# Blood viscosity

Blood viscosity is a measure of the resistance of blood to flow. It can be described as the thickness and stickiness of blood. This dynamic biophysical property of blood makes it a critical determinant of friction against the vessel walls, the rate of venous return, the work required for the heart to pump blood, and how much oxygen is transported to tissues and organs. These functions of the cardiovascular system are directly related to vascular resistance, preload, afterload, and perfusion, respectively.

Unlike water and other Newtonian fluids, blood is a complex suspension of cells, nutrients, ions, gases, and other molecules which plasma and among themselves. Consequently, blood behaves as a non-Newtonian fluid. As such, the viscosity of blood varies with shear rate. Shear rate can be thought of as a velocity gradient. Unbalanced forces such as pressure gradients in the vasculature owe to a continuous deformation of the blood, causing adjacent layers of the blood to slide past each other at a certain velocity, altering its shear rate. When shear rate increases, a tangential force called shear stress acts against vessel walls. Blood becomes physically thinner at high shear rates like those experienced in peak-systole. Contrarily, during end-diastole, blood moves more slowly and becomes thicker and stickier. Blood is a shear-thinning fluid because its viscosity decreases as shear rate and shear stress increase.

The primary determinants of blood viscosity are hematocrit, red blood cell deformability, red blood cell aggregation, and plasma viscosity. Of these, hematocrit has the strongest impact on whole blood viscosity. One unit increase in hematocrit can cause up to a 4% increase in blood viscosity.[1] This relationship becomes increasingly sensitive as hematocrit increases. When the hematocrit rises to 60 or 70, which it often does in polycythemia,[2]  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.[3] This will lead to decreased oxygen delivery.[4]

Many conventional cardiovascular risk factors and outcomes have been independently correlated with whole blood viscosity. Hypertension, total cholesterol, LDL-cholesterol, triglycerides, chylomicrons, VLDL-cholesterol, diabetes and metabolic syndrome, obesity, cigarette smoking, male gender, and aging have all been positively linked to whole blood viscosity. HDL-cholesterol has been negatively correlated to whole blood viscosity.[5]

In pascal-seconds (Pa·s), the viscosity of blood at 37 °C is normally 3 × 10−3 to 4 × 10−3,[6] respectively 3 - 4 centipoise (cP) in the centimetre gram second system of units.

$\mu = (3 \sim 4) \cdot 10^{-3} \, Pa \cdot s$

$\nu = \frac{\mu}{\rho} = \frac{(3 \sim 4) \cdot 10^{-3}}{1.06\cdot 10^{3}} = (2.8 \sim 3.8) \cdot 10^{-6} \, \frac{m^2}{s}$

Plasma’s viscosity is determined by water-content and macromolecular components, so these factors that affect blood viscosity are the plasma protein concentration and types of proteins in the plasma, but these effects are so much less than the effect of hematocrit that they are not significant,[7] and elevation of plasma viscosity correlates to the progression of coronary and peripheral vascular diseases.[2][7] Anemia can lead to decrease blood viscosity, which may lead to heart failure.

Other factors influencing blood viscosity include temperature, where an increase in temperature results in a decrease in viscosity. This is particularly important in hypothermia, where an increase in blood viscosity will cause problems with blood circulation.

## Measurement

Blood viscosity can be measured by viscometers capable of measurements at various shear rates, such as a rotational viscometer.[8]

## Hemorheology

Hemorheology is the study of flow properties of blood and its elements (plasma and formed elements, including red blood cells, white blood cells and platelets). There is increasing evidence indicating that flow properties of blood are among the main determinants of proper tissue perfusion and alterations in these properties play significant roles in disease processes; hence, knowledge of them is vital to any understanding of hemorheology.[9] Blood is a suspension of cellular elements in plasma, therefore exhibit non-Newtonian flow behavior. That is, its viscosity is shear rate dependent. Blood viscosity decrease with increased shear rate, known as shear thinning. Blood viscosity is determined by plasma viscosity, hematocrit (volume fraction of red blood cell, which constitute 99.9% of the cellular elements) and mechanical behavior of red blood cells. Therefore, red blood cell mechanics is the major determinant of flow properties of blood. Red blood cells have unique mechanical behavior, which can be discussed under the terms “erythrocyte deformability” and “erythrocyte aggregation”.[10] The term hemorheology was first introduced by scientist Alfred L. Copley.

