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Showing content from https://link.springer.com/article/10.1007/s10439-014-0970-3 below:

Fractional-Order Viscoelasticity in One-Dimensional Blood Flow Models

References
  1. Alastruey, J., A. W. Khir, K. S. Matthys, P. Segers, S. J. Sherwin, P. R. Verdonck, K. H. Parker, and J. Peiró. Pulse wave propagation in a model human arterial network: assessment of 1-D visco-elastic simulations against in vitro measurements. J. Biomech. 44:2250–2258, 2011.

    Article  PubMed Central  PubMed  Google Scholar 

  2. Atanacković, T. M., S. Konjik, L. Oparnica, and D. Zorica. Thermodynamical restrictions and wave propagation for a class of fractional order viscoelastic rods. Abstr. Appl. Anal. 2011:1–32, 2011.

  3. Bia, D., I. Aguirre, Y. Zócalo, L. Devera, E. Cabrera Fischer, and R. L. Armentano. Regional differences in viscosity, elasticity, and wall buffering function in systemic arteries: pulse wave analysis of the arterial pressure–diameter relationship. Rev. Esp. Cardiol. (Engl. Ed.) 58:167–174, 2005.

    Google Scholar 

  4. Čanić, S., C. J. Hartley, D. Rosenstrauch, J. Tambača, G. Guidoboni, and A. Mikelić. Blood flow in compliant arteries: an effective viscoelastic reduced model, numerics, and experimental validation. Ann. Biomed. Eng. 34(4):575–592, 2006.

    Article  PubMed  Google Scholar 

  5. Craiem, D. O., and R. L. Armentano. A fractional derivative model to describe arterial viscoelasticity. Biorheology 44:251–263, 2007.

    PubMed  Google Scholar 

  6. Craiem, D. O., F. J. Rojo, J. M. Atienza, R. L. Armentano, and G. V. Guinea. Fractional-order viscoelasticity applied to describe uniaxial stress relaxation of human arteries. Phys. Med. Biol. 53:4543, 2008.

    Article  PubMed  Google Scholar 

  7. Craiem, D. O., F. J. Rojo, J. M. Atienza, G. V. Guinea, and R. L. Armentano. Fractional calculus applied to model arterial viscoelasticity. Latin Am. Appl. Res. 38:141–145, 2008.

    Google Scholar 

  8. DeVault, K., P. A. Gremaud, V. Novak, M. S. Olufsen, G. Vernieres, and P. Zhao. Blood flow in the circle of willis: modeling and calibration. SIAM Multiscale Model. Simul. 7(2):888–909, 2008.

    Article  Google Scholar 

  9. Doehring, T. C., A. D. Freed, E. O. Carew, I. Vesely, et al. Fractional order viscoelasticity of the aortic valve cusp: an alternative to quasilinear viscoelasticity. J. Biomech. Eng.-Trans. ASME 127:700, 2005.

    Google Scholar 

  10. Eringen, A. C. Mechanics of Continua. Huntington, NY: Robert E. Krieger, 1980.

  11. Formaggia, L., A. Quarteroni, and A. Veneziani. Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System, Vol. 1. New York: Springer, 2009.

  12. Fung, Y. Biomechanics: Mechanical Properties of Living Tissues. New York: Springer, 1993.

  13. Grinberg, L., E. Cheever, T. Anor, J. R. Madsen, and G. E. Karniadakis. Modeling blood flow circulation in intracranial arterial networks: a comparative 3D/1D simulation study. Ann. Biomed. Eng. 39:297–309, 2011.

    Article  PubMed  CAS  Google Scholar 

  14. López-Fernández, M., C. Lubich, and A. Schädle. Adaptive, fast, and oblivious convolution in evolution equations with memory. SIAM J. Sci. Comput. 30:1015–1037, 2008.

    Article  Google Scholar 

  15. Lubich, C., and A. Schädle. Fast convolution for nonreflecting boundary conditions. SIAM J. Sci. Comput. 24:161–182, 2002.

    Article  Google Scholar 

  16. Lundkvist, A., E. Lilleodden, W. Siekhaus, J. Kinney, L. Pruitt, and M. Balooch. Viscoelastic properties of healthy human artery measured in saline solution by AFM-based indentation technique. In: MRS Proceedings, Vol. 436, 1996.

  17. Magin, R. L. Fractional Calculus in Bioengineering. Redding: Begell House, 2006.

  18. Mainardi, F. Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. London: Imperial College Press, 2010.

  19. Näsholm, S. P., and S. Holm. On a fractional Zener elastic wave equation. Fract. Calc. Appl. Anal. 16:26–50, 2013.

    Article  Google Scholar 

  20. Podlubny, I. Fractional Differential Equations, Vol. 198. San Diego: Academic Press, 1998.

  21. Podlubny, I. Calculation of the Mittag-Leffler function with desired accuracy. http://www.mathworks.com/matlabcentral/fileexchange/8738-mittag-leffler-function, 2012. Accessed 12 September 2012.

  22. Raghu, R., I. E. Vignon-Clementel, C. A. Figueroa, and C. A. Taylor. Comparative study of viscoelastic arterial wall models in nonlinear one-dimensional finite element simulations of blood flow. J. Biomech. Eng.-Trans. ASME 133(8):081003–081003, 2011.

    Article  Google Scholar 

  23. Reymond, P., F. Merenda, F. Perren, D. Rüfenacht, and N. Stergiopulos. Validation of a one-dimensional model of the systemic arterial tree. Am. J. Physiol. Heart Circ. Physiol. 297:208, 2009.

    Article  CAS  Google Scholar 

  24. Reymond, P., F. Perren, F. Lazeyras, and N. Stergiopulos. Patient-specific mean pressure drop in the systemic arterial tree, a comparison between 1-D and 3-D models. J. Biomech. 45(15):2499–2505, 2012.

    Article  PubMed  Google Scholar 

  25. Sherwin, S. J., V. Franke, J. Peiro, and K. H. Parker. One-dimensional modelling of a vascular network in space–time variables. J. Eng. Math. 47:217–250, 2012.

    Article  Google Scholar 

  26. Shu, C. W. Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput. 9(6):1073–1084, 1988.

    Article  Google Scholar 

  27. Smith, N. P., A. J. Pullan, and P. J. Hunter. An anatomically based model of transient coronary blood flow in the heart. SIAM J. Appl. Math. 62:990–1018, 2001.

    Article  Google Scholar 

  28. Steele, B. N., D. Valdez-Jasso, M. A. Haider, and M. S. Olufsen. Predicting arterial flow and pressure dynamics using a 1D fluid dynamics model with a viscoelastic wall. SIAM J. Appl. Math. 71(4):1123–1143, 2011.

    Article  Google Scholar 

  29. Valdez-Jasso, D., D. Bia, Y. Zócalo, R. L. Armentano, M. Haider, and M. Olufsen. Linear and nonlinear viscoelastic modeling of aorta and carotid pressure–area dynamics under in vivo and ex vivo conditions. Ann. Biomed. Eng. 39(5):1–19, 2011.

    Google Scholar 

  30. Witthoft, A., and G. E. Karniadakis. A bidirectional model for communication in the neurovascular unit. J. Theor. Biol. 311:80–93, 2012.

    Article  PubMed  Google Scholar 

  31. Xiu, D., and D. E. Karniadakis. The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24:619–644, 2002.

    Article  Google Scholar 

  32. Yang, X., M. Choi, G. Lin, and G. E. Karniadakis. Adaptive anova decomposition of stochastic incompressible and compressible flows. J. Comput. Phys. 231:1587–1614, 2012.

    Article  Google Scholar 

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