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CHAPTER 14 Overview of the Circulation: Pressure,...

CHAPTER 14 Overview of the Circulation: Pressure, UNIT IV Flow, and Resistance The function of the circulation is to serve the needs of The function of the capillaries is to exchange fluid, nutri- the body tissues—to transport nutrients to the tissues, to ents, electrolytes, hormones, and other substances between transport waste products away, transport hormones from the blood and interstitial fluid. To serve this role, the capil- one part of the body to another and, in general, to main- lary walls are thin and have numerous minute capillary pores tain an appropriate environment in all the tissue fluids for permeable to water and other small molecular substances. survival and optimal function of the cells. The venules collect blood from the capillaries and The rate of blood flow through many tissues is controlled gradually coalesce into progressively larger veins. mainly in response to their need for nutrients and removal of The veins function as conduits for transport of blood from waste products of metabolism. In some organs, such as the the venules back to the heart. The veins also serve as a major kidneys, the circulation serves additional functions. Blood reservoir of extra blood. Because the pressure in the venous flow to the kidney, for example, is far in excess of its metabolic system is low, the venous walls are thin. Even so, they are requirements and is related to its excretory function, which muscular enough to contract or expand and thereby serve as requires that a large volume of blood be filtered each minute. Pulmonary circulation The heart and blood vessels, in turn, are controlled to 9% provide the cardiac output and arterial pressure needed to supply adequate tissue blood flow. What are the mecha- nisms for controlling blood volume and blood flow, and how does this process relate to the other functions of the circulation? These are some of the topics and questions that we discuss in this section on the circulation. Aorta Superior vena cava PHYSICAL CHARACTERISTICS OF THE CIRCULATION The circulation, shown in Figure 14-1, is divided into Heart 7% the systemic circulation and the pulmonary circulation. Inferior Because the systemic circulation supplies blood flow to all vena cava the tissues of the body except the lungs, it is also called the Systemic greater circulation or peripheral circulation. vessels Functional Parts of the Circulation. Before discussing Arteries Systemic 13% the details of circulatory function, it is important to un- circulation derstand the role of each part of the circulation. 84% Arterioles The function of the arteries is to transport blood under and capillaries high pressure to the tissues. For this reason, the arter- 7% ies have strong vascular walls, and blood flows at a high velocity in the arteries. The arterioles are the last small branches of the arterial system; they act as control conduits through which blood is Veins, venules, and released into the capillaries. Arterioles have strong muscular venous sinuses walls that can close the arterioles completely or, by relax- 64% ing, can dilate the vessels severalfold; thus, the arterioles can Figure 14-1. Distribution of blood (in percentage of total blood) in vastly alter blood flow in each tissue in response to its needs. the different parts of the circulatory system. 171 UNIT IV The Circulation 120 Left Right Pulmonary 100 ventricular ventricular artery 80 pressure pressure pressure 60 Aortic pressure 40 20 0 120 100 Pulmonary Pulmonary Capillaries Capillaries Arterioles 80 ventricle Venules arteries atrium Veins Right Right veins 60 40 20 0 Arterioles ventricle arteries arteries atrium Large Small Aorta Left Left 0 Systemic Pulmonary Figure 14-2. Normal blood pressures (in mm Hg) in the different portions of the circulatory system when a person is lying in the horizontal position. a controllable reservoir for the extra blood, either a small or Note particularly that the cross-sectional areas of the a large amount, depending on the needs of the circulation.␣ veins are much larger than those of the arteries, averag- ing about four times those of the corresponding arteries. Volumes of Blood in the Different Parts of the This difference explains the large blood storage capac- Circulation. Figure 14-1 provides an overview of the cir- ity of the venous system in comparison with the arterial culation and lists the percentages of total blood volume system. in major segments of the circulation. For example, about Because the same volume of blood flow (F) must pass 84% of the entire blood volume of the body is in the sys- through each segment of the circulation each minute, the temic circulation, and 16% is in the heart and lungs. Of velocity of blood flow (v) is inversely proportional to the the 84% in the systemic circulation, approximately 64% is vascular cross-sectional area (A): in the veins, 13% is in the arteries, and 7% is in the sys- temic arterioles and capillaries. The heart contains 7% of v = F/A the blood, and the pulmonary vessels contain 9%. Thus, under resting conditions, the velocity averages Most surprising is the low blood volume in the capillaries. about 33 cm/sec in the aorta but is only 1/1000 as rapid It is here, however, that the most important function of the in the capillaries—about 0.3 mm/sec. However, because circulation occurs—diffusion of substances back and forth the capillaries have a typical length of only 0.3 to 1 mil- between the blood and tissues, as discussed in Chapter 16.