The relationships between shear stress and shear rate for blood must be determined experimentally and expressed by constitutive equations. 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, 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 model where has a constant viscosity at all shear rates. This approach is valid for high shear rates ($\dot{\gamma} > 700\, s^{-1}$) where the vessel diameter is much bigger than the blood cells.[11]
• Bingham fluid 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.
• 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.
$\mu_a = {{\mu_0} \times {(1+kH)}}$
• 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.
${\tau}^{0.5} = {{a}{|\gamma|}^{0.5} + b^ {0.5}}$
• Quemada model where k0, k and γc are constants. This equation accurately fits blood data over a very wide range of shear rates.
$\mu_a = {{\mu_0} {{(1-0.5kH)}^{-2}}}$
$k = {{k_0 + k_\inf {\gamma^{0.5}}_r } \over {1+{\gamma^{0.5}}_r}}$
$\gamma_r = {{\gamma} \over {\gamma_c}}$

### 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.[9]

### 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 Fåhraeus-Lindqvist effect.[9]

## References

1. ^ Baskurt, Oguz K., and Herbert J. Meiselman. "Blood rheology and hemodynamics." Seminars in thrombosis and hemostasis. Vol. 29. No. 5. New York: Stratton Intercontinental Medical Book Corporation, c1974-, 2003. PMID: 14631543
2. ^ a b Tefferi A (May 2003). "A contemporary approach to the diagnosis and management of polycythemia vera". Curr. Hematol. Rep. 2 (3): 237–41. PMID 12901345.
3. ^ Lenz C, Rebel A, Waschke KF, Koehler RC, Frietsch T (2008). "Blood viscosity modulates tissue perfusion: sometimes and somewhere". Transfus Altern Transfus Med 9 (4): 265–272. doi:10.1111/j.1778-428X.2007.00080.x. PMC 2519874. PMID 19122878.
4. ^ Kwon O, Krishnamoorthy M, Cho YI, Sankovic JM, Banerjee RK (February 2008). "Effect of blood viscosity on oxygen transport in residual stenosed artery following angioplasty". J Biomech Eng 130 (1): 011003. doi:10.1115/1.2838029. PMID 18298179.
5. ^ Jeong, Seul-Ki, et al. "Cardiovascular risks of anemia correction with erythrocyte stimulating agents: should blood viscosity be monitored for risk assessment?." Cardiovascular Drugs and Therapy 24.2 (2010): 151-160. PMID: 20514513
6. ^ Viscosity. The Physics Hypertextbook. by Glenn Elert
7. ^ a b Késmárky G, Kenyeres P, Rábai M, Tóth K (2008). "Plasma viscosity: a forgotten variable". Clin. Hemorheol. Microcirc. 39 (1-4): 243–6. PMID 18503132.
8. ^ Baskurt OK, Boynard M, Cokelet GC, et al (2009). "New Guidelines for Hemorheological Laboratory Techniques". Clinical Hemorheology and Microcirculation 42: 75–97.
9. ^ a b c Baskurt, OK; Hardeman M, Rampling MW, Meiselman HJ (2007). Handbook of Hemorheology and Hemodynamics. Amsterdam, Netherlands: IOS Press. ISBN 978-1-58603-771-0.
10. ^ Baskurt OK, Meiselman HJ (2003). "Blood rheology and hemodynamics". Seminars in Thrombosis and Haemostasis 29: 435–450. doi:10.1055/s-2003-44551. PMID 14631543.
11. ^ Fung, Y.C. (1993). Biomechanics: mechanical properties of living tissues (2. ed. ed.). New York, NY: Springer. ISBN 9780387979472.