., and Patitucci, P. J., 1980, "Visco-Elasticity of Passive Cardiac Muscle," J. Biomech. Eng., 102, pp. 57-61.
3. Woo, S. L., Simon, B. R., Kuei, S. C., and Akeson, W. H., 1980, "Quasi-Linear Viscoelastic Properties of Normal Articular Cartilage," J. Biomech. Eng., 102, pp. 85-90.
4. 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, pp. 293-298.
5. Johnson, G. A., Tramaglini, D. M., Levine, R. E., Ohno, K., Choi, N. Y., and Woo, S. L., 1994, "Tensile and Viscoelastic Properties of Human Patellar Tendon," J. Orthop. Res., 12, pp. 796-803.
6. Carew, E. O., Talman, E. A., Boughner, D. R., and Vesely, I., 1999, "Quasi-Linear Viscoelastic Theory Applied to Internal Shearing of Porcine Aortic Valve Leaflets," J. Biomech. Eng., 121, pp. 386-392.
7. Thomopoulos, S., Williams, G. R., and Soslowsky, L. J., 2003, "Tendon to Bone Healing: Differences in Biomechanical, Structural, and Compositional Properties Due to a Range of Activity Levels," J. Biomech. Eng., 125, pp. 106-113.
8. Elliott, D. M., Robinson, P. S., Gimbel, J. A., Sarver, J. J., Abboud, J. A., Iozzo, R. V., and Soslowsky, L. J., 2003, "Effect of Altered Matrix Proteins on Quasilinear Viscoelastic Properties in Transgenic Mouse Tail Tendons," Ann. Biomed. Eng., 31, pp. 599-605.
9. Han, L., Noble, J. A., and Burcher, M., 2003, "A Novel Ultrasound Indentation System For Measuring Biomechanical Properties Of In Vivo Soft Tissue," Ultrasound Med. Biol., 29, pp. 813-823.
10. 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, pp. 447-452.
11. Podlubny, I., 1999, in Mathematics in Science and Engineering (Academic Press, San DiegoVol), Vol. 198, pp. 268-277.
12. Glockle, W. G., and Nonnenmacher, T. F., 1995, "A Fractional Calculus Approach to Self-Similar Protein Dynamics," Biophys. J., 68, pp. 46-53.
13. Suki, B., Barabasi, A. L., and Lutchen, K. R., 1994, "Lung Tissue Viscoelasticity: A Mathematical Framework and Its Molecular Basis," J. Appl. Physiol., 76, pp. 2749-2759.
14. Carew, E. O., Doehring, T. C., Barber, J. E., Freed, A. D., and Vesely, I., 2003, in ASME Summer Bioengineering Conference, Key Biscayne, FL.
15. Ross, B., 1977, "The Development of Fractional Calculus 1695-1900," Hist. Math., 4, pp. 75-89.
16. Miller, K. S., and Ross, B., 1993, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley, New York, NY).
17. Douglas, J. F., 2000, in Applications of Fractional Calculus in Physics, edited by R. Hilfer (World Scientific, Singapore) pp. 241-330.
18. Heymans, N., and Bauwens, J. C., 1994, "Fractal Rheological Models and Fractional Differential Equations for Viscoelastic Behavior," Rheol. Acta, 33, pp. 210-219.
19. Doehring, T. C., Carew, E. O., and Vesely, I., 2004, "The Effect of Strain Rate on the Viscoelastic Response of Aortic Valve Tissue: A Direct-Fit Approach," Ann. Biomed. Eng., 32, pp. 223-232.
20. Fung, Y. C., 1993, Biomechanics: Mechanical Properties of Living Tissues (Springer-Verlag, New York, NY).
21. Mitton, R. G., 1945, "Mechanical Properties of Leather Fibres," J. Soc. Leather Trades' Chem., 29, pp. 169-194.
22. Carew, E. O., and Vesely, I., 1998, "Alternative Relaxation Spectra for Quasi-Linear Viscoelastic Theory Models," Ann. Biomed. Eng., 26, p. S-65.
23. Gorenflo, R., Loutchko, I., and Luchko, Y., 2002, "Computation of the Mittag-Leffler Function E(Z) and its Derivatives," Fractional Calculus Appl. Anal., 5, pp. 491-518.
24. 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.
25. Rousseau, E. P., Sauren, A. A., van Hout, M. C., and van Steenhoven, A. A., 1983, "Elastic and Viscoelastic Material Behaviour of Fresh and Glutaraldehyde-Treated Porcine Aortic Valve Tissue," J. Biomech., 16, pp. 339-48.
26. Haut, R. C., and Little, R. W., 1972, "A Constitutive Equation For Collagen Fibers," J. Biomech., 5, pp. 423-430.
27. Provenzano, P., Lakes, R., Keenan, T., and Vanderby, R. Jr., 2001, "Nonlinear Ligament Viscoelasticity," Ann. Biomed. Eng., 29, pp. 908-14.