Determination of rheological properties of red blood cells by Couette viscometry

About: The article was published on 1980-08-01 and is currently open access. It has received 18 citations till now. The article focuses on the topics: Viscometer & Viscosity.

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Determination of rheological properties of red blood
cells by Couette viscometry
J. Dufaux, D. Quemada, P. Mills
To cite this version:
J. Dufaux, D. Quemada, P. Mills. Determination of rheological properties of red blood cells by
Couette viscometry. Revue de Physique Appliquée, Société française de physique / EDP, 1980, 15 (8),
pp.1367-1374. �10.1051/rphysap:019800015080136700�. �jpa-00244860�

1367
Determination
of
rheological
properties
of
red
blood
cells
by
Couette
viscometry
J.
Dufaux,
D.
Quemada
and
P.
Mills
L.B.H.P.,
Université
Paris
VII,
2,
place
Jussieu,
75221
Paris
Cedex
05,
France
(Reçu
le
17 janvier
1980,
révisé
le
5
mai
1980,
accepté
le
9
mai
1980)
Résumé.
2014
L’utilisation
d’un
viscosimètre
Couette
à
cylindres
coaxiaux
permet
la
mesure
de
la
viscosité
de
suspensions
de
globules
rouges
dans
une
gamme
de
cisaillement
variant
de
0,017
5
s-1
à
128
s-1.
L’état
d’agré-
gation
et
l’état
de
déformation
des
globules
sont
obtenus
en
adaptant
les
paramètres
d’une
relation
rhéologique
aux
résultats
expérimentaux.
Différents
types
de
suspensions
de
globules
rouges
sont
étudiés.
Une
application
aux
cas
pathologiques
est
proposée.
Abstract.
2014
The
use
of
a
Couette
viscometer
with
coaxial
cylinders
enables
us
to
measure
the
viscosity
of
red
blood
cell
suspensions,
the
shear
rate
varying
from
0.017 5
s-1
to
128
s-1.
Red
blood
cells
aggregation
and
defor-
mation
states
are
obtained
by
fitting
a
rheological
relation
on
experimental
results.
Different
types
of
suspensions
are
studied.
An
application
to
pathological
cases
is
proposed.
Revue
Phys.
Appl.
15
(1980)
1367-1374
AOÛT
1980.
Classification
Physics
Abstracts
46. 30R
1.
Introduction.
-
The
use
of
low
shear
rate
vis-
cometers
in
the
field
of
biorheology
has
enabled
scientists
to
show
that
the
viscosity
of
whole
human
blood
collected
on
anticoagulant
increases
greatly
when
the
shear
rate y
decreases
below
10 s-1.
The
non-newtonian
characteristic
of
this
fluid
is
due
to
several
factors
which
play
a
very
important
part,
such
as :
-
the
deformability
of
the
red
blood
cells
(RBCs),
--
the
aggregation
of
RBCs
(formation
of
rou-
leaux),
-
the
electrical
level
of
the
RBCs
membrane,
-
the
composition
of
plasma
and
its
physico-
chemical
state.
The
study
of
the
influence
of
blood
viscosity
on
blood
flow
has
always
been
main
topic
of
interest.
The
importance
of
stasis
in
inflammatory
reactions
and
of
RBCs
aggregation
in
shock
due
to
haemor-
rhagics
or
burns
has
clearly
been
shown
[1].
Unfortunately
the
quantitative
aspect
of
the
problem
brought
about
in
rheology
for
concentrated
medium
has
until
the
past
few
years
come
up
against
the
lack
of
satisfactory
theoretical
studies.
Many
of
the
laws
relating
the
viscosity
to
concen-
tration 11
=
11(C)
that
we
may
call
empiric
or
partially
empiric
have
been
put
forward.
These
laws
give
the
Einstein
relation
when
the
volumic
concentration
e
~
0,
such
as :
-
the
Brinkman-Roscoe
law
[2]
-
the
Mooney
law
[3]
where
03BB
= 1 cM,
c
being
the
packing
concentration
and
non-newtonian
laws
i
=
~.03B3
=
03C4(03B3),
such
as
the
Casson
law
[4]
where
i -
shear
stress,
03C4y
=
yield
shear
stress,
03B3
=
shear
rate.
