VENTILATION PERFUSION RELATIONSHIPS

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1 CHAPTER 17 VENTILATION PERFUSION RELATIONSHIPS Peter D. Wagner STRUCTURAL AND FUNCTIONAL BASIS OF VENTILATION, PERFUSION, AND GAS EXCHANGE The lung exists for gas exchange, that is, the transfer of oxygen from the air to the blood and carbon dioxide from the blood to the air. Its basic structural unit is the alveolus a roughly polygonal gas-filled tissue bubble whose walls are filled with capillaries. The human lung contains some 300 million alveoli, and their diameters average about 300 m. The strategy of dividing the lung up into a massive number of very small units keeps the total gas volume low enough for the lungs to fit inside the chest while at the same time creating an enormous interfacial surface area for exchange of oxygen and carbon dioxide between gas and blood. To enable gas exchange, alveoli are supplied with both inspired gas via the airways and venous blood from the right side of the heart. The gas and blood must be kept in very close proximity to one another for gas exchange to occur, but they must still remain physically completely separated. Separation is accomplished via the blood gas barrier a thin (about 0.3 m) layer of cells and supporting matrix. Oxygen and carbon dioxide exchange occurs by diffusion through the blood gas barrier along partial pressure gradients between alveolar gas and capillary blood. As a gas exchanger, the lung is the servant of the body tissues. Under steady-state conditions, the lungs absorb from the air exactly that amount of oxygen per minute needed to support tissue metabolism no more and no less. This is true also for the elimination of carbon dioxide produced by metabolism. The first step in this process is ventilation, a process of sequential inhalation and exhalation of gas. During each inspiration, oxygen is inhaled from the air, at a concentration of about 21% (or partial pressure, PO 2, of about 150 mm Hg). Inhalation is accomplished by the fall in alveolar gas pressure to below atmospheric pressure following contraction of the diaphragm and chest wall muscles, which expand the thoracic cavity, thus reducing intrathoracic pressure. When intrathoracic pressure falls, so too does alveolar pressure. As alveolar pressure falls below atmospheric pressure, air flows from the environment along the airways to reach the alveoli, where it mixes with alveolar gas remaining from prior breaths. Because oxygen molecules move continually across the blood gas barrier into the pulmonary capillary blood, the alveolar oxygen level from prior breaths is considerably lower than inspired. The freshly inhaled oxygen thus tops up the alveolar oxygen store, replacing the molecules that have moved into the blood. This process serves to stabilize the alveolar oxygen concentration over time at about 14%, or about 100 mm Hg. An analogy would be adding 1 gallon of gasoline every 20 miles to the tank of a car that does 20 miles per gallon: the amount of gasoline in the tank will oscillate around 0.5 gallons about a constant level as long as topping up is continued. Each gallon added is the equivalent of each breath raising alveolar oxygen levels; continued driving depletes the fuel level at a steady rate, much as oxygen molecules constantly move into the blood to supply the cells of the body. If the fuel tank is large relative to the 1-gallon tidal volume of gasoline, the fuel level oscillations are relatively small, allowing a simple view of the tank as having an essentially constant amount of gasoline over time. Since tidal volume is normally only about 500 ml, whereas functional residual capacity (FRC) is some 4,000 ml, the oscillations of oxygen about the mean are indeed very small. Thus, if average alveolar PO 2 is about 100 mm Hg, each inspiration raises this to about 102 mm Hg. During each expiration, it is obvious that no oxygen can move from the air to the alveoli, but oxygen still moves from the alveolar gas into the blood, reducing the alveolar PO 2 to about 98 mm Hg by the end of the exhalation. For most purposes, it is entirely satisfactory to consider the alveolar PO 2 to be constant over time, despite the tidal nature of breathing and the 2mmHg PO 2 oscillation. 1 Once oxygen has moved across the blood gas barrier into the pulmonary capillary blood, a process of passive diffusion, 2 almost all of it ( 98%) binds to hemoglobin in the red blood cells. The remainder is physically dissolved in the water of the plasma and red cells. These cells spend only about 0.75 seconds 3 in the pulmonary microcirculation taking on oxygen molecules. This period of time reflects the high rate of bloodflow through the pulmonary vascular bed (about 6 L/min) and the small capillary blood volume at any instant (about 75 ml). The ratio of capillary volume to

2 166 Ventilation, Pulmonary Circulation and Gas Exchange bloodflow [75 ml/(6 L/min)] is the average transit time, and this indeed comes to 0.75 seconds. In normal lungs at rest, the time required to fully load oxygen onto hemoglobin is only about 0.25 seconds, 4 and thus there is considerable reserve capacity in the oxygen-diffusing capacity of the lung. This is explained by the very large alveolar wall surface area through which the oxygen diffuses, some 80 m 2 in all, and the very short diffusion distance separating alveolar gas from capillary blood, both mentioned above. The end result is that in normal lungs at rest, the PO 2 in the blood exiting the pulmonary capillary network is virtually equal to that of the alveolar gas (100 mm Hg) and diffusion equilibration is said to be complete. The PO 2 in the blood leaving the lungs is thus also about 100 mm Hg. Because of the shape of the oxygen hemoglobin dissociation curve, essentially all oxygen-binding sites (98 of every 100) contain oxygen at this pressure of 100 mm Hg. In other words, the oxygen saturation of blood leaving the lungs is 98%. Whereas the process of ventilation is tidal, with sequential inspiration and expiration occurring through the same system of airways, bloodflow through the lung vasculature is unidirectional. Thus, the right ventricle pumps partially deoxygenated blood returned from the various body tissues through the pulmonary arterial