Blood viscosity
   HOME

TheInfoList



OR:

Hemorheology, also spelled haemorheology (from
Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...
‘αἷμα, ''haima'' '
blood Blood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood in the cir ...
' and
rheology Rheology (; ) is the study of the flow of matter, primarily in a fluid (liquid or gas) state, but also as "soft solids" or solids under conditions in which they respond with Plasticity (physics), plastic flow rather than deforming Elasticity (phy ...
, from Greek ῥέω ''rhéō'', ' flow' and -λoγία, ''-logia'' 'study of'), or blood rheology, is the study of flow properties of blood and its elements of plasma and cells. Proper tissue perfusion can occur only when blood's rheological properties are within certain levels. Alterations of these properties play significant roles in disease processes. Blood
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
is determined by plasma viscosity,
hematocrit The hematocrit () (Ht or HCT), also known by several other names, is the volume percentage (vol%) of red blood cells (RBCs) in blood, measured as part of a blood test. The measurement depends on the number and size of red blood cells. It is norm ...
(volume fraction of red blood cell, which constitute 99.9% of the cellular elements) and mechanical properties of
red blood cell Red blood cells (RBCs), also referred to as red cells, red blood corpuscles (in humans or other animals not having nucleus in red blood cells), haematids, erythroid cells or erythrocytes (from Greek ''erythros'' for "red" and ''kytos'' for "holl ...
s. Red blood cells have unique mechanical behavior, which can be discussed under the terms
erythrocyte deformability Erythrocyte deformability refers to the ability of erythrocytes (red blood cells, RBC) to change shape under a given level of applied stress, without hemolysing (rupturing). This is an important property because erythrocytes must change their shape ...
and
erythrocyte aggregation Erythrocyte aggregation is the reversible clumping of red blood cells (RBCs) under low shear forces or at stasis. Erythrocytes aggregate in a special way, forming rouleaux. Rouleaux are stacks of erythrocytes which form because of the unique discoi ...
. Because of that, blood behaves as a
non-Newtonian fluid A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for ex ...
. As such, the viscosity of blood varies with
shear rate In physics, shear rate is the rate at which a progressive shearing deformation is applied to some material. Simple shear The shear rate for a fluid flowing between two parallel plates, one moving at a constant speed and the other one stationary ...
. Blood becomes less viscous at high shear rates like those experienced with increased flow such as during exercise or in peak- systole. Therefore, blood is a shear-thinning fluid. Contrarily, blood viscosity increases when shear rate goes down with increased vessel diameters or with low flow, such as downstream from an obstruction or in
diastole Diastole ( ) is the relaxed phase of the cardiac cycle when the chambers of the heart are re-filling with blood. The contrasting phase is systole when the heart chambers are contracting. Atrial diastole is the relaxing of the atria, and ventri ...
. Blood viscosity also increases with increases in red cell aggregability.


