Velocity of the Bloodstream

Velocity, as relates to fluid movement, is the distance that a particle of fluid travels with respect to time, and it is expressed in units of distance per unit time (e.g., cm/sec). This is in contrast to flow, which is the rate of displacement of a volume of fluid, and it is expressed in units of volume per unit time (e.g., cm³/sec). In a rigid tube, velocity (v) and flow (Q) are related to one another by the cross-sectional area (A) of the tube:

Equation 17-1

The interrelationships among velocity, flow, and area are shown in Figure 17-1. Because conservation of mass requires that the fluid flowing through a rigid tube be constant, the velocity of the fluid will vary inversely with the cross-sectional area. Thus, fluid flow velocity is greatest in the section of the tube with the smallest cross-sectional area and slowest in the section of the tube with the greatest cross-sectional area.

Figure 17-1 As fluid flows through a tube of variable cross-sectional area, A, the linear velocity, v, varies inversely with the cross-sectional area.

As shown in Figure 15-3, velocity decreases progressively as blood traverses the arterial system. At the capillaries, velocity decreases to a minimal value. As the blood then passes centrally through the venous system toward the heart, velocity progressively increases again. The relative velocities in the various components of the circulatory system are related only to the respective cross-sectional areas.

Relationship between Velocity and Pressure

The total energy in a hydraulic system consists of three components: pressure, gravity, and velocity. The velocity of blood flow can have an important effect on the pressure within the tube. Consider the effect of velocity on pressure in a tube with different cross-sectional areas (Fig. 17-2). An ideal fluid flows in this system, in which the total energy remains constant. The total pressure within the tube equals the lateral (static) pressure plus the dynamic pressure. The gravitational component can be neglected because the tube is horizontal. The total pressures in segments A, B, and C will be equal, provided that the energy loss from viscosity is negligible (viz., this fluid is an “ideal fluid”). The effect of velocity on the dynamic component (P_dyn) can be estimated from

Figure 17-2 In a narrow section, B, of a tube, the linear velocity, v, and hence the dynamic component of pressure, ρv²/2, are greater than in the wide sections, A and C, of the same tube. If the total energy is virtually constant throughout the tube (i.e., if the energy loss because of viscosity is negligible), the lateral pressure in the narrow section will be less than the lateral pressure in the wide sections of the tube.

Equation 17-2

where ρ is the density of the fluid (g/cm³) and v is velocity (cm/sec). The fluid has a density of 1 g/cm³. In section A, the lateral pressure is 100 mm Hg; note that 1 mm Hg equals 1330 dynes/cm². From Equation 17-2, P_dyn = 5000 dynes/cm², or 3.8 mm Hg. In the narrow section B of the tube where the velocity is twice as great, P_dyn = 20,000 dynes/cm², or 15 mm Hg. Thus, the lateral pressure in section B will be 15 mm Hg less than the total pressure, whereas the lateral pressure in sections A and C will be only 3.8 mm Hg less. In most arterial locations, the dynamic component will be a negligible fraction of the total pressure. However, at sites of an arterial constriction or obstruction, the high flow velocity is associated with a large kinetic energy, and therefore the dynamic pressure component may increase significantly. Hence, the pressure would be reduced and perfusion of distal segments will be correspondingly decreased. This example helps explain how pressure changes in a vessel that is narrowed by atherosclerosis or spasm of the blood vessel wall. That is, in narrowed sections of a tube, the dynamic component increases significantly because the flow velocity is associated with a large kinetic energy.

Relationship between Pressure and Flow

The most fundamental law that governs the flow of fluids through cylindrical tubes was derived empirically by the French physiologist Poiseuille. He was primarily interested in the physical determinants of blood flow, but he replaced blood with simpler liquids in his measurements of flow through glass capillary tubes. His work was so precise and important that his observations have been designated Poiseuille’s law.

Poiseuille’s Law

Poiseuille’s law applies to the steady (i.e., nonpulsatile) laminar flow of newtonian fluids through rigid cylindrical tubes. A newtonian fluid is one whose viscosity remains constant, and laminar flow is the type of motion in which the fluid moves as a series of individual layers, with each layer moving at a velocity different from that of its neighboring layers (Fig. 17-3). In the case of laminar flow through a tube, the fluid consists of a series of infinitesimally thin concentric tubes sliding past one another. Despite the differences between the vascular system (i.e., flow is pulsatile, the vessels are not rigid cylinders, and blood is not a newtonian fluid), Poiseuille’s law does provide valuable insight into the determinants of blood flow through the vascular system.

Figure 17-3 When flow is laminar, all elements of the fluid move in streamlines that are parallel to the axis of the tube; the fluid does not move in a radial or circumferential direction. The layer of fluid in contact with the wall is motionless; the fluid that moves along the central axis of the tube has the maximal velocity.