tree to the capillary bed, where reoxygenation takes place as described. The oxygenated blood then is collected in the pulmonary veins, which forward the blood to the left heart for distribution to the tissues. What enables passive diffusion to accomplish the transfer of oxygen from alveolar gas into the blood is the fact that alveolar PO 2 is much higher (at 100 mm Hg) than the PO 2 of the blood returning from the tissues (normally about 40 mm Hg). The fall in PO 2 from 100 (arterial) to 40 mm Hg (venous) as blood traverses the body reflects the extraction of oxygen by each tissue to support its metabolic needs. Figure 17-1 depicts the entire process in a homogeneous or one-compartment lung. The processes of ventilation, diffusion, and bloodflow are indicated, along with the normal oxygen and carbon dioxide partial pressures in alveolar gas and pulmonary arterial and venous blood. The gas exchange process is intrinsically inefficient. Thus, exhaled alveolar gas has considerable oxygen in it (14% of expired gas is oxygen, equivalent to 100 mm Hg as mentioned), and inspired air contains 21% oxygen at 150 mm Hg. Thus, only about one-third of the inhaled oxygen is absorbed, and considerable ventilatory effort is therefore wasted (compared with a hypothetically perfectly efficient lung, in which all of the inhaled oxygen would be taken up). Similarly, since blood returning from the tissues still has a PO 2 of 40 mm Hg (which corresponds to an oxygen hemoglobin saturation of about 75%), only about 25% of the oxygen in each red blood cell is transferred to the tissues to support metabolism. Considerable cardiac contractile effort is therefore wasted as well. In addition, the process of diffusion appears overendowed, when we consider that the transit time, at 0.75 seconds, is three times as long as required. One could hypothetically survive the removal of two-thirds of the lung tissue and still have sufficient time for diffusion equilibration (at rest). Pulmonary artery P v O 2 = 40 P v CO 2 = 45 Alveoli Conducting airways Ventilation P A O 2 = 100 P A CO 2 = 40 Diffusion Capillaries Bloodflow There are reasons, however, why the body imposes these taxes on itself. First, maintaining alveolar PO 2 at 100 mm Hg is important because when the arterial blood reaches the various tissue beds, the unloading of oxygen is, as in the lung, a process of passive diffusion. This requires a high incoming PO 2 in the arterial blood to provide the diffusion gradient to the tissues. Thus, when arterial PO 2 is reduced, such as at altitude, exercise capacity is also reduced, in large part because of the reduction in the blood tissue gradient of oxygen driving diffusion. Second, the reserve capacity in capillary transit time seen at rest reflects the need for greatly increased oxygen uptake during exercise. If the lungs were not overbuilt for resting conditions, little exercise could be accomplished because during exercise oxygen would not be able to be transferred from alveolar gas to capillary blood sufficiently quickly. Third, the low tissue extraction rate of 25% noted above also reflects the need to be able to extract more oxygen from each red cell during exercise to support much higher metabolic rates. CHALLENGES TO GAS EXCHANGE CAUSED BY THE STRUCTURE OF THE LUNGS Pulmonary vein P c O 2 = 100 P c CO 2 = 40 FIGURE 17-1 The principal structures involved in pulmonary gas exchange and their functions. Gas exchange is an integrated process involving ventilation, bloodflow, and diffusion. In the section above, I pointed out intrinsic inefficiencies, seen at rest, based on the need to provide the body with sufficient oxygen when metabolic needs increase. However, the fact that the lung accomplishes gas exchange by a process dependent on ventilation, passive diffusion, and bloodflow has led to pulmonary structural characteristics that have considerable potential to interfere with gas exchange, even in the healthy lung. These potential problems are thus additional to those described above. That such interferences rarely seem to happen in health is remarkable. However, they collectively form the basis of why gas exchange can be so severely compromised in pulmonary disease (see Chapter 18, Ventilation Perfusion Distributions in Disease ). The potentially deleterious effects of lung structure on gas exchange include the following. LUNG COLLAPSE: PNEUMOTHORAX Because breathing is a tidal process, a mechanism is required for alternately inflating and deflating the lungs with each

3 Ventilation Perfusion Relationships 167 breath. The left and right lungs lie in physically separate parts of the thoracic cavity. The intrapleural space between the surface of the lungs and the inner surface of the chest wall contains only a thin film of liquid. Since the lungs are elastic, they have a natural tendency to collapse away from the chest wall. The lungs are kept inflated and do not collapse, by virtue of the subatmospheric pressure in the intrapleural space. This pressure is below atmospheric because the lungs tend to collapse whereas the chest wall tends to spring out. These opposing tendencies create a stable state of lung inflation with a negative intrapleural pressure. If the integrity of the intrapleural space on either side of the chest is violated (as may happen in chest wall trauma or with spontaneous pneumothorax), the lung on that side will collapse like a punctured balloon. In such a situation, breathing efforts will be ineffectual, and thus the lung will remain unventilated, obviously compromising gas exchange, with potentially fatal consequences. The need for sequential inflation and deflation in a system where gas exchange occurs by diffusion through very thin alveolar capillary membranes imposes constraints on lung structure that result in a delicate tissue framework susceptible to pneumothorax. DEAD SPACE Because gas exchange occurs by passive diffusion, a very large alveolar surface area is needed in order for sufficient oxygen to reach the pulmonary capillaries. Suppose that the lung, with a volume (V) at FRC of 4,000 ml, were a single spherical large alveolus. Since volume is given by the formula V (4/3) x r 3, the radius, r, would be about 10 cm. Since the surface area (A) of this sphere is given