␣ limeter, the blood remains in the capillaries for only 1 to 3 seconds, which is surprising because all diffusion Cross-Sectional Areas and Velocities of Blood Flow. If of nutrient food substances and electrolytes that occurs all the systemic vessels of each type were put side by side, through the capillary walls must be performed in this their approximate total cross-sectional areas for the aver- short time.␣ age human would be as follows: Vessel Cross-Sectional Area (cm2) Pressures in the Various Portions of the Circula- Aorta 2.5 tion. Because the heart pumps blood continually into the aorta, the mean pressure in the aorta is high, aver- Small arteries 20 aging about 100 mm Hg. Also, because heart pumping Arterioles 40 is pulsatile, the arterial pressure normally alternates Capillaries 2500 between an average systolic pressure level of 120 mm Venules 250 Hg and a diastolic pressure level of 80 mm Hg un- Small veins 80 der resting conditions, as shown on the left side of Venae cavae 8 Figure 14-2. 172  Chapter 14 Overview of the Circulation: Pressure, Flow, and Resistance As the blood flows through the systemic circulation, P1 Pressure gradient P2 its mean pressure falls progressively to about 0 mm Hg Blood flow by the time it reaches the termination of the superior and inferior venae cavae where they empty into the right Resistance atrium of the heart. UNIT XIV The pressure in many of the systemic capillaries varies Figure 14-3. Interrelationships of pressure, resistance, and blood from as high as 35 mm Hg near the arteriolar ends to as flow. P1, Pressure at the origin of the vessel; P2, pressure at the other end of the vessel. low as 10 mm Hg near the venous ends, but their aver- age functional pressure in most vascular beds is about 17 mm Hg, a pressure low enough that little of the plasma 2. Cardiac output is the sum of all the local tissue leaks through the minute pores of the capillary walls, even flows. When blood flows through a tissue, it imme- though nutrients can diffuse easily through these same diately returns by way of the veins to the heart. The pores to the outlying tissue cells. In some capillaries, such heart responds automatically to this increased in- as the glomerular capillaries of the kidneys, the pressure is flow of blood by pumping it immediately back into considerably higher, averaging about 60 mm Hg and caus- the arteries. Thus, as long as the heart is functioning ing much higher rates of fluid filtration. normally, it acts as an automaton, responding to the At the far-right side of Figure 14-2, note the respective demands of the tissues. The heart, however, often pressures in the different parts of the pulmonary circula- needs help in the form of special nerve signals to tion. In the pulmonary arteries, the pressure is pulsatile, make it pump the required amounts of blood flow. just as in the aorta, but the pressure is far less; pulmo- 3. Arterial pressure regulation is generally independent nary artery systolic pressure averages about 25 mm Hg of either local blood flow control or cardiac output and diastolic pressure averages about 8 mm Hg, with a control. The circulatory system is provided with an mean pulmonary arterial pressure of only 16 mm Hg. The extensive system for controlling the arterial blood mean pulmonary capillary pressure averages only 7 mm pressure. For example, if at any time the pressure Hg. Yet, the total blood flow through the lungs each min- falls significantly below the normal level of about ute is the same as through the systemic circulation. The 100 mm Hg, a barrage of nervous reflexes elicits a low pressures of the pulmonary system are in accord with series of circulatory changes to raise the pressure the needs of the lungs because all that is required is to back toward normal within seconds. The nervous expose the blood in the pulmonary capillaries to oxygen signals especially do the following: (a) increase the and other gases in the pulmonary alveoli.␣ force of heart pumping; (b) cause contraction of the large venous reservoirs to provide more blood to the heart; and (c) cause generalized constric- BASIC PRINCIPLES OF CIRCULATORY tion of the arterioles in many tissues so that more FUNCTION blood accumulates in the large arteries to increase Although the details of circulatory function are com- the arterial pressure. Then, over more prolonged plex, three basic principles underlie all functions of the periods—hours and days—the kidneys play an ad- system. ditional major role in pressure control by secret- 1. Blood flow to most tissues is controlled according to ing pressure-controlling hormones and regulating the tissue needs. When tissues are active, they need blood volume. an increased supply of nutrients and therefore more Thus, the needs of the individual tissues are served blood flow than when at rest, occasionally as much specifically by the circulation. In the remainder of this as 20 to 30 times the resting level. However, the heart chapter, we begin to discuss the basic control of tissue normally cannot increase its cardiac output more blood flow, cardiac output, and arterial pressure.