Technical Brief

Characterizations and Correlations of Wall Shear Stress in Aneurysmal Flow

[+] Author and Article Information
Amirhossein Arzani

Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720-1740

Shawn C. Shadden

Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720-1740
e-mail: shadden@berkeley.edu

1Corresponding author.

Manuscript received May 6, 2015; final manuscript received November 5, 2015; published online December 8, 2015. Assoc. Editor: Jonathan Vande Geest.

J Biomech Eng 138(1), 014503 (Dec 08, 2015) (10 pages) Paper No: BIO-15-1221; doi: 10.1115/1.4032056 History: Received May 06, 2015; Revised November 05, 2015

Wall shear stress (WSS) is one of the most studied hemodynamic parameters, used in correlating blood flow to various diseases. The pulsatile nature of blood flow, along with the complex geometries of diseased arteries, produces complicated temporal and spatial WSS patterns. Moreover, WSS is a vector, which further complicates its quantification and interpretation. The goal of this study is to investigate WSS magnitude, angle, and vector changes in space and time in complex blood flow. Abdominal aortic aneurysm (AAA) was chosen as a setting to explore WSS quantification. Patient-specific computational fluid dynamics (CFD) simulations were performed in six AAAs. New WSS parameters are introduced, and the pointwise correlation among these, and more traditional WSS parameters, was explored. WSS magnitude had positive correlation with spatial/temporal gradients of WSS magnitude. This motivated the definition of relative WSS gradients. WSS vectorial gradients were highly correlated with magnitude gradients. A mix WSS spatial gradient and a mix WSS temporal gradient are proposed to equally account for variations in the WSS angle and magnitude in single measures. The important role that WSS plays in regulating near wall transport, and the high correlation among some of the WSS parameters motivates further attention in revisiting the traditional approaches used in WSS characterizations.

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Grahic Jump Location
Fig. 1

Unit vector field et is defined as the unit tangent vector that is most aligned with the centerline direction. The binormal vector eb is computed as the cross product of this unit tangent vector and the unit normal vector.

Grahic Jump Location
Fig. 7

Sum of WSS vectors in the binormal direction (∫0Tτbdt) for two representative cases (patients 4 and 6). Anterior views are shown. Positive values show regions with dominant counterclockwise near wall rotating flow. Negative values show regions with dominant clockwise near wall rotating flow. The colorbar range does not represent peak values.

Grahic Jump Location
Fig. 6

Sum of WSS vectors in the tangent direction (∫0Tτtdt) for a representative case (patient 4). Positive values show regions with dominant forward near wall flow. Negative values show regions with dominant backward near wall flow. The colorbar range does not represent peak values.

Grahic Jump Location
Fig. 5

WSS parameters for a representative case (patient 3). The posterior view is shown in this figure. All units are based on dynes/cm2 for WSS magnitude, rad for WSS angle, cm for spatial gradients, and seconds for time. OSI, Δ90 and mix parameters are dimensionless.

Grahic Jump Location
Fig. 4

WSS parameters for a representative case (patient 3). The anterior view is shown in this figure. All units are based on dynes/cm2 for WSS magnitude, radians for WSS angle, cm for spatial gradients, and seconds for time. OSI, Δ90 and mix parameters are dimensionless.

Grahic Jump Location
Fig. 3

Instantaneous complex WSS vectors, and the corresponding WSS streamlines for three patients. To improve visualization, the WSS vectors are scaled differently in each patient; however the same color mapping was used among all cases.

Grahic Jump Location
Fig. 2

Patient-specific models used in this study. The shaded region shows the aneurysmal region, where the WSS correlations were performed.

Grahic Jump Location
Fig. 8

(a) Changes in WSS angle can be computed wrong in regions near the transition of the coordinate (between 0 and 2π using the convention shown). (b) Quantification of changes in WSS angle can be achieved by computation of WSS angle with respect to two reference directions and taking the minimum of the two differences.



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