Polymer/Fluids Research Group

Department of Chemical Engineering
University of Cambridge

R. M. de Roeck & M. R. Mackley


The Rheology and Microstructure of Equine Blood













The rheological nature of blood has been studied for many years. However, the ability to predict its behaviour in complex geometries (i.e. in artificial organs) is still eluding the medical engineers of today. Blood is a system rich in rheological properties, exhibiting shear-thinning, visco-elastic and sedimenting behaviour. The works of Thurston1, Chien2 et al., Schmid-Schönbein3 et al. and Copley4 et al. have already gone a long way in documenting these behaviours. Furthermore, a number of these authors have performed microscopic observations of blood under shear, reporting the presence of shear induced aggregates. But still, there have only ever been qualitative correlations made between the observed micro-structure and the reported rheology. Consequently, it is the aim of the current study to address some of the fundamental issues involved in gaining a more quantitative understanding of the blood system. Central to this issue is the determination of the intrinsic link between the rheology and the microstructure.

In an effort to model the behaviour of blood, trials of the Maxwell model have been made. Although originally designed for polymer systems, Mackley5 et al., have shown that the Maxwell model can also be used for other fluids exhibiting visco-elastic properties.

The material presented here represents only a short synopsis of the current research being undertaken.

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The Blood System

As a physiological fluid, blood is a highly complex suspension of polydisperse, flexible, chemically and electrostatically active cells suspended in an electrolytic fluid of a critical pH, in which there are numerous active proteins and organic substances. To further complicate matters, the composition of the sample blood varies from day to day, even from minute to minute, depending on the environment and activeness of the donor.

On the most simple level, blood can be broken down into four main constituent parts: red blood cells (RBCs, erythrocytes), white blood cells (leukocytes), platelets, and the suspending plasma. The phase volume (haematocrit) can be quite variable but is normally in the range 30-55%. Platelets occupy about 2% of the total blood volume, and white blood cells approximately 0.5%.

Structurally, equine red blood cells are biconcave discs of dimensions 6-7mm diameter, 2.5 mm thick at the edge and 1 mm thick at the centre. They can be envisaged as soft bags containing haemoglobin. The RBC is a highly deformable entity, as can be demonstrated when cells pass through capillaries within the body, the diameters of which are of the order 2-4 mm.

A membrane provides the cell with its shape, strength and flexibility. It consists of lipid bi-layer supported by an extensive filamentous protein network (the cytoskeleton). A number of proteins anchor the cytoskeleton to the lipid bi-layer. These proteins also provide binding sites for glycolytic enzymes that endow the RBC with its negative surface charge.




- Rouleaux





A scanning electron microscope image of equine
red blood cells stacked in a 'rouleaux.'

Aggregation is a reversible process involving the mutual binding of red blood cells. It is known that the ability of a particular blood type to aggregate is dependent on a number of factors: The presence of particular plasma proteins, notably fibrinogen and the immuno-globulins, play an important role, as do the imposed flow conditions. RBC deformability has also been seen to effect the aggregation process.

Clear differences can be seen when inter-species comparisons are made. Equine blood is a highly aggregating system, whereas bovine blood can not be induced to aggregate under any imposed flow conditions. Human blood fits somewhere in the centre of this spectrum.

The aggregates themselves have a characteristic structure, taking on the appearance of a stacked pile of coins. These formations have been named rouleaux. When the numbers of cells in a rouleaux becomes reasonably large (>10), cross links between rouleaux can be formed, resulting in an extended network.

Numerous studies have been performed in order to investigate the mechanisms of red cell aggregation, resulting in two popular hypotheses: the bridging mechanism and the depletion layer hypothesis.

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Experimental Techniques

The blood samples in the current study are heparinised (at a concentration of 50i.u./ml.) and used within six hours of withdrawal. When not in use, the blood is kept still and at room temperature. Prior to experimentation, the blood is hand agitated for 2-3 minutes in order to resuspend the cells, before further dispersion protocols within the apparatus: a pre-shear rate of 1000s-1 for at least 30 seconds immediately before an experimental run. All experiments were undertaken at 38.5C ± 1C (Temperature of equine blood in vivo).


Rheological Experiments

Rheological characterisation is performed using a Rheometrics RDSII controlled strain rheometer. Initial attempts to gain data were hampered by the very small torque transmitted through the sample. In order to increase the range of shear rates experimentally accessible, a new geometry was designed and constructed within the department. This consisted of an annulus parallel plate geometry with outer and inner diameters of 100mm and 50mm respectively. Using this geometry, it has been possible to gain almost an order of magnitude better torque resolution in steady and oscillatory experiments.

Steady shear investigations were performed to determine the shear thinning behaviour of blood, as well as thixotropic effects. Strain and frequency sweeps were also made to examine the visco-elastic response.


Microscopic Observations

Microscopic observations of blood were performed under controlled shear conditions using the Cambridge Shear System (CSS450). The system employs a similar configuration used in the RDSII except that the plates are transparent, allowing the use of an Olympus BH2 microscope. A CCD camera is mounted on the microscope column enabling the use of a video recorder and an image capture system. High resolution images were produced, providing the opportunity for an in depth analysis of the dynamics of aggregation under steady or oscillatory shear conditions

The gap width used in all CSS450 experiments was 50mm. A x20 objective was used in conjunction with a x10 column lens giving an overall magnification of approximately 200.

The Linkam Cambridge Shear System: Designed and developed in the Department of
Chemical Engineering, within the Polymer/Fluids Group.


Examples of the types of images that can be obtained from the Linkam CSS450 can be seen on the web page Nice_pics.