␣ than four to seven times higher than resting levels. Therefore, it is not possible simply to increase blood INTERRELATIONSHIPS OF PRESSURE, flow everywhere in the body when a particular tissue FLOW, AND RESISTANCE demands increased flow. Instead, the microvessels of each tissue, especially the arterioles, continuously Blood flow through a blood vessel is determined by two monitor tissue needs, such as the availability of oxy- factors: (1) pressure difference of the blood between the gen and other nutrients and the accumulation of car- two ends of the vessel, also sometimes called the pressure bon dioxide and other tissue waste products. These gradient along the vessel, which pushes the blood through microvessels, in turn, dilate or constrict to control the vessel; and (2) the impediment to blood flow through local blood flow at the level required for the tissue the vessel, which is called vascular resistance. Figure 14-3 activity. Also, nervous control of the circulation from demonstrates these relationships, showing a blood vessel the central nervous system and hormones provides segment located anywhere in the circulatory system. additional help in controlling tissue blood flow. 173 UNIT IV The Circulation + + 0 0 N S N S − + − + − − A B Figure 14-4. A, Electromagnetic flowmeter showing generation of an electrical voltage in a wire as it passes through an electromagnetic field. B, Generation of an electrical voltage in electrodes on a blood vessel when the vessel is placed in a strong magnetic field, and blood flows through the vessel. C, Modern electromag- netic flowmeter probe for chronic implantation around blood vessels. N and S refer to the mag- C net’s north and south poles. P1 represents the pressure at the origin of the vessel Ordinarily, blood flow is expressed in milliliters per and P2 is the pressure at the other end. Resistance occurs minute or liters per minute, but it can be expressed in as a result of friction between the flowing blood and the milliliters per second or in any other units of flow and intravascular endothelium all along the inside of the ves- time. sel. The flow through the vessel can be calculated by the The overall blood flow in the total circulation of an following formula, which is called Ohm’s law: adult person at rest is about 5000 ml/min. This is called ∆P the cardiac output because it is the amount of blood F= pumped into the aorta by the heart each minute. R in which F is blood flow, ∆P is the pressure difference (P1 Methods for Measuring Blood Flow. Many mechanical − P2) between the two ends of the vessel, and R is the resis- and mechanoelectrical flowmeter devices can be inserted in se- tance. This formula states that the blood flow is directly ries with a blood vessel or, in some cases, applied to the outside proportional to the pressure difference but inversely pro- of the vessel to measure blood flow.␣ portional to the resistance. Electromagnetic Flowmeter. An electromagnetic flow- Note that it is the difference in pressure between the meter, the principles of which are illustrated in Figure two ends of the vessel, not the absolute pressure in the 14-4, can be used to measure blood flow experimentally vessel, that determines flow rate. For example, if the pres- without opening the blood vessel. Figure 14-4A shows sure at both ends of a vessel is 100 mm Hg and no differ- the generation of electromotive force (electrical voltage) in a wire that is moved rapidly in a cross-wise direction ence exists between the two ends, there will be no flow, through a magnetic field. This is the well-known princi- despite the presence of 100 mm Hg pressure. ple for production of electricity by the electric generator. Ohm’s law, illustrated in the preceding formula, Figure 14-4B shows that the same principle applies for expresses one of the most important of all the relation- generation of electromotive force in blood that is mov- ships that the reader needs to understand to compre- ing through a magnetic field. In this case, a blood vessel hend the hemodynamics of the circulation. Because is placed between the poles of a strong magnet, and elec- of the extreme importance of this formula, the reader trodes are placed on the two sides of the vessel perpen- should also become familiar with its other algebraic dicular to the magnetic lines of force. When blood flows forms: through the vessel, an electrical voltage proportional to the rate of blood flow is generated between the two electrodes, ∆P = F × R and this voltage is recorded using an appropriate voltmeter or electronic recording apparatus. Figure 14-4C shows an ∆P R= actual probe that is placed on a large blood vessel to record F its blood flow. The probe contains both the strong magnet and the electrodes. BLOOD FLOW A special advantage of the electromagnetic flowmeter is that it can record changes in flow in less than 1/100 of Blood flow rate means the quantity of blood that passes a second, allowing for the accurate recording of pulsatile a given point in the circulation in a given period of time. changes in flow, as well as steady flow.␣ 174  Chapter 14 Overview of the Circulation: Pressure, Flow, and Resistance Ultrasonic Doppler Flowmeter. Another type of flow- meter that can be applied to the outside of the vessel and that has many of the same advantages as the electro- A magnetic flowmeter is the ultrasonic Doppler flowmeter, shown in Figure 14-5. A minute piezoelectric crystal is UNIT XIV mounted at one end in the wall of the device. This crystal, when energized with an appropriate electronic apparatus, transmits ultrasound at a frequency of several hundred B thousand cycles per second downstream along the flow- ing blood. A portion of the sound is reflected by the red blood cells in the flowing blood. The reflected ultrasound waves then travel backward from the blood cells toward C the crystal. These reflected waves have a lower frequency Figure 14-6. A, Two fluids (one dyed red, and the other clear) before than the transmitted wave because the red blood cells are flow begins. B, The same fluids 1 second after flow begins. C, Turbu- moving away from the transmitter crystal. This effect is lent flow, with elements of the fluid moving in