It
seems
that
these
laws
only
allow
the
rheological
behaviour
of
human
blood
within
a
limited
range
of
concentration
and
shear
rates.
On
a
basis
of
the
optimization
of
viscous
energy
dissipation,
a
new
theoretical
approach
has
been
developed
by
one
of’
us
[5].
It
has
led
to
the
rheological
relation :
where
il, =
relative
viscosity,
fi
=
suspension
viscosity,
fi p
=
plasma
viscosity,
H
=
suspension
hematocrit,
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:019800015080136700

1368
k =
the
effective
intrinsic
viscosity
that
can
be
considered
as
a
function
of
maximum
concen-
tration
Hm
relating
to
the
packing
of
RBCs
that
solidify
the
suspension :
This
law
has
been
extended
to
the
non-newtonian
behaviour
[6].
The
relation
(1)
becomes :
The
parameters
ko
and
koo
characterize
the
beha-
viour
of
the
suspension
at
zero
and
infinite
shear
rate.
When ÿ
=
0
the
RBCs
aggregation
is
the
predo-
minant
process.
When y
is
large,
rouleaux
are
dispersed
and
single
cells
are
deformed
and
oriented
in
the
flow.
The
critical
shear
rate
03B3c defines
a
characteristic
value
which
separates
the
domain
where
RBCs
aggregation
occurs
to
the
one
where
RBCs
are
dispersed
as
single
cells.
Within
the
limit 03B3
03B3c,
the
equation
fi
= f(03B3)
which
is
deduced
from
(2)
is
in
agree-
ment
with
the
Casson
law
and
allows
us
to
find
a
yield
shear
stress
[7]
given
by :
The
experimental
study
performed
in
our
laboratory
shows
the
interest
of
these
three
parameters
that
characterize
the
rheological
properties
of
different
samples
of
blood
or
RBCs
suspensions.
2.
Methodology.
- 2.1
VISCOMETRY.
-
Viscosity
measurements
are
done
by
the
means
of
a
Couette
viscometer
with
coaxial
cylinders
(L:S.
30
Contraves,
inner
and
outer
cylinders 0
= 11
mm
and 0
= 12
mm
respectively,
height = 20 mm,
Fig.
1).
The
shear
Fig.
1.
-
Body
(1
and
2)
and
its
guard
ring
3.
rate
can
vary
from
0.017
5
s-’
to
128
s-’
1
by
30
dis-
crete
values.
The
amount
of
liquid
needed
is
approxi-
matively
2
cm3.
The
apparatus
temperature
is
regulat-
ed.
The
results
that
will
be
presented
were
achieved
for
23°
+ 0.1
OC.
A
plexiglas
protection
isolates
the
measurement
cup
from
outer
disturbances
(draughts,
sound
vibrations...).
It
is
difficult
to
get
altogether
rid
of
mechanical
vibrations
transmitted
by
the
building.
We
obtained
the
most
acceptable
results
by
setting
the
viscometer
on
a
tank
that
had
been
filled
with
300
kg
of
sand.
The
setting
of
the
apparatus
was
done
and
the
manufacturer’s
testing
was
verified
with
different
newtonian
liquids
such
as
aceton,
water,
Dow
chemical
oils
(il
=
5
cP,
50
cP,
100
cP).
The
error
of the
appa-
ratus
is
lower
than
5
%
for
the
zones
of
the
diagram
il
=
f(03B3)
which
are
related
to
the
rheogram
of human
blood.
When
we
actived
the
first
measurements
with
plasma
and
human
blood
(H
=
0.30)
we
faced
the
same
problems
other
experimenters
met.
It
is
known
that
low
viscosity
measurements
are
modified
by
the
formation
of
a
semi
solid
protein
film
on
the
air
blood
interface.
A
few
drops
of
duo-
decyl
sodium
sulfate
[8]
temporely
suppresses
these
interfering
effects.
Unfortunately
microscopic
obser-
vation
shows
that
the
RBCs
are
deformed
by
this
substance.