by the formula A 4 x r 2, total surface area would be about 1,200 cm 2. Given the thickness (about 0.3 m) of the blood gas barrier, it was noted above that an area of about 80 m 2 is required to enable the rates of oxygen uptake required for heavy exercise. This is 800,000 cm 2. Thus, a single large alveolus would have more than 600-fold too small a surface area to support gas exchange during exercise. From the above area and volume formulae, it should be apparent that the surface area/volume ratio of a sphere (A/V) increases as its diameter is reduced. Thus, to achieve a sufficient surface area for gas exchange within a 4 L total volume, the lung must be constructed not as a single sphere but rather as a parallel collection of many smaller spheres the alveoli. It turns out that to have an 80 m 2 surface area with a 4 L total volume, about 300 million spheres of diameter about 300 m would be needed. The consequence of this requirement is the herculean task of ventilating each alveolus with relatively equal amounts of air on each breath. Much like a bunch of grapes on a branched stem, the alveoli (grapes) are connected to a branched system of conducting airways (stem). This treetrunk-like system of airways has to branch some 23 times in order to supply such a large number of alveoli. The total volume of these conducting airways is considerable, and it should be clear that all inhaled air must negotiate these airways before it reaches the alveoli where gas exchange takes place. Down to about the sixteenth branch point, the airways are constructed robustly only for delivery of air, and no oxygen crosses the thick walls of these first 16 branches to contribute to overall oxygen uptake. The total volume of these 16 generations of airways in the average person is about 150 ml 5 and is called the anatomic dead space. Of every tidal breath taken, normally about 500 ml, only 350 ml of fresh air will reach the alveoli and take part in oxygen uptake. If there are 15 breaths/min, total ventilation will be ml /min, or 7.5 L /min. However, alveolar ventilation (that amount of fresh air reaching the alveoli) is only 15 ( ) ml /min, or 5.3 L /min. The normal dead space is thus about 30% of the tidal volume, and the ventilation associated with it (2.2 L /min in this example) is termed wasted ventilation. One must ventilate some 40% more to achieve a given level of oxygen uptake than if there were no conducting airway system. This requirement may be problematic in patients with severe lung disease and is the basis for the use of transtracheal catheter administration of air or oxygen to patients with impaired ventilation. Direct insufflation of air into the trachea functionally eliminates that part of the anatomic dead space above the trachea (the larynx and oropharynx). This reduces the amount of ventilation needed to support a given metabolic rate. AIRWAY INFECTION/INFLAMMATION The progressive branching of the airways imposes not only dead space but also ever-narrowing and increasing numbers of airways with each generation (or branching). In the small bronchioles, because of their enormous number, the total cross-sectional area is so high that the linear velocity of gas becomes very low. This favors the settling out of large, inhaled particles (such as dust particles, bacteria, or viruses), which may adhere to the airway wall and initiate inflammation. Here, as elsewhere in the airways, edema and secretions can develop. In the small airways in particular, the lumen cross-section can then be significantly reduced, impairing distal alveolar ventilation. VENTILATION AND PERFUSION INEQUALITY RESULTING FROM MULTIPLE BRANCHING Yet another intrinsic disadvantage of such a progressively branching airway system is that the dimensions of all members of each generation cannot be identical. Since these airways are arranged in parallel with one another, those airways that are for some reason longer and narrower than others will impose higher resistance to airflow, and thus there may be inequality in the distribution of ventilation to distal alveoli. This concept applies equally to the pulmonary vascular tree, which also branches progressively and will give rise to inequality in the distribution of alveolar bloodflow. DYNAMIC COMPRESSION OF THE AIRWAYS Yet another consequence of the branching airway system is that smaller peripheral airways (which lack cartilage in their walls), in particular, become susceptible to compression during exhalation. During quiet breathing at rest this does not occur, but during forceful exhalations, such as seen during

4 168 Ventilation, Pulmonary Circulation and Gas Exchange exercise, the resulting positive intrapleural pressure can compress these airways, resulting in limitation of airflow. This problem is known as dynamic compression. To the extent that this phenomenon occurs unevenly throughout the lung, as a result of both gravitational and nongravitational influences, it will add to the possibility of inequality of ventilation. In young healthy people, it is not of much concern. It is seen more with advancing age, as the elastic recoil of the lungs diminishes, 6 and is a hallmark of emphysema, where elastic recoil is greatly reduced. Reduced elastic recoil is a factor because dynamic compression is to some extent counteracted by outward radial traction imposed on airways by alveoli connected to them, and the strength of such radial traction depends on elastic recoil. ALVEOLAR COLLAPSE The alveolar epithelial surface is wet, as are all body tissues. Yet this surface, on the inside of each alveolus, is in direct contact with air. This creates a (roughly spherical) air liquid interface, and surface tension must therefore exist. As with soap bubbles, such surface tension acts to reduce the surface area of the interface, so that alveoli are intrinsically prone to collapse. The law of LaPlace shows that the smaller the alveolar radius, the greater will be the tendency for collapse to occur because of this surface tension. Thus, having a great many small bubbles rather than fewer large ones may serve gas exchange well but puts the lungs at risk of collapse. Without special molecules that greatly reduce the surface tension of the alveolar lining fluid (surfactant), widespread