a disorderly pattern. called the Doppler effect. (It is the same effect that one experiences when a train approaches and passes by while at the right a clear fluid, but there is no flow in the blowing its whistle. Once the whistle has passed by the vessel. When the fluids are made to flow, a parabolic person, the pitch of the sound from the whistle suddenly interface develops between them, as shown 1 second becomes much lower than when the train is approaching.) For the flowmeter shown in Figure 14-5, the high- later in Figure 14-6B. The portion of fluid adjacent to frequency ultrasound wave is intermittently cut off, and the the vessel wall has hardly moved, the portion slightly reflected wave is received back onto the crystal and greatly away from the wall has moved a small distance, and amplified by the electronic apparatus. Another portion of the portion in the center of the vessel has moved a long the electronic apparatus determines the frequency difference distance. This effect is called the parabolic profile for between the transmitted wave and the reflected wave, thus velocity of blood flow. determining the velocity of blood flow. As long as the diam- The cause of the parabolic profile is as follows. The eter of a blood vessel does not change, changes in blood flow fluid molecules touching the wall move slowly because in the vessel are directly related to changes in flow velocity. of adherence to the vessel wall. The next layer of mol- Like the electromagnetic flowmeter, the ultrasonic ecules slips over these, the third layer over the second, Doppler flowmeter is capable of recording rapid pulsatile the fourth layer over the third, and so forth. Therefore, changes in flow, as well as steady flow.␣ the fluid in the middle of the vessel can move rapidly because many layers of slipping molecules exist between Laminar Flow of Blood in Vessels. When blood flows at the middle of the vessel and the vessel wall. Thus, each a steady rate through a long smooth blood vessel, it flows layer toward the center flows progressively more rapidly in streamlines, with each layer of blood remaining the than the outer layers.␣ same distance from the vessel wall. Also, the centralmost portion of the blood stays in the center of the vessel. This Turbulent Flow of Blood Under Some Conditions. type of flow is called laminar flow or streamline flow, in When the rate of blood flow becomes too great, when it contrast to turbulent flow, which is blood flowing in all passes by an obstruction in a vessel, when it makes a sharp directions in the vessel and continually mixing in the ves- turn, or when it passes over a rough surface, the flow may sel, as discussed subsequently.␣ then become turbulent, or disorderly, rather than stream- lined (Figure 14-6C). Turbulent flow means that the blood Parabolic Velocity Profile During Laminar Flow. flows crosswise in the vessel and along the vessel, usually When laminar flow occurs, the velocity of flow in the forming whorls in the blood, called eddy currents. These center of the vessel is far greater than that toward the eddy currents are similar to the whirlpools that can be outer edges. This phenomenon is demonstrated in seen in a rapidly flowing river at a point of obstruction. Figure 14-6. In Figure 14-6A, a vessel contains two When eddy currents are present, the blood flows with fluids, the one at the left colored by a dye and the one much greater resistance than when the flow is streamlined because eddies add to the overall friction of flow in the vessel tremendously. Crystal The tendency for turbulent flow increases in direct pro- portion to the velocity of blood flow, the diameter of the blood vessel, and the density of the blood and is inversely proportional to the viscosity of the blood, in accordance with the following equation: Transmitted Reflected ν⋅d⋅ρ wave wave Re = η Figure 14-5. Ultrasonic Doppler flowmeter. 175 UNIT IV The Circulation where Re is Reynolds’ number, the measure of the ten- recording the electrical signals on a high-speed electrical record- dency for turbulence to occur, v is the mean velocity of er. Each of these transducers uses a very thin, highly stretched blood flow (in cm/sec), d is the vessel diameter (in centi- metal membrane that forms one wall of the fluid chamber. The meters), ρ is density (in grams/ml), and η is the viscosity fluid chamber, in turn, is connected through a needle or cath- (in poise). The viscosity of blood is normally about 1/30 eter inserted into the blood vessel in which the pressure is to poise, and the density is only slightly greater than 1. When be measured. When the pressure is high, the membrane bulges Reynolds’ number rises above 200 to 400, turbulent flow slightly and, when it is low, it returns toward its resting position. will occur at some branches of vessels but will die out In Figure 14-7A, a simple metal plate is placed a few along the smooth portions of the vessels. However, when hundredths of a centimeter above the membrane. When Reynolds’ number rises above approximately 2000, turbu- the membrane bulges, the membrane comes closer to the lence will usually occur, even in a straight, smooth vessel. plate, which increases the electrical capacitance between Reynolds’ number for flow in the vascular system these two, and this change in capacitance can be recorded normally rises to 200 to 400, even in large arteries. As a using an appropriate electronic system. result, there is almost always some flow turbulence at the In Figure 14-7B, a small iron slug rests on the mem- branches of these vessels. In the proximal portions of the brane, and this slug can be displaced