Blood viscosity

Blood viscosity is a measure of the resistance of blood to flow. It can also be described as the thickness and stickiness of blood. This
biophysical Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. Bi ...
property makes it a critical determinant of friction against the vessel walls, the rate of
venous return Venous return is the rate of blood flow back to the heart. It normally limits cardiac output. Superposition of the cardiac function curve and venous return curve is used in one hemodynamic model. __TOC__ Physiology Venous return (VR) is the flow o ...
, the work required for the
heart The heart is a muscular organ in most animals. This organ pumps blood through the blood vessels of the circulatory system. The pumped blood carries oxygen and nutrients to the body, while carrying metabolic waste such as carbon dioxide to t ...
to pump blood, and how much
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as ...
is transported to tissues and organs. These functions of the cardiovascular system are directly related to
vascular resistance Vascular resistance is the resistance that must be overcome to push blood through the circulatory system and create flow. The resistance offered by the systemic circulation is known as the systemic vascular resistance (SVR) or may sometimes be cal ...
, preload, afterload, and perfusion, respectively. The primary determinants of blood viscosity are
hematocrit The hematocrit () (Ht or HCT), also known by several other names, is the volume percentage (vol%) of red blood cells (RBCs) in blood, measured as part of a blood test. The measurement depends on the number and size of red blood cells. It is norm ...
, red blood cell deformability, red blood cell aggregation, and plasma viscosity. Plasma's viscosity is determined by water-content and
macromolecular A macromolecule is a very large molecule important to biophysical processes, such as a protein or nucleic acid. It is composed of thousands of covalently bonded atoms. Many macromolecules are polymers of smaller molecules called monomers. The ...
components, so these factors that affect blood viscosity are the
plasma protein Blood-proteins, also termed plasma proteins, are proteins present in blood plasma. They serve many different functions, including transport of lipids, hormones, vitamins and minerals in activity and functioning of the immune system. Other blood pr ...
concentration and types of proteins in the plasma. Nevertheless, hematocrit has the strongest impact on whole blood viscosity. One unit increase in hematocrit can cause up to a 4% increase in blood viscosity. This relationship becomes increasingly sensitive as hematocrit increases. When the hematocrit rises to 60 or 70%, which it often does in
polycythemia Polycythemia (also known as polycythaemia) is a laboratory finding in which the hematocrit (the volume percentage of red blood cells in the blood) and/or hemoglobin concentration are increased in the blood. Polycythemia is sometimes called eryth ...
, the blood viscosity can become as great as 10 times that of water, and its flow through blood vessels is greatly retarded because of increased resistance to flow. This will lead to decreased oxygen delivery. Other factors influencing blood viscosity include
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
, where an increase in temperature results in a decrease in viscosity. This is particularly important in
hypothermia Hypothermia is defined as a body core temperature below in humans. Symptoms depend on the temperature. In mild hypothermia, there is shivering and mental confusion. In moderate hypothermia, shivering stops and confusion increases. In severe ...
, where an increase in blood viscosity will cause problems with blood circulation.


Clinical significance

Many conventional cardiovascular risk factors have been independently linked to whole blood viscosity.
Anemia Anemia or anaemia (British English) is a blood disorder in which the blood has a reduced ability to carry oxygen due to a lower than normal number of red blood cells, or a reduction in the amount of hemoglobin. When anemia comes on slowly, t ...
can reduce blood viscosity, which may lead to heart failure. Furthermore, elevation of plasma viscosity correlates to the progression of
coronary Coronary () may, as shorthand in English, be used to mean: * Coronary circulation, the system of arteries and veins in mammals ** Coronary artery disease **Coronary occlusion ** A myocardial infarction, a heart attack As adjective * Referring to ...
and
peripheral artery disease Peripheral artery disease (PAD) is an abnormal narrowing of arteries other than those that supply the heart or brain. When narrowing occurs in the heart, it is called coronary artery disease, and in the brain, it is called cerebrovascular dis ...
s.


Normal level

In pascal- seconds (Pa·s), the
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
of blood at 37 °C is normally 3 × 10−3 to 4 × 10−3, respectively 3 - 4 centi poise (cP) in the
centimetre gram second system of units 330px, Different lengths as in respect to the Electromagnetic spectrum, measured by the Metre and its deriveds scales. The Microwave are in-between 1 meter to 1 millimeter. A centimetre (international spelling) or centimeter (American spellin ...
. \mu = (3 \sim 4) \cdot 10^ \, Pa \cdot s \nu = \frac = \frac = (2.8 \sim 3.8) \cdot 10^ \, \frac Blood viscosity can be measured by viscometers capable of measurements at various shear rates, such as a rotational
viscometer A viscometer (also called viscosimeter) is an instrument used to measure the viscosity of a fluid. For liquids with viscosities which vary with flow conditions, an instrument called a rheometer is used. Thus, a rheometer can be considered as a spe ...
.


