Page 95 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

72 BIOMECHANICS OF THE HUMAN BODY

3.2 PHYSICAL PROPERTIES OF BLOOD

3.2.1 Constituents of Blood
Blood is a suspension of cellular elements—red blood cells (erythrocytes), white cells (leuko-
cytes), and platelets—in an aqueous electrolyte solution, the plasma. Red blood cells (RBC)
are shaped as a biconcave saucer with typical dimensions of 2 × 8 mm. Erythrocytes are slightly
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heavier than the plasma (1.10 g/cm against 1.03 g/cm ); thus they can be separated by cen-
trifugation from the plasma. In normal blood they occupy about 45 percent of the total volume.
Although larger than erythrocytes, the white cells are less than 1/600th as numerous as the red
cells. The platelet concentration is 1/20th of the red cell concentration, and their dimensions
are smaller (2.5 mm in diameter). The most important variable is the hematocrit, which defines
the volumetric fraction of the RBCs in the blood. The plasma contains 90 percent of its mass
in water and 7 percent in the principal proteins albumin, globulin, lipoprotein, and fibrinogen.
Albumin and globulin are essential in maintaining cell viability. The lipoproteins carry lipids
(fat) to the cells to provide much of the fuel of the body. The osmotic balance controls the fluid
exchange between blood and tissues. The mass density of blood has a constant value of
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1.05 g/cm for all mammals and is only slightly greater than that of water at room temperature
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(about 1 g/cm ).

3.2.2 Blood Rheology

The macroscopic rheologic properties of blood are determined by its constituents. At a normal phys-
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iological hematocrit of 45 percent, the viscosity of blood is m = 4 × 10 −2 dyne . s/cm (or poise),
which is roughly 4 times that of water. Plasma alone (zero hematocrit) has a viscosity of m = 1.1 ×
10 −2 to 1.6 × 10 −2 poise, depending upon the concentration of plasma proteins. After a heavy meal,
when the concentration of lipoproteins is high, the plasma viscosity is quite elevated (Whitmore,
1968). In large arteries, the shear stress (t) exerted on blood elements is linear with the rate of shear,
and blood behaves as a newtonian fluid, for which,

⎛ du ⎞
τ = μ − (3.1)
⎝ dr ⎠
where u is blood velocity and r is the radial coordinate perpendicular to the vessel wall.
In the smaller arteries, the shear stress acting on blood elements is not linear with shear rate,
and the blood exhibits a nonnewtonian behavior. Different relationships have been proposed for the
nonnewtonian characteristics of blood, for example, the power-law fluid,

n
⎛ du ⎞
τ = K − n ( > ) (3.2)
0
⎝ dr ⎠
where K is a constant coefficient. Another model, the Casson fluid (Casson, 1959), was proposed
by many investigators as a useful empirical model for blood (Cokelet, 1980; Charm and Kurland,
1965),

/
/
/
τ 12 = K ⎛ du ⎞ 12 + τ 12 (3.3)
−
y
⎝ dr ⎠
where t is the fluid yield stress.
y