Journal
of the
University
of Chemical
Technology
Metallurgy,
1, 2009
Journal
of the
University
of Chemical
Technology
andand
Metallurgy,
44,44,
1, 2009,
50-54
BLOOD RHEOLOGY - A KEY FOR BLOOD CIRCULATION IN HUMAN BODY
M. Karsheva, P. Dinkova, I. Pentchev, T. Ivanova
University of Chemical Technology and Metallurgy
8 Kl. Ohridski, 1756 Sofia, Bulgaria
E-mail: [email protected]
Received 19 December 2008
Accepted 16 February 2009
ABSTRACT
In the present work the rheological behaviour of the whole blood of healthy persons in relation to its parameters
(hematocrite, hemoglobin and RBC) was investigated. It was found that the whole blood exhibits non-Newtonian behaviour
which can be described by the power law rheological model. The blood apparent viscosity in women is lower than that in
men which can be explained by lower HCT values for the females. The observed HCT values are not always directly
related to the erythrocytes number it depends also on the RBC dimensions. The dependencies of the rheological parameters K and n on the hematocrite values are found. Both dependencies could be described by linear relationship with HCT.
The dependencies of the rheological parameters on the RBC concentration are also found. The dependency of K on RBC
could be described by 2nd degree polynomial relationship. On the other hand the flow index values are almost unaffected
by the erythrocytes’ concentration. So it could be taken a mean value for n.
Keywords: blood rheology, hematocrite, RBC concentration.
INTRODUCTION
Biorheology is the branch of biological sciences
that studies the flow and deformation of biological material under the influence of constraints applied to it.
The part of the biorheology focusing on blood is termed
hemorheology. Its purpose is therefore to study the flow
of the blood in interaction with its surrounding environment, in both macro- and microcirculation. The
blood is a fluid circulating in the human body and transferring the oxygen from the lungs to all important organs of the body. As a tissue the blood consists of cells
and intracellular substance – plasma, i.e. the blood can
be treated as a suspension. The blood cells are: erythrocytes or red blood cells (Er or RBC), leucocytes (leuc)
and trombocytes (Trh) suspended in the blood plasma.
One of the most important characteristics of the
blood is the hematocrite which is the relationship be-
50
tween the cellular volumes as compared with the total
blood volume. Thus the normal hematocrite values are
between 40 and 45 %, meaning that that corresponds to
the globular volume. The hematocrite rises with the
plasma volume decrease, or the globular volume increase, or both. The increased hematocrite values are
observed when the organism was dehydrated. Decreasing of these values is observed when the globular level
lowers, case typical for the anaemia disease. The normal hematocrite values for the men are higher then for
the women. For the vein blood having normally higher
hematocrite then the arterial blood its mean value for
man is 0.45, for woman it is 0.40. This difference is due
to the larger erythrocyte number in man’s blood.
The hematocrite gives valuable information about
the changes in the number and the dimensions of RBC
as well as about the volume of the blood plasma. Its
values decrease not only with the decrease of the total
M. Karsheva, P. Dinkova, I. Pentchev, T. Ivanova
erythrocyte number, but also when more liquid enters
in the intravasale space (hydration). In the contrary, the
increase in its values is observed when the total RBC
amount increases or when the organism loses liquids,
so decreasing the plasma volume (dehydration due to
diarea, burning of a large surface of the body, etc.). The
blood viscosity increases rapidly with the hematocrit
increase.
Blood formed elements [1]. Erythrocytes, hematite or
red globules
These cells are 93 to 99 % of blood formed elements and about 45 % of blood volume, influencing
seriously the blood rheology. Its normal amount is of
5 200000 (± 300000) in men and 4 700000 (± 300000)
in women for every blood cubic millimeter
or 4.5 ÷ 5.5.1012 / l in men and 4.0 ÷ 5.0.1012 / l in
women. The total mass of circulating erythrocytes is
regulated within narrow limits, since they are responsible for carrying oxygen. However, its figure cannot be
also elevated in order not to impede the adequate blood
flow. As all blood cells do erythrocytes derivate from the
bone medulla. It is a no-nucleic cell and it possesses a biconcave disk shape. This shape allows it to have a larger
surface than if it was round. In order to get across the
capillary the red globules must deform themselves. They
are able to do it because its membrane high flexibility
which is given by a protein named spectrin. Erythrocytes
main function is transportation of oxygen and carbon dioxide. Its cytoplasm possesses a high concentration of that
protein. Blood viscosity is one of its most important properties, giving us information on the state of the human
health. Blood viscosity depends almost exclusively on blood
erythrocyte concentration (as we already mentioned the
blood is a suspension). In acute anemia, for example, blood
viscosity might reduce in half. This diminishes blood flow
resistance in peripheral vessels in such a way that the blood
amounts which flow towards the tissues and return to the
heart are much higher than normal.