Therefore,
such
adding
has
not
been
used.
The
technique
of
the
guard
ring
[9]
enables
us
to
avoid
this
drawback.
By
slightly
penetrating
into
the
surface
of
the
suspension
it
protects
the
bob
from
the
effects
due
to
the
film
(Figs.
1
and
2).
Fig.
2. - Guard
ring
influence.
Bovine
blood
H =
0.26.
Log 1
=
f (log
r).
a)
Without
guard
ring.
b)
With
the
guard
ring.
The
fluid
is
newtonian.
The
human
RBCs
sediment
quickly
(sedimentation
rate
=
5
mm/h
at 03B3
=
0).
Therefore
the
measurements
on
a
sample
must
be
achieved
during
a
limited
period
in
order
to
diminish
the
influence
of
this
effect.
For
normal
samples
a
period
less
than
15
seconds
for
performing
each
measurement
enables
the
obtention
of
a
rheogram
with
no
problem
whatsoever
[10].

1369
The
question
whether
during
measurements
the
shear
rate
has
to
be
increased
or
decreased
has
also
arise.
The
fact
that
we
have
chosen
the
decreasing
variation
is
justified
by
,the
fact
that
the
progressive
formation
of
rouleaux
occurs
more
regularly
when
the
shear
rate
decreases
than
they
dissociate
when
the
shear
increases.
On
one
hand
we
begin
with
a
homo-
geneous
liquid
in
which
all
the
dispersed
blood
cells
are
oriented
along
the
flow
lines.
This
structure
is
reproducible
for
different
experiments
and
various
samples.
On
the
other
hand the
structure
at
the
outset
can
be
complex,
the
network
of
rouleaux
varying
from
one
measurement
to
another.
2.2
METHOD
OF
DATA
PROCESSING.
-
The
gap
of
the
measurement
system
being
500
03BC,
we
may
suppose
that
there
is
no
plasma
layer
effects
[11].
Moreover
we
may
consider
that
in
first
approximation,
shear
rate
is
constant
inside
the
gap.
We
therefore
don’t
need
to
use
a
Krieger
and
Elrod’s
correction
[12].
The
number
of
data
we
must
analyse
is
great,
since
they
concem
the
following
relations :
~r = f(03B3),
~r = f(H),
for
normal
samples,
pathological
samples
and
samples
to
which
drugs
had
been
added.
The
use
of
a
small
computer
(H.P.
9821
A)
allows
us
to
overcome
this
processing.
A
first
program
has
been
taken
into
account
the
sensitivity
level
of
the
apparatus
and
enable
us
to
draw
the
diagram q =
f(03B3),
log q
=
f (log
),
1:
= f(03B3),
03C4
=
f(03B3)
and
to
record
the
values
of
fI,
03B3, 03C4
for
each
measurement.
A
second
program
using
a
least
squares
method
leads
to
the
parameters
ko,
k~,
03B3c
by
fitting
the
equation
(2)
on
the
resulting
data ~
= f(03B3).
Figure
3
Fig.
3.
-
Test
the
law
(2) :
0
Mr
X, e
Mr
Y.
shows
the
comparison
of
the
experimental
curve
log n
=
f (log
)
(from
which
the
3
coefficients
are
calculated)
to
corresponding
theoretical
curve.
We
can
notice
a
good
agreement.
2.3
THE
SUSPENSIONS.
-
We
have
prepared
the
suspensions
(kind
of
anticoagulants,
number
of
washings,
speed
and
duration
of
centrifugation,
duration
and
temperature
of
incubation)
in
accor-
dance
to
literature
recipes.
Viscometric
measurements
have
been
performed
on
the
following
RBCs
sus-
pensions :
-
RBCs
in
a
isotonic
physiological
serum,
-
RBCs
centrifugated
and
resuspended
in
plasma
(from
which
the
white
blood
cells
have been
pre-
viously
eliminated),
-
RBCs
hardened
by
glutaraldehyde,
-
washed
RBCs
suspended
in
Dextran
solutions
of
various
molecular
weights,
at
various
concen-
trations
and
different
ionic
strengths,
-
RBCs
ghosts
(after
hemoglobin
extraction
by
hemolysis
[13]).
