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Blood Flow in Compliant Arteries: An Effective Viscoelastic Reduced Model, Numerics, and Experimental Validation

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Abstract

The focus of this work is on modeling blood flow in medium-to-large systemic arteries assuming cylindrical geometry, axially symmetric flow, and viscoelasticity of arterial walls. The aim was to develop a reduced model that would capture certain physical phenomena that have been neglected in the derivation of the standard axially symmetric one-dimensional models, while at the same time keeping the numerical simulations fast and simple, utilizing one-dimensional algorithms. The viscous Navier–Stokes equations were used to describe the flow and the linearly viscoelastic membrane equations to model the mechanical properties of arterial walls. Using asymptotic and homogenization theory, a novel closed, “one-and-a-half dimensional” model was obtained. In contrast with the standard one-dimensional model, the new model captures: (1) the viscous dissipation of the fluid, (2) the viscoelastic nature of the blood flow – vessel wall interaction, (3) the hysteresis loop in the viscoelastic arterial walls dynamics, and (4) two-dimensional flow effects to the leading-order accuracy. A numerical solver based on the 1D-Finite Element Method was developed and the numerical simulations were compared with the ultrasound imaging and Doppler flow loop measurements. Less than 3% of difference in the velocity and less than 1% of difference in the maximum diameter was detected, showing excellent agreement between the model and the experiment.

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ACKNOWLEDGMENTS

Research of Čanić, Hartley, Rosenstrauch, Tambača and Mikelić is supported in part by the joint National Science Foundation and the National Institutes of Health grant DMS-0443826. In addition, research of Čanić is supported in part by the National Science Foundation under grants DMS-0245513, DMS-0337355, and the research of Hartley is supported in part by the National Institutes of Health under Grant HL22512. The experimental design and the in vitro work at Dr. Rosenstrauch's laboratory at the Texas Heart Institute was partially supported by a grant from the Roderick Duncan McDonald Foundation at the St. Luke's Episcopal Hospital. Kent Elastomer Inc. donation of latex tubing is also acknowledged. The authors would like to thank undergraduate student Joy Chavez for the help with data collection and flow loop experiments. Chavez's research was supported by the NSF under grant DMS-0337355.

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, TX, 77204-3008, USA

    Sunčica Čanić & Giovanna Guidoboni

  2. Sections of Cardiovascular Sciences, Department of Medicine, Baylor College of Medicine, Houston, TX, 77030, USA

    Craig J. Hartley

  3. Texas Heart Institute and the University of Texas Health Science Center at Houston, Houston, TX, 77204, USA

    Doreen Rosenstrauch

  4. Department of Mathematics, University of Zagreb, Bijenička 30, Zagreb, Croatia

    Josip Tambača

  5. Department of Mathematics, Université Claude Bernard Lyon 1, 69622, Villeurbanne Cedex, France

    Andro Mikelić

Authors
  1. Sunčica Čanić
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  2. Craig J. Hartley
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  3. Doreen Rosenstrauch
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  4. Josip Tambača
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  5. Giovanna Guidoboni
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  6. Andro Mikelić
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Correspondence to Sunčica Čanić.

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Čanić, S., Hartley, C.J., Rosenstrauch, D. et al. Blood Flow in Compliant Arteries: An Effective Viscoelastic Reduced Model, Numerics, and Experimental Validation. Ann Biomed Eng 34, 575–592 (2006). https://doi.org/10.1007/s10439-005-9074-4

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  • DOI: https://doi.org/10.1007/s10439-005-9074-4

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