Leucocytes or white globules
They are one per cent of the blood cells (between 5000 and 10000 per cubic millimeter). Leucocytes
intervene in the organism immunologic defense. So they
are mobile units and transport themselves towards specific areas of infection or inflammation.
Plaques or trombocytes
Leucocytes and erythrocytes have their origin in
cell’s maturation. In the contrary, plackets form through
the fragmentation process. Blood’s plaques amount is
150000 to 300000 per mm3. They are in charge of avoiding blood’s extravasations if an eventual damage takes
place. Plaques get together over a damage forming a
plaque cap. They also play an important role in protein
activation during coagulation since they free
tromboplastine and on the other side – serotonin (vessel
constrictor) acting over straight muscle cells of the vessels, thus helping to diminish blood’s flow in the injured area.
Plasma: an intracellular substance
Plasma is a colloidal solution, or a system of
proteins dissolved in an aqueous medium. These proteins are called plasmatic proteins and are mostly synthesized by the liver. The most abundant and the largest
is the albumin. Its main function is to transport different molecules. It possesses different electrical charges
on its surface which allows establishing unions between
the different elements it carries. Thus, molecules with
low solubility can be carried. The albumin also, joins
water molecules which produce an aqueous retention
within the intravascular compartment. Water is the largest component of plasma and acts as a solvent of plasmatic proteins and inorganic salts. These three components regulate arterial pressure.
It is evident that the hydrodynamic and mass
transfer functions of the blood are closely related to its
composition and the amount of the suspended in it red
blood cells. It could be estimated by measurement of
the rheological properties of the blood.
Recently the number of publications on this question
increases [2-7]. They are dedicated to the relationship between the blood viscosity and its other parameters (hematocrite,
lactates, etc.) in trained and untrained persons as well as to
the effect of the exercise on these properties.
In the literature different experimental conditions and methods are reported. Different rheometers
were used for the studies (capillary, rotational, oscillating, etc.) the blood samples were prepared by different
methods, and their properties were followed for temperatures of 37 0C or of 20 0C. Therefore the data are to
be treated carefully to avoid possible errors.
51
Journal of the University of Chemical Technology and Metallurgy, 44, 1, 2009
and 3 are for the females, 4 and 5 – for male persons. It
is evident that the blood samples of the women are situated under those of the men because of their lower apparent viscosities.
The reason for this phenomenon is the lower
hematocrite of women in comparison of men with about
9 %. This fact coincides with that the RBC number in
women is lower that that in men. However the sample 2
of one female person has a RBC of 5.42 t/l and HCT of
0.385 (even lower than the normal value) and for instance, the sample 4 (male) has RBC of 4.51 and HCT of
0.471. A possible explanation of this observation could
be a certain hemodilution of the blood for sample 2.
100
τ , mPa
Blood rheology
Rheological measurements of whole blood and
red blood cell suspensions demonstrate unique nonNewtonian behaviour, i.e. yield stress, shear thinning,
thixotropy and viscoelasticity. However, few studies have
quantitatively considered the viscoelastic relaxation of
blood cells and links with bulk rheology are not established [8].
A number of the literature data concern the blood
rheology studied with rotational viscometers with coaxial cylinders or cone-and-plate [2, 9,12], falling ball
viscometers at high shear rates [10], tube viscometers
[11] at low shear rates, and oscillating flow tube viscometers to measure the elastic properties of blood [12].
Different shear rates and temperatures, as well as different methods for blood preservation are used, so it is
quite difficult to make a direct comparison of the results of different authors. Usually, only an apparent viscosity for a given shear rate (or shear stress, depending
on the measuring device) are presented, not the whole
flow curves.
The aim of the present work was to study the
rheological behaviour of the whole blood of healthy
persons in relation to its parameters (hematocrite, hemoglobin and RBC).
