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Viscoelastic behaviour of human blood and polyacrylamide model fluids for heart valve testing
Dietmar Lerche, Georgios Vlastos, Brigitte Koch, Manfred Pohl, Klaus Affeld
To cite this version:
Dietmar Lerche, Georgios Vlastos, Brigitte Koch, Manfred Pohl, Klaus Affeld. Viscoelastic behaviour of human blood and polyacrylamide model fluids for heart valve testing. Journal de Physique III, EDP Sciences, 1993, 3 (6), pp.1283-1289. �10.1051/jp3:1993198�. �jpa-00248998�
Classification Physic-s Abstracts
46.60 87.45 87.45F
Viscoelastic behaviour of human blood and polyacrylamide
model fluids for heart valve testing (*)
Dietmar Lerche(I), Georgios Vlastos(I), Brigitte Kochl'), Manfred Pohll') and
Klaus Affeld (2)
(1) Inst. Med. Phys. Biophysics, Med. Faculty Charitd, Humboldt University, 0-1040 Berlin, Germany
(2) Biofluid Lab., Virchow Hospital, Free University, Berlin, Germany
(Receii,ed 19 October 1992, revised 21 January 1993, accepted 8 March 1993)
Abstract. New heart valves and other cardiovascular assist systems have to be tested for
hydrodynamic performance. In place of human blood simple model fluids like glycerol solutions
are employed often due to ethical and practical reasons. But blood exhibits complex non- Newtonian and viscoelastic behaviour. Rheological blood properties are reviewed based on literature and own experimental results. Furthermore we studied polymer solutions with respect to blood-like flow behaviour. Rheology was assessed by means of the low shear rotational viscometer (LS 40, Mettler-Toledo, Switzerland) under stationary and dynamic shear conditions (variation of
frequency and angular displacement).
Introduction.
Based on ISO- as well as FDA-standards, artificial blood pumps, artificial heart valves but %lso grafts have to be tested for hydrodynamic performance [1, 2]. Furthermore, fluid dynamic
hypothesis of atherogenesis [3], based on the finding that atherosclerotic lesions are found
primarily at arterial bends and bifurcations, motivated numerous studies to link flow disturbances at these sites to vessel (graft) geometry and wall elasticity, to pulsatility of flow and local shear stress values [4, 5].
As human blood is not always available due to ethic reasons or in quantities necessary and, additionally, some measurements and visualization techniques are not applicable to blood, different model fluids are employed e.g. [6]. However, these model fluids used are often very different from the rheological behaviour of normal and even more of pathological blood, which is known to exhibit non-Newtonian, thixotropic and viscoelastic properties [7-9]. As was shown theoretically, flow fields of non-Newtonian fluids in relevant geometries differ from those of Newtonian liquids [10, 11] and this was as well demonstrated experimentally [12,
(*) Paper in part presented at Intemational Conference Fluid Mechanics, Alexandria, April 28-30, 1992.
1284 JOURNAL DE PHYSIQUE III N° 6
13]. Furthermore, any « blood-like » model fluid should not only mimic the shear rate
dependent energy dissipation, but also the storage/release of energy as shear rates change with time or position.
Therefore, hydrodynamic studies in vitro have to employ model fluids, which match the shear dependent viscous energy dissipation and the storage/release of elastic energy, to get flow pattem of high relevance to hemodynamic in vivo events.
Materials and methods.
Static and dynamic viscosity determinations were performed by means of the computer
controlled rotational viscometerLS40 (Mettler-Toledo, Switzerland) with the DIN 412
measuring system at 25 °C. Shear dependent apparent viscosity was measured starting from 100 s~l and decreasing the shear rate by 41 steps within 400 s (automatic sensitivity change, preshearing time 15 s at loo s-'). Complex viscosity was determined by measuring protocols incrementing the frequency from 0.2 Hz to 6 Hz (20 steps) while holding angular displacement fixed, or incrementing the angular displacement from I° to 60° at a given frequency. In some series a stationary shear rate (I s~'-5 s~') was superposed to the oscillatory shear. Data
analysis was performed by means of the software package LS 40 AT (1.0).
Human blood from healthy volunteers was drawn by venipuncture and anti-coagulated with
heparin. Volume concentration of red blood cells (RBC) was adjusted to 0.45 (hematocrit) by autologous plasma, samples stored at room temperature and measured within 5 hours.