lung collapse would occur. This is indeed seen clinically in premature infants, whose surfactant system is immature, and in acute lung injury at any age, when the surfactant system malfunctions. PULMONARY EDEMA The balance of hydrostatic and osmotic forces between the blood in the pulmonary capillaries and the fluid in the interstitium around them is such that there is a net force driving fluid out of the capillaries into the interstitium of the blood gas barrier. Were this fluid to accumulate, the blood gas barrier would thicken, and this would reduce the rate of diffusive equilibration for oxygen and carbon dioxide between the alveolar gas and capillary blood. It would also make affected alveolar walls stiffer and thus more difficult to inflate during inspiration. That such fluid does not normally accumulate is because of the pulmonary lymphatic system, which collects such fluid and facilitates its transport back into the systemic venous system along a lymph vessel tree that follows the airway branching pattern centrally and ends in the superior vena cava. Lymphatic obstruction or overwhelming the system with high rates of fluid transudation does, in fact, cause pulmonary edema, and lung function can accordingly be impaired. CAPILLARY INTEGRITY Finally, the very delicate nature of the blood gas barrier (about 0.3 m thick) makes it vulnerable to disruption when stressed. 7 This can result from high intracapillary blood pressure (as happens frequently in race horses when they are galloping, for example 8 ). It could also possibly result from excessive stretch of the alveolar wall (as happens during mechanical ventilation of ill patients when inflation pressures are excessive). Since the blood gas barrier is predominantly formed of capillary walls (mated to alveolar epithelium), its disruption leads to local inflammation, edema, and, when severe, even frank hemorrhage of blood into the alveoli. Any of these effects may impair gas exchange. It is remarkable that in the face of all these challenges, gas exchange proceeds as smoothly as it does, even in health. It is testament to the success of evolutionary countermeasures to these problems phenomena such as making the alveoli support each other mechanically by being physically joined together; reducing surface tension by surfactant production; clearing inhaled particles by means of scavenger cells (macrophages) and the mucociliary airway clearance system; and a pulmonary microvasculature that keeps blood pressures low (when flow is increased) by mechanisms of recruitment and distention of blood vessels. GRAVITATIONAL DETERMINANTS OF VENTILATION PERFUSION DISTRIBUTION As if these challenges were not enough, the presence of gravity imposes systematic gradients in the distribution of ventilation and bloodflow in the lung. These gradients are in the same direction but are unequal in magnitude. Thus, (1) both bloodflow and ventilation are generally higher in dependent than in nondependent regions, and (2) the inequality of bloodflow considerably exceeds that of ventilation. As a result, the ratio of ventilation to bloodflow, a critical determinant of gas exchange, is not uniform. In the upright lung, it is systematically higher at the apex than at the base. 9 The gradient in ventilation can be explained by the weight of the lung itself causing some sagging of the lung within the thorax. Thus, the nondependent alveoli will be more expanded than the dependent alveoli, much like a slinky, or coiled spring, hanging under its own weight: the upper coils are further apart than the lower coils, due to its weight. This uneven expansion is considered in the context of the pressure volume behavior of the lung. More expanded alveoli, further up the pressure volume curve, are stiffer than less expanded alveoli. Thus, the larger, nondependent alveoli expand less with each breath and thus receive less ventilation than their dependent neighbors. As a result, the ventilation of alveoli near the bottom of the upright human lung is about twice the ventilation of alveoli near the top. Gravity also explains the gradient in perfusion, wherein the bloodflow in alveoli at the bottom of the upright human lung is perhaps 10 times higher than at the top of the lung. This is explained in large part by the hydrostatic properties of a column of liquid and Ohm s law. Ohm s law states that flow will vary directly with pressure (assuming constant resistance). Since pulmonary artery pressure falls by 1 cm H 2 O with each centimeter increase in height up the lung, because blood has a density of about 1 g/cm, bloodflow will fall with increasing height up the lung. This concept suffices for the general explanation of bloodflow variation with vertical

5 Ventilation Perfusion Relationships 169 Ventilation (L/min), bloodflow (L/min) and ventilation/bloodflow ratio Ventilation Top Ventilation/bloodflow ratio Bloodflow Relative position from top to bottom of the lung position throughout the lung, but the details are more complex because the blood vessels are exposed to alveolar gas pressure. Accordingly, as first described by West and Dollery, 10 lung perfusion is functionally described by relationships among three pressures: pulmonary arterial, pulmonary venous, and alveolar. In this way, three functional zones are defined. But from the operational point of view, one sees an essentially linear fall in bloodflow across zones from the bottom to the top of the upright lung. Figure 17-2 shows this classic variation in ventilation, bloodflow, and the ratio between them with vertical distance, drawn from the data of West. 9 Figure 17-2 reminds us that the systematic variation in ventilation and bloodflow implies obligate variation in the ratio of ventilation (V A) to bloodflow (Q ) with vertical distance, also shown in Figure This critical concept is discussed later. NONGRAVITATIONAL DETERMINANTS OF V A/Q DISTRIBUTION Bottom FIGURE 17-2 Data from West 9 showing the systematic changes in ventilation, bloodflow, and their ratio with distance up and down the upright human lung. Whereas ventilation and bloodflow are both lower at the top than the bottom, there is relatively more ventilation than bloodflow at the top and relatively more bloodflow than ventilation at the bottom. As a result, ventilation/perfusion ratios are higher at the top than at the bottom. It has been known for almost 40 years that gravity is not the only factor responsible for uneven distribution of ventilation and bloodflow in the lungs. For example, ventilation and bloodflow fall off serially with distance along the airways, independently of gravity. 