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.

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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.

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Fig. 2

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

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Fig. 3

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

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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)

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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

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Fig. 6

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

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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.




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