Blood viscoelasticity

Blood is a
viscoelastic In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly ...
fluid, meaning that it possesses both viscous and fluid characteristics. The viscous component arises primarily through the
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
of blood plasma, while the
elastic Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rubber used to hold objects togeth ...
component arises from deformation of the red blood cells. As the heart contracts,
mechanical energy In physical sciences, mechanical energy is the sum of potential energy and kinetic energy. The principle of conservation of mechanical energy states that if an isolated system is subject only to conservative forces, then the mechanical energy is ...
is transferred from the heart to the blood; a small part of the energy is dissipated by the viscosity of the
suspension Suspension or suspended may refer to: Science and engineering * Suspension (topology), in mathematics * Suspension (dynamical systems), in mathematics * Suspension of a ring, in mathematics * Suspension (chemistry), small solid particles suspende ...
, another part is stored as elastic energy in the red blood cells, and the remaining energy is used to drive blood circulation and is thus converted to
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acc ...
. Viscoelastic fluids make up a larger class of fluids called
non-Newtonian fluids A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for ex ...
. The red blood cells occupy about half of the volume of blood and possess elastic properties. This elastic property is the largest contributing factor to the viscoelastic behavior of blood. The large volume percentage of red blood cells at a normal
hematocrit The hematocrit () (Ht or HCT), also known by several other names, is the volume percentage (vol%) of red blood cells (RBCs) in blood, measured as part of a blood test. The measurement depends on the number and size of red blood cells. It is norm ...
level leaves little room for cell motion and deformation without interacting with a neighboring cell. Calculations have shown that the maximum volume percentage of red blood cells without deformation is 58% which is in the range of normally occurring levels. Due to the limited space between red blood cells, it is obvious that in order for blood to flow, significant cell to cell interaction will play a key role. This interaction and tendency for cells to aggregate is a major contributor to the viscoelastic behavior of blood. Red blood cell deformation and aggregation is also coupled with flow-induced changes in the arrangement and orientation as a third major factor in its viscoelastic behavior. Other factors contributing to the viscoelastic properties of blood is the plasma viscosity, plasma composition, temperature, and the rate of flow or shear rate. Together, these factors make human blood
viscoelastic In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly ...
, non- Newtonian, and
thixotropic Thixotropy is a time-dependent shear thinning property. Certain gels or fluids that are thick or viscous under static conditions will flow (become thinner, less viscous) over time when shaken, agitated, shear-stressed, or otherwise stressed ( ...
. When the red cells are at rest or at very small shear rates, they tend to aggregate and stack together in an energetically favorable manner. The attraction is attributed to charged groups on the surface of cells and to the presence of fibrinogen and globulins. This aggregated configuration is an arrangement of cells with the least amount of deformation. With very low shear rates, the viscoelastic property of blood is dominated by the aggregation and cell deformability is relatively insignificant. As the shear rate increases the size of the aggregates begins to decrease. With a further increase in shear rate, the cells will rearrange and orient to provide channels for the plasma to pass through and for the cells to slide. In this low to medium shear rate range, the cells wiggle with respect to the neighboring cells allowing flow. The influence of aggregation properties on the viscoelasticity diminish and the influence of red cell deformability begins to increase. As shear rates become large, red blood cells will stretch or deform and align with the flow. Cell layers are formed, separated by plasma, and flow is now attributed to layers of cells sliding on layers of plasma. The cell layer allows for easier flow of blood and as such there is a reduced viscosity and reduced elasticity. The viscoelasticity of the blood is dominated by the deformability of the red blood cells.


