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

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.

Shear Stress on the Vessel Wall

As blood flows through a vessel, it exerts a force on the vessel wall parallel to the wall. This force is called a shear stress (τ). Shear stress is directly proportional to the flow rate and viscosity of the fluid:

Equation 17-13

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.

Functional Properties of Capillaries

In metabolically active organs, such as the heart, skeletal muscle, and glands, capillary density is high. In less active tissues, such as subcutaneous tissue or cartilage, capillary density is low. Capillary diameter also varies. Some capillaries have diameters smaller than those of erythrocytes. Passage through these tiny vessels requires the erythrocytes to become temporarily deformed. Fortunately, normal erythrocytes are quite flexible.

Blood flow in capillaries depends chiefly on the contractile state of arterioles. The average velocity of blood flow in capillaries is approximately 1 mm/sec; however, it can vary from zero to several millimeters per second in the same vessel within a brief period. These changes in capillary blood flow may be random or rhythmic. The rhythmic oscillatory behavior of capillaries is caused by contraction and relaxation (vasomotion) of the precapillary vessels (i.e., the arterioles and small arteries).

Vasomotion is an intrinsic contractile behavior of vascular smooth muscle and is independent of external input. Changes in transmural pressure (intravascular minus extravascular pressure) also influence the contractile state of precapillary vessels. An increase in transmural pressure, caused either by an increase in venous pressure or by dilation of arterioles, results in contraction of the terminal arterioles. A decrease in transmural pressure causes precapillary vessel relaxation (see Chapter 18). Humoral and possibly neural factors also affect vasomotion. For example, when increased transmural pressure causes the precapillary vessels to contract, the contractile response can be overridden and vasomotion abolished. This effect is accomplished by metabolic (humoral) factors when the O₂ supply becomes too low for the requirements of parenchymal tissue, as occurs in skeletal muscle during exercise.

Although a reduction in transmural pressure relaxes the terminal arterioles, blood flow through the capillaries cannot increase if the reduction in intravascular pressure is caused by severe constriction of the upstream microvessels. Large arterioles and metarterioles also exhibit vasomotion. However, their contraction does not usually completely occlude the lumen of the vessel and arrest blood flow, whereas contraction of the terminal arterioles may arrest blood flow. Thus, the flow rate in capillaries may be altered by contraction and relaxation of small arteries, arterioles, and metarterioles.

Blood flow through the capillaries has been called nutritional flow because it provides for exchange of gases and solutes between blood and tissue. Conversely, blood flow that bypasses the capillaries as it passes from the arterial to the venous side of the circulation has been termed nonnutritional, or shunt, flow (Fig. 17-24). In some areas of the body (e.g., fingertips, ears), true AV shunts exist (see Chapter 18). However, in many tissues, such as muscle, anatomic shunts are lacking. Even in the absence of these shunts, nonnutritional flow can occur. In tissues with metarterioles, nonnutritional flow may be continuous from arteriole to venule during low metabolic activity, when many precapillary vessels are closed. When metabolic activity increases in these tissues, more precapillary vessels open to permit capillary perfusion.

True capillaries lack smooth muscle and are therefore incapable of active constriction. Nevertheless, the endothelial cells that form the capillary wall contain actin and myosin, and they can alter their shape in response to certain chemical stimuli.

Because of their narrow lumens (i.e., small radius), the thin-walled capillaries can withstand high internal pressures without bursting. This property can be explained in terms of the law of Laplace:

Equation 17-16

where

The Laplace equation applies to very thin-walled vessels, such as capillaries. Wall tension opposes the distending force (Pr) that tends to pull apart a theoretical longitudinal slit in the vessel (Fig. 17-25). Transmural pressure in a blood vessel in vivo is essentially equal to intraluminal pressure because extravascular pressure is generally negligible. To calculate wall tension, pressure in mm Hg is converted to dynes per square centimeter according to the equation P = hρg, where h is the height of an Hg column in centimeters, ρ is the density of Hg in g/cm³, and g is gravitational acceleration in cm/s². For a capillary with a pressure of 25 mm Hg and a radius of 5 × 10⁻⁴ cm, the pressure (2.5 cm Hg × 13.6 g/cm³ × 980 cm/sec²) is 3.33 × 10⁴ dyne/cm. Wall tension is then 16.7 dyne/cm². For an aorta with a pressure of 100 mm Hg and a radius of 1.5 cm, wall tension is 2 × 10⁵ dyne/cm. Thus, at the pressures normally found in the aorta and capillaries, the wall tension of the aorta is about 12,000 times greater than that of the capillaries. In a person standing quietly, capillary pressure in the feet may reach 100 mm Hg. Even under such conditions, capillary wall tension increases to a value that is still only one three-thousandth of the wall tension in the aorta at the same internal pressure.

Figure 17-25 Diagram of a small blood vessel to illustrate the law of Laplace: T = Pr, where P = intraluminal pressure, r = radius of the vessel, and T = wall tension as the force per unit length tangential to the vessel wall. Wall tension acts to prevent rupture along a theoretical longitudinal slit in the vessel.

The diameter of the resistance vessels (arterioles) is determined by the balance between the contractile force of the vascular smooth muscle and the distending force produced by intraluminal pressure. The greater the contractile activity of the vascular smooth muscle of an arteriole, the smaller its diameter. In small arterioles, contraction can continue to the point at which the vessel is completely occluded. Occlusion is caused by infolding of the endothelium and by trapping of blood cells in the vessel.

With a progressive reduction in intravascular pressure, vessel diameter decreases (as does vessel wall tension—the law of Laplace) and blood flow eventually ceases, although pressure within the arteriole is still greater than tissue pressure. The pressure that causes flow to cease has been called the critical closing pressure, and its mechanism is still controversial. This critical closing pressure is low when vasomotor activity is reduced by inhibition of sympathetic nerve activity in the vessel and is increased when vasomotor tone is enhanced by activation of the vascular sympathetic nerve fibers.

Vasoactive Role of the Capillary Endothelium

For many years, the endothelium of capillaries was thought to be an inert single layer of cells that served solely as a passive filter to permit the passage of water and small molecules across the blood vessel wall and to retain blood cells and large molecules (proteins) within the vascular compartment. However, the endothelium is now recognized to be an important source of substances that cause contraction or relaxation of vascular smooth muscle.

One of these substances is prostacyclin (PGI₂). PGI₂ can relax vascular smooth muscle via an increase in cAMP (Fig. 17-26). PGI₂ is formed in the endothelium from arachidonic acid, and the process is catalyzed by PGI₂ synthase. The mechanism that triggers synthesis of PGI₂ is not known. However, PGI₂ may be released by an increase in shear stress caused by accelerated blood flow. The primary function of PGI₂ is to inhibit platelet adherence to the endothelium and platelet aggregation and thus prevent intravascular clot formation. PGI₂ also causes relaxation of vascular smooth muscle.