Poiseuille’s law describes the flow of fluids through cylindrical tubes in terms of flow, pressure, the dimensions of the tube, and the viscosity of liquid.

Equation 17-3

where

Q = flow

P_i − P_o = pressure gradient from the inlet (i) of the tube to the outlet (o)

r = radius of the tube

l = length of the tube

η = viscosity of the fluid

As is clear from the equation, flow through the tube will increase as the pressure gradient is increased, and it will decrease as either the viscosity of the fluid or the length of the tube increases. The radius of the tube is a critical factor in determining flow because it is raised to the fourth power. As described later, the radius of a tube is a major determinant of the resistance to flow.

Resistance to Flow

In electrical theory, Ohm’s law states that the resistance, R, equals the ratio of voltage drop, E, to current flow, I.

Equation 17-4

Similarly, in fluid mechanics, hydraulic resistance, R, may be defined as the ratio of the pressure drop, P_i − P_o, to flow, Q.

Equation 17-5

For the steady, laminar flow of a newtonian fluid through a cylindrical tube, the physical components of hydraulic resistance may be appreciated by rearranging Poiseuille’s law to give the hydraulic resistance equation:

Equation 17-6

Thus, when Poiseuille’s law applies, the resistance to flow depends only on the dimensions of the tube and the characteristics of the fluid.

The principal determinant of resistance to blood flow through any vessel is the caliber of the vessel because resistance varies inversely as the fourth power of the radius of the tube. In Figure 17-4, the resistance to flow through small blood vessels was measured and the resistance per unit length of vessel (R/l) was plotted against the vessel diameter. As shown, resistance is highest in the capillaries (diameter of 7 μm), and it diminishes as the vessels increase in diameter on the arterial and venous sides of the capillaries. Values of R/l are virtually proportional to the fourth power of the diameter (or radius) of the larger vessels on both sides of the capillaries.

Figure 17-4 Resistance per unit length (R/l) for individual small blood vessels. The capillaries, with a diameter of 7 μm, are denoted by the vertical dashed line. Resistances of the arterioles are plotted to the left and resistances of the venules to the right of the vertical dashed line. For both types of vessels, the resistance per unit length is inversely proportional to the fourth power of the vessel diameter (D).

(Redrawn from Lipowsky HH et al: Circ Res 43:738, 1978.)

Changes in vascular resistance occur when the caliber of vessels changes. The most important factor that leads to a change in vessel caliber is contraction of the circular smooth muscle cells in the vessel wall. Changes in internal pressure also alter the caliber of blood vessels and therefore alter the resistance to blood flow through these vessels. Blood vessels are elastic tubes. Hence, the greater the transmural pressure (i.e., the difference between internal and external pressure) across the wall of a vessel, the greater the caliber of the vessel and the less its hydraulic resistance.

It is apparent from Figure 15-3 that the greatest drop in pressure occurs in the very small arteries and arterioles. However, capillaries, which have a mean diameter of about 7 μm, have the greatest resistance to blood flow. Nevertheless, it is the arterioles, not the capillaries, that have the greatest resistance of all the different varieties of blood vessels that lie in series with one another (as in Fig. 15-3). This seeming paradox is related to the relative numbers of parallel capillaries and parallel arterioles. Most simply, there are far more capillaries than arterioles in the systemic circulation, and total resistance across the many capillaries arranged in parallel is much less than total resistance across the fewer arterioles arranged in parallel. In addition, arterioles have a thick coat of circularly arranged smooth muscle fibers that can vary the lumen radius. Even small changes in radius alter resistance greatly, as can be seen from the hydraulic resistance equation (Equation 17-6), wherein R varies inversely with r⁴.

Resistances in Series and in Parallel

In the cardiovascular system, the various types of vessels listed along the horizontal axis in Figure 15-3 lie in series with one another. The individual members of each category of vessels are ordinarily arranged in parallel with one another (Fig. 15-1). Thus, capillaries throughout the body are in most instances parallel elements, except for the renal vasculature (in which the peritubular capillaries are in series with the glomerular capillaries) and the splanchnic vasculature (in which the intestinal and hepatic capillaries are aligned in series with each other). The total hydraulic resistance of components arranged in series or in parallel can be derived in the same manner as those for analogous combinations of electrical resistance.

Resistance of Vessels in Series.

Three hydraulic resistances, R₁, R₂, and R₃, are arranged in series in the system depicted in Figure 17-5. The pressure drop across the entire system (i.e., the difference between inflow pressure, P_i, and outflow pressure, P_o) consists of the sum of the pressure drops across each of the individual resistances (equation a). In steady state, the flow, Q, through any given cross section must equal the flow through any other cross section. By dividing each component in equation a by Q (equation b), it is evident from the definition of resistance (Equation 17-5) that for resistances in series, the total resistance, R_t, of the entire system equals the sum of the individual resistances, that is,

Figure 17-5 For resistances (R₁, R₂, and R₃) arranged in series, total resistance, R_t, equals the sum of the individual resistances. P, pressure; Q, flow.

