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Research Papers

# Rheological Effects of Blood in a Nonplanar Distal End-to-Side Anastomosis

[+] Author and Article Information
Qian-Qian Wang

Medical Engineering Division, School of Engineering and Materials Science, Queen Mary,  University of London, London E1 4NS, UK

Bao-Hong Ping

Department of Hematology, Nanfang Hospital, Southern Medical University, 1838 Guangzhou Avenue North, Guangzhou 510515, China

Qing-Bo Xu

Vascular Biology Unit, Department of Cardiology, King’s College London, Strand, London WC2R 2LS, UK

Wen Wang1

Medical Engineering Division, School of Engineering and Materials Science, Queen Mary,  University of London, London E1 4NS, UKwen.wang@qmul.ac.uk

1

Corresponding author.

J Biomech Eng 130(5), 051009 (Aug 12, 2008) (9 pages) doi:10.1115/1.2948418 History: Received August 08, 2007; Revised February 18, 2008; Published August 12, 2008

## Abstract

This study investigates rheological effects of blood on steady flows in a nonplanar distal end-to-side anastomosis. The shear-thinning behavior of blood is depicted by a Carreau–Yasuda model and a modified power-law model. To explore effects of nonplanarity in vessel geometry, a curved bypass graft is considered that connects to the host artery with a $90deg$ out-of-plane curvature. Navier–Stokes equations are solved using a finite volume method. Velocity and wall shear stress (WSS) are compared between Newtonian and non-Newtonian fluids at different flow rates. At low flow rate, difference in axial velocity profiles between Newtonian and non-Newtonian fluids is significant and secondary flows are weaker for non-Newtonian fluids. At high flow rate, non-Newtonian fluids have bigger peak WSS and WSS gradient. The size of the flow recirculation zone near the toe is smaller for non-Newtonian fluids and the difference is significant at low flow rate. The nonplanar bypass graft introduces helical flow in the host vessel. Results from the study reveal that near the bed, heel, and toe of the anastomotic junction where intimal hyperplasia occurs preferentially, WSS gradients are all very big. At high flow rates, WSS gradients are elevated by the non-Newtonian effect of blood but they are reduced at low flow rates. At these locations, blood rheology not only affects the WSS and its gradient but also secondary flow patterns and the size of flow recirculation near the toe. This study reemphasizes that the rheological property of blood is a key factor in studying hemodynamic effects on vascular diseases.

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## Figures

Figure 6

Velocity vectors of the secondary flow at the cross section x∕D=2.0 for Newtonian, CY, and PL fluids at different flow rates. Orientation is the same as that in Fig. 1.

Figure 7

Normalized axial WSS in the host vessel for Newtonian, CY, and PL fluids at different flow rates. The vessel is cut open along the toe wall. The y axis represents the circumferential length and is normalized by πR. The x axis is the axial distance in the host vessel. The location of the “bed” is denoted by X.

Figure 8

Zero WSS contours for Newtonian, CY, and PL fluids at different flow rates in the host vessel. In the figure, the host vessel is cut open along the bed wall, unlike in the previous figure where the host vessel is opened up along the toe wall (i.e., the middle dashed line in this figure). — Newtonian; ------ CY; ⋯⋯⋯ PL

Figure 9

Normalized WSS along the bed wall (left panel) and the toe wall (right panel) of the host vessel at three flow rates. — Newtonian; ------ CY; ⋯⋯⋯ PL

Figure 1

Model geometry of the nonplanar end-to-side anastomosis. The bypass graft and the host vessel have the same diameter (D) and intersect at 45deg angle. The curved bypass graft has three sections: from the inlet, a straight tube of 1D in length connects to a 90deg torus with a ratio of curvature of 1∕4, which in turn connects to a straight tube of 1.5D in length. The torus is in a plane perpendicular to that of the intersection. The x axis is at the center of the host vessel and x=0 is where the toe exists. The host vessel is fully occluded at x=−3D with the outlet at x=10D. (a) Mesh grid and locations of the heel, toe, and bed in the Cartesian coordinates. (b) Mesh grid in a cross section of the vessel and locations of four walls.

Figure 2

Blood viscosity at different shear rates. Comparison between Newtonian and non-Newtonian model predictions and experimental data by Biro (33).

Figure 3

Axial velocity profiles of a Newtonian fluid in the symmetric plane in a 90deg curved tube at Re=700. The inner and the outer walls are denoted by I and O. Velocity is normalized by the mean velocity. Open circles (○) represent experimental data by Bovendeerd (35). Solid circles (●) are numerical results by Rindt (36). Solid lines are results from the current study.

Figure 4

Normalized axial velocity profiles for Newtonian and non-Newtonian fluids in the x‐y (top panel) and x‐z (bottom panel) planes at eight axial distances in the host vessel. (a) Q=5.16ml∕s (Re=250 for the Newtonian fluid); (b) Q=8.26ml∕s (Re=400 for the Newtonian fluid). — Newtonian; ------ CY; ⋯⋯⋯ PL

Figure 5

Normalized axial velocity contours and secondary flow streamlines at four cross sections in the host vessel at Q=12.39ml∕s (Re=600 for the Newtonian fluid). Orientation is the same as that in Fig. 1.

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