Figure 17-26 Endothelium- and non–endothelium-mediated vasodilation. Prostacyclin (PGI₂) is formed from arachidonic acid (AA) by the action of cyclooxygenase (Cyc Ox) and prostacyclin synthase (PGI₂ Syn) in the endothelium and elicits relaxation of the adjacent vascular smooth muscle via increases in cAMP. Stimulation of the endothelial cells with acetylcholine (ACh) or other agents (see text) results in the formation and release of an endothelium-derived relaxing factor identified as nitric oxide (NO). NO stimulates guanylyl cyclase (G Cyc) to increase cGMP in the vascular smooth muscle to produce relaxation. The vasodilator agent nitroprusside (NP) acts directly on vascular smooth muscle. Substances such as adenosine, H⁺, CO₂, and K⁺ can arise in the parenchymal tissue and elicit vasodilation by direct action on vascular smooth muscle.

Of far greater importance in endothelium-mediated vascular dilation is the formation and release of nitric oxide (NO), a component of endothelium-derived relaxing factor (Fig. 17-26). When endothelial cells are stimulated by acetylcholine or other vasodilator agents (ATP, bradykinin, serotonin, substance P, histamine), NO is released. These agents do not cause vasodilation in blood vessels lacking the endothelium. NO (synthesized from L-arginine) activates guanylyl cyclase in vascular smooth muscle to increase [cGMP], which produces relaxation by decreasing myofilament sensitivity to [Ca⁺⁺]. Release of NO can be stimulated by the shear stress of blood flow on the endothelium. The drug nitroprusside also increases cGMP by acting directly on vascular smooth muscle; it is not endothelium mediated. Vasodilator agents such as adenosine, H⁺, CO₂, and K⁺ may be released from parenchymal tissue and act locally on resistance vessels (Fig. 17-26).

Acetylcholine also causes the release of an endothelium-dependent hyperpolarizing factor that underlies the relaxation of adjacent smooth muscle. Although arachidonic acid metabolites have been suggested, the factor remains unknown. Moreover, how the factor reaches vascular smooth muscle (diffusion through the extracellular space or passage via myoepithelial junctions) is unclear. Nevertheless, there are diverse ways by which endothelial cells communicate with vascular smooth muscle.

The endothelium can also synthesize endothelin, a potent vasoconstrictor peptide. Endothelin can affect vascular tone and blood pressure in humans and may be involved in such pathological states as atherosclerosis, pulmonary hypertension, congestive heart failure, and renal failure.

Passive Role of the Capillary Endothelium

Transcapillary Exchange.

Solvent and solute move across the capillary endothelial wall by three processes: diffusion, filtration, and pinocytosis. Diffusion is the most important process for transcapillary exchange and pinocytosis is the least important.

DIFFUSION

Under normal conditions, only about 0.06 mL of water per minute moves back and forth across the capillary wall per 100 g of tissue as a result of filtration and absorption. In contrast, 300 mL of water per minute per 100 g of tissue moves across the capillary wall by diffusion, a 5000-fold difference.

When filtration and diffusion are related to blood flow, about 2% of the plasma passing through the capillaries is filtered. In contrast, the diffusion of water is 40 times greater than the rate at which it is brought to the capillaries by blood flow. The transcapillary exchange of solutes is also primarily governed by diffusion. Thus, diffusion is the key factor in providing exchange of gases, substrates, and waste products between capillaries and tissue cells.

The process of diffusion is described by Fick’s law (see also Chapter 1):

Equation 17-17

where

J = quantity of a substance moved per unit time

D = free diffusion coefficient for a particular molecule

A = cross-sectional area of the diffusion pathway

= concentration gradient of the solute

For diffusion across a capillary wall, Fick’s law can also be expressed as

Equation 17-18

where

P = capillary permeability to the substance

S = capillary surface area

C_i=concentration of the substance inside the capillary

C_o=concentration of the substance outside the capillary

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The PS product provides a convenient expression of available capillary surface area because the intrinsic permeability of the capillary is rarely altered much under physiological conditions (capillary permeability may be altered as with a bee sting).

In capillaries, diffusion of lipid-insoluble molecules is restricted to water-filled channels or pores. Movement of solute across the capillary endothelium is complex and involves corrections for attractions between solute and solvent molecules, interactions between solute molecules, pore configuration, and charge on the molecules relative to charge on the endothelial cells. Such solute motion is not simply a matter of random thermal movement of molecules down a concentration gradient. For small molecules, such as water, NaCl, urea, and glucose, the capillary pores offer little restriction to diffusion (i.e., they have a low reflection coefficient—see later). Diffusion of these substances is so rapid that the mean concentration gradient across the capillary endothelium is extremely small. The greater the size of the lipidinsoluble molecules, the more restricted their diffusion through capillaries. Diffusion eventually becomes minimal when the molecular weight of the molecules exceeds about 60,000. With small molecules, the only limitation to net movement across the capillary wall is the rate at which blood flow transports the molecules to the capillary. Transport of these molecules is said to be flow limited.

With flow-limited small molecules, the concentration of the molecule in blood reaches equilibrium with its concentration in interstitial fluid at a location near the origin of the capillary from its parent arteriole. Its concentration falls to negligible levels near the arterial end of the capillary (Fig. 17-27, A). If the flow is large, the small molecule can still be present at a distant locus downstream in the capillary. A somewhat larger molecule will move farther along the capillary before it reaches an insignificant concentration in blood. Furthermore, the number of still larger molecules that enter the arterial end of the capillary but cannot pass through the capillary pores equals the number that leaves the venous end of the capillary (see Fig. 17-27, A).

Figure 17-27 Flow- and diffusion-limited transport from capillaries (Cap) to tissue. A, Flow-limited transport. The smallest water-soluble inert tracer particles (blue dots) reach negligible concentrations after passing only a short distance down the capillary. Larger particles (circles) with similar properties travel farther along the capillary before reaching an insignificant intracapillary concentration. Both substances cross the interstitial fluid (ISF) and reach the parenchymal tissue (Cell). Because of their size, more of the smaller particles are taken up by the tissue cells. The largest particles cannot penetrate the capillary pores and hence do not escape from the capillary lumen except by pinocytotic vesicle transport. An increase in the volume of blood flow or an increase in capillary density increases tissue supply of the diffusible solutes. Note that capillary permeability is greater at the venous end of the capillary (also in the venule, not shown) because of the larger number of pores in this region. B, Diffusion-limited transport. When the distance between the capillaries and parenchymal tissue is large as a result of edema or low capillary density, diffusion becomes a limiting factor in the transport of solutes from capillary to tissue, even at high rates of capillary blood flow.

With large molecules, diffusion across the capillaries becomes the limiting factor (diffusion limited). That is, the permeability of a capillary to a large solute molecule limits its transport across the capillary wall. Diffusion of small lipid-insoluble molecules is so rapid that diffusion limits blood-tissue exchange only when distances between capillaries and parenchymal cells are great (e.g., tissue edema or very low capillary density) (Fig. 17-27, B).