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Experiments were performed on whole blood of haematocrit (phase volume) 40%. The shear rate sweep presented here can be seen to demonstrate the well documented shear thinning characteristics of whole blood. However, also to be noted is an 'anomaly' seen in the shear rate region of 2-100s-1, where there appears to be a deviation from the otherwise smooth curve; the steady decrease in apparent viscosity stops abruptly at 3s-1 and is seen to rise and fall twice before a further steady decrease is seen after 100s-1. No comment on this behaviour has previously been made in the literature.

As a consequence of this observation, time was spent performing steady shear experiments at different shear rates to look for possible thixotropy, as well as to determine the validity of the observed point of inflection. The results (not shown) demonstrated a strong time dependency in viscosity in the shear rate range 1-25s-1. These findings, in conjunction with observations made using the Linkam CSS450, confirmed the presence of large scale structural changes occurring in the system. This offered a reasonable explanation of the observed anomaly observed in the shear rate sweep.


Oscillatory shear conditions were applied to the whole blood system in order to investigate its elastic and viscous response. These properties are quantified in terms of the elastic modulus (G') and the viscous modulus (G"). The relative magnitudes of the two moduli are closely related to the internal structures existing in the system.

Initially, strain sweeps were performed at different frequencies. As can be seen in the presented data, the strain sweep performed at 1rads-1 demonstrates a region of linear visco-elasticity up to a critical strain of about 10%. However, when the same experiment is performed at 10rads-1, the linear visco-elastic region is no longer seen. It is very likely that this is a function of long range ordering present at small frequencies which is broken up as the conditions become more 'violent'. This is hypothesis is reflected in the images captured on the CSS450.

When looking at the frequency sweep data, particular attention should be drawn to the way in which the G' and G" moduli behave as a function of the experimental strain parameter. As the strain parameter is increased from 1% to 100%, quite clear and distinct behaviours are exhibited in the frequency sweeps. At 10% strain,the moduli are seen to form a plateau region in the frequency range 1-10rads-1. This plateau is later seen to reduce in extent and finally vanishes at a strain of 100%, accompanied with an inversion of the G', G" traces.

The onset of this plateau region is indicative of the onset, or reordering, of structure within the system. In accordance with this statement, micro-structural observations have offered further evidence to suggest a rheological window in which conditions are more favourable for the formation of microstructure.


In almost all the reported literature, plasma is assumed to be Newtonian. However, plasma is essentially a polymeric solution, and for that reason, a number of experiments have been performed to investigate its possible visco-elastic nature.

The implications of visco-elasticity within the suspending media are far reaching. It is probable that the dynamics of the aggregation process will be effected by any visco-elasticity in plasma, and it is certain that these effects will be apparent in the flow of whole blood through complex geometries. At the moment, however, investigations are still under way.

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Cross referencing the steady shear rheological experiments with the video-captured images, it can be seen that the shear rate region spanning the observed anomaly corresponds to images depicting an extended structure. Between 1s-1 and 50s-1, the different types of structure formed are seen mainly as orientated cigar shaped clumps that decrease in size as the shear rate increases. The considerable shear thinning observed over this range is no-doubt closely related to the hydrodynamic behaviour of these different aggregate forms. A dynamic coalescence/break-up of aggregates was also observed, probably contributing to the anomalous effect. The roles of sedimentation and the formation of a cell-free plasma layers will certainly play a role in the observed rheology and hence both these areas are currently under investigation.

In contrast to the steady shear structures, the effect of oscillation can be seen to induce a network type structure in the blood sample. It is very likely that this is responsible for an enhanced elastic component observed when the blood is subject to certain oscillatory flow conditions. The effect of performing frequency sweeps at different strains has also been seen to yield markedly different results, even at strains within the classical linear visco-elastic region. With reference to the video footage, it can be seen that the type of structure formed is very much dependent on the imposed strain.


It has been known for many years that certain shear conditions can accelerate the aggregation process. The current investigations hope to take a closer look at these well documented phenomena by trying to more accurately determine the controlling rheological factors involved in this process.

On inspection of the video footage, it can be seen that there are a number of different structures formed, controlled by various flow parameters. Efforts are currently being made to quantify the structure types as well as determine the exact controlling conditions.

The protocols so far used for the rheological characterisation of blood have been loosely based on fitting resultant data to the Maxwell model. It can be seen, however, that the blood system does not exhibit the linear visco-elastic behaviour intrinsic to this model. As a consequence, investigations are being made to adapt the standard Maxwell model to incorporate structural evolution terms. This future model must be able to reflect visco-elasticity, thixotropy, the various types of structures observed, and their rheological consequences.

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1. Thurston G.B. (1970) The visco-elasticity of blood and plasma during coagulation in circular tubes. Proceedings of the Sixth Conference of the European Society for Microcirculation, Aalborg. S. Karger Basel. 1971 pp. 12-15.

2. Chien S., King R.G., Skalak R., Usami S., Copley A.L. (1975) Viscoelastic properties of human blood and red cell suspensions. Biorheology 12 pp. 341-346.

3. Schmid-Schönbein H., Gosen J.V., Heinich L., Klose H.J., Volger E. (1973) A counter-rotating 'rheoscope chamber' for the study of the microrheology of blood cell aggregation by microscopic observation and microphotometry. Microvascular Research 6 pp. 366-376.

4. Copley A.L., King R.G., Chien S., Usami S., Skalak R. (1975) Microscopic observations of visco-elasticity of human blood in steady and oscillatory shear. Biorheology 12 pp. 257-263.

5. Mackley M.R., Marshall R.T.J., Smeulders B.A.F., & Zhao F.D. (1994) The rheological characterisation of polymeric and colloidal fluids. Chem. Eng. Sci. 49 pp. 2551-2565.

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