Maxwell model

Maxwell Model concerns Maxwell fluids or
Maxwell material A Maxwell material is the most simple model viscoelastic material showing properties of a typical liquid. It shows viscous flow on the long timescale, but additional elastic resistance to fast deformations. It is named for James Clerk Maxwell w ...
. The material in Maxwell Model is a fluid which means it respects continuity properties for conservative equations : Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids. Maxwell model is made to estimate local conservative values of viscoelasticity by a global measure in the integral volume of the model to be transposed to different flow situations. Blood is a complex material where different cells like red blood cells are discontinuous in plasma. Their size and shape are irregular too because they are not perfect spheres. Complicating moreover blood volume shape, red cells are not identically distributed in a blood sample volume because they migrate with velocity gradients in direction to the highest speed areas calling the famous representation of the
Fåhræus–Lindqvist effect The Fåhraeus–Lindqvist effect describes how the viscosity of a fluid, in this case blood, changes with the diameter of the tube it travels through. In particular there is a 'decrease in viscosity as the tube's diameter ''decreases (although on ...
, aggregate or separate in sheath or plug flows described by Thurston. Typically, the Maxwell Model described below is uniformly considering the material (uniform blue color) as a perfect distributed particles fluid everywhere in the volume (in blue) but Thurston reveals that packs of red cells, plugs, are more present in the high speed region, if ''y'' is the height direction in the Maxwell model figure, (''y''~H) and there is a free cells layer in the lower speed area (''y''~0) what means the plasma fluid phase that deforms under Maxwell Model is strained following inner linings that completely escape from the analytical model by Maxwell. In theory, a fluid in a Maxwell Model behaves exactly similarly in any other flow geometry like pipes, rotating cells or in rest state. But in practice, blood properties vary with the geometry and blood has shown being an inadequate material to be studied as a fluid in common sense. So Maxwell Model gives trends that have to be completed in real situation followed by Thurston model in a vessel regarding distribution of cells in sheath and plug flows. If a small cubical volume of blood is considered, with forces being acted upon it by the heart pumping and shear forces from boundaries. The change in shape of the cube will have 2 components: * Elastic deformation which is recoverable and is stored in the structure of the blood. * Slippage which is associated with a continuous input of viscous energy. When the force is removed, the cube would recover partially. The elastic deformation is reversed but the slippage is not. This explains why the elastic portion is only noticeable in unsteady flow. In steady flow, the slippage will continue to increase and the measurements of non time varying force will neglect the contributions of the elasticity. Figure 1 can be used to calculate the following parameters necessary for the evaluation of blood when a force is exerted. :::Shear Stress: \tau = \frac :::Shear Strain: \gamma = \frac :::Shear Rate: \dot \gamma = \frac A sinusoidal time varying flow is used to simulate the pulsation of a heart. A viscoelastic material subjected to a time varying flow will result in a phase variation between \tau and \gamma represented by \phi. If \phi = 0, the material is a purely elastic because the stress and strain are in phase, so that the response of one caused by the other is immediate. If \phi = 90°, the material is a purely viscous because strain lags behind stress by 90 degrees. A viscoelastic material will be somewhere in between 0 and 90 degrees. The sinusoidal time variation is proportional to e^. Therefore, the size and phase relation between the stress, strain, and shear rate are described using this relationship and a radian frequency, \omega = 2 \pi f were f is the frequency in
Hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that o ...
. :::Shear Stress: \tau^* = \tau e ^ :::Shear Strain: \gamma^* = \gamma e^ :::Shear Rate: \dot \gamma^* = \dot \gamma e^ The components of the complex shear stress can be written as: :::\tau^* = \tau'-i \tau'' Where \tau' is the viscous stress and \tau'' is the elastic stress. The complex coefficient of viscosity \eta^* can be found by taking the ratio of the complex shear stress and the complex shear rate: ::: \eta^*= \frac = ( \frac +i \frac)=\eta'+i\eta'' Similarly, the complex dynamic modulus G can be obtained by taking the ratio of the complex shear stress to the complex shear strain. :::G = \frac =( \frac +i \frac) Relating the equations to common viscoelastic terms we get the storage modulus, G', and the loss modulus, G". :::G = G' + iG'' A viscoelastic
Maxwell material A Maxwell material is the most simple model viscoelastic material showing properties of a typical liquid. It shows viscous flow on the long timescale, but additional elastic resistance to fast deformations. It is named for James Clerk Maxwell w ...
model is commonly used to represent the viscoelastic properties of
blood Blood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood in the cir ...
. It uses purely viscous damper and a purely elastic spring connected in series. Analysis of this model gives the complex viscosity in terms of the dashpot constant and the spring constant. ::: \eta^*=\frac = \eta'-i\eta''