80
TAU2j
60
TAU3j
40
TAU4m
20
TAU5m
0
0
500
1000
γ ,s
1500
-1
Fig. 1. Typical flow curves for whole blood of males and
females.
EXPERIMENTAL
Materials and methods
Blood was sampled from 10 healthy male and
female volunteers in vacuteiners containing EDTA as
anticoagulant. The rheological measurements were made
using a co-axial cylinder viscometer Rheotest RV2.1
(Germany) with N cylinder (sample volume of 11 cm3).
The flow curves were taken at temperature of 200C.
Unique analysis with Z cylinder showed no slip effect
on the wall, but it was found that sensibility of the device was not enough for that experiments. That was the
reason to continue the experiments with N cylinder.
The hematological analyses were done in authorized
laboratory, where the values of hematocrite, RBC and
hemoglobin were determined.
RESULTS AND DISCUSSION
In Fig. 1 four typical flow curves: two for male
and two for female persons, are presented. Samples 2
52
From the figure it can be seen that the flow
curves are non linear without intercept and can be described by the power law rheological model:
τ = Kγ n
Here K is the consistency index, characterizing
n
the sample consistency, mPas ;
n is the rheological flow index (more it differs
unity, more the fluid is non-Newtonian);
τ is the shear stress, mPa;
γ is the shear rate, s-1.
The rheological parameters of the samples were
found statistically using MSExcell.
In Fig. 2 the dependencies of the rheological parameters on the hematocrite values are presented. It was
found that both dependencies could be described by
linear relationship with HCT. The equations found give
satisfactory accuracy: Maximal relative error for K being 14 %, for n – 4.9 %
M. Karsheva, P. Dinkova, I. Pentchev, T. Ivanova
1,4
K
1,2
n
K,n
1
0,8
Linear (n)
0,6
Linear (K)
0,4
0,2
K,n
1,4
1,2
1
0,8
0,6
0,4
0,2
0
K
n
Linear (n)
Poly. (K)
4
0
0,3
0,4
5
6
7
8
RBC,T/L
0,5
HCT
Fig. 2. Dependency of rheological parameters of the power
law model on the HCT values.
The equations obtained are:
K = 0.8693HCT + 0.6707
n = 0.4604 HCT + 0.3994
In Fig. 3 the dependencies of the rheological parameters on the RBC concentration are presented. It
was found that the dependency of K on RBC could be
described by 2nd degree polynomial relationship:
K = 0.0955RBC 2 − 1.0278RBC + 3.7423
On the other hand the flow index values are almost unaffected by the erythrocytes’ concentration. So
it could be taken a mean value for n. The equation found
give satisfactory accuracy: maximal relative error for K
being 19,8 %, for n – 6.9 % compared to its mean value.
Some interesting observations could be done from
the data. The male person with a hematocrite value of
0.482 has a RBC concentration of 4.51 (the highest HCT
with not very high RBC). The possible explanation of
this observation could be the dimensions of RBC: is they
are large; the volume RBC concentration (hematocrite)
will be high. On the other hand, the same person exhibits
not very high values of the consistency index and quite
high flow indexes n, which confirms the proposed explanation. The already commented observation for low HCT
values at high RBC concentration may has similar explanation – smaller erythrocytes would give low vol/vol concentration at quite large number per volume.
Fig. 3. Dependency of rheological parameters of the power
law model on the RBC concentration.
CONCLUSIONS
From the experiments done the following conclusions could be driven:
• The whole blood exhibits non-Newtonian
behaviour which can be described by the power law
rheological model.
• The blood apparent viscosity in women is lower
than that in men which can be explained by lower HCT
values for the females.
• The observed HCT values are not always directly related to the erythrocytes number it depends also
on the RBC dimensions.
• The dependencies of the rheological parameters K and n on the hematocrite values are found. Both
dependencies could be described by linear relationship
with HCT.
• The dependencies of the rheological parameters on the RBC concentration are also found. The
dependency of K on RBC could be described by 2nd
degree polynomial relationship. On the other hand the
flow index values are almost unaffected by the erythrocytes’ concentration. So it could be taken a mean
value for n.
Acknowledgements
This work was supported financially by the Research Sector of UCTM-Sofia, contract No 2/87-2009.
53
Journal of the University of Chemical Technology and Metallurgy, 44, 1, 2009
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