The
hematocrit
has
been
measured
by
centrifugation
in
microhematocrit
tubes
at
2
000
g
during
15
min.
This
acceleration
is
insufficient
and
results
in
hemato-
crit
values
which
have
to
be
reduced
by
5
%
to
get
the
true
values.
It
would
be
necessary
to
use
a
15
000
g
centrifugation
in
order
to
eliminate
that
cause
of error.
The
data
processing
will
be
simplified
and
speeded
up
by
the
achievement
presently
underway
in
our
laboratory
of
an
interface
between
the
viscometer
and
the
computer.
This
interface
will
control
the
viscometer
and
after,
will
analyse
the
data
[14].
3.
Results.
-
3.1
SUSPENSIONS
OF
BOVINE
RBCS.
- 3.1.1
Suspensions
of
RBCs
in
autologous
plasma
and
in
saline
solution.
-
A
first
group
of
measurements
was
achieved
with
bovine
blood
and
different
sus-
pensions
of
bovine
RBCs.
Although
one
of
the
characteristics
of
human
blood,
that
is
the
formation
of rouleaux
no
occurs
in
bovine
blood,
the
importance
of
this
measurements
(Fig.
4)
was
to
test
the
metho-
dology
with
a
less
precious
fluid
than
human
blood.
The
absence
of
yield
shear
stress
on
the
figure
5
can
be
noticed.
The
results
obtained
with
the
same
blood
sample
are
shown
on
table
I.
Table
I.

1370
Fig.
4.
-
a)
Rheograms
of
washed
bovine
RBCs
suspended
in
their
plasma
for
various
hematocrits.
b)
Rheograms
for
washed
bovine
RBCs
in
saline
for
various
hematocrits.
Fig.
5.
-
Shear
stress-shear
rate
relation
03C4
=
f(03B3).
The
absence
of
yield
shear
stress
was
noticed.
These
results
support
the
meaning
of
ko
as
a
para-
meter
related
to
the
aggregating
ability
of
the
RBCs.
We
notice
hereby,
that
it
is
almost
the
same
value
for
the
two
suspensions
in
agreement
with
the
lack
of
formation
of
rouleaux.
In
this
case
ko
only
depends
on
the
concentration
without
deformation
(CM
=
0.61
for
H
0.42).
However
with
highly
concentrated
hematocrits
ko
decreases
because
of
the
RBCs
deformation
by
crowding
phenomenon
(CM
=
0.69
for
H
=
0.66
and
even
CM
=
0.77
for
H
=
0.77).
The
meaning
of
k.
as
a
parameter
of
RBCs
defor-
mation
and
therefore
of
RBCs
orientation
is
also
supported
by
these
results
which
offer,
at
same
hematocrit,
lower
values
for
plasma
(ilp
=
1.2 cP)
than
for
saline
solution
(ilp
=
0.95
cP),
the
defor-
mation
and
orientation
being
higher
in
the
former
than
in
the
latter.
Moreover
the
orientation
effect
being
greater
and
greater
as
H
increases
we
obtain
decreasing
koo
in
both
cases.
3.1.2
Suspensions
of
RBCs
hardened
by
glutaral-
dehyde.
-
RBCs
washed
three
times
in
isotonic
saline
have
been
suspended
into
a
2
%
glutaraldehyde
in
saline.
For
all
shear
rates
at
which
measurements
can
be
done,
newtonian
behaviour
is
evident
(Fig.
6).
Fig.
6.
-
Rheograms
of
bovine
RBCs
hardened
by
glutaraldehyde.
We
can
notice
the
absence
of
measurements
beyond
1
s-1
for
H
=
0.56.
It
was
impossible
to
centre
the
bob.
Applying
the
law
(1)
for
the
variation
of
viscosity
versus
concentration
gives
k
values.
Taking
into
account
hematocrit
correction
by
thé
factor
0.60
[15],
the
results
shown
in
table
II
are
obtained.
Table
II.
The
value
of k
depends
upon
the
duration
of
incubation
of
the
suspension
in
agreement
with
other
observation
[16].