upward into a center aorta and pulmonary artery, Reynolds’ number can rise space inside an electrical wire coil. Movement of the iron to several thousand during the rapid phase of ejection into the coil increases the inductance of the coil, and this by the ventricles, which causes considerable turbulence too can be recorded electronically. in the proximal aorta and pulmonary artery, where many Finally, in Figure 14-7C, a very thin, stretched resist- conditions are appropriate for turbulence, such as the fol- ance wire is connected to the membrane. When this wire lowing: (1) high velocity of blood flow; (2) pulsatile nature is stretched greatly, its resistance increases; when it is of the flow; (3) sudden change in vessel diameter; and (4) stretched less, its resistance decreases. These changes can large vessel diameter. However, in small vessels, Reynolds’ also be recorded by an electronic system. number is almost never high enough to cause turbulence.␣ The electrical signals from the transducer are sent to an amplifier and then to an appropriate recording device. With some of these high-fidelity types of recording systems, pres- BLOOD PRESSURE sure cycles up to 500 cycles/sec have been recorded accu- rately. In common use are recorders capable of registering Standard Units of Pressure. Blood pressure almost al- pressure changes that occur as rapidly as 20 to 100 cycles/ ways is measured in millimeters of mercury (mm Hg) sec in the manner shown on the recorder in Figure 14-7C.␣ because the mercury manometer has been used as the standard reference for measuring pressure since its inven- tion in 1846 by Poiseuille. Actually, blood pressure means the force exerted by the blood against any unit area of the vessel wall. If the pressure in a vessel is 100 mm Hg, this A means that the force exerted is sufficient to push a col- umn of mercury against gravity up to a level 50 millim- eters high. Occasionally, pressure is measured in centimeters of water (cm H2O). A pressure of 10 cm H2O means a pres- B sure sufficient to raise a column of water against gravity to a height of 10 centimeters. One millimeter of mercury pressure equals 1.36 centimeters of water pressure because the specific gravity of mercury is 13.6 times that of water, and 1 centimeter is 10 times as great as 1 millimeter.␣ High-Fidelity Methods for Measuring Blood Pres- sure. The mercury in a manometer has so much inertia that it cannot rise and fall rapidly. For this reason, the mercury manometer, although excellent for recording steady pres- sures, cannot respond to pressure changes that occur more rapidly than about one cycle every 2 to 3 seconds. When- ever it is desired to record rapidly changing pressures, some other type of pressure recorder is necessary. Figure 14-7 demonstrates the basic principles of three electronic pressure C transducers commonly used for converting blood pressure and/ Figure 14-7. A–C, Principles of three types of electronic transducers or rapid changes in pressure into electrical signals and then for recording rapidly changing blood pressures (see text). 176  Chapter 14 Overview of the Circulation: Pressure, Flow, and Resistance RESISTANCE TO BLOOD FLOW d=1 1 ml/min Units of Resistance. Resistance is the impediment to P= d=2 16 ml/min blood flow in a vessel, but it cannot be measured by any 100 mm Hg direct means. Instead, resistance must be calculated from d=4 256 ml/min UNIT XIV measurements of blood flow and pressure difference be- A tween two points in the vessel. If the pressure difference between two points is 1 mm Hg and the flow is 1 ml/sec, the resistance is said to be 1 peripheral resistance unit, usually abbreviated PRU.␣ Small vessel Expression of Resistance in CGS Units. Occasionally, a basic physical unit called the CGS (centimeters, grams, seconds) unit is used to express resistance. This unit is B Large vessel dyne sec/cm5. Resistance in these units can be calculated Figure 14-8. A, Demonstration of the effect of vessel diameter on by the following formula: blood flow. B, Concentric rings of blood flowing at different veloci- ties; the farther away from the vessel wall, the faster the flow. d, diameter; P, pressure difference between the two ends of the vessels. ⎛ dyne sec ⎞ 1333 × mm Hg R ⎜ in ⎝ ⎟= cm5 ⎠ ml sec Small Changes in Vessel Diameter Markedly Change Its Conductance. Slight changes in the diameter of a vessel ␣Total Peripheral Vascular Resistance and Total Pul- cause tremendous changes in the vessel’s ability to conduct monary Vascular Resistance. The rate of blood flow blood when the blood flow is streamlined. This phenom- through the entire circulatory system is equal to the rate enon is illustrated in Figure 14-8A, which shows three ves- of blood pumping by the heart—that is, it is equal to the sels with relative diameters of 1, 2, and 4 but with the same cardiac output. In an adult human, this averages approx- pressure difference of 100 mm Hg between the two ends of imately 100 ml/sec. The pressure difference from the the vessels. Although the diameters of these vessels increase systemic arteries to the systemic veins is about 100 mm only fourfold, the respective flows are 1, 16, and 256 ml/ Hg. Therefore, the resistance of the entire systemic cir- min, which is a 256-fold increase in flow. Thus, the conduct- culation, called the total peripheral resistance, is about ance of the vessel increases in proportion to the fourth pow- 100/100, or 1 PRU. er of the diameter, in accordance with the following formula: In conditions in which all the blood vessels throughout Conductance ∝ Diameter 4 the body become strongly constricted, the total periph- eral