Equation 17-7

Resistance of Vessels in Parallel.

For resistances in parallel, as illustrated in Figure 17-6, inflow and outflow pressure is the same for all tubes. In steady state, the total flow, Q_t, through the system equals the sum of the flows through the individual parallel elements (equation a). Because the pressure gradient (P_i − P_o) is identical for all parallel elements, each term in equation a may be divided by that pressure gradient to yield equation b. From the definition of resistance, equation c may be derived. This equation states that for resistances in parallel, the reciprocal of the total resistance, R_t, equals the sum of the reciprocals of the individual resistances, that is,

Figure 17-6 For resistances (R₁, R₂, and R₃) arranged in parallel, the reciprocal of the total resistance, R_t, equals the sum of the reciprocals of the individual resistances. P, pressure; Q, flow.

Equation 17-8

By considering a few simple illustrations, some of the fundamental properties of parallel hydraulic systems become apparent. For example, if the resistances of the three parallel elements in Figure 17-6 were all equal, then

Equation 17-9

Therefore, from Equation 17-8,

Equation 17-10

By equating the reciprocals of these terms,

Equation 17-11

Thus, the total resistance is less than the individual resistances. For any parallel arrangement, the total resistance must be less than that of any individual component. For example, consider a system in which a tube with very high resistance is added in parallel to a low-resistance tube. The total resistance of the system must be less than that of the low-resistance component by itself because the high-resistance component affords an additional pathway, or conductance, for flow of fluid.

Consider the physiological relationship between the total peripheral resistance (TPR) of the entire systemic vascular bed and the resistance of one of its components, such as the renal vasculature. TPR is the ratio of the arteriovenous (AV) pressure difference (P_a − P_v) to the flow through the entire systemic vascular bed (i.e., the cardiac output, Q_t). The renal vascular resistance (R_r) would be the ratio of the same AV pressure difference (P_a − P_v) to renal blood flow (Q_r).

In an individual with an arterial pressure of 100 mm Hg, a peripheral venous pressure of 0 mm Hg, and a cardiac output of 5000 mL/min, TPR will be 0.02 mm Hg/mL/min, or 0.02 PRU (peripheral resistance units). Normally, blood flow through one kidney would be approximately 600 mL/min. Renal resistance would therefore be 100 mm Hg ÷ 600 mL/min, or 0.17 PRU, which is 8.5 times greater than TPR. An organ such as the kidney, which weighs only about 1% as much as the whole body, has a vascular resistance much greater than that of the entire systemic circulation. Hence, it is not surprising that the resistance to flow would be greater for a component organ, such as the kidney, than for the entire systemic circulation because the systemic circulation has many more alternative pathways for blood to flow than just one kidney.

Laminar and Turbulent Flow

Under certain conditions, fluid flow in a cylindrical tube will be laminar, as illustrated in Figure 17-3. As the fluid moves through the tube, a thin layer of fluid in contact with the tube wall adheres to the wall and hence is motionless. The layer of fluid just central to this external lamina must shear against this motionless layer, and therefore the layer moves slowly, but with a finite velocity. Similarly, the next more central layer moves still more rapidly; the longitudinal velocity profile is that of a paraboloid (Fig. 17-3). The fluid elements in any given lamina remain in that lamina as the fluid moves longitudinally along the tube. The velocity at the center of the stream is maximal and equal to twice the mean velocity of flow across the entire cross section of the tube.

Irregular motions of the fluid elements may develop in the flow of fluid through a tube; such flow is called turbulent. In these conditions, fluid elements do not remain confined to definite laminae, but rapid, radial mixing occurs (Fig. 17-7). Greater pressure is required to force a given flow of fluid through the same tube when the flow is turbulent than when it is laminar. In turbulent flow, the pressure drop is approximately proportional to the square of the flow rate, whereas in laminar flow, the pressure drop is proportional to the first power of the flow rate. Hence, to produce a given flow, a pump such as the heart must do considerably more work if turbulence develops.

Figure 17-7 In turbulent flow the elements of the fluid move irregularly in axial, radial, and circumferential directions. Vortices frequently develop.

Whether turbulent or laminar flow will exist in a tube under given conditions may be predicted on the basis of a dimensionless number called Reynold’s number (N_R). This number represents the ratio of inertial to viscous forces. For a fluid flowing through a cylindrical tube,

Equation 17-12

where ρ = fluid density, D = tube diameter, v = mean velocity, and η = viscosity. For N_R of 2000 or greater, the flow will usually be laminar; for N_R of 3000 or greater, the flow will be turbulent; and for N_R between 2000 and 3000, the flow will be transitional between laminar and turbulent. Equation 17-12 indicates that high fluid densities, large tube diameters, high flow velocities, and low fluid viscosities predispose to turbulence. In addition to these factors, abrupt variations in tube dimensions or irregularities in the tube walls may produce turbulence.