11 Variation in ventilation and bloodflow at a given horizontal level also occurs because of intrinsic anatomic variation in airway and vascular geometry, and there may also be random or even systematic differences in airway and vascular smooth muscle responses that further modify distribution. Furthermore, the repeated branching pattern of the airways and blood vessels gives rise to fractal behavior in distribution, such that spatial correlation of both ventilation and bloodflow occurs. 12 That is, there is clustering such that adjacent areas of the lung are generally more similar with regard to both ventilation and bloodflow than are distant areas. The degree of variation in both ventilation and bloodflow has been shown to be substantial, and it has been claimed that, as a result, nongravitational causes of both ventilation and perfusion inequality are more important than those based on gravity. If that were true, it would imply that whereas ventilation and bloodflow were each nonuniform, variations in each must correlate, such that the nonuniformity in their ratio (ventilation/perfusion ratio) is far less. This conclusion is based on the fact that the gravitational gradient in ventilation/ perfusion ratios accounts for the majority of the normal alveolar arterial PO 2 difference, 9 leaving very little that can be due to other, nongravitational causes. PRINCIPLES OF PULMONARY GAS EXCHANGE A central theme emerging from the preceding discussion is the importance of the ratio of ventilation to bloodflow (the ventilation/perfusion or V A/Q ratio) in determining gas exchange. This section provides the quantitative basis for this claim. It relies on a single, fundamental, yet simple principle: conservation of mass. The most well-known treatises on the subject can be found in the literature of the immediate post World War II period. This is when Riley and Cournand 13 and Rahn and Fenn 14 separately laid out the principles of gas exchange, converting them into useful relationships that have given us our current understanding of how gas exchange takes place and what factors are involved. The problem is approached by recognizing that oxygen is taken out of the respired air at a rate exactly equal to the rate of its uptake into the pulmonary capillary blood, so long as the lung exchange process is in a steady state. With this explicit assumption, we can write one equation depicting the removal of oxygen from respired gas and a second depicting its uptake into capillary blood, as follows: V O 2 V IF I O 2 V AF A O 2 (17-1) V O 2 Q C a O 2 Q C v O 2 (17-2) In these two equations, V O 2 represents the rate of oxygen uptake, which is equal to the body metabolic rate, V I and V A are, respectively, inspired and expired alveolar ventilation, and F I O 2 and F A O 2 are, respectively, inspired and expired fractional alveolar oxygen concentrations. Equation 17-1 thus states that the amount of oxygen taken out of respired air per minute is the amount inhaled per minute (V IF I O 2 ) minus the amount exhaled (V AF A O 2 ). Equation 17-2 is very similar but refers to the blood. Thus, Q is total pulmonary bloodflow (essentially equal to cardiac output), and C a O 2 and C v O 2 are, respectively, the oxygen concentrations in arterial and mixed venous blood. Here, oxygen taken into the blood is the difference between the rate at which oxygen leaves the lungs (Q C a O 2 ) and the rate at which it enters (Q C v O 2 ). Because of the steady-state assumption, the VO 2 values in the two equations are identical. Thus, Equations 17-1 and 17-2 can themselves be equated: V IF I O 2 V AF A O 2 Q C a O 2 Q C v O 2 (17-3) If we assume for simplicity that V I and V A are numerically identical (and they normally differ by no more than 1%), we

6 170 Ventilation, Pulmonary Circulation and Gas Exchange can replace V I with V A and simplify Equation 17-3 as follows: V A(F I O 2 F A O 2 ) Q (C a O 2 C v O 2 ) (17-4) This can be rearranged, yielding: V A/Q (C a O 2 C v O 2 )/(F I O 2 F A O 2 ) (17-5) It is more usual to convert the fractional concentrations F I O 2 and F A O 2 to their corresponding partial pressures P I O 2 and P A O 2 (using Dalton s Law of Partial Pressures), which simply involves a proportionality constant that we can call k, such that: V A/Q k(c a O 2 C v O 2 )/(P I O 2 P A O 2 ) (17-6) Exactly the same reasoning leads to a similar equation for carbon dioxide: V A/Q k(c v CO 2 C a CO 2 )/(P A CO 2 P I CO 2 ) (17-7) Both the numerator and denominator terms are reversed for carbon dioxide, simply reflecting the fact that whereas oxygen moves from air to blood, carbon dioxide moves from blood to air. In addition, P I CO 2 is so low (air normally contains only 0.03% carbon dioxide) that it can be neglected. Equations 17-6 and 17-7 describe the necessary quantitative relationships between V A/Q ratio and gas concentrations in the alveolar gas and capillary blood. It is critical to understanding these equations to realize that they contain both independent and dependent variables. Most commonly, we use Equation 17-6 to find, for given values of V A/Q ratio and of mixed venous and inspired oxygen levels (the independent variables), what the alveolar (and hence end-capillary) oxygen levels (the dependent variables) must be to satisfy the equation. The same applies for P A CO 2 in Equation The answer is given in Figure Here, the numerical solution to Equation 17-6 is presented for all possible values of V A/Q, using normal values for inspired and mixed venous PO 2. The lowest possible V A/Q value is zero, corresponding to a perfused alveolus that has no ventilation (ie, a shunt). Such a unit exchanges no gas, and so the end-capillary blood leaving that unit has a PO 2 equal to that of mixed venous blood (40 Torr in this example). The highest possible V A/Q value is infinite, representing a ventilated alveolus without any bloodflow (called alveolar dead