resistance occasionally rises to as high as 4 PRU. Conversely, when the vessels become greatly dilated, the ␣Poiseuille’s Law. The cause of this great increase in con- resistance can fall to as little as 0.2 PRU. ductance when the diameter increases can be explained In the pulmonary system, the mean pulmonary arterial by referring to Figure 14-8B, which shows cross sections pressure averages 16 mm Hg and the mean left atrial pres- of a large and small vessel. The concentric rings inside the sure averages 2 mm Hg, giving a net pressure difference of vessels indicate that the velocity of flow in each ring is 14 mm. Therefore, when the cardiac output is normal at different from that in the adjacent rings because of lami- about 100 ml/sec, the total pulmonary vascular resistance nar flow, which was discussed earlier in the chapter. That calculates to be about 0.14 PRU (about one seventh that in is, the blood in the ring touching the wall of the vessel is the systemic circulation).␣ barely flowing because of its adherence to the vascular en- dothelium. The next ring of blood toward the center of the Conductance of Blood in a Vessel Is the Reciprocal vessel slips past the first ring and, therefore, flows more of Resistance. Conductance is a measure of the blood rapidly. Likewise, the third, fourth, fifth, and sixth rings flow through a vessel for a given pressure difference. This flow at progressively increasing velocities. Thus, the blood measurement is generally expressed in terms of ml/sec that is near the wall of the vessel flows slowly, whereas per mm Hg pressure, but it can also be expressed in terms that in the middle of the vessel flows much more rapidly. of L/sec per mm Hg or in any other units of blood flow In the small vessel, essentially all the blood is near the and pressure. wall, so the extremely rapidly flowing central stream of It is evident that conductance is the exact reciprocal of blood simply does not exist. By integrating the velocities resistance in accord with the following equation: of all the concentric rings of flowing blood and multiply- ing them by the areas of the rings, one can derive the fol- lowing formula, known as Poiseuille’s law: 1 Conductance = π∆ Pr 4 Resistance␣ F= 8 ηl 177 UNIT IV The Circulation in which F is the rate of blood flow, ∆P is the pressure dif- R1 R2 ference between the ends of the vessel, r is the radius of the vessel, l is length of the vessel, and η is viscosity of the blood. A Note particularly in this equation that the rate of blood R1 R flow is directly proportional to the fourth power of the 2 radius of the vessel, which demonstrates once again that the diameter of a blood vessel (which is equal to twice the radius) plays the greatest role of all factors in determining the rate of blood flow through a vessel.␣ B R3 R4 Importance of the Vessel Diameter Fourth Power Figure 14-9. Vascular resistance (R). A, In series. B, In parallel. Law in Determining Arteriolar Resistance. In the systemic circulation, about two thirds of the total sys- temic resistance to blood flow is resistance in the small arterioles. The internal diameters of the arterioles range from as little as 4 micrometers to as much as 25 mi- It is obvious that for a given pressure gradient, far crometers. However, their strong vascular walls allow greater amounts of blood will flow through this parallel the internal diameters to change tremendously, often as system than through any of the individual blood vessels. much as fourfold. From the fourth power law discussed Therefore, the total resistance is far less than the resis- earlier, which relates blood flow to diameter of the ves- tance of any single blood vessel. Flow through each of the sel, one can see that a fourfold increase in vessel diam- parallel vessels in Figure 14-9B is determined by the pres- eter can increase the flow as much as 256-fold. Thus, sure gradient and its own resistance, not the resistance of this fourth power law makes it possible for the arteri- the other parallel blood vessels. However, increasing the oles, responding with only small changes in diameter to resistance of any of the blood vessels increases the total nervous signals or local tissue chemical signals, either to vascular resistance. turn off the blood flow to the tissue almost completely It may seem paradoxical that adding more blood ves- or, at the other extreme, to cause a vast increase in flow. sels to a circuit reduces the total vascular resistance. Many Ranges of blood flow of more than 100-fold in separate parallel blood vessels, however, make it easier for blood to tissue areas have been recorded between the limits of flow through the circuit because each parallel vessel pro- maximum arteriolar constriction and maximum arteri- vides another pathway, or conductance, for blood flow. olar dilation.␣ The total conductance (Ctotal) for blood flow is the sum of the conductance of each parallel pathway: Resistance to Blood Flow in Series and Parallel Vas- cular Circuits. Blood pumped by the heart flows from the high- pressure part of the systemic circulation (i.e., For example, brain, kidney, muscle, gastrointestinal, aorta) to the low- pressure side (i.e., vena cava) through skin, and coronary circulations are arranged in parallel, many miles of blood vessels arranged in series and in and each tissue contributes to the overall conductance parallel. The arteries, arterioles, capillaries, venules, of the systemic circulation. Blood flow through each and veins are collectively arranged in series. When tissue is a fraction of the total blood flow (cardiac out- blood vessels are arranged in series, flow through each put) and is determined by the resistance (the reciprocal blood vessel is the same, and the total resistance to of conductance) for blood flow in the tissue, as well as blood flow (Rtotal) is equal to the sum of the resistances the pressure gradient. Therefore, amputation of a limb or of each vessel: surgical removal of a kidney also removes a parallel cir- cuit and reduces the total vascular conductance and total blood flow (i.e., cardiac output) while increasing the total The total peripheral vascular resistance is therefore peripheral vascular resistance.