Biomedical Engineering Reference
In-Depth Information
4.3
Viscosity of Blood
In general the viscosity of blood is a function of plasma viscosity (which is rela-
tively constant) and viscosity of the formed elements (not constant). When the ve-
locity is constant, blood behaves like a Newtonian fluid since the blood cells do not
deform. But this is not the case for large velocity changes where blood cells deform
and move in different proximity to the vessel walls, both of which influence its vis-
cosity. Viscosity of blood is influenced mainly by the red blood cells and to a lesser
extent, blood vessel diameter, shear rate, and temperature.
Red blood cells occupy 99.7 % of all formed elements, and are a major determi-
nant for the difference between plasma and blood viscosity. The remaining volumes
contain white blood cells and platelets which contribute 0.16% and 0.12 % of the
total formed elements, respectively (Popel and Johnson 2005). The percentage of
whole blood occupied by the formed elements is called the
haematocrit
. Since red
blood cells occupy almost the entire formed elements, the haematocrit is commonly
reported as the volume of packed red cells. In adult males the average haematocrit
value is 46 (range: 40-54), while for females it is 42 (range: 37-47).
The viscosity of plasma is
µ
− −−
3
11
=× ⋅
and this increases when red
blood cells are considered. The size, shape, and flexibility of red blood cells are
influencing factors to its viscosity. The viscosity of whole blood at hematocrit of
45 % is approximately
1.2
10
kg m
s
µ
− −−
3
11
=×
about 4-5 times of water. A change
in haematocrit means that the volume occupied by the red bloods changes and this
has a significant effect on viscosity; one unit increase in haematocrit can cause
up to a 4 % increase in blood viscosity (Baskurt et al. 2007). Figure
4.2a
high-
lights the influence of haematocrit levels on viscosity which shows a non-linear
relationship.
When exposed to increasing shear, the viscosity decreases. The rate of shear (i.e.
rate of deformation) of a fluid flowing between the centre of a blood vessel and its
walls is defined by
3.2
10
kgm
s
u
h
γ=
(4.1)
where
γ
is the shear rate, measured in reciprocal seconds;
u
is the velocity of the
fluid; and
h
is the distance from the vessel wall. Increased shear rates occur when
there are high velocities in the vessels. This causes red blood cells to move towards
the centre of the vessel and orient in the flow direction, reducing its viscosity. For
low velocities, the viscosity is highest as the red blood cells become more evenly
distributed throughout the vessel. For extremely low velocities, red blood cells can
aggregate, which increases the viscosity dramatically. The influence of shear rate is
shown in Fig.
4.2b
.
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