Rheologic Properties of Blood

The viscosity of a given newtonian fluid at a specified temperature will be constant over a wide range of tube dimensions and flows. However, for a non-newtonian fluid such as blood, viscosity may vary considerably as a function of tube dimensions and flows. Therefore, the term viscosity does not have a unique meaning for blood. The term apparent viscosity is frequently used for the derived value of blood viscosity obtained under the particular conditions of measurement.

Rheologically, blood is a suspension of formed elements, principally erythrocytes, in a relatively homogeneous liquid, the blood plasma. Because blood is a suspension, the apparent viscosity of blood varies as a function of the hematocrit (ratio of the volume of red blood cells to the volume of whole blood). The viscosity of plasma is 1.2 to 1.3 times that of water. The upper curve in Figure 17-8 shows that blood with a normal hematocrit ratio of 45% has an apparent viscosity 2.4 times that of plasma.^* In severe anemia, blood viscosity is low. With greater hematocrit ratios, the slope of the curve increases progressively; it is especially steep at the upper range of erythrocyte concentrations.

Figure 17-8 The apparent viscosity of whole blood, relative to that of plasma, increases at a progressively greater rate as the hematocrit ratio increases. For any given hematocrit ratio, the apparent viscosity of blood is less when measured in a biological viscometer (such as the blood vessels) than in a conventional capillary tube viscometer.

(Redrawn from Levy MN, Share L: Circ Res 1:247, 1953.)

For any given hematocrit ratio, the apparent viscosity of blood, relative to that of water, depends on the dimensions of the tube used in estimating the viscosity. Figure 17-9 demonstrates that the apparent viscosity of blood diminishes progressively as tube diameter decreases below a value of about 0.3 mm. The diameters of the highest-resistance blood vessels, the arterioles, are considerably less than this critical value. This phenomenon therefore reduces the resistance to flow in blood vessels that possess the greatest resistance. The influence of tube diameter on apparent viscosity is explained in part by the actual change in blood composition as it flows through small tubes. The composition of blood changes because the red blood cells tend to accumulate in the faster axial stream, whereas plasma tends to flow in the slower marginal layers. Because the axial portions of the bloodstream contain a greater proportion of red cells and this axial portion will move at greater velocity, the red cells tend to traverse the tube in less time than plasma does. Measurement has shown that red cells do travel faster than plasma through these vascular beds. Furthermore, the hematocrit ratios of the blood contained in the small blood vessels of various tissues are lower than those in blood samples withdrawn from large arteries or veins.

Figure 17-9 The viscosity of blood relative to that of water increases as a function of tube diameter up to a diameter of about 0.3 mm.

(Redrawn from Fåhraeus R, Lindqvist T: Am J Physiol 96:562, 1931.)

The physical forces responsible for the drift of erythrocytes toward the axial stream and away from the vessel walls when blood is flowing at normal rates are not fully understood. One factor is the great flexibility of red blood cells. At low flow rates, like those in the microcirculation, rigid particles do not migrate toward the central axis of a tube, whereas flexible particles do. The concentration of flexible particles near the tube’s central axis is enhanced by increasing the shear rate.

The apparent viscosity of blood diminishes as the flow rate is increased (Fig. 17-10), a phenomenon called shear thinning. The greater the flow, the greater the rate that one lamina of fluid shears against an adjacent lamina. The greater tendency for erythrocytes to accumulate in the axial laminae at higher flow rates is partly responsible for this non-newtonian behavior. However, a more important factor is that at very slow flow rates, the suspended cells tend to form aggregates, which increases blood viscosity. As flow is increased, this aggregation decreases, and so also does the apparent viscosity of blood (Fig. 17-10).

Figure 17-10 Decrease in the viscosity of blood (centipoise) at increasing rates of shear (sec⁻¹). The shear rate refers to the velocity of one layer of fluid relative to that of the adjacent layers and is directionally related to the rate of flow.

(Redrawn from Amin TM, Sirs JA: Q J Exp Physiol 70:37, 1985.)

The tendency for erythrocytes to aggregate at low flow depends on the concentration of the larger protein molecules in plasma, especially fibrinogen. For this reason, changes in blood viscosity with flow rate are much more pronounced when the concentration of fibrinogen is high. In addition, at low flow rates, leukocytes tend to adhere to the endothelial cells of the microvessels and thereby increase the apparent viscosity of the blood.