Movement of lipid-soluble molecules across the capillary wall is not limited to capillary pores (only about 0.02% of the capillary surface) but also occurs directly through the lipid membranes of the entire capillary endothelium. Consequently, lipid-soluble molecules move rapidly between blood and tissue. The degree of lipid solubility (oil-to-water partition coefficient) provides a good index of the ease of transfer of lipid molecules through the capillary endothelium.

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O₂ and CO₂ are both lipid soluble, and they readily pass through endothelial cells. Calculations based on (1) the diffusion coefficient for O₂, (2) capillary density and diffusion distances, (3) blood flow, and (4) tissue O₂ consumption indicate that the O₂ supply of normal tissue at rest and during activity is not limited by diffusion or by the number of open capillaries.

Measurements of the partial pressure of O₂ (PO₂) and O₂ saturation of blood in microvessels indicate that in many tissues, O₂ saturation at the entrance of capillaries has decreased to about 80% as a result of diffusion of O₂ from arterioles and small arteries. Moreover, CO₂ loading and the resulting intravascular shifts in the oxyhemoglobin dissociation curve occur in the precapillary vessels. Hence, in addition to gas exchange at the capillaries, O₂ and CO₂ pass directly between adjacent arterioles and venules and possibly between arteries and veins (countercurrent exchange). This countercurrent exchange represents a diffusional shunt of gas away from the capillaries; this shunt may limit the supply of O₂ to the tissue at low blood flow rates.

CAPILLARY FILTRATION.

The permeability of the capillary endothelial membrane is not uniform. Thus, the liver capillaries are quite permeable, and albumin escapes from them at a rate several times greater than that from the less permeable muscle capillaries. Furthermore, permeability is not uniform along the length of the capillary. The venous ends are more permeable than the arterial ends, and permeability is greatest in the venules, a property attributed to the greater number of pores in these regions.

Where does filtration occur? Some water passes through the capillary endothelial cell membranes, but most flows through apertures (pores) in the endothelial walls of the capillaries (Figs. 17-28 and 17-29). The pores in skeletal and cardiac muscle capillaries have diameters of about 4 nm. There are clefts between adjacent endothelial cells in mouse cardiac muscle, and the gap at the narrowest point is about 4 nm. The clefts (pores) are sparse and represent only about 0.02% of the capillary surface area. Pores are absent in cerebral capillaries, where the blood-brain barrier blocks the entry of many small molecules.

Figure 17-28 A, Cross-sectioned capillary in a mouse ventricular wall. The luminal diameter is approximately 4 μm. In this thin section, the capillary wall is formed by a single endothelial cell (Nu, endothelial nucleus), which forms a functional complex (arrow) with itself. The thin pericapillary space is occupied by a pericyte (PC) and a connective tissue (CT) cell (“fibroblast”). Note the numerous endothelial vesicles (V). B, Detail of the endothelial cell in A showing plasmalemmal vesicles (V) attached to the endothelial cell surface. These vesicles are especially prominent in vascular endothelium and are involved in transport of substances across the blood vessel wall. Note the complex alveolar vesicle (asterisk). BM, basement membrane. C, Junctional complex in a capillary of a mouse heart. “Tight” junctions (TJ) typically form in these small blood vessels and appear to consist of fusions between apposed endothelial cell surface membranes. D, Interendothelial junction in a muscular artery of monkey papillary muscle. Although tight junctions similar to those of capillaries are found in these large blood vessels, extensive junctions that resemble gap junctions in the intercalated disks between myocardial cells often appear in arterial endothelium (example shown at GJ).

Figure 17-29 Diagrammatic sketch of an electron micrograph of a composite capillary in cross section.

In addition to clefts, some of the more porous capillaries (e.g., in the kidney, intestine) contain fenestrations 20 to 100 nm wide, whereas other capillaries (e.g., in the liver) have a discontinuous endothelium (Fig. 17-29). Fenestrations and discontinuous endothelium permit the passage of molecules that are too large to pass through the intercellular clefts of the endothelium.

The direction and magnitude of water movement across the capillary wall can be estimated as the algebraic sum of the hydrostatic and osmotic pressure that exists across the membrane. An increase in intracapillary hydrostatic pressure favors movement of fluid from the vessel interior to the interstitial space, whereas an increase in the concentration of osmotically active particles within vessels favors movement of fluid into the vessels from the interstitial space (Fig. 17-30).

Figure 17-30 Schematic representation of the factors responsible for filtration and absorption across the capillary wall and the formation of lymph.

Hydrostatic Forces.

Hydrostatic pressure (blood pressure) within capillaries is not constant. Instead, it depends on arterial and venous pressure and on precapillary (arterioles) and postcapillary (venules and small veins) resistance. An increase in arterial or venous pressure elevates capillary hydrostatic pressure, whereas a reduction in arterial or venous pressure has the opposite effect. An increase in arteriolar resistance or closure of arteries reduces capillary pressure, whereas a greater resistance to flow in venules and veins increases capillary pressure.

Hydrostatic pressure is the principal force in capillary filtration. A given change in venous pressure produces a greater effect on capillary hydrostatic pressure than does the same change in arterial pressure. About 80% of an increase in venous pressure is transmitted back to the capillaries.

Capillary hydrostatic pressure (P_c) varies from tissue to tissue. Average values, obtained from direct measurements in human skin, are about 32 mm Hg at the arterial end of capillaries and about 15 mm Hg at the venous end of capillaries at the level of the heart (Fig. 17-30). As discussed previously, when a person stands, hydrostatic pressure increases in the legs and decreases in the head.

Tissue pressure, or more specifically interstitial fluid pressure (P_i) outside the capillaries, opposes capillary filtration. P_c − P_i constitutes the driving force for filtration. Normally, P_i is close to zero, so P_c essentially represents the hydrostatic driving force.

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Osmotic Forces.

The key factor that restrains fluid loss from capillaries is the osmotic pressure of plasma proteins (such as albumin). This osmotic pressure is called colloid osmotic pressure or oncotic pressure (π_p). The total osmotic pressure of plasma is about 6000 mm Hg (reflecting the presence of electrolytes and other small molecules), whereas oncotic pressure is only about 25 mm Hg. This small oncotic pressure is an important factor in fluid exchange across the capillary because plasma proteins are essentially confined to the intravascular space, whereas electrolytes are virtually equal in concentration on both sides of the capillary endothelium. The relative permeability of solute to water influences the actual magnitude of osmotic pressure. The reflection coefficient (σ) is the relative impediment to the passage of a substance through the capillary membrane. The reflection coefficient of water is zero and that of albumin (to which the endothelium is essentially impermeable) is 1. Filterable solutes have reflection coefficients between 0 and 1. In addition, different tissues have different reflection coefficients for the same molecule. Hence, movement of a given solute across the endothelial wall varies with the tissue. True oncotic pressure (π) is defined by the following equation (see also Chapter 1):

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Equation 17-19

where

σ = reflection coefficient

R = gas constant

T = temperature in degrees Kelvin

C_i and C_o = solute concentration inside and outside the capillary, respectively