␣ equal to the sum of resistances of the arteries, arterioles, capillaries, venules, and veins. In the example shown in Effect of Blood Hematocrit and Blood Figure 14-9A, the total vascular resistance is equal to the Viscosity on Vascular Resistance and sum of R1 and R2. Blood Flow Blood vessels branch extensively to form parallel cir- Note that another important factor in Poiseuille’s equa- cuits that supply blood to the many organs and tissues of tion is the viscosity of the blood. The greater the viscosity, the body. This parallel arrangement permits each tissue the lower the flow in a vessel if all other factors are con- to regulate its own blood flow, to a great extent, indepen- stant. Furthermore, the viscosity of normal blood is about dently of flow to other tissues. three times as great as the viscosity of water. For blood vessels arranged in parallel (Figure 14-9B), What makes the blood so viscous? It is mainly the the total resistance to blood flow is expressed as follows: large numbers of suspended red cells in the blood, each 178  Chapter 14 Overview of the Circulation: Pressure, Flow, and Resistance 10 Viscosity of whole blood 9 100 100 100 8 Viscosity (water = 1) 7 90 90 90 UNIT XIV 6 80 80 80 5 4 70 70 70 Normal blood 3 2 Viscosity of plasma 60 60 60 1 Viscosity of water 50 50 50 0 0 10 20 30 40 50 60 70 40 40 40 Hematocrit 30 30 30 Figure 14-11. Effect of hematocrit on blood viscosity (water vis- cosity = 1). 20 20 20 2.5 10 10 10 2.0 Blood flow (× normal) 0 0 0 1.5 Normal Anemia Polycythemia Normal Figure 14-10. Hematocrit values in a healthy (normal) person and ol 1.0 contr in patients with anemia and polycythemia. The numbers refer to the Local percentage of the blood composed of red blood cells. Vasoconstrictor 0.5 of which exerts frictional drag against adjacent cells and 0 against the wall of the blood vessel. 0 50 100 150 200 Mean arterial pressure (mm Hg) Hematocrit—the Proportion of Blood That Is Red Figure 14-12. Effect of changes in arterial pressure over a period Blood Cells. If a person has a hematocrit of 40, this of several minutes on blood flow in a tissue such as skeletal muscle. means that 40% of the blood volume is cells, and the Note that between pressures of 70 and 175 mm Hg, blood flow is remainder is plasma. The hematocrit of adult men aver- autoregulated. The blue line shows the effect of sympathetic nerve ages about 42, whereas that of women averages about stimulation or vasoconstriction by hormones such as norepineph- rine, angiotensin II, vasopressin, or endothelin on this relationship. 38. These values can vary greatly, depending on wheth- Reduced tissue blood flow is rarely maintained for more than a few er the person has anemia, the degree of bodily activ- hours because of the activation of local autoregulatory mechanisms ity, and the altitude at which the person resides. These that eventually return blood flow toward normal. changes in hematocrit are discussed in relationship to the red blood cells and their oxygen transport function of hematocrit that they are not significant considerations in Chapter 33. in most hemodynamic studies. The viscosity of blood Hematocrit is determined by centrifuging blood in a plasma is about 1.5 times that of water.␣ calibrated tube, as shown in Figure 14-10. The calibra- tion allows direct reading of the percentage of cells.␣ EFFECTS OF PRESSURE ON VASCULAR RESISTANCE AND TISSUE BLOOD FLOW Increasing Hematocrit Markedly Increases Blood Vis- cosity. The viscosity of blood increases markedly as the Autoregulation Attenuates the Effect of Arterial hematocrit increases, as shown in Figure 14-11. The vis- Pressure on Tissue Blood Flow. From the discussion cosity of whole blood at a normal hematocrit is about 3 to thus far, one might expect an increase in arterial pres- 4, which means that three to four times as much pressure sure to cause a proportionate increase in blood flow is required to force whole blood as to force water through through the body’s tissues. However, the effect of arte- the same blood vessel. When the hematocrit rises to 60 rial pressure on blood flow in many tissues is usually far or 70, which it often does in persons with polycythemia, less than one might expect, as shown in Figure 14-12. the blood viscosity can become as great as 10 times that This is because an increase in arterial pressure not only of water, and its flow through blood vessels is greatly re- increases the force that pushes blood through the ves- tarded. sels, but also initiates compensatory increases in vascu- Other factors that affect blood viscosity are the lar resistance within a few seconds through activation of plasma protein concentration and types of proteins in the the local control mechanisms, discussed in Chapter 17. plasma, but these effects are so much less than the effect Conversely, with reductions in arterial pressure, vascular 179 UNIT IV The Circulation External (tissue) 7 pressure Pt Wall 6 Sympathetic thickness (h) inhibition Blood flow (ml/min) 5 Internal 4 (intravascular) Normal Critical Vessel pressure Pi 3 closing