Research Papers

Linear and Nonlinear Viscoelastic Arterial Wall Models: Application on Animals

[+] Author and Article Information
Arthur R. Ghigo, Xiao-Fei Wang, Jose-Maria Fullana, Pierre-Yves Lagrée

CNRS UMR 7190,
Institut Jean le Rond ∂'Alembert,
UPMC Univ Paris 06,
Sorbonne Universités,
Paris F-75005, France

Ricardo Armentano

Faculty of Engineering and
Natural and Exact Sciences,
Favaloro University,
Buenos Aires C1078AAI, Argentina

Manuscript received April 28, 2016; final manuscript received September 17, 2016; published online November 4, 2016. Assoc. Editor: Alison Marsden.

J Biomech Eng 139(1), 011003 (Nov 04, 2016) (7 pages) Paper No: BIO-16-1175; doi: 10.1115/1.4034832 History: Received April 28, 2016; Revised September 17, 2016

This work deals with the viscoelasticity of the arterial wall and its influence on the pulse waves. We describe the viscoelasticity by a nonlinear Kelvin–Voigt model in which the coefficients are fitted using experimental time series of pressure and radius measured on a sheep's arterial network. We obtained a good agreement between the results of the nonlinear Kelvin–Voigt model and the experimental measurements. We found that the viscoelastic relaxation time—defined by the ratio between the viscoelastic coefficient and the Young's modulus—is nearly constant throughout the network. Therefore, as it is well known that smaller arteries are stiffer, the viscoelastic coefficient rises when approaching the peripheral sites to compensate the rise of the Young's modulus, resulting in a higher damping effect. We incorporated the fitted viscoelastic coefficients in a nonlinear 1D fluid model to compute the pulse waves in the network. The damping effect of viscoelasticity on the high-frequency waves is clear especially at the peripheral sites.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Wang, X. , Nishi, S. , Matsukawa, M. , Ghigo, A. , Lagrée, P.-Y. , and Fullana, J.-M. , 2016, “ Fluid Friction and Wall Viscosity of the 1D Blood Flow Model,” J. Biomech., 49(4), pp. 565–571. [CrossRef] [PubMed]
Fung, Y. , 1993, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York.
Steele, B. , Valdez-Jasso, D. , Haider, M. , and Olufsen, M. , 2011, “ Predicting Arterial Flow and Pressure Dynamics Using a 1D Fluid Dynamics Model With a Viscoelastic Wall,” SIAM J. Appl. Math., 71(4), pp. 1123–1143. [CrossRef]
Holenstein, R. , Niederer, P. , and Anliker, M. , 1980, “ A Viscoelastic Model for Use in Predicting Arterial Pulse Waves,” ASME J. Biomech. Eng., 102(4), pp. 318–325. [CrossRef]
Reymond, P. , Bohraus, Y. , Perren, F. , Lazeyras, F. , and Stergiopulos, N. , 2011, “ Validation of a Patient-Specific One-Dimensional Model of the Systemic Arterial Tree,” Am. J. Physiol.: Heart Circ. Physiol., 301(3), pp. H1173–H1182. [CrossRef] [PubMed]
Reymond, P. , Merenda, F. , Perren, F. , Rüfenacht, D. , and Stergiopulos, N. , 2009, “ Validation of a One-Dimensional Model of the Systemic Arterial Tree,” Am. J. Physiol.: Heart Circ. Physiol., 297(1), pp. H208–H222. [CrossRef] [PubMed]
Raghu, R. , Vignon-Clementel, I. , Figueroa, C. , and Taylor, C. , 2011, “ Comparative Study of Viscoelastic Arterial Wall Models in Nonlinear One-Dimensional Finite Element Simulations of Blood Flow,” ASME J. Biomech. Eng., 133(8), p. 081003. [CrossRef]
Segers, P. , Stergiopulos, N. , Verdonck, P. , and Verhoeven, R. , 1997, “ Assessment of Distributed Arterial Network Models,” Med. Biol. Eng. Comput., 35(6), pp. 729–736. [CrossRef] [PubMed]
Armentano, R. , Barra, J. , Levenson, J. , Simon, A. , and Pichel, R. , 1995, “ Arterial Wall Mechanics in Conscious Dogs Assessment of Viscous, Inertial, and Elastic Moduli to Characterize Aortic Wall Behavior,” Circ. Res., 76(3), pp. 468–478. [CrossRef] [PubMed]
Alastruey, J. , Khir, A. W. , Matthys, K. S. , Segers, P. , Sherwin, S. J. , Verdonck, P. R. , Parker, K. H. , and Peiró, J. , 2011, “ Pulse Wave Propagation in a Model Human Arterial Network: Assessment of 1-D Visco-Elastic Simulations Against In Vitro Measurements,” J. Biomech., 44(12), pp. 2250–2258. [CrossRef] [PubMed]
Valdez-Jasso, D. , Haider, M. , Banks, H. , Santana, D. , Germán, Y. , Armentano, R. , and Olufsen, M. , 2009, “ Analysis of Viscoelastic Wall Properties in Ovine Arteries,” IEEE Trans. Biomed. Eng., 56(2), pp. 210–219. [CrossRef] [PubMed]
Erbay, H. , Erbay, S. , and Dost, S. , 1992, “ Wave Propagation in Fluid Filled Nonlinear Viscoelastic Tubes,” Acta Mech., 95(1–4), pp. 87–102. [CrossRef]
Bird, R. B. , Armstrong, R. C. , Hassager, O. , and Curtiss, C. F. , 1977, Dynamics of Polymeric Liquids, Vol. 1, Wiley, New York.
Fischer, E. C. , Bia, D. , Camus, J. , Zócalo, Y. , De Forteza, E. , and Armentano, R. , 2006, “ Adventitia-Dependent Mechanical Properties of Brachiocephalic Ovine Arteries in In Vivo and In Vitro Studies,” Acta Physiol., 188(2), pp. 103–111. [CrossRef]
Fung, Y. , 1997, Biomechanics: Circulation, Springer Verlag, New York.
Smith, N. , Pullan, A. , and Hunter, P. , 2002, “ An Anatomically Based Model of Transient Coronary Blood Flow in the Heart,” SIAM J. Appl. Math., 62(3), pp. 990–1018. [CrossRef]
Wang, X. , Delestre, O. , Fullana, J.-M. , Saito, M. , Ikenaga, Y. , Matsukawa, M. , and Lagrée, P.-Y. , 2012, “ Comparing Different Numerical Methods for Solving Arterial 1D Flows in Networks,” Comput. Methods Biomech. Biomed. Eng., 15(Suppl. 1), pp. 61–62. [CrossRef]
Wang, X. , Fullana, J.-M. , and Lagrée, P.-Y. , 2015, “ Verification and Comparison of Four Numerical Schemes for a 1D Viscoelastic Blood Flow Model,” Comput. Methods Biomech. Biomed. Eng., 18(15), pp. 1704–1725. [CrossRef]
Bessems, D. , Giannopapa, C. , Rutten, M. , and van de Vosse, F. , 2008, “ Experimental Validation of a Time-Domain-Based Wave Propagation Model of Blood Flow in Viscoelastic Vessels,” J. Biomech., 41(2), pp. 284–291. [CrossRef] [PubMed]
Valdez-Jasso, D. , Bia, D. , Zócalo, Y. , Armentano, R. , Haider, M. , and Olufsen, M. , 2011, “ Linear and Nonlinear Viscoelastic Modeling of Aorta and Carotid Pressure–Area Dynamics Under In Vivo and Ex Vivo Conditions,” Ann. Biomed. Eng., 39(5), pp. 1438–1456. [CrossRef] [PubMed]
Nichols, W. , O'Rourke, M. , and Vlachopoulos, C. , 2011, McDonald's Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles, CRC Press, Boca Raton, FL.