Albumin is the most important plasma protein determining oncotic pressure. The average albumin molecule (molecular weight of 69,000) is approximately half the size of the average globulin molecule, and it is present at almost twice the concentration as that of globulins (4.5 versus 2.5 g/dL of plasma). Albumin also exerts a greater osmotic force than can be accounted for solely on the basis of its concentration in plasma. Therefore, it cannot be completely replaced by inert substances of appropriate molecular size, such as dextran. This additional osmotic force becomes disproportionately great at high concentrations of albumin (as in plasma), and this force is weak to absent in dilute solutions of albumin (as in interstitial fluid). The reason for this activity of albumin is its negative charge at normal blood pH. Albumin binds a small number of Cl⁻ ions, which increases the negative charge and hence the ability to retain more Na⁺ inside the capillaries (see Chapter 2). This small increase in the electrolyte concentration of plasma over that of interstitial fluid produced by the negatively charged albumin enhances its osmotic force to that of an ideal solution containing a solute with a molecular weight 37,000. If albumin had a molecular weight of 37,000, it would not be retained by the capillary endothelium because of its small size. Hence, albumin could not function as a counterforce to capillary hydrostatic pressure. If albumin did not exert this enhanced osmotic force, a concentration of about 12 g of albumin/dL of plasma would be required to achieve a plasma oncotic pressure of 25 mm Hg. Such a high albumin concentration would greatly increase blood viscosity and hence would increase resistance to blood flow through the vascular system.

IN THE CLINIC

With prolonged standing, particularly when associated with some elevation of venous pressure in the legs (such as that caused by pregnancy) or with sustained increases in venous pressure (as seen in congestive heart failure), filtration is greatly enhanced, and it exceeds the capacity of the lymphatic system to remove the capillary filtrate from the interstitial space.

The concentration of plasma proteins may also change in different pathological states and thus alter the osmotic force and movement of fluid across the capillary membrane. The plasma protein concentration is increased in dehydration (e.g., water deprivation, prolonged sweating, severe vomiting, diarrhea). In this condition, water moves by osmotic force from the tissues to the vascular compartment. In contrast, the plasma protein concentration is reduced in some renal diseases because of its loss in urine, and edema may occur.

When capillary injury is extensive, as in severe burns, intravascular fluid and plasma protein leak into the interstitial space in the damaged tissues. The protein that escapes from the vessel lumen increases the oncotic pressure of the interstitial fluid. This greater osmotic force outside the capillaries leads to additional fluid loss and possibly to severe dehydration of the patient.

Small amounts of albumin escape from the capillaries and enter the interstitial fluid, where they exert a very small osmotic force (0.1 to 5 mm Hg). This force, π_i, is small because the concentration of albumin in interstitial fluid is low and because at low concentrations, albumin cannot enhance the osmotic force as much as it does at high concentrations.

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Balance of Hydrostatic and Osmotic Forces.

The relationship between hydrostatic pressure and oncotic pressure and the role of these forces in regulating fluid passage across the capillary endothelium were expounded by Starling in 1896. This relationship constitutes the Starling hypothesis. It can be expressed by the equation

Equation 17-20

where

Q_f = fluid movement

P_c = capillary hydrostatic pressure

P_i = interstitial fluid hydrostatic pressure

π_p = plasma oncotic pressure

π_i = interstitial fluid oncotic pressure

k = filtration constant for the capillary membrane

Filtration occurs when the algebraic sum is positive; absorption occurs when it is negative.

Traditionally, filtration was considered to occur at the arterial end of the capillary and absorption was considered to occur at its venous end because of the gradient of hydrostatic pressure along the capillary. This scheme is true for an idealized capillary (Fig. 17-30). However, in well-perfused capillaries, arteriolar vasoconstriction can reduce P_c such that absorption is allowed transiently. With continued vasoconstriction, absorption will diminish with time because fluid absorption increases π_i (the interstitial protein concentration rises) and decreases P_i. Direct observations have revealed that many capillaries only filter, whereas others only absorb. In some vascular beds (e.g., the renal glomerulus), hydrostatic pressure in the capillary is high enough to cause filtration along the entire length of the capillary. In other vascular beds (e.g., the intestinal mucosa), the hydrostatic and oncotic forces are such that absorption occurs along the whole capillary.

Capillary pressure depends on several factors, the principal one being the contractile state of the precapillary vessel. Normally, arterial pressure, venous pressure, postcapillary resistance, interstitial fluid hydrostatic and oncotic pressure, and plasma oncotic pressure are relatively constant. A change in precapillary resistance influences fluid movement across the capillary wall. Because water moves so quickly across the capillary endothelium, the hydrostatic and osmotic forces equilibrate along the entire capillary. Hence, in the normal state, filtration and absorption across the capillary wall are well balanced. Only a small percentage (2%) of the plasma that flows through the vascular system is filtered. Of this, about 85% is absorbed in the capillaries and venules. The remainder returns to the vascular system as lymph fluid, along with the albumin that escapes from the capillaries.

In the lungs, mean capillary hydrostatic pressure is only about 8 mm Hg (see Chapter 22). Because plasma oncotic pressure is 25 mm Hg and lung interstitial fluid pressure is approximately 15 mm Hg, the net force slightly favors reabsorption. Despite the predominance of reabsorption, pulmonary lymph is formed. This lymph consists of fluid that is osmotically withdrawn from the capillaries by the small amount of plasma protein that escapes through the capillary endothelium.

IN THE CLINIC

In pathological conditions, such as left ventricular failure or mitral valve stenosis, pulmonary capillary hydrostatic pressure may exceed plasma oncotic pressure. When this occurs, it may cause pulmonary edema, a condition in which excessive fluid accumulates in the pulmonary interstitium. This fluid accumulation seriously interferes with gas exchange in the lungs.

Capillary Filtration Coefficient.

The rate of fluid movement (Q_f) across the capillary membrane depends not only on the algebraic sum of the hydrostatic and osmotic forces across the endothelium (ΔP) but also on the area (A_m) of the capillary wall available for filtration, the distance (Δx) across the capillary wall, the viscosity (η) of the filtrate, and the filtration constant (k) of the membrane. These factors may be expressed by the equation

Equation 17-21

The dimensions of Q_r are units of flow per unit of pressure gradient across the capillary wall per unit of capillary surface area. This expression, which describes the flow of fluid through the membrane pores, is essentially Poiseuille’s law for flow through tubes.

Because the thickness of the capillary wall and the viscosity of the filtrate are relatively constant, they can be included in the filtration constant k. If the area of the capillary membrane is not known, the rate of filtration can be expressed per unit weight of tissue. Hence, the equation can be simplified to

Equation 17-22

where k_t is the capillary filtration coefficient for a given tissue and the units for Q_f are milliliters per minute per 100 g of tissue per mm Hg pressure.

In any given tissue, the filtration coefficient per unit area of capillary surface, and hence capillary permeability, is not changed by various physiological conditions, such as arteriolar dilation and capillary distention, or by such adverse conditions as hypoxia, hypercapnia, or reduced pH. When capillaries are injured (as by toxins or severe burns), significant amounts of fluid and protein leak out of the capillaries into the interstitial space. This increase in capillary permeability is reflected by an increase in the filtration coefficient.