The deformability of erythrocytes is also a factor in shear thinning, especially when hematocrit ratios are high. The mean diameter of human red blood cells is about 7 μm, yet they are able to pass through openings with a diameter of only 3 μm. As blood with densely packed erythrocytes flows at progressively greater rates, the erythrocytes become more and more deformed. Such deformation diminishes the apparent viscosity of blood. The flexibility of human erythrocytes is enhanced as the concentration of fibrinogen in plasma increases (Fig. 17-11). If the red blood cells become hardened, as they are in certain spherocytic anemias, shear thinning may diminish.

Figure 17-11 Effect of the plasma fibrinogen concentration on the flexibility of human erythrocytes.

(Redrawn from Amin TM, Sirs JA: Q J Exp Physiol 70:37, 1985.)

Arterial Elasticity

The systemic and pulmonary arterial systems distribute blood to the capillary beds throughout the body. The arterioles are high-resistance vessels of this system that regulate the distribution of flow to the various capillary beds. The aorta, the pulmonary artery, and their major branches have a large amount of elastin in their walls, which makes these vessels highly distensible (i.e., compliant). This distensibility serves to dampen the pulsatile nature of blood flow that results from the heart pumping blood intermittently. When blood is ejected from the ventricles during systole, these vessels distend, and during diastole, they recoil back and propel the blood forward (Fig. 17-12). Thus, the intermittent output of the heart is converted to a steady flow through the capillaries.

Figure 17-12 A to D, When the arteries are normally compliant, blood flows through the capillaries throughout the cardiac cycle. When the arteries are rigid, blood flows through the capillaries during systole, but flow ceases during diastole.

IN THE CLINIC

As people age, the elastin content of the large arteries is reduced and replaced by collagen. This reduces arterial compliance (Fig. 17-13). Thus, with age, systolic pressure increases, as does the difference between systolic and diastolic blood pressure, called the pulse pressure (see below).

Figure 17-13 Pressure-volume relationships of aortas obtained at autopsy from humans in different age groups (denoted by the numbers at the right end of each of the curves). Note how compliance (ΔV/ΔP) decreases with age.

(Redrawn from Hallock P, Benson IC: J Clin Invest 16:595, 1937.)

The elastic nature of the large arteries also reduces the work of the heart. If these arteries were rigid rather than compliant, the pressure would rise dramatically during systole. This increased pressure would require the ventricles to pump against a large load (i.e., afterload) and thus increase the work of the heart. Instead, as blood is ejected into these vessels, they distend, and the resultant increase in systolic pressure, and thus the work of the heart, is reduced.

Determinants of Arterial Blood Pressure

Arterial blood pressure is routinely measured in patients, and it provides a useful estimate of their cardiovascular status. Arterial pressure can be defined as mean arterial pressure, which is the pressure averaged over time, and as systolic (maximal) and diastolic (minimal) arterial pressure within the cardiac cycle (Fig. 17-14). The difference between systolic and diastolic pressure is termed pulse pressure.

Figure 17-14 Arterial systolic, diastolic, pulse, and mean pressure. Mean arterial pressure () represents the area under the arterial pressure curve (shaded area) divided by the duration of the cardiac cycle (t₂ − t₁).

The determinants of arterial blood pressure are arbitrarily divided into “physical” and “physiological” factors (Fig. 17-15). The two physical factors or fluid mechanical characteristics are fluid volume (i.e., blood volume) within the arterial system and the static elastic characteristics (compliance) of the system. The physiological factors are cardiac output (which equals heart rate × stroke volume) and peripheral resistance.

Figure 17-15 Arterial blood pressure is determined directly by two major physical factors: arterial blood volume and arterial compliance. These physical factors in turn are affected by certain physiological factors, namely, cardiac output (heart rate × stroke volume) and peripheral resistance.

Mean Arterial Pressure

Mean arterial pressure, , may be estimated from an arterial blood pressure tracing by measuring the area under the pressure curve and dividing this area by the time interval involved (Fig. 17-14). Alternatively, can be satisfactorily approximated from the measured values of systolic (P_s) and diastolic (P_d) pressure by means of the following formula:

Equation 17-14

Consider that mean arterial pressure depends on only two physical factors: mean blood volume in the arterial system and arterial compliance (Fig. 17-16). Arterial volume, V_a, in turn depends on the rate of inflow, Q_h, into the arteries from the heart (cardiac output) and on the rate of outflow, Q_r, from the arteries through the resistance vessels (peripheral runoff). These relationships are expressed mathematically as

Figure 17-16 The two physical determinants of pulse pressure are arterial compliance (C_a) and the change in arterial volume. The two physiological determinants of mean arterial pressure () are cardiac output and total peripheral resistance.

Equation 17-15

where dV_a/dt is the change in arterial blood volume per unit time. If Q_h exceeds Q_r, arterial volume increases, the arterial walls are stretched further, and pressure rises. The converse happens when Q_r exceeds Q_h. When Q_h equals Q_r, arterial pressure remains constant. Thus, increases in cardiac output raise mean arterial pressure, as do increases in peripheral resistance. Conversely, decreases in cardiac output or peripheral resistance decrease mean arterial pressure.