Oldroyd-B model

One of the most frequently used constitutive models for the
viscoelasticity In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearl ...
of blood is the Oldroyd-B model. There are several variations of the Oldroyd-B non-Newtonian model characterizing shear thinning behavior due to red blood cell aggregation and dispersion at low shear rate. Here we consider a three-dimensional Oldroyd-B model coupled with the momentum equation and the total stress tensor. A non Newtonian flow is used which insures that the viscosity of blood \mu(h, d) is a function of vessel diameter d and hematocrit h. In the Oldroyd-B model, the relation between the shear stress tensor B and the orientation stress tensor A is given by: S + \gamma \left \frac- \Delta V \cdot S-S \cdot^T \right \mu (h,d) \left B + \gamma \left( \frac- \Delta V \cdot B - B \cdot ^T \right) \right- gA + C_1\left(gA - \frac \right) where D/Dt is the material derivative, V is the velocity of the fluid, C1, C2, g, \gamma are constants. S and B are defined as follows: ::: S = \mu B + gA :::B = \Delta V + (\Delta V )^T


Viscoelasticity of red blood cells

Red blood cells are subjected to intense mechanical stimulation from both blood flow and vessel walls, and their rheological properties are important to their effectiveness in performing their biological functions in the microcirculation. Red blood cells by themselves have been shown to exhibit viscoelastic properties. There are several methods used to explore the mechanical properties of red blood cells such as: ::* micropipette aspiration ::* micro indentation ::* optical tweezers ::* high frequency electrical deformation tests These methods worked to characterize the deformability of the red blood cell in terms of the shear, bending, area expansion moduli, and relaxation times. However, they were not able to explore the viscoelastic properties. Other techniques have been implemented such as photoacoustic measurements. This technique uses a single-pulse laser beam to generate a photoacoustic signal in tissues and the decay time for the signal is measured. According to the theory of linear viscoelasticity, the decay time is equal to the viscosity-elasticity ratio and therefore the viscoelasticity characteristics of the red blood cells could be obtained. Another experimental technique used to evaluate viscoelasticity consisted of using Ferromagnetism beads bonded to a cells surface. Forces are then applied to the magnetic bead using optical magnetic twisting cytometry which allowed researchers to explore the time dependent responses of red blood cells. T_s(t) is the mechanical torque per unit bead volume (units of stress) and is given by: ::: T_s(t)=c H \cos \theta where H is the applied magnetic twisting field, is the angle of the bead’s magnetic moment relative to the original magnetization direction, and c is the bead constant which is found by experiments conducted by placing the bead in a fluid of known viscosity and applying a twisting field. Complex
Dynamic modulus Dynamic modulus (sometimes complex modulusThe Open University (UK), 2000. ''T838 Design and Manufacture with Polymers: Solid properties and design'', page 30. Milton Keynes: The Open University.) is the ratio of stress to strain under ''vibratory c ...
G can be used to represent the relations between the oscillating stress and strain: :::G = G' + iG'' where G' is the ''storage modulus'' and G'' is the ''loss modulus'': ::: G' = \frac \cos \phi ::: G'' = \frac \sin \phi where \sigma_0 and \varepsilon_0 are the amplitudes of stress and strain and \phi is the phase shift between them. From the above relations, the components of the complex modulus are determined from a loop that is created by comparing the change in torque with the change in time which forms a loop when represented graphically. The limits of T_s(t) - d(t) loop and the area, A, bounded by the T_s(t) - d(t) loop, which represents the energy dissipation per cycle, are used in the calculations. The phase angle \phi, storage modulus G', and loss modulus G'' then become: ::: \phi = \sin^ \frac ::: G' = \frac \cos \phi ::: G'' = \frac \sin \phi = \frac where d is the displacement. The hysteresis shown in figure 3 represents the viscoelasticity present in red blood cells. It is unclear if this is related to membrane molecular fluctuations or metabolic activity controlled by intracellular concentrations of ATP. Further research is needed to fully explore these interaction and to shed light on the underlying viscoelastic deformation characteristics of the red blood cells.