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Because capillary permeability is constant under normal conditions, the filtration coefficient can be used to determine the relative number of open capillaries (i.e., the capillary surface area available for filtration in tissue). For example, the increased metabolic activity of contracting skeletal muscle relaxes the precapillary resistance vessels and hence opens more capillaries. This process, called capillary recruitment, increases the filtering surface area.

Disturbances in Hydrostatic-Osmotic Balance.

Relatively small changes in arterial pressure may have little effect on filtration. The change in pressure may be countered by adjustments in precapillary resistance vessels (autoregulation; see Chapter 18) so that hydrostatic pressure remains constant in the open capillaries. However, a severe reduction in mean arterial pressure usually evokes arteriolar constriction mediated by the sympathetic nervous system. This response may occur in hemorrhage, and it is often accompanied by a fall in venous pressure. These changes reduce capillary hydrostatic pressure. However, the low blood pressure in hemorrhage causes a decrease in blood flow (and hence in O₂ supply) to the tissue, with the result that vasodilator metabolites accumulate and relax the arterioles. Precapillary vessel relaxation also occurs because of the reduced transmural pressure (autoregulation, see Chapter 18). Consequently, absorption predominates over filtration, and fluid moves from the interstitium into the capillary. These responses to hemorrhage constitute one of the compensatory mechanisms used by the body to restore blood volume (see Chapter 19).

An increase in venous pressure alone, as occurs in the feet when a person stands up, would elevate capillary pressure and enhance filtration. However, the increase in transmural pressure closes precapillary vessels (myogenic mechanism; see Chapter 18), and hence the capillary filtration coefficient actually decreases. This reduction in capillary surface available for filtration prevents large amounts of fluid from leaving the capillaries and entering the interstitial space.

In a normal individual, the filtration coefficient (k_t) for the whole body is about 0.006 mL/min/100 g of tissue/mm Hg. For a 70-kg man, an elevation in venous pressure of 10 mm Hg for 10 minutes would increase filtration from capillaries by 342 mL. Edema does not usually occur because the fluid is returned to the vascular compartment by the lymphatic vessels. When edema develops, it usually appears in the dependent parts of the body, where the hydrostatic pressure is greatest, but its location and magnitude are also determined by the type of tissue. Loose tissues, such as the subcutaneous tissue around the eyes or in the scrotum, are more prone than firm tissues, such as in a muscle, or encapsulated structures, such as in a kidney, to collect larger quantities of interstitial fluid.

PINOCYTOSIS

Some transfer of substances across the capillary wall can occur in tiny pinocytotic vesicles. These vesicles (Figs. 17-28 and 17-29), formed by pinching off of the endothelial cell membrane, can take up substances on one side of the capillary wall, move them across the cell by kinetic energy, and deposit their contents on the other side—a process termed transcytosis. The amount of material transported in this way is very small relative to that moved by diffusion. However, pinocytosis may be responsible for the movement of large (30 nm) lipid-insoluble molecules between blood and interstitial fluid. The number of pinocytotic vesicles in endothelium varies among tissues (muscle > lung > brain), and the number increases from the arterial to the venous end of the capillary.

Physical Factors

The primary factor responsible for perfusion of the myocardium is aortic pressure. Changes in aortic pressure generally evoke parallel directional changes in coronary blood flow. This is caused in part by changes in coronary perfusion pressure. However, the major factor in the regulation of coronary blood flow is a change in arteriolar resistance engendered by changes in the metabolic activity of the heart. When the metabolic activity of the heart increases, coronary resistance decreases; when cardiac metabolism decreases, coronary resistance increases (see Chapter 18).

If a cannulated coronary artery is perfused by blood from a pressure-controlled reservoir, perfusion pressure can be altered without changing aortic pressure and cardiac work. The relationship between initial and steady-state blood flow is shown in the experiment in Figure 17-32. This is an example of autoregulation of blood flow, which is discussed in Chapter 18. Blood pressure is kept within narrow limits by baroreceptor reflex mechanisms. Hence, changes in coronary blood flow are mainly caused by changes in the diameter of coronary resistance vessels in response to the metabolic demands of the heart.

Figure 17-32 Pressure-flow relationships in the coronary vascular bed. At constant aortic pressure, cardiac output, and heart rate, coronary artery perfusion pressure was abruptly increased or decreased from the control level indicated by the point where the two lines cross. The closed circles represent the flows that were obtained immediately after the change in perfusion pressure; the open circles represent the steady-state flows at the new pressures. There is a tendency for flow to return toward the control level (autoregulation of blood flow), and this is most prominent over the intermediate pressure range (about 60 to 180 mm Hg).

(From Berne RM, Rubio R: Coronary circulation. In Handbook of Physiology (sect 2): The Cardiovascular System: The Heart, vol 1. Bethesda, MD, American Physiological Society, 1979.)

In addition to providing the pressure to move blood through the coronary vessels, the heart also affects its blood supply by the squeezing effect (extravascular compression) of the contracting myocardium on its own blood vessels. The patterns of coronary flow in the left and right coronary arteries are shown in Figure 17-33.

Figure 17-33 Comparison of phasic coronary blood flow in the left and right coronary arteries. Extravascular compression is so great during early ventricular systole that blood flow in the large coronary arteries supplying the left ventricle is briefly reversed. Maximal left coronary inflow occurs in early diastole, when the ventricles have relaxed and extravascular compression of the coronary vessels is virtually absent. After an initial reversal in early systole, left coronary blood flow follows the aortic pressure until early diastole, when it rises abruptly and then declines slowly as aortic pressure falls during the remainder of diastole.

Left ventricular myocardial pressure (pressure within the wall of the left ventricle) is greatest near the endocardium and least near the epicardium. This pressure gradient does not normally impair endocardial blood flow because the greater blood flow to the endocardium during diastole compensates for the greater blood flow to the epicardium during systole. Measurements of coronary blood flow indicate that blood flow to the epicardial and endocardial halves of the left ventricle is approximately equal under normal conditions. Because extravascular compression is greatest at the endocardial surface of the ventricle, the equality of epicardial and endocardial blood flow indicates that the tone of the endocardial resistance vessels is less than that of the epicardial vessels.

The flow pattern in the right coronary artery is similar to that in the left coronary artery (Fig. 17-33). In contrast to the left ventricle, reversal of blood flow does not occur in the right ventricle in early systole because the thin right ventricle develops a lower pressure during systole. Hence, systolic blood flow constitutes a much greater proportion of total coronary inflow than it does in the left coronary artery.

The extent to which extravascular compression restricts coronary inflow can be readily seen when the heart is suddenly arrested in diastole or with the induction of ventricular fibrillation. Figure 17-34, A, depicts mean left coronary flow when the vessel was perfused with blood at a constant pressure from a reservoir. When ventricular fibrillation was electrically induced, an immediate and substantial increase in blood flow occurred. A subsequent increase in coronary resistance over a period of many minutes reduced myocardial blood flow to below the level that existed before induction of ventricular fibrillation (Fig. 17-34, B, just before stellate ganglion stimulation).