space). This unit also exchanges no gas, and thus the alveolar PO 2 equals that of the inspired gas (150 Torr in this case). Between these extremes, there is a smooth relationship where P A O 2 increases nonlinearly with increasing V A/Q ratio as shown. A major assumption in solving Equation 17-6 is that the alveolar and end-capillary PO 2 values are the same. This implies complete equilibration by diffusion for oxygen across the blood gas barrier. A justification for this assumption, at least at rest, was provided earlier. Identical assumptions are used for carbon dioxide in solving Equation Figure 17-4 shows the solution to Equation 17-7 for carbon dioxide in a manner similar to Figure 17-3 for oxygen. Again, the extremes of V A/Q ratio produce PCO 2 values corresponding to that of mixed venous blood when the V A/Q ratio is zero and to that of inspired gas (essentially zero) when the V A/Q ratio is infinite, whereas between there is a smooth relationship, with PCO 2 falling as V A/Q is increased. Equations 17-6 and 17-7 are very useful. Under the prevailing major assumptions (steady-state conditions and complete diffusion equilibration), they show that alveolar (and thus end-capillary) PO 2 and PCO 2 values are determined by three interacting factors. These are (1) the V A/Q ratio, (2) the so-called boundary conditions mixed venous and inspired oxygen and carbon dioxide levels, and (3) the oxygen hemoglobin and carbon dioxide dissociation curves because they determine the relationships between oxygen and carbon dioxide concentrations (numerator of Equations 17-6 and 17-7) and partial pressures (denominator of Equations 17-6 and 17-7). Alterations in any one of these three factors thus have the potential to affect alveolar and hence arterial PO 2. Figures 17-3 and 17-4 showed how the first of these three (V A/Q ratio) affects PO 2 and PCO 2. Figure 17-5 shows how changes in mixed venous PO 2 and Alveolar PO 2 (Torr) Inspired PO Mixed venous PO FIGURE 17-3 Dependence of alveolar PO 2 on ventilation/perfusion (V A/Q ) ratio. At low V A/Q, alveolar PO 2 is close to mixed venous PO 2 ; at high V A/Q, it is close to inspired PO 2. Alveolar PO 2 is most sensitive to V A/Q in the normal range (V A/Q of about 1). Alveolar PCO 2 (Torr) Mixed venous PCO 2 Inspired PCO FIGURE 17-4 Dependence of alveolar PCO 2 on ventilation/ perfusion (V A/Q ) ratio. At low V A/Q, alveolar PCO 2 is close to mixed venous PCO 2 ; at high V A/Q, it is close to inspired PCO 2. Alveolar PO 2 is most sensitive to V A/Q in the above-normal range (V A/Q of about 1 to 10).

7 Ventilation Perfusion Relationships 171 A Alveolar PO 2 (Torr) B Mixed venous PO 2 : Alveolar PO 2 (Torr) Hemoglobin P 50 : FIGURE 17-6 Dependence of alveolar PO 2 on hemoglobin P 50. As P 50 varies, alveolar PO 2 changes (at given mixed venous and inspired PO 2 ). Changes in P 50 affect alveolar PO 2 mostly in the normal range of V A/Q, around Alveolar PO 2 (Torr) Inspired PO 2 : FIGURE 17-5 Relationship of alveolar PO 2 to V A/Q depends on both mixed venous PO 2 (A) and inspired PO 2 (B). In particular, PO 2 in areas of low V A/Q reflects mixed venous PO 2, whereas areas of high V A/Q reflect inspired PO 2. inspired PO 2 affect PO 2. A fall in mixed venous PO 2 reduces alveolar PO 2 in all alveoli, but much more so in alveoli whose V A/Q ratio is low. Such units have their PO 2 tied to that of mixed venous blood, as shown. Correspondingly, a fall in inspired PO 2 also reduces alveolar PO 2, but more so when V A/Q ratio is high. The curve for carbon dioxide behaves correspondingly when venous or inspired PCO 2 is changed. Figure 17-6 shows how changes in the PO 2 corresponding to hemoglobin oxygen saturation of 50% (P 50 ) affect alveolar PO 2 when mixed venous and inspired PO 2 are maintained at normal values. Thus, a fall in P 50 leads to a higher alveolar PO 2 at any V A/Q ratio, and vice versa. The effects are clearly greatest in the normal range of V A/Q and are negligible when V A/Q is either very low or very high. Solving Equations 17-6 and 17-7 by hand or graphically, as done originally, 14 is very laborious, due mostly to the nonlinear and interdependent nature of the oxygen and carbon dioxide dissociation curves. Today, these equations are easily solved by computer, and the necessary algorithms are well established 15,16 and available. GAS EXCHANGE IN THE PERFECTLY HOMOGENEOUS LUNG To apply these concepts to the lungs, it is useful to begin with an ideal lung that is completely homogeneous. Even though the lungs of young healthy subjects contain V A/Q inequality from several sources, as discussed above, the degree of inequality normally present has very little detrimental effect on arterial PO 2 and PCO 2. Commonly, arterial PO 2 is only about 5 to 10 Torr below alveolar PO 2 ; this has negligible effects on arterial oxygen saturation and concentration and no measurable effect on arterial PCO 2. Thus, the normal lung is not far from being homogeneous in terms of overall gas exchange, and the following analysis therefore can be used with little error. Once again, it is the concept of which variables in the system are independent and which are dependent that should first be considered when applying Equations 17-1 through Restating Equations 17-1 and 17-2, we have: V O 2 V IF I O 2 V AF A O 2 kv A(P I O 2 P A O 2 ) (17-8) (remember that taking V I V A is reasonable; k converts fractional concentration F to partial pressure P) and V O 2 Q (C a O 2 C v O 2 ) (17-9) When considering Equation 17-8, recall that the lung remains the servant of the body, such that the body, not the lung, sets VO 2 as an independent variable in the current context. Likewise, P I O 2 is set by the environmental conditions, and V A is determined by the integrated respiratory control system and mechanical properties of the lungs and chest wall. Thus, the single dependent variable is alveolar PO 2 (P A O 2 ). What Equation 17-8 tells us is as follows: given the VO 2, P I O 2, and amount of alveolar ventilation (V A), the alveolar PO 2 takes a unique, dependent value that must satisfy Equation These are the only determinants of alveolar PO 2 in a homogeneous lung. Let us now proceed to Equation The same value of VO 2 must exist as for Equation Total pulmonary bloodflow will also be determined, like ventilation, by complex