Polyacrylamide of different molecular weights (Nordfloc AP 273E, AP 45E, AP 30E ; Nordmann, Rassmann GmbH & Co., Hamburg) was used to prepare model fluids. To study
the influence of different solvents on viscoelastic behaviour of polyacrylamide solutions
especially with regard to the long-term stability of the model fluids, the dry powder was
dissolved in water or Mgcl~-solutions (ionic strength effects) with or without isopropanol (2.6w/w%) under permanent stirring for 4 hours. Solutions prepared were stored at a
temperature of 4 °C and measured the next day. Short term stability of these solutions was
proved in preliminary studies.
Viscosity and viscoelasticity of blood and model fluids.
It is well known and experimentally documented that human blood exhibits non-Newtonian
viscosity and nonlinear viscoelasticity [7-9, 14, 15]. Steady shear absolute apparent viscosity
of normal and abnormal blood exhibits a large variability (Fig. I) and depends beside the plasma viscosity (Newtonian fluid) and RBC volume concentration on microrheological properties of RBC as there are aggregability (rouleaux formation, especially pronounced at low shear rates) as well as deformability and orientability due to high shear stress [7, 9]. There are
numerous theoretical, semi-empirical and empirical constitutive viscosity equations to
describe stationary and dynamic blood viscosity [15]. The Quemada approach has its
advantage due to rheological interpretation of the different parameters involved [7]. The hematocrit dependent and shear rate dependent intrinsic viscosity depends on a coefficient, closely related to RBC deformation and orientation at high shear rate, k~, as well as on a
parameter related to RBC-RBC interaction (rouleaux formation and particle crowding) at low shear rates, ko. Furthermore, a critical shear rate f~ is defined, which may be interpreted as a
mean relaxation time of shear dependent structural transitions of the flowing blood. Quemada equation [7] was fitted to relative apparent blood viscosity at native hematocrit (0.45 ± 0.03) for healthy controls (Fig. I) and the corresponding mean intrinsic viscosities and standard
deviations (n =19) for high and low shear rates as well as the critical shear rate read
k~
= 1.53 ± 0.43, ko = 4.01 ± 0.29 and j~ = (7.4 ± 8.9 ) s~ ' Nowadays independent
~
i oo
)
~
o i
o
fir
i
o.oi o-i i io ioo
Steady Shear Rate [I/sl
Fig. I. Apparent absolute steady shear blood viscosity of normal, healthy subjects (~l, mean ± s-d-,
n = 19), of a hypercholesterolic patient (O) and of a blood sample incubated with X-ray contrast media (li). Solid line is the nonlinear regression curve fitting the Quemada equation to experimental data points.
methods are employed to analyze the rheological behaviour and to get a better insight into the
microrheological properties of blood [9]. Viscoelasticity of human blood is also an important feature. As figure 2 reveals, there is a very strong dependence of complex and elastic viscosity
on maximal oscillatory shear rate (f~~,). The component of elastic viscosity decreases
markedly with increasing f~~~ and for f~~~~20s~' complex viscosity is predominatly determined by the viscous component. This is true independently whether the j~~~ is obtained by changing angular displacement at constant oscillatory frequency (in the above case 0.5 Hz)
or altering frequency at constant displacement (data not shown). Viscous component does not
depend on j~~~ up to about I s~' and decreases than steadily approaching values of the
complex viscosity for j~~, m 20 s~' These results
are principally in agreement with findings
obtained by oscillatory tube flow at constant frequency [8, 141. We investigated furthermore the influence of a superposed steady shear rate on viscoelasticity. As shown in figure 2 for j =
2 s~ ~, the elastic component of complex viscosity is dramatically reduced especially in
the low shear region. Complex viscosity is altered accordingly, whereas the viscous
component did not change (data not shown). This is an important finding taking into account that blood flow in the most arterial trees is, despite its pulsatility, a foreward flow.
Solutions of polyacrylamideAP273E, AP45E and AP30E were used at different
concentrations. In general, as higher the molecular weight and concentration, as higher the
steady shear viscosity. With respect to shear rate dependence all of these solutions are non- Newtonian and exhibit pseudo-plastic or shear rate thinning behaviour (Fig. 3). As higher the polymer concentration as well as the molecular weight, as lower is the critical shear rate to reach the limiting low shear condition, that means. a shear rate independent viscosity. But in
general, if the non-Newtonian behaviour is in the corresponding shear rate region of blood, apparent viscosity is higher than the blood one. If however, ionic strength is increased by
1286 JOURNAL DE PHYSIQUE III N° 6
20
$ ~ ~-4-&-A~
~s~
O
~
~§
W iQ
_@
= W O U
£
~ 5
o
o-i i i o ioo
Osci. Shear Rate [I /s]
Fig. 2. Complex viscosity (O), viscous (li) and elastic (~l) component of blood (Hct 0.45) in
dependence on maximal oscillatory shear rate (representative data). Full and blank symbols represent data of the same sample but of different sensitivity ranges of LS 40. The full line indicates measurements of only oscillatory shear (0.5 Hz, angular displacement 0.30°-60°) and the broken line those with
superposed steady shear (f 2 s~ ').
iooo
I ioo
?