Effects of blood vessels

When looking at viscoelastic behavior of blood
in vivo Studies that are ''in vivo'' (Latin for "within the living"; often not italicized in English) are those in which the effects of various biological entities are tested on whole, living organisms or cells, usually animals, including humans, and ...
, it is necessary to also consider the effects of
arteries An artery (plural arteries) () is a blood vessel in humans and most animals that takes blood away from the heart to one or more parts of the body (tissues, lungs, brain etc.). Most arteries carry oxygenated blood; the two exceptions are the pu ...
,
capillaries A capillary is a small blood vessel from 5 to 10 micrometres (μm) in diameter. Capillaries are composed of only the tunica intima, consisting of a thin wall of simple squamous endothelial cells. They are the smallest blood vessels in the body: ...
, and
veins Veins are blood vessels in humans and most other animals that carry blood towards the heart. Most veins carry deoxygenated blood from the tissues back to the heart; exceptions are the pulmonary and umbilical veins, both of which carry oxygenated b ...
. The viscosity of blood has a primary influence on flow in the larger arteries, while the elasticity, which resides in the elastic deformability of red blood cells, has primary influence in the arterioles and the capillaries. Understanding wave propagation in arterial walls, local hemodynamics, and wall shear stress gradient is important in understanding the mechanisms of cardiovascular function. Arterial walls are anisotropic and heterogeneous, composed of layers with different bio-mechanical characteristics which makes understanding the mechanical influences that arteries contribute to blood flow very difficult.


Medical reasons for a better understanding

From a medical standpoint, the importance of studying the viscoelastic properties of blood becomes evident. With the development of cardiovascular prosthetic devices such as heart valves and blood pumps, the understanding of pulsating blood flow in complex geometries is required. A few specific examples are the effects of viscoelasticity of blood and its implications for the testing of a pulsatile Blood Pumps. Strong correlations between blood viscoelasticity and regional and global cerebral blood flow during cardiopulmonary bypass have been documented. This has also led the way for developing a blood analog in order to study and test prosthetic devices. The classic analog of glycerin and water provides a good representation of viscosity and inertial effects but lacks the elastic properties of real blood. One such blood analog is an aqueous solution of Xanthan gum and glycerin developed to match both the viscous and elastic components of the complex viscosity of blood. Normal red blood cells are deformable but many conditions, such as
sickle cell disease Sickle cell disease (SCD) is a group of blood disorders typically inherited from a person's parents. The most common type is known as sickle cell anaemia. It results in an abnormality in the oxygen-carrying protein haemoglobin found in red b ...
, reduce their elasticity which makes them less deformable. Red blood cells with reduced deformability have increasing impedance to flow, leading to an increase in red blood cell aggregation and reduction in oxygen saturation which can lead to further complications. The presence of cells with diminished deformability, as is the case in sickle cell disease, tends to inhibit the formation of plasma layers and by measuring the viscoelasticity, the degree of inhibition can be quantified.


History

In early theoretical work, blood was treated as a non-Newtonian viscous fluid. Initial studies had evaluated blood during steady flow and later, using oscillating flow. Professor George B. Thurston, of the University of Texas, first presented the idea of blood being viscoelastic in 1972. The previous studies that looked at blood in steady flow showed negligible elastic properties because the elastic regime is stored in the blood during flow initiation and so its presence is hidden when a flow reaches steady state. The early studies used the properties found in steady flow to derive properties for unsteady flow situations.G. Thurston, The Viscosity and Viscoelasticity of Blood in Small Diameter Tubes, Microvascular Research, 1975, 11, 133-146. Advancements in medical procedures and devices required a better understanding of the mechanical properties of blood.


