Biomedical Engineering Reference
In-Depth Information
30% to 35%). This is caused by the overall slow velocity in these blood vessels and the
increase in the cell to tube ratio. It has been suggested that the endothelial cell glycocalyx
(a region of glycated membrane bound proteins that extends into the lumen) also plays a
role in the decreased hematocrit. This region may force the flow of red blood cells to the
centerline in blood vessels with a smaller diameter, but have little to no effect in blood
vessels with larger diameters. A typical glycocalyx extends for approximately 100 nm.
Upon removal of the endothelial cell glycocalyx, it has been seen that the capillary hemat-
ocrit increases, but not back to the inflow hematocrit levels.
Taken together, blood vessels with a relatively high ratio of blood cell diameter to tube
diameter have a lower than normal hematocrit. This is partially caused by the fluid
dynamics (velocities, no-slip boundary condition, and diameter relationship), but may also
be partially regulated by biological factors (such as the glycocalyx).
In the early 1930s, a number of studies were conducted by Fahraeus and Lindquist to
determine the effects of vessel radius on viscosity and hematocrit. For these experiments,
the diameter of the tube was restricted to be less than 250
m and the shear rate was rela-
tively high as compared to the normal microcirculation, approximately 100 s
2
1
. The shear
rate was this large so that the flow in the feeding tube would be Newtonian. The pressure
difference across the tube and the volumetric flow rate were quantified and fit to the
Hagen-Poiseuille equation. Interestingly, the normal relationship was not dependent on
the bulk viscosity of the fluid, but instead it was dependent on an effective fluid viscosity.
It has been experimentally shown that the new Hagen-Poiseuille relationship that is valid
for flows within the microcirculation is represented as
μ
5
πΔ
Pr
4
Q
ð
6
:
13
Þ
8
μ
eff
L
where
μ
eff
is the effective viscosity of the fluid within the microcirculation. The effective
viscosity is highly dependent on the diameter of the blood vessel and the pressure drop
across the blood vessel.
In general, the effective viscosity reduces with a decreasing tube radius. For a hemato-
crit of 40%, the normal blood viscosity is in the range of 3.5 cP. As the diameter of the
blood vessels reduces to 1 mm, the effective viscosity will reduce by approximately 5%.
However, for blood vessels that are smaller than 500
m, the reduction in viscosity is
much more pronounced, and it approaches 2 cP in blood vessels with a diameter less than
50
μ
m. Within blood vessels with a diameter in the range of the red blood cell diameter,
the viscosity increases rapidly again due to plug flow principles (see
Section 6.8
). These
results were explained by the presence of a plasma layer along the blood vessel wall. This
layer is void of red blood cells, consisting solely of plasma, which has a viscosity of
approximately 1 cP (i.e., water). Because this low viscosity solution is next to the wall,
where the shear stresses would be the highest, the overall viscosity of the fluid reduces.
Also as discussed above, red blood cells stream to the centerline and move with the rapid
flow.
To more accurately describe the presence of a plasma layer, one must consider the
hemodynamic forces that act on a red blood cell. Because a red blood cell has a size associ-
ated with it (i.e., it is not a particle), then the forces that act on the cell must satisfy
μ
Search WWH ::
Custom Search