Arterial Pulse Pressure

Arterial pulse pressure is systolic pressure minus diastolic pressure. It is principally a function of just one physiological factor, stroke volume, which determines the change in arterial blood volume (a physical factor) during ventricular systole. This physical factor, plus a second physical factor (arterial compliance), determines the arterial pulse pressure (Fig. 17-16).

Stroke Volume.

As described previously, mean arterial pressure depends on cardiac output and peripheral resistance. During the rapid ejection phase of systole, the volume of blood introduced into the arterial system exceeds the volume that exits the system through the arterioles. Arterial pressure and volume therefore rise to a peak pressure, which is systolic pressure. During the remainder of the cardiac cycle (i.e., ventricular diastole), cardiac ejection is zero, and peripheral runoff now greatly exceeds cardiac ejection. The resultant decrement in arterial blood volume thus causes pressure to fall to a minimum, which is diastolic pressure. The effect of stroke volume on pulse pressure when arterial compliance is constant is illustrated in Figure 17-17.

Figure 17-17 Effect of a change in stroke volume on pulse pressure in a system in which arterial compliance remains constant over the prevailing range of pressures and volumes. A larger volume increment [(V₄ − V₃) > (V₂ − V₁)] results in a greater mean pressure and a greater pulse pressure [(P₄ − P₃) > (P₂ − P₁)].

Arterial Compliance.

Arterial compliance also affects pulse pressure. This relationship is illustrated in Figure 17-18. When cardiac output and TPR are constant, a decrease in arterial compliance results in an increase in pulse pressure. Diminished arterial compliance also imposes a greater workload on the left ventricle (i.e., increased afterload), even if stroke volume, TPR, and mean arterial pressure are equal in the two individuals.

Figure 17-18 For a given volume increment (V₂ − V₁), reduced arterial compliance (compliance B < compliance A) results in increased pulse pressure [(P₄ − P₁) > (P₃ − P₂)].

Total Peripheral Resistance and Arterial Diastolic Pressure.

As previously discussed, if the heart rate and stroke volume remain constant, an increase in TPR will increase mean arterial pressure. When arterial compliance is constant, an increase in TPR leads to proportional increases in systolic and diastolic pressure such that the pulse pressure is unchanged (Fig. 17-19, A). However, arterial compliance is not linear. As mean arterial pressure increases and the artery is stressed, compliance decreases (Fig. 17-19, B). Because of the decrease in arterial compliance with increased arterial pressure, pulse pressure will increase when arterial pressure is elevated.

Figure 17-19 Comparison of the effects of a given change in peripheral resistance on pulse pressure when the pressure-volume curve for the arterial system is either rectilinear (A) or curvilinear (B). The increment in arterial volume is the same for both conditions [(V₄ − V₃) = (V₂ −V₁)].

IN THE CLINIC

Arterial pulse pressure affords valuable clues about a person’s stroke volume, provided that arterial compliance is essentially normal. Patients who have severe congestive heart failure or who have suffered a severe hemorrhage are likely to have a very small arterial pulse pressure because their stroke volumes are abnormally small. Conversely, individuals with large stroke volumes, as in aortic valve regurgitation, are likely to have an increased arterial pulse pressure. Similarly, well-trained athletes at rest tend to have large stroke volumes because their heart rates are usually low. The prolonged ventricular filling times in these individuals induce the ventricles to pump a large stroke volume, and hence their pulse pressure is large.

Peripheral Arterial Pressure Curves

The radial stretch of the ascending aorta brought about by left ventricular ejection initiates a pressure wave that is propagated down the aorta and its branches. The pressure wave travels much faster than the blood itself does. This pressure wave is the “pulse” that can be detected by palpating a peripheral artery.

IN THE CLINIC

In chronic hypertension, a condition characterized by a persistent elevation in TPR, the arterial pressure-volume curve resembles that shown in Figure 17-19, B. Because arteries become substantially less compliant when arterial pressure rises, an increase in TPR will elevate systolic pressure more than it will elevate diastolic pressure. Diastolic pressure is elevated in such individuals, but ordinarily not more than 10 to 40 mm Hg above the average normal level of 80 mm Hg. Not uncommonly, however, systolic pressure is elevated by 50 to 100 mm Hg above the average normal level of 120 mm Hg. The combination of increased resistance and diminished arterial compliance is represented in Figure 17-20.

Figure 17-20 Changes in aortic pressure induced by changes in arterial compliance and peripheral resistance (R_p) in an isolated heart preparation. As compliance was reduced from 43 to 14 to 3.6 units, pulse pressure increased significantly.

(Modified from Elizinga G, Westerhof N: Circ Res 32:178, 1973.)