Grahic Jump Location
Fig. 1

Arterial tree of a sheep. Experimental data are collected from 11 sheep at the following seven locations: ascending aorta (AA), proximal descending aorta (PD), medial descending aorta (MD), distal descending aorta (DD), brachiocephalic trunk (BT), carotid artery (CA), and femoral artery (FA). There are three virtual arteries (VAs), which are indicated by dashed lines, to model the side branches when pulse waves are simulated. Parameters for all the arteries are shown in Table 1.

Grahic Jump Location
Fig. 2

Pressure–radius loop of ascending aorta: experimental data and prediction of (left) linear Kelvin–Voigt model and (right) nonlinear Kelvin–Voigt model

Grahic Jump Location
Fig. 3

Experimental data and the fitted nonlinear Kelvin–Voigt model. Parameter values are in Table 1.

Grahic Jump Location
Fig. 4

Optimal unstressed radius R0, predicted and measured for the seven arteries (ascending aorta, proximal descending aorta, medial descending aorta, distal descending aorta, brachiocephalic trunk, carotid artery, and femoral artery)

Grahic Jump Location
Fig. 5

Mean values of the reference Young's modulus E (left), and viscosity coefficient ϕ0 (right) with standard deviations among the group of sheep at the seven locations of the arterial network

Grahic Jump Location
Fig. 6

Relaxation time ϕ0/E with standard deviations at the seven locations of the arterial network

Grahic Jump Location
Fig. 7

Time series of flow rate at medial descending aorta (left) and carotid artery (right). The viscoelastic model predicts a smoother waveform than the elastic model.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In