Vascular Cell Physiology Under Shear Flow: Role of Cell Mechanics and Mechanotransduction - Mechanical and Chemical Signaling in Angiogenesis - page 128

Fig. 4 Fluid shear stress acts
longitudinally on the
endothelial cells; cyclic
stretch acts perpendicular to
the flow direction caused by
the pulse pressure of the flow

mechanical constraints, wall thickness, and geometry. Pressure extends the artery
like a balloon, the best way to measure the circumferential stretch caused by this
distension is the mean circumferential hoop stress [ 17 ]. The circumferential hoop
stress is given by, r ¼ Pr = h, where P is the blood pressure, r is the vessel inner
radius and h is the vessel wall thickness. Circumferential strains usually affect the
smooth muscle cells and the tunica media. The pulsatile nature of blood flow
forces the artery to stretch with every heart beat, and therefore stretch is affected
by the compliance of the arteries through the level of pulsation [ 37 ].
Shear stress directly affects endothelial cells that make up the intima layer [ 38 ].
Fluid shear stress is the result of friction created by blood flow and is also affected
by arterial stiffness. Shear stress is a product of blood viscosity and the velocity
gradient at the vessel wall. Although blood is a non-Netonian fluid, an assumption
can be made that the non-Newtonian behavior of blood in the circulation does not
affect the dynamics of the circulation as a whole. While this assumption may not
hold true at specific points, such as in a vessel junction, in general, fluid shear
stress can be calculated from the shear rate and the viscosity of the blood, through
the change in velocity in the vessel over the change in radius, s ¼ l d dr : For laminar
steady flow of a Newtonian fluid, the calculation of shear stress is given by:
s ¼ 4lQ

pr 2 ; where l is the viscosity, Q is the flow rate and r is the lumen radius. Shear
stress depends on the diameter of the vessel, therefore an increase or decrease in
the shear stress is associated with the increase and decrease of vessel diameter.
Thus, when compared to stiff vessels, elastic vessels with an increased diameter
could reduce the shear rate up to 30 % [ 39 ]. In a physiological artery, the mag-
nitude of shear stress is in the range of 10-40 dynes/cm 2 , whereas in a diseased
state, the shear stress can dramatically increase relative to normal levels [ 40 ]. The
shear stress influences many vascular functions, such as the permeability of
the vessel, the activity of the endothelial cells, the integrity of formed elements in
the blood, and coagulation of blood [ 41 ].
Stiffness of the proximal arteries alters the flow stress. Changes in the upstream
flow pattern are transferred to the downstream arteries affecting the mechanical
stresses on the microcirculation. Increases in pulsations caused by a stiffer artery
will result in increased shear stress and increased circumferential stress in the
microcirculation. These mechanical changes not only affect the blood flow, but
they also affect the cells and fibers embedded in the tissue walls.