E (
~
~~~~~~
i ~~~
,°' 10
>
50
o.oi o-i i io ioo
Steady Shear Rate [I /s]
Fig. 3. Apparent steady shear viscosity of different aqueous polyacrylamide solutions (O, AP 273E X, AP 30E) of different polymer concentrations (indicated in ppm). Full circles (.) represent data of
250ppm AP 273E dissolved in an isopropanol (2.6 %)-electrolyte (0.98 mmolfl Mgcl~)-solvent. For
reason of cleamess curve fitting (solid linesl in accordance with Quemada equation is only shown for
AP 273E (250 ppm) and AP 30E (50 ppm).
adding Mgcl~, steady shear viscosity may gradually be decreased (data not shown). A 250 ppm solution of AP 273 E (Mgcl~-electrolyte solvent, 0.98 mmol/I) behaves, on the one hand, at high shear rates (~ 50 s~ ~) like a 125 ppm solution and, on the other hand, at low shear rates (< 0.05 s~') similar to 80ppm AP273E-solution. In general, an appropriate MgC12-concentration decreases the shear rate region, in which the non-Newtonian behaviour is exhibited and the rheology of polyacrylamide solution renders more the blood one as shown in figure I and quantitatively described by means of the three parameters of the Quemada model at given hematocrit (volumen concentration). As shown in figure 3, the relative
viscosity to shear rate dependence may be also fitted to the Quemada model. From a
rheological point of view a direct comparison of the intrinsic viscosities as well as of the critical shear rate with the corresponding values of blood is not very meaningful as these
parameters depend on volume concentration, which differs considerably between both fluids.
But the corresponding fit parameters obtained at a apparent volume concentration of 0.45 are useful with respect to a pragmatic quantitative comparison.
Complex viscosity, their viscous and elastic components, respectively, are demonstrated at
figure 4. Linear viscoelastic behaviour was found to be different for the viscous and elastic component and, in general, depending on the polymer concentration. In the low shear region
under most experimental conditions elastic component of complex viscosity was found to be
higher than the viscous one, as shown in figure 4. This behaviour reverses as a steady shear rate (j
= 2 s~') is superposed due to a pronounced reduction of the elastic component. As
higher oscillatory shear rates (f~~~) as more the complex viscosity and the elastic viscosity approaches those values which were obtained without a superposed steady shear rate. In
20
_
5
o~
~i
D-
E
u~
w 10
~w
wI
~D,a-a-a,a-D-°-°-°
m*«m~
w D
m
5 5
'
o
o-i i io ioo
Osci. Shear Rate [I /s]
Fig. 4. Complex viscosity (O), viscous (li) and elastic (~l) component of AP 273E (Isopropanol (2.6 %)-electrolyte (0.98 mmolfl MgC12)-solvent) in dependence on maximal oscillatory shear rate. Full and blank symbols represent data of the same sample but of different sensitivity ranges of LS 40. The full line indicates measurements of only oscillatory shear (0.5 Hz, angular displacement 0.18°-60° ) and the
broken line those with superposed steady shear (j = 2 s~ ').
1288 JOURNAL DE PHYSIQUE III N° 6
contrast, viscous component is not affected by a superposed steady shear rate of
f w 2 s~ In future experiments, the behaviour of other « model fluids » [14, 161 have to be
investigated with respect to the above results.
Conclusion.
Non-Newtonian steady shear viscosity of normal blood may be mimicked by polyacrylamide
solutions of appropriate concentration and molecular weight. The low shear to high shear
viscosity ratio is reduced by increasing salt concentration (ionic strength). But, in general, if the high shear rate region (I s~'-10D s~') is modeled also quantitatively, limiting low shear
viscosity of model fluids investigated is rather low compared to blood. Viscoelastic behaviour
of model fluids chosen shows principally the same features as blood does. But at low
oscillatory shear rates, in contrast to blood, the elastic component often dominates the viscous component of polyacrylamide solutions. If a steady shear ratb of up to f
= 5 s~' is superposed
to oscillatory shearing, generally, viscous component is hardly changed but elastic component of viscosity is considerably reduced. For normal blood this alteration is more pronounced than for polyacrylamide solutions.
Acknowledgments.
This work was supported in part by the Deutsche Forschungsgemeinschaft (Af3/10-1).
Polyacrylamide was graciously supplied by Nordmann, Rassmann GmbH & Co (Hamburg).
References
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