radius (r) pressure 2 Sympathetic 1 stimulation A Transmural pressure 0 ∆P = Pi – Pt 0 20 40 60 80 100 120 140 160 180 200 Tension (T) = ∆P(r/h) Arterial pressure (mm Hg) Figure 14-13. Effect of arterial pressure on blood flow through a passive blood vessel at different degrees of vascular tone caused by Shear stress increased or decreased sympathetic stimulation of the vessel. resistance is promptly reduced in most tissues, and blood B flow is maintained at a relatively constant rate. The abil- Figure 14-14. Illustration of the effects of vessel wall tension and ity of each tissue to adjust its vascular resistance and to shear stress on blood vessels. Wall tension develops in response to maintain normal blood flow during changes in arterial transmural pressure gradients and causes stretch of endothelial and pressure between approximately 70 and 175 mm Hg is vascular smooth muscle cells in all directions. Shear stress is the fric- called blood flow autoregulation. tional force or drag on endothelial cells caused by flowing blood. Note in Figure 14-12 that changes in blood flow can Shear stress results in unidirectional endothelial cell deformation. be caused by strong sympathetic stimulation, which constricts the blood vessels. Likewise, hormonal vaso- twofold or more. Conversely, very strong sympathetic constrictors, such as norepinephrine, angiotensin II, vaso- stimulation can constrict the vessels so much that blood pressin, or endothelin, can also reduce blood flow, at least flow occasionally decreases to as low as zero for a few sec- transiently. onds, despite high arterial pressure. Blood flow changes rarely last for more than a few hours In reality, there are few physiological conditions in in most tissues, even when increases in arterial pressure which tissues display the passive pressure-flow relation- or increased levels of vasoconstrictors are sustained. The ship shown in Figure 14-13. Even in tissues that do not reason for the relative constancy of blood flow is that each effectively autoregulate blood flow during acute changes tissue’s local autoregulatory mechanisms eventually over- in arterial pressure, blood flow is regulated according to ride most of the effects of vasoconstrictors to provide a the needs of the tissue when the pressure changes are sus- blood flow that is appropriate for the needs of the tissue.␣ tained, as discussed in Chapter 17.␣ Pressure-Flow Relationship in Passive Vascular Beds. Vascular Wall Tension. Tension on the blood vessel wall In isolated blood vessels or in tissues that do not exhibit develops in response to transmural pressure gradients autoregulation, changes in arterial pressure may have and causes vascular smooth muscle and endothelial cells important effects on blood flow. The effect of pressure to stretch in all directions (Figure 14-14A). According to on blood flow may be greater than that predicted by Poi- the law of Laplace, wall tension (T) for a thin-walled tube seuille’s equation, as shown by the upward curving lines is proportional to the transmural pressure gradient (∆P) in Figure 14-13. The reason for this is that increased ar- times the radius (r) of the blood vessel divided by its wall terial pressure not only increases the force that pushes thickness (h): blood through the vessels, but also distends the elastic T = ∆P × (r/h) vessels, actually decreasing vascular resistance. Con- versely, decreased arterial pressure in passive blood ves- Thus, larger blood vessels exposed to high pressures, sels increases resistance as the elastic vessels gradually such as the aorta, must have stronger walls to withstand collapse due to reduced distending pressure. When pres- higher levels of tension and are generally reinforced with sure falls below a critical level, called the critical closing fibrous bands of collagen. In contrast, capillaries have a pressure, flow ceases because the blood vessels are com- much smaller radii and therefore are exposed to much pletely collapsed. lower wall tension, permitting them to withstand pres- Sympathetic stimulation and other vasoconstrictors sures as high as 65 to 70 mm Hg in some organs such as can alter the passive pressure-flow relationship shown the kidneys. As discussed in Chapter 17, chronic changes in Figure 14-13. Thus, inhibition of sympathetic activity in blood pressure lead to remodeling of blood vessels to greatly dilates the vessels and can increase the blood flow accommodate the associated changes in wall tension.␣ 180  Chapter 14 Overview of the Circulation: Pressure, Flow, and Resistance Vascular Shear Stress. As blood flows it creates a fric- to accommodate the blood flow requirements of the tis- tional force, or drag, on the endothelial cells lining the sues. Endothelial cells contain multiple proteins that to- blood vessels (see Figure 14-14B). This force, called shear gether serve as mechanical sensors and regulate signaling stress, is proportional to the flow velocity and viscosity of pathways that shape the vasculature during embryonic the blood, inversely related to the radius cubed, and gen- development and continue altering blood vessel morphol- UNIT XIV erally is expressed in force/unit area (e.g., dynes/cm2). In ogy to optimize delivery of blood to tissues in adult life, as clinical practice, there is no single commonly used meth- discussed further in Chapter 17. od for measuring shear stress. However, despite its rela- tively low magnitude compared to contractile forces or wall stretch from blood pressure, shear stress is important Bibliography in the development and adaptation of the vascular system See the bibliography for Chapter 15. 181