The velocity of the pressure wave varies inversely with arterial compliance. In general, transmission velocity increases with age, thus confirming the observation that the arteries become less compliant with advancing age. Velocity also increases progressively as the pulse wave travels from the ascending aorta toward the periphery. This increase in velocity reflects the decrease in vascular compliance in the more distal than in the more proximal portions of the arterial system.

The arterial pressure contour becomes distorted as the wave is transmitted down the arterial system. This distortion in the pressure wave contour is demonstrated in Figure 17-21. These changes in contour are pronounced in young individuals, but they diminish with age. In elderly patients, the pulse wave may be transmitted virtually unchanged from the ascending aorta to the periphery.

Figure 17-21 Arterial pressure curves recorded from various sites. Aside from the increasing delay in the onset of the initial pressure rise, three major changes occur in the arterial pulse contour as the pressure wave travels distally. First, the systolic portions of the pressure wave become narrowed and elevated. In the figure, the systolic pressure at the level of the knee was 39 mm Hg greater than that recorded in the aortic arch. Second, the high-frequency components of the pulse, such as the incisura (i.e., the notch that appears at the end of ventricular ejection), are damped out and soon disappear. Third, a hump may appear on the diastolic portion of the pressure wave, at a point in the pressure wave just beyond the locus at which the incisura had initially appeared.

(From Remington JW, O’Brien LJ: Am J Physiol 218:437, 1970.)

Damping of the high-frequency components of the arterial pulse is largely caused by the elastic properties of the arterial walls. Several factors, including wave reflection and resonance, vascular tapering, and pressure-induced changes in transmission velocity, contribute to peaking of the arterial pressure wave.

Blood Pressure Measurement in Humans

In hospital intensive care units, needles or catheters may be introduced into the peripheral arteries of patients to measure arterial blood pressure directly by means of strain gauges. Ordinarily, blood pressure is estimated indirectly by means of a sphygmomanometer.

When blood pressure readings are taken from the arm, systolic pressure may be estimated by palpating the radial artery at the wrist (palpatory method). While pressure in the cuff exceeds the systolic level, no pulse is perceived. As pressure falls just below the systolic level (Fig. 17-22, A), a spurt of blood passes through the brachial artery under the cuff during the peak of systole, and a slight pulse will be felt at the wrist.

Figure 17-22 A to C, Measurement of arterial blood pressure with a sphygmomanometer.

The auscultatory method is a more sensitive and therefore a more precise technique for measuring systolic pressure, and it also permits diastolic pressure to be estimated. The practitioner listens with a stethoscope applied to the skin of the antecubital space over the brachial artery. While the pressure in the cuff exceeds systolic pressure, the brachial artery is occluded and no sounds are heard (Fig. 17-22, B). When the inflation pressure falls just below the systolic level (120 mm Hg in Fig. 17-22, A), a small spurt of blood escapes the occluding pressure of the cuff, and slight tapping sounds (called Korotkoff sounds) are heard with each heartbeat. The pressure at which the first sound is detected represents systolic pressure. It usually corresponds closely with the directly measured systolic pressure. As the inflation pressure of the cuff continues to fall, more blood escapes under the cuff per beat and the sounds become louder. When the inflation pressure approaches the diastolic level, the Korotkoff sounds become muffled. When the inflation pressure falls just below the diastolic level (80 mm Hg in Fig. 17-22, A), the sounds disappear; the pressure reading at this point indicates diastolic pressure. The origin of the Korotkoff sounds is related to the discontinuous spurts of blood that pass under the cuff and meet a static column of blood beyond the cuff; the impact and turbulence generate audible vibrations. Once the inflation pressure is less than diastolic pressure, flow is continuous in the brachial artery, and sounds are no longer heard (Fig. 17-22, C).

Capacitance and Resistance

Veins are elements of the circulatory system that return blood to the heart from tissues. Moreover, veins constitute a very large reservoir that contains up to 70% of the blood in the circulation. The reservoir function of veins makes them able to adjust blood volume returning to the heart, or preload, so that the needs of the body can be matched when cardiac output is altered (see Chapter 19). This high capacitance is an important property of veins.

The hydrostatic pressure in postcapillary venules is about 20 mm Hg, and it decreases to around 0 mm Hg in the thoracic venae cavae and right atrium. Hydrostatic pressure in the thoracic venae cavae and right atrium is also termed central venous pressure. Veins are very distensible and have very low resistance to blood flow. This low resistance allows movement of blood from peripheral veins to the heart with only small reductions in central venous pressure. Moreover, veins control filtration and absorption by adjusting postcapillary resistance (see later) and assist in the cardiovascular adjustments that accompany changes in body position.

The ability of veins to participate in these various functions depends on their distensibility, or compliance. Venous compliance varies with the position in the body such that veins in the lower limb are less compliant than those at or above the level of the heart. Veins in the lower limbs are also thicker than those in the brain or upper limbs. The compliance of veins, like that of arteries, decreases with age, and the vascular thickening that occurs is accompanied by a reduction in elastin and an increase in collagen content.

