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Research Papers

Evaluation of Hemodynamics in a Prestressed and Compliant Tapered Femoral Artery Using an Optimization-Based Inverse Algorithm

[+] Author and Article Information
Rupak K. Banerjee

Department of Mechanical and
Materials Engineering,
College of Engineering and Applied Science,
University of Cincinnati,
593 Rhodes Hall, ML 0072
Cincinnati, OH 45221

Gavin A. D'Souza, Anup K. Paul, Ashish Das

Department of Mechanical and
Materials Engineering,
College of Engineering and Applied Science,
University of Cincinnati,
Cincinnati, OH 45221

1Corresponding author.

Manuscript received May 22, 2016; final manuscript received January 23, 2017; published online February 23, 2017. Assoc. Editor: Jonathan Vande Geest.

J Biomech Eng 139(4), 041002 (Feb 23, 2017) (11 pages) Paper No: BIO-16-1215; doi: 10.1115/1.4035916 History: Received May 22, 2016; Revised January 23, 2017

The important factors that affect the arterial wall compliance are the tissue properties of the arterial wall, the in vivo pulsatile pressure, and the prestressed condition of the artery. It is necessary to obtain the load-free geometry for determining the physiological level of prestress in the arterial wall. The previously developed optimization-based inverse algorithm was improved to obtain the load-free geometry and the wall prestress of an idealized tapered femoral artery of a dog under varying arterial wall properties. The compliance of the artery was also evaluated over a range of systemic pressures (72.5–140.7 mmHg), associated blood flows, and artery wall properties using the prestressed arterial geometry. The results showed that the computed load-free outer diameter at the inlet of the tapered artery was 6.7%, 9.0%, and 12% smaller than the corresponding in vivo diameter for the 25% softer, baseline, and 25% stiffer arterial wall properties, respectively. In contrast, the variations in the prestressed geometry and circumferential wall prestress were less than 2% for variable arterial wall properties. The computed compliance at the inlet of the prestressed artery for the baseline arterial wall property was 0.34%, 0.19%, and 0.13% diameter change/mmHg for time-averaged pressures of 72.5, 104.1, and 140.7 mmHg, respectively. However, the variation in compliance due to the change in arterial wall property was less than 6%. The load-free and prestressed geometries of the idealized tapered femoral artery were accurately (error within 1.2% of the in vivo geometry) computed under variable arterial wall properties using the modified inverse algorithm. Based on the blood-arterial wall interaction results, the arterial wall compliance was influenced significantly by the change in average pressure. In contrast, the change in arterial wall property did not influence the arterial wall compliance.

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Figures

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Fig. 1

Cross-sectional view of the 3D tapered femoral artery of a dog showing mean dimensions of the artery obtained from in vivo angiographic images

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Fig. 2

Cross-sectional view of the FE model of the in vivo tapered femoral artery showing (a) the boundary conditions used in the inverse algorithm, (b) rigid contact surface scaled by −δr, (c) the radially shrunk artery with its outer surface coincident with the rigid surface, and (d) the radially and axially shrunk artery showing the load-free geometry

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Fig. 3

(a) Experimental data (Attinger, 1968) of a dog femoral artery. (b) Experimental data and theoretical Cauchy stress versus stretch ratio. (c) Contour plot of the strain energy density function for the baseline arterial property constants.

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Fig. 4

(a) Outlet pressure wave forms used to compute arterial wall compliance for in vivo and elevated pressures. (b) Measured and extrapolated pressure drop wave forms for in vivo and elevated outlet pressures.

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Fig. 7

Pressure versus midwall radius at the inlet and outlet for time-averaged pressures of (a) 72.5 mmHg, (b) 104.1 mmHg, and (c) 140.7 mmHg computed using the baseline arterial wall property

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Fig. 9

Variation of the tapered artery midwall: (a) circumferential stress and (b) axial stress for in vivo and elevated pressures computed using the baseline arterial wall property

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Fig. 10

Flow chart of the inverse algorithm

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Fig. 5

Results from the inverse algorithm for the tapered dog femoral artery with in vivo time-averaged pressure of 72.5 mmHg, 48% axial stretch and baseline arterial wall property. Dimensions of: (a) in vivo wall, (b) load-free wall, and (c) prestressed arterial wall with the load-free wall superimposed on it.

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Fig. 6

(a) Spatially averaged axial velocity at the cuff location for experimentally measured, computed compliant, and computed rigid tapered dog femoral artery at in vivo pressure with baseline arterial wall property. (b) Computed spatially averaged axial velocity for the in vivo and elevated pressures with the baseline arterial wall property.

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Fig. 8

Computed compliance versus pressure at the inlet and outlet. The computed results are compared with the in vivo data [22].

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