Constitutive equations

The relationships between shear stress and shear rate for blood must be determined experimentally and expressed by
constitutive equations In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and app ...
. Given the complex macro-rheological behavior of blood, it is not surprising that a single equation fails to completely describe the effects of various rheological variables (e.g.,
hematocrit The hematocrit () (Ht or HCT), also known by several other names, is the volume percentage (vol%) of red blood cells (RBCs) in blood, measured as part of a blood test. The measurement depends on the number and size of red blood cells. It is norm ...
, shear rate). Thus, several approaches to defining these equations exist, with some the result of curve-fitting experimental data and others based on a particular rheological model. *
Newtonian fluid A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of chang ...
model where has a constant viscosity at all shear rates. This approach is valid for high shear rates (\dot > 700\, s^) where the vessel diameter is much bigger than the blood cells. *
Bingham fluid A Bingham plastic is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is named after Eugene C. Bingham who proposed its mathematical form. It is used as a common mathematical mo ...
model takes into account the aggregation of red blood cells at low shear rates. Therefore, it acts as an elastic solid under threshold level of shear stress, known as
yield stress In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and w ...
. * Einstein model where η0 is the suspending fluid Newtonian viscosity, "k" is a constant dependent on particle shape, and H is the volume fraction of the suspension occupied by particles. This equation is applicable for suspensions having a low volume fraction of particles. Einstein showed k=2.5 for spherical particles. : \mu_a = * Casson model where "a" and "b" are constants; at very low shear rates, b is the yield shear stress. However, for blood, the experimental data can not be fit over all shear rates with only one set of constants "a" and "b", whereas fairly good fit is possible by applying the equation over several shear rate ranges and thereby obtaining several sets of constants. : ^ = * Quemada model where k0, k and γc are constants. This equation accurately fits blood data over a very wide range of shear rates. : \mu_a = : k = : \gamma_r =


Other characteristics


The Fåhraeus effect

The finding that, for blood flowing steadily in tubes with diameters of less than 300 micrometres, the average hematocrit of the blood in the tube is less than the hematocrit of the blood in the reservoir feeding the tube is known as the Fåhræus effect. This effect is generated in the concentration entrance length of the tube, in which erythrocytes move towards the central region of the tube as they flow downstream. This entrance length is estimated to be about the distance that the blood travels in a quarter of a second for blood where red blood cell aggregation is negligible and the vessel diameter is greater than about 20 micrometres.


The Fåhræus–Lindqvist effect

As the characteristic dimension of a flow channel approaches the size of the particles in a suspension; one should expect that the simple continuum model of the suspension will fail to be applicable. Often, this limit of the applicability of the continuum model begins to manifest itself at characteristic channel dimensions that are about 30 times the particle diameter: in the case of blood with a characteristic RBC dimension of 8 μm, an apparent failure occurs at about 300 micrometres. This was demonstrated by Fåhraeus and Lindqvist, who found that the apparent viscosity of blood was a function of tube diameter, for diameters of 300 micrometres and less, when they flowed constant-hematocrit blood from a well-stirred reservoir through a tube. The finding that for small tubes with diameters below about 300 micrometres and for faster flow rates which do not allow appreciable erythrocyte aggregation, the effective viscosity of the blood depends on tube diameter is known as the Fåhræus–Lindqvist effect.


See also

* Alfred L. Copley * Blood hammer * Biorheology, the study of flow properties(rheology) of biological fluids. *
Hemodynamics Hemodynamics or haemodynamics are the dynamics of blood flow. The circulatory system is controlled by homeostatic mechanisms of autoregulation, just as hydraulic circuits are controlled by control systems. The hemodynamic response continuously m ...
*
Hyperviscosity syndrome Hyperviscosity syndrome is a group of symptoms triggered by an increase in the viscosity of the blood. Symptoms of high blood viscosity include spontaneous bleeding from mucous membranes, visual disturbances due to retinopathy, and neurologic sympt ...
*
Rouleaux Rouleaux (singular is rouleau) are stacks or aggregations of red blood cells (RBCs) that form because of the unique discoid shape of the cells in vertebrates. The flat surface of the discoid RBCs gives them a large surface area to make contact wi ...
, is a configuration that RBC aggregates take.


References

{{Authority control Blood Blood tests Hematology Non-Newtonian fluids Rheology