Variations in venous return are achieved by adjustments in venomotor tone, respiratory activity (see Chapter 19), and orthostatic stress or gravity.

Gravity

Gravitational forces may profoundly affect cardiac output. For example, soldiers standing at attention for a long time may faint because gravity causes blood to pool in the dependent blood vessels and thereby reduces cardiac output. Warm ambient temperatures interfere with the compensatory vasomotor reactions, and the absence of muscular activity exaggerates these effects. Gravitational effects are amplified in airplane pilots during pullout from dives. The centrifugal force in the footward direction may be several times greater than the force of gravity. Pilots characteristically black out momentarily during the pullout maneuver as blood is drained from the cephalic regions and pooled in the lower parts of the body.

Some explanations that have been advanced to explain the gravitationally induced reduction in cardiac output are inaccurate. For example, it has been argued that when an individual is standing, the force of gravity impedes venous return to the heart from the dependent regions of the body. This statement is incomplete because it ignores the gravitational counterforce on the arterial side of the same vascular circuit, and this counterforce facilitates venous return. Moreover, it ignores the effect of gravity in causing venous pooling. When standing upright, gravity will cause blood to accumulate in the lower extremities and distend both the arteries and veins. Because venous compliance is so much greater than arterial compliance, this distention occurs more on the venous than on the arterial side of the circuit.

The hemodynamic effects of such venous distention (venous pooling) resemble those caused by the hemorrhage of an equivalent volume of blood from the body. When an adult person shifts from a supine position to a relaxed standing position, 300 to 800 mL of blood pools in the legs. This pooling may reduce cardiac output by about 2 L/min. The compensatory adjustments to assumption of a standing position are similar to the adjustments to blood loss (see also Chapter 19). There is a reflex increase in heart rate and cardiac contractility. In addition, both arterioles and veins constrict, with the arterioles being affected to a greater extent than the veins.

Muscular Activity and Venous Valves

When a recumbent person stands but remains at rest, the pressure in the veins rises in the dependent regions of the body (Fig. 17-23). The venous pressure (P_v) in the legs increases gradually and does not reach an equilibrium value until almost 1 minute after standing. The slowness of this rise in P_v is attributable to the venous valves, which permit flow only toward the heart. When a person stands, the valves prevent blood in the veins from falling toward the feet. Hence, the column of venous blood is supported at numerous levels by these valves. Because of these valves, the venous column can be thought of as consisting of many discontinuous segments. However, blood continues to enter the column from many venules and small tributary veins, and the pressure continues to rise. As soon as the pressure in one segment exceeds that in the segment just above it, the intervening valve is forced open. Ultimately, all the valves are open and the column is continuous.

Figure 17-23 Mean pressures (±95% confidence intervals) in the foot veins of 18 human subjects during quiet standing, walking, and running.

(From Stick C et al: J Appl Physiol 72:2063, 1992.)

Precise measurement reveals that the final level of P_v in the feet during quiet standing is only slightly greater than that in a static column of blood extending from the right atrium to the feet. This finding indicates that the pressure drop caused by blood flow from the foot veins to the right atrium is very small. This very low resistance justifies considering all the veins as a common venous compliance in the circulatory system model illustrated in Chapter 19.

When an individual who has been standing quietly begins to walk, venous pressure in the legs decreases appreciably (Fig. 17-23). Because of the intermittent venous compression exerted by the contracting leg muscles and because of the operation of the venous valves, blood is forced from the veins toward the heart. Hence, muscular contraction lowers the mean venous pressure in the legs and serves as an auxiliary pump. Furthermore, muscular contraction prevents venous pooling and lowers capillary hydrostatic pressure. In this way, muscular contraction reduces the tendency for edema fluid to collect in the feet during standing.

Microcirculation

The microcirculation is defined as the circulation of blood through the smallest vessels of the body—arterioles, capillaries, and venules. Arterioles (5 to 100 μm in diameter) have a thick smooth muscle layer, a thin adventitial layer, and an endothelial lining (see Fig. 15-2). Arterioles give rise directly to capillaries (5 to 10 μm in diameter) or in some tissues to metarterioles (10 to 20 μm in diameter), which then give rise to capillaries (Fig. 17-24). Metarterioles can either bypass the capillary bed and connect to venules or directly connect to the capillary bed. Arterioles that give rise directly to capillaries regulate flow through these capillaries by constriction or dilation. The capillaries form an interconnecting network of tubes with an average length of 0.5 to 1 mm.

Figure 17-24 Composite schematic drawing of the microcirculation. The circular structures on the arteriole and venule represent smooth muscle fibers, and the branching solid lines represent sympathetic nerve fibers. The arrows indicate the direction of blood flow.