8 172 Ventilation, Pulmonary Circulation and Gas Exchange control systems external to the lungs. Given that alveolar and end-capillary (here arterial) PO 2 are equal in this homogeneous lung, arterial oxygen concentration (C a O 2 ) must be that value read off the oxygen hemoglobin dissociation curve for the value of alveolar PO 2 determined from Equation Hence, the remaining unknown, mixed venous oxygen concentration must be that value that satisfies Equation In sum, Equation 17-8 shows that it is only metabolic rate, ventilation, and inspired PO 2 that together influence arterial PO 2 when the lungs are completely homogeneous. Cardiac output does not influence arterial PO 2 under such circumstances but does affect mixed venous PO 2. Again, these conclusions pertain only to steady-state conditions and when there is complete diffusion equilibration across the blood gas barrier. Although this is strictly true only for a homogeneous lung, these conclusions are also approximately correct for the normal human lung, as discussed above. When this approach is taken, and as can be inferred from Figures 17-3 and 17-4, we can see that normal arterial PO 2 is about 100 Torr, and arterial PCO 2 is about 40 Torr. This is based on (1) alveolar ventilation at 5 to 6 L/min and cardiac output at 5 to 6 L /min, such that overall V A /Q ratio is close to 1, and (2) a metabolic rate resulting in a VO 2 of 300 ml/min and a VCO 2 of 240 ml/min. GAS EXCHANGE IN THE PRESENCE OF V A/Q INEQUALITY V A/Q inequality is defined as the state wherein not all alveoli enjoy the same V A/Q ratio. However, all of the principles laid out in Equations 17-1 to 17-7 apply when V A/Q inequality develops, just as in the homogeneous lung. In the presence of V A/Q inequality, these equations can be applied in turn to each different V A/Q ratio unit in the lung. The performance of the whole lung is then found simply by summing the contributions from each unit. In reality, there are (as stated earlier) some 300 million alveoli in the lungs. However, due to their small size and anatomic proximity to each other, it is thought that many adjacent alveoli together form a functional unit of gas exchange. Evidence points to the acinus (all alveoli distal to the last terminal bronchiole) as the anatomic basis of a functional unit, 17 and there are about 100,000 such acini in the lung, consistent with about 17 generations 18 of dichotomously branching airways up to the last terminal bronchiole ( ,072). Although this number is very much lower than 300 million, it is still far too high to deal with experimentally. Since each unit is characterized by two independent variables (ventilation and bloodflow), it would take some 260,000 measurements to fully describe the functional V A/Q distribution! We have neither the technology nor the resources to do this, and thankfully it turns out not to be necessary to understand V A/Q inequality in the lung. In fact, the simplest model of inequality, the two-compartment model, is quite adequate for illustration of how V A/Q inequality affects gas exchange. I show this below. To work through this more difficult analysis, it is most instructive to use particular examples. It is easiest to start from the homogeneous lung and then use the above equations to determine how a two-compartment model with a defined degree of V A/Q mismatch affects gas exchange. What will be found is that V A/Q inequality causes hypoxemia, hypercapnia, and reductions in the rates of both oxygen uptake and carbon dioxide elimination. Such a result is not compatible with life in the long term because the lung cannot supply enough oxygen for the metabolic needs of the body or keep up with the associated rate of carbon dioxide elimination. Usually, the body employs one or more compensatory mechanisms (discussed below), which can return VO 2 and VCO 2 to levels matching the tissue metabolic rate. However, sometimes this does not happen. And, occasionally, the degree of inequality may be too severe for available compensatory mechanisms to cope with. In either case, death will ensue. I will begin with a homogeneous lung, using values for the variables that correspond to those of a typical normal resting adult breathing air at sea level. I will stipulate the following independent variables: F I O ; F I CO 2 0; barometric pressure 760 Torr; VO ml/min; VCO ml/min; alveolar ventilation 5.2 L/min; cardiac output 6.0 L/min. Additional secondary information required includes hemoglobin concentration (taken to be normal, 15 g/dl), hemoglobin P 50 (normal at 27 Torr), and acid base status, which will also be taken to be normal. That is, there is no metabolic acidosis or alkalosis. Applying first Equations 17-1 and 17-2 for oxygen and using the corresponding approach simultaneously for carbon dioxide, we find that, for the given V A/Q ratio of 5.2/6.0, or 0.87, P A O Torr and P A CO 2 40 Torr. This is compatible with Figures 17-3 and Mixed venous PO 2 is about 40 Torr, and mixed venous PCO 2 is 46 Torr. These unique values (here rounded to the nearest integer) fit the equations and allow for the requisite VO 2 and VCO 2 specified above. Figure 17-7 shows these results in diagrammatic form, where the lung is drawn as two alveoli that are equally perfused and equally ventilated. Thus, although two alveoli are drawn, they have the same V A/Q ratio, and thus the system is really a homogeneous lung. The trachea is represented by the single vertical line at the top of the figure. It divides into two bronchi that connect the trachea to the two circular alveoli. Beneath each alveolus is its vasculature, drawn as a curved vessel on each side that touches its alveolus, forming the blood gas barrier at the points of contact. Blood flows from the outside inwards for each alveolus, and the two blood vessels join at the foot of the figure to form the left atrial and hence systemic arterial bloodstreams. Suppose we now suddenly create severe airway obstruction in the bronchus of the left-hand alveolus. This could, in fact, happen, for example, from inhalation of a foreign body into a main bronchus, and is depicted in Figure If we analyze the effects of this inequality, assuming first that the mixed venous blood oxygen and carbon dioxide levels remain normal, the results are as shown in Figure 17-8A. The large black dot indicates the obstruction, which has reduced ventilation on the left side from 2.6 to just