Figure 17-34 A, Unmasking of the restricting effect of ventricular systole on mean coronary blood flow by induction of ventricular fibrillation during perfusion of the left coronary artery at constant pressure. With the onset of ventricular fibrillation, coronary blood flow increases abruptly because extravascular compression is removed. Flow then gradually returns toward and often falls below the prefibrillation level. This increase in coronary resistance that occurs despite the removal of extravascular compression demonstrates the heart’s ability to adjust its blood flow to meet its energy requirements. B, Effect of cardiac sympathetic nerve stimulation on coronary blood flow and coronary sinus blood O₂ tension in a fibrillating heart during perfusion of the left coronary artery at constant pressure. (Berne RM: Unpublished observations.)

When diastolic pressure in the coronary arteries is abnormally low (such as in severe hypotension, partial coronary artery occlusion, or severe aortic stenosis), the ratio of endocardial to epicardial blood flow falls below a value of 1. This ratio indicates that blood flow to the endocardial regions is more severely impaired than that to the epicardial regions of the ventricle. There is also an increase in the gradient of myocardial lactic acid and myocardial adenosine concentrations from epicardium to endocardium. For this reason, the myocardial damage observed in atherosclerotic heart disease (e.g., after coronary occlusion) is greatest in the inner wall of the left ventricle.

Tachycardia and bradycardia have dual effects on coronary blood flow. A change in heart rate mainly alters diastole. In tachycardia, the proportion of time spent in systole, and consequently the period of restricted inflow, increases. However, this mechanical effect is overridden by the dilation of coronary resistance vessels associated with the increased metabolic activity of the more rapidly beating heart. With bradycardia the opposite occurs; coronary inflow is less restricted (more time in diastole), but so are the metabolic (O₂) requirements of the myocardium.

Neural and Neurohumoral Factors

Stimulation of cardiac sympathetic nerves markedly increases coronary blood flow. However, the increase in flow is associated with an increased heart rate and more forceful systole. The stronger contraction and the tachycardia tend to restrict coronary flow. The increase in myocardial metabolic activity, however, tends to dilate coronary resistance vessels. The increase in coronary blood flow evoked by cardiac sympathetic nerve stimulation reflects the sum of these factors. In perfused hearts in which the mechanical effect of extravascular compression is eliminated by cardiac arrest or by ventricular fibrillation, an initial coronary vasoconstriction is often observed. After this initial vasoconstriction, the metabolic effect evokes vasodilation (see Fig. 17-34, B).

Furthermore, when β-adrenergic receptor blockade eliminates the positive chronotropic and inotropic effects, activation of the cardiac sympathetic nerves increases coronary resistance. These observations indicate that the primary action of the sympathetic nerve fibers on the coronary resistance vessels is vasoconstriction.

α-Adrenergic receptors (constrictors) and βadrenergic receptors (dilators) are present on the coronary vessels. Coronary resistance vessels also participate in the baroreceptor and chemoreceptor reflexes, and the sympathetic constrictor tone of the coronary arterioles can be modulated by such reflexes. Nevertheless, coronary resistance is predominantly under local nonneural control.

Vagus nerve stimulation slightly dilates the coronary resistance vessels, and activation of the carotid and aortic chemoreceptors can slightly decrease coronary resistance via the vagus nerves to the heart. Failure of strong vagal stimulation to increase coronary blood flow is not due to lack of muscarinic receptors on the coronary resistance vessels because intracoronary administration of acetylcholine elicits marked vasodilation.

Metabolic Factors

A striking characteristic of the coronary circulation is the close relationship between the level of myocardial metabolic activity and the magnitude of coronary blood flow (Fig. 17-35). This relationship is also found in a denervated heart and in a completely isolated heart, either in the beating or in the fibrillating state. The fibrillating ventricles can fibrillate for many hours when the coronary arteries are perfused with arterial blood from some external source. As already noted, a fibrillating heart uses less O₂ than a pumping heart does, and blood flow to the myocardium is reduced accordingly.

Figure 17-35 Relationship between myocardial O₂ consumption and coronary blood flow during a variety of interventions that increase or decrease the myocardial metabolic rate.

(From Berne RM, Rubio R: Coronary circulation. In Handbook of Physiology (sect 2): The Cardiovascular System: The Heart, vol 1. Bethesda, MD, American Physiological Society, 1979.)

The mechanisms that link the cardiac metabolic rate and coronary blood flow remain unsettled. However, it appears that a decrease in the ratio of O₂ supply to O₂ demand releases vasodilator substances from the myocardial cells into the interstitial fluid, where they relax the coronary resistance vessels. Decreases in arterial blood O₂ content or in coronary blood flow and increases in metabolic rate all decrease the O₂ supply-demand ratio (Fig. 17-36). As a consequence, vasodilator substances are released. These substances dilate the arterioles and thereby adjust the O₂ supply to the O₂ demand. A decrease in O₂ demand diminishes the release of vasodilators and permits greater expression of basal tone.

Figure 17-36 Imbalance in the O₂ supply–O₂ demand ratio alters coronary blood flow by the rate of release of a vasodilator metabolite from cardiomyocytes. A decrease in the ratio elicits an increase in vasodilator release, whereas an increase in the ratio has the opposite effect.

Numerous metabolites mediate the vasodilation that accompanies increased cardiac work. Accumulation of vasoactive metabolites can also account for the increase in blood flow that results from a brief period of ischemia (i.e., reactive hyperemia—see Chapter 18). The duration of the enhanced coronary flow after release of the briefly occluded vessel is, within certain limits, proportional to the duration of the period of occlusion. Among the factors implicated in reactive hyperemia are ATP-sensitive K⁺ (K_ATP) channels, NO, CO₂, H⁺, K⁺, hypoxia, and adenosine.

Of these agents, the key factors appear to be adenosine, NO, and opening of the K_ATP channels. The contributions of each of these agents and their interaction under basal conditions and during increased myocardial activity are complex. A reduction in oxidative metabolism in vascular smooth muscle reduces ATP synthesis, which in turn opens K_ATP channels and causes hyperpolarization. This change in potential reduces entry of Ca⁺⁺ and relaxes coronary vascular smooth muscle to increase flow. A reduction in ATP also opens K_ATP channels in cardiac muscle and generates an outward current that reduces the duration of the action potential and limits entry of Ca⁺⁺ during phase 2 of the action potential. This action may serve a protective role during periods of imbalance between O₂ supply and demand. Additionally, the release of vasodilators, such as NO and adenosine, dilates the arterioles and thereby adjusts the O₂ supply to the O₂ demand. At low concentrations, adenosine appears to activate endothelial K_ATP channels and to enhance release of NO. Conversely, at higher concentrations, adenosine acts directly on vascular smooth muscle by activating K_ATP channels. Decreased O₂ demand would sustain the ATP level, as well as reduce the amount of vasodilator substances released and permit greater expression of basal tone. If production of all three agents is inhibited, coronary blood flow is reduced, both at rest and during exercise. Furthermore, contractile dysfunction and signs of myocardial ischemia become evident.

