Page 104 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

PHYSICAL AND FLOW PROPERTIES OF BLOOD 81

FIGURE 3.8 Schematic description of the skewed axial velocity profile and
the secondary motions developed in a laminar flow in a curved tube.

where r is the tube radius and R is the radius of curvature. As De increases, the maximal
curve
axial velocity is more skewed toward the outer wall. Dean’s analytic solutions are limited to
small ratios of radius to radius of curvature for which De < 96. However, numerical solutions
extended the range up to 5000. Blood flow in the aortic arch is complex and topics such as
entry flow from the aortic valve, pulsatile flow, and their influence on wall shear stress have
been the subject of numerous experimental and numerical studies (Pedley, 1980; Berger et al.,
1983; Chandran, 2001).

3.3.7 Flow in Bifurcating and Branching Systems
The arterial system is a complex asymmetric multigeneration system of branching and bifurcating
tubes that distribute blood to all organs and tissues. A simplified arterial bifurcation may be repre-
sented by two curved tubes attached to a straight mother tube. Accordingly, the pattern of blood flow
downstream of the flow divider (i.e., bifurcating region) is in general similar to flow in curved tubes
(Fig. 3.9). Typically, a boundary layer is generated on the inside wall downstream from the flow
divider, with the maximum axial velocity just outside the boundary layer. As in flow in curved tubes,
the maximal axial velocity is skewed toward the outer curvature, which is the inner wall of the
bifurcation.
Comprehensive experimental and computational studies were conducted to explore the pattern
of blood flow in a branching vessel, energy losses, and the level of wall shear stress in the branch
region (Ku and Giddens, 1987; Pinchak and Ostrach, 1976; Liepsch et al., 1989; Liepsch, 1993;
Pedley, 1995; Perktold and Rappitsch, 1995). Of special interest are the carotid bifurcation and the
lower extremity bypass graft-to-artery anastomosis whose blockage may induce stroke and walking
inability, respectively. A recent review of computational studies of blood flow through bifurcating
geometries that may aid the design of carotid endartectomy for stroke prevention and graft-to-artery
configuration may be found in Kleinstreuer et al., 2001.