9 Ventilation Perfusion Relationships 173 Normal lungs Ventilation L/min P A O 2 P A CO 2 Perfusion L/min Arterial PO Torr Arterial PCO 2 40 Torr P V O 2 40 P V CO VO VCO FIGURE 17-7 Gas exchange function in a homogeneous lung that is normally perfused and ventilated. Arterial PO 2 and PCO 2 are 100 and 40 Torr, respectively, and the lung is able to take up the normal amount of oxygen (300 ml/min) and eliminate the normal amount of carbon dioxide (240 ml/min). These results all come from solving the mass conservation equations (Equations 17-1 and 17-2 for oxygen and the corresponding equations for carbon dioxide). 0.3 L /min. As a result, the rest of the ventilation is diverted to the right side, keeping total ventilation constant. In reality, both ventilation and mixed venous gas levels would change, as too may cardiac output, and these changes are discussed below. However, to understand the effects of V A/Q inequality on gas exchange, we will first assume no changes in any of these variables. The redistribution of ventilation gives rise to two different V A/Q ratios, as Figure 17-8 shows: 0.1 on the left and 1.6 on the right. Since overall ventilation and bloodflow are unchanged, the overall V A/Q ratio remains at 5.2/6.0, or Note that the V A/Q ratio of the left side is lower, and that of the right side is higher, than this overall value. At first sight, one might think that, for this reason, the two would offset one another, and overall gas exchange would be unaffected. This is not the case, as the following analysis demonstrates. When Equations 17-1 and 17-2 are applied separately to both alveoli, the resulting alveolar PO 2 values are, as shown, 47 and 119 Torr (see Figure 17-3). Similar calculations for carbon dioxide reveal that alveolar PCO 2 values are 46 and 35 Torr, respectively (see Figure 17-4). The bloodflow remains equally distributed between the alveoli (3 L/min each), and so the mixed arterial blood is a 50:50 mixture of the bloodstreams from the two alveoli. Because the oxygen dissociation curve is so nonlinear, this mixture does not produce a PO 2 halfway between the two alveolar PO 2 values of 47 and 119 (which would be 83) but gives rise to a much lower PO 2, 58 Torr. Similar calculations for carbon dioxide give a rather different result: because the carbon dioxide dissociation curve is nearly linear, the PCO 2 of mixed arterial blood is essentially the average of the two alveolar PCO 2 values, at 41 Torr. Although this is a small absolute increase from normal (of only about 1 Torr), even a 1-Torr increase is a significant percentage (about 20%) of the mixed venous arterial PCO 2 difference, suggesting that carbon dioxide elimination is indeed compromised, even though the change in arterial PCO 2 seems trivial. Thus, in this particular model, where the primary lesion corresponds to areas of greatly reduced V A/Q ratio, the effects on arterial PO 2 are shown to be far greater than those on arterial PCO 2. These results also imply that total oxygen uptake must have been reduced (same mixed venous PO 2 but lower than normal arterial PO 2 ), and Figure 17-8A indicates this, with V O 2 falling from its normal value of 300 ml/min (Figure 17-7) to 200 ml/min, a 33% reduction. There is also a reduction in carbon dioxide elimination as implied above, from 240 ml/min in the normal lung to 210 ml/min here, but the interference is less than for oxygen, a reduction of only 13%. The next step in the analysis is to determine the effect of this hypoxic and (slightly) hypercapnic blood on oxygen transport to (and carbon dioxide transport from) the peripheral tissues. Since tissue metabolic rate continues unchanged, the tissues will attempt to extract sufficient oxygen from the blood for their metabolic needs. Extracting the same amount of oxygen from arterial blood with a lower PO 2 must result in a fall in venous PO 2 draining the tissues. This must cause a fall in mixed venous PO 2 in the pulmonary artery. Returning to Figure 17-5A, it becomes clear that this fall in mixed venous PO 2 must reduce alveolar PO 2, especially in the low-v A/Q alveolus, which will further lower systemic arterial PO 2 as well. However, this strategy does enable restoration of V O 2 to normal. Figure 17-8B shows the result of this process, and it can be seen that V O 2 is indeed restored to 300 ml/min, but the penalty is a fall in both mixed venous and arterial PO 2 (to 33 and 48 Torr, respectively). In a similar manner, because arterial PCO 2 was increased by V A/Q inequality, adding all the metabolically produced carbon dioxide to tissue blood raises mixed venous PCO 2, which will lead to a further increase in arterial PCO 2. Arterial PCO 2 is now 45 Torr, up from 41 Torr. However, as for oxygen, the lungs are again able to eliminate all of the carbon dioxide produced (240 ml/min). Figure 17-8B shows this as well. We thus have what at first sight appears to be a paradox: overall lung function (ie, V O 2 and V CO 2 ) has been restored, but the hypoxemia and hypercapnia are both worse than before the changes in venous PO 2 and PCO 2 that allowed V O 2 and V CO 2 to be normalized. Actually, this is typical of other functional systems in the body and is not a paradox. For example, in stable chronic renal failure, the total amount of urea excreted in the urine per unit time exactly matches tissue urea production, but this can happen only in the case of a higher than normal blood urea level when some nephrons are diseased and functionally compromised. To this point, the body tissues have been protected (V O 2 and V CO 2 normalized), but hypoxemia and hypercapnia are both significant. The next likely response is therefore an increase in ventilation resulting from chemoreceptor activation in response to the low PO 2 and high PCO 2. Figure 17-8C shows that if the normal (right-hand) alveolus has its ventilation increased by just 0.6 L/min (ie, by just 12%), arterial PCO 2 is returned to the normal value of 40 Torr, even if the

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