According to the adenosine hypothesis, a reduction in myocardial O₂ tension produced by inadequate coronary blood flow, hypoxemia, or increased metabolic activity of the heart leads to release of adenosine from the myocardium. Adenosine enters the interstitial fluid space to reach the coronary resistance vessels and induces vasodilation by activating adenosine receptors. However, it cannot be responsible for the increased coronary flow observed during prolonged enhancement of cardiac metabolic activity because release of adenosine from cardiac muscle is transitory. Little evidence exists that CO₂, H⁺, or O₂ play a significant direct role in the regulation of coronary blood flow. Factors that alter coronary vascular resistance are illustrated in Figure 17-37.

Figure 17-37 Schematic representation of factors that increase (+) or decrease (−) coronary vascular resistance. Intravascular pressure (arterial blood pressure) stretches the vessel wall.

Neural Factors

The skin contains essentially two types of resistance vessels: arterioles and arteriovenous anastomoses. AV anastomoses shunt blood from the arterioles to the venules and venous plexuses; hence, they bypass the capillary bed. Such anastomoses are found in the fingertips, palms of the hands, toes, soles of the feet, ears, nose, and lips. AV anastomoses differ morphologically from arterioles; the anastomoses are either short, straight, or long coiled vessels, about 20 to 40 μm in luminal diameter, and they have thick muscular walls richly supplied with nerve fibers (Fig. 17-39). These vessels are almost exclusively under sympathetic neural control, and they dilate maximally when their nerve supply is interrupted. Conversely, reflex stimulation of the sympathetic fibers to these vessels may constrict them and obliterate the vascular lumen. Although AV anastomoses do not exhibit basal tone, they are highly sensitive to vasoconstrictor agents such as epinephrine and norepinephrine. Furthermore, AV anastomoses are not under metabolic control, and they do not show reactive hyperemia or autoregulation of blood flow. Thus, regulation of blood flow through these anastomotic channels is governed principally by the nervous system in response to reflex activation by temperature receptors or from higher centers of the central nervous system.

Figure 17-39 AV anastomosis in the ear injected with Berlin blue. A, artery; V, vein; arrow points to an AV anastomosis. The walls of the AV anastomosis in the fingertips are thicker and more cellular.

(From Pritchard MML, Daniel PM: J Anat 90:309, 1956.)

Most of the resistance vessels in the skin exhibit some basal tone and are under dual control of the sympathetic nervous system and local regulatory factors. However, neural control predominates. Stimulation of sympathetic nerve fibers induces vasoconstriction, and cutting the sympathetic nerves induces vasodilation. After chronic denervation of the cutaneous blood vessels, the degree of tone that existed before denervation is gradually regained over a period of several weeks. This restoration of tone is accomplished by an enhancement of basal tone. Denervation of the skin vessels results in enhanced sensitivity to catecholamines in circulation (denervation hypersensitivity).

Parasympathetic vasodilator nerve fibers do not innervate cutaneous blood vessels. However, stimulation of the sweat glands, which are innervated by sympathetic cholinergic fibers, dilates the skin resistance vessels. Sweat contains an enzyme that lyses a protein (kallidin) in the tissue fluid to produce bradykinin, a polypeptide with potent vasodilator properties. Bradykinin, formed locally, dilates the arterioles and increases blood flow to the skin.

Certain skin vessels, particularly those in the head, neck, shoulders, and upper part of the chest, are regulated by higher centers in the brain. Blushing, in response to embarrassment or anger, and blanching, in response to fear or anxiety, are examples of cerebral inhibition and stimulation, respectively, of the sympathetic nerve fibers to the affected cutaneous regions.

In contrast to AV anastomoses in the skin, the resistance vessels display autoregulation of blood flow and reactive hyperemia. If the arterial inflow to a limb is stopped by inflating a blood pressure cuff briefly, the skin becomes bright red below the point of vascular occlusion when the cuff is subsequently deflated. The increased cutaneous blood flow (reactive hyperemia) is also manifested by distention of the superficial veins in the affected extremity.

The Role of Temperature in the Regulation of Skin Blood Flow

The primary function of the skin is to maintain a constant internal environment and protect the body from adverse changes. Ambient temperature is one of the most important external variables with which the body must contend. Exposure to cold elicits a generalized cutaneous vasoconstriction that is especially pronounced in the hands and feet. This response is chiefly mediated by the nervous system. Arrest of the circulation to a hand by a pressure cuff plus immersion of that hand in cold water induces vasoconstriction in the skin of the other extremities that are exposed to room temperature. When the circulation to the chilled hand is not occluded, the reflex generalized vasoconstriction is caused in part by the cooled blood that returns to the general circulation. This returned blood then stimulates the temperature-regulating center in the anterior hypothalamus, which also responds to direct application of cold to evoke cutaneous vasoconstriction.

The skin vessels of the cooled hand also respond directly to cold. Moderate cooling or a brief exposure to severe cold (0° C to 15° C) constricts the resistance and capacitance vessels, including the AV anastomoses. Prolonged exposure to severe cold evokes a secondary vasodilator response. Prompt vasoconstriction and severe pain are elicited by immersion of the hand in ice water. However, this response is soon followed by dilation of the skin vessels, with reddening of the immersed part and alleviation of the pain. With continued immersion of the hand, alternating periods of constriction and dilation occur, but the skin temperature rarely drops as much as it did in response to the initial vasoconstriction. Prolonged severe cold, of course, damages tissue. The rosy faces of people exposed to a cold environment are examples of cold vasodilation. However, blood flow through the skin of the face may be greatly reduced despite the flushed appearance. The red color of the slowly flowing blood is mainly caused by reduced O₂ uptake by the cold skin and the cold-induced shift of the oxyhemoglobin dissociation curve to the left (see Chapter 23).

Direct application of heat to the skin not only dilates the local resistance and capacitance vessels and AV anastomoses but also reflexly dilates blood vessels in other parts of the body. The local effect is independent of the vascular nerve supply, whereas the reflex vasodilation is a combined response to stimulation of the anterior hypothalamus by the returning warmed blood and stimulation of cutaneous heat receptors in the heated regions of the skin.

The close proximity of the major arteries and veins permits countercurrent heat exchange between them. Cold blood that flows in veins from a cooled hand toward the heart takes up heat from adjacent arteries; this warms the venous blood and cools the arterial blood. Heat exchange takes place in the opposite direction when the extremity is exposed to heat. Thus, heat conservation is enhanced during exposure of extremities to cold environments, and heat conservation is minimized during exposure of the extremities to warm environments.

Neural Factors

The resistance vessels of muscle possess a high degree of basal tone; they also display tone in response to continuous low-frequency activity in the sympathetic vasoconstrictor nerve fibers. The basal firing frequency of sympathetic vasoconstrictor fibers is only about 1 to 2 per second, and maximal vasoconstriction occurs at frequencies of about 10 per second.

Vasoconstriction evoked by sympathetic nerve activity is caused by the local release of norepinephrine. Intraarterially injected norepinephrine elicits only vasoconstriction (α-adrenergic receptor). In contrast, low doses of epinephrine produce vasodilation (β-adrenergic receptor), whereas large doses cause vasoconstriction.

Baroreceptor reflexes greatly influence the tonic activity of the sympathetic nerves. An increase in carotid sinus pressure dilates the muscle vascular bed, whereas a decrease in carotid sinus pressure elicits vasoconstriction (Fig. 17-40). When sympathetic constrictor tone is high, the decrease in blood flow evoked by common carotid artery occlusion is small, but the increase in flow after the release of occlusion is large. The vasodilation produced by baroreceptor stimulation is caused by inhibition of sympathetic vasoconstrictor activity.

Figure 17-40 Evidence for participation of the muscle vascular bed in vasoconstriction and vasodilation mediated by the carotid sinus baroreceptors after common carotid artery occlusion and release. In this preparation, the sciatic and femoral nerves constituted the only direct connection between the hind leg muscle mass and the rest of the dog. The muscle was perfused by blood at a constant pressure that was completely independent of the animal’s arterial pressure.

(Redrawn from Jones RD, Berne RM: Am J Physiol 204:461, 1963.)

The resistance vessels in skeletal muscle contribute significantly to maintenance of arterial blood pressure because skeletal muscle constitutes a large fraction of the body’s mass and hence the muscle vasculature constitutes the largest vascular bed. Participation of the skeletal muscle vessels in vascular reflexes is important in maintaining normal arterial blood pressure.

A comparison of the sympathetic neural effects on the blood vessels of muscle and skin is summarized in Figure 17-41. Note that the lower the basal tone of the skin vessels, the greater their constrictor response; also note the absence of active cutaneous vasodilation.

Figure 17-41 Basal tone and the range of response of resistance vessels in muscle (dashed lines) and skin (shaded area) to stimulation and section of sympathetic nerves. Peripheral resistance is plotted on a logarithmic scale.

(Redrawn from Celander O, Folkow B: Acta Physiol Scand 29:241, 1953.)

Local Factors

In active skeletal muscle, blood flow is regulated by metabolic factors. In resting muscle, neural factors predominate, and they superimpose neurogenic tone on basal tone (Fig. 17-41). Cutting the sympathetic nerves to muscle abolishes the neural component of vascular tone, and it unmasks the intrinsic basal tone of the blood vessels. The neural and local mechanisms that regulate blood flow oppose each other, and during muscle contraction the local vasodilator mechanism supervenes. However, during exercise, strong sympathetic nerve stimulation slightly attenuates the vasodilation induced by locally released metabolites.

Neural Factors

The cerebral vessels are innervated by cervical sympathetic nerve fibers that accompany the internal carotid and vertebral arteries into the cranial cavity. The importance of neural regulation of the cerebral circulation is controversial. The sympathetic control of cerebral vessels appears to be weaker than that in other vascular beds, and the contractile state of cerebrovascular smooth muscle appears to depend mainly on local metabolic factors.

Local Factors

Generally, total cerebral blood flow is relatively constant. However, regional blood flow in the brain is associated with regional neural activity. For example, movement of one hand results in increased blood flow only in the hand area of the contralateral sensorimotor and premotor cortex. In addition, talking, reading, and other stimuli to the cerebral cortex are associated with increased blood flow in the appropriate regions of the contralateral cortex (Fig. 17-42). Glucose uptake also corresponds with regional cortical neuronal activity. Thus, when the retina is stimulated by light, uptake of glucose is enhanced in the visual cortex.

Figure 17-42 Effects of different stimuli on regional blood flow in the contralateral human cerebral cortex. Sens 1, low-intensity electrical stimulation of the hand; Sens 2, high-intensity electrical stimulation of the hand (pain).

(Redrawn from Ingvar DH: Brain Res 107:181, 1976.)

The cerebral vessels are very sensitive to CO₂ tension. Increases in arterial blood CO₂ tension (PCO₂) elicit marked cerebral vasodilation; inhalation of 7% CO₂ increases cerebral blood flow twofold. Conversely, decreases in PCO₂, as caused by hyperventilation, diminish cerebral blood flow. CO₂ causes these changes by altering perivascular (and probably intracellular vascular smooth muscle) pH, which in turn alters arterial resistance to flow. By independently changing PCO₂ and the bicarbonate concentration, pial vessel (vessels of the pia mater) diameter and blood flow were shown to be inversely related to pH, regardless of the level of PCO₂.

CO₂ can diffuse to vascular smooth muscle from brain tissue or from the lumen of the vessels, whereas H⁺ in blood is prevented from reaching arteriolar smooth muscle by the blood-brain barrier. Hence, the cerebral vessels dilate when the [H⁺] of cerebrospinal fluid is increased, but these vessels dilate only minimally in response to an increase in the [H⁺] of arterial blood.

[K⁺] also affects cerebral blood flow. Hypoxia, electrical stimulation of the brain, and seizures elicit rapid increases in cerebral blood flow and in perivascular [K⁺]. The increases in [K⁺] are similar in magnitude to those that produce pial arteriolar dilation when K⁺ is applied topically to these vessels. However, the increase in [K⁺] is not sustained throughout the period of cerebral stimulation. Thus, only the initial increase in cerebral blood flow can be attributed to the release of K⁺.

Adenosine affects cerebral blood flow. Adenosine levels in the brain increase in response to ischemia, hypoxemia, hypotension, hypocapnia, electrical stimulation of the brain, and induced seizures. Topically applied adenosine is a potent dilator of the pial arterioles. Any intervention that either reduces the O₂ supply to the brain or increases the O₂ requirements of the brain results in the rapid (within 5 seconds) formation of adenosine in cerebral tissue. Unlike the changes in pH or K⁺, the adenosine concentration of the brain increases with initiation of the change in O₂ supply, and it remains elevated throughout the period of O₂ imbalance. The adenosine that is released into cerebrospinal fluid during cerebral ischemia becomes incorporated into adenine nucleotides in cerebral tissue. These local factors—pH, K⁺, and adenosine—may all act in concert to adjust cerebral blood flow to the metabolic activity of the brain.

The cerebral circulation displays reactive hyperemia and excellent autoregulation when arterial blood pressure is between 60 and 160 mm Hg. Mean arterial pressures below 60 mm Hg result in reduced cerebral blood flow and then syncope, whereas mean pressures above 160 mm Hg may lead to increased permeability of the blood-brain barrier and consequently to cerebral edema. Hypercapnia or any other potent vasodilator abolishes autoregulation of cerebral blood flow. None of the candidates for metabolic regulation of cerebral blood flow account for this phenomenon. Hence, autoregulation of cerebral blood flow is probably mediated by a myogenic mechanism, but experimental proof is still lacking.