ch17

STRUCTURAL AND FUNCTIONAL BASIS OF VENTILATION, PERFUSION, AND GAS EXCHANGE

The lung exists for gas exchange, that is, the transfer of oxy-gen from the air to the blood and carbon dioxide from theblood to the air. Its basic structural unit is the alveolus—aroughly polygonal gas-filled tissue “bubble” whose walls arefilled with capillaries. The human lung contains some 300million alveoli, and their diameters average about 300 �m.The strategy of dividing the lung up into a massive numberof very small units keeps the total gas volume low enoughfor the lungs to fit inside the chest while at the same timecreating an enormous interfacial surface area for exchange ofoxygen and carbon dioxide between gas and blood.

To enable gas exchange, alveoli are supplied with bothinspired gas via the airways and venous blood from the rightside of the heart. The gas and blood must be kept in veryclose 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—athin (about 0.3 �m) layer of cells and supporting matrix.Oxygen and carbon dioxide exchange occurs by diffusionthrough the blood–gas barrier along partial pressure gradi-ents between alveolar gas and capillary blood.

As a gas exchanger, the lung is the servant of the body tis-sues. Under steady-state conditions, the lungs absorb fromthe air exactly that amount of oxygen per minute needed tosupport tissue metabolism—no more and no less. This istrue also for the elimination of carbon dioxide produced bymetabolism. The first step in this process is ventilation, aprocess of sequential inhalation and exhalation of gas.During each inspiration, oxygen is inhaled from the air, at aconcentration of about 21% (or partial pressure, PO2, ofabout 150 mm Hg). Inhalation is accomplished by the fall inalveolar gas pressure to below atmospheric pressure follow-ing contraction of the diaphragm and chest wall muscles,which expand the thoracic cavity, thus reducing intratho-racic pressure. When intrathoracic pressure falls, so too doesalveolar pressure. As alveolar pressure falls below atmos-pheric pressure, air flows from the environment along theairways to reach the alveoli, where it mixes with alveolar gas

remaining from prior breaths. Because oxygen moleculesmove continually across the blood–gas barrier into the pul-monary capillary blood, the alveolar oxygen level from priorbreaths is considerably lower than inspired. The freshlyinhaled 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 concen-tration 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 iscontinued. Each gallon added is the equivalent of eachbreath raising alveolar oxygen levels; continued drivingdepletes the fuel level at a steady rate, much as oxygen mol-ecules constantly move into the blood to supply the cells ofthe body. If the fuel tank is large relative to the 1-gallon“tidal volume” of gasoline, the fuel level oscillations are rel-atively small, allowing a simple view of the tank as havingan 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 verysmall. Thus, if average alveolar PO2 is about 100 mm Hg,each inspiration raises this to about 102 mm Hg. During eachexpiration, it is obvious that no oxygen can move from theair to the alveoli, but oxygen still moves from the alveolar gasinto the blood, reducing the alveolar PO2 to about 98 mm Hgby the end of the exhalation. For most purposes, it is entirelysatisfactory to consider the alveolar PO2 to be constant overtime, despite the tidal nature of breathing and the �2 mm HgPO2 oscillation.1

Once oxygen has moved across the blood–gas barrier intothe pulmonary capillary blood, a process of passive diffu-sion,2 almost all of it (�98%) binds to hemoglobin in thered blood cells. The remainder is physically dissolved in thewater of the plasma and red cells. These cells spend onlyabout 0.75 seconds3 in the pulmonary microcirculation tak-ing on oxygen molecules. This period of time reflects thehigh rate of bloodflow through the pulmonary vascular bed(about 6 L/min) and the small capillary blood volume at anyinstant (about 75 mL). The ratio of capillary volume to

CHAPTER 17

VENTILATION–PERFUSIONRELATIONSHIPS

Peter D. Wagner

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 atrest, the time required to fully load oxygen onto hemoglobinis only about 0.25 seconds,4 and thus there is considerablereserve capacity in the “oxygen-diffusing capacity” of thelung. This is explained by the very large alveolar wall surfacearea through which the oxygen diffuses, some 80 m2 in all,and the very short diffusion distance separating alveolar gasfrom capillary blood, both mentioned above.

The end result is that in normal lungs at rest, the PO2 inthe blood exiting the pulmonary capillary network is virtu-ally equal to that of the alveolar gas (100 mm Hg) and diffu-sion equilibration is said to be complete. The PO2 in theblood leaving the lungs is thus also about 100 mm Hg.Because of the shape of the oxygen–hemoglobin dissociationcurve, essentially all oxygen-binding sites (98 of every 100)contain oxygen at this pressure of 100 mm Hg. In otherwords, the oxygen saturation of blood leaving the lungs is 98%.

Whereas the process of ventilation is “tidal,” with sequen-tial inspiration and expiration occurring through the samesystem of airways, bloodflow through the lung vasculature isunidirectional. Thus, the right ventricle pumps partiallydeoxygenated blood returned from the various body tissuesthrough the pulmonary arterial tree to the capillary bed,where reoxygenation takes place as described. The oxy-genated blood then is collected in the pulmonary veins,which forward the blood to the left heart for distribution tothe tissues. What enables passive diffusion to accomplish thetransfer of oxygen from alveolar gas into the blood is the factthat alveolar PO2 is much higher (at 100 mm Hg) than thePO2 of the blood returning from the tissues (normally about40 mm Hg). The fall in PO2 from 100 (arterial) to 40 mm Hg(venous) as blood traverses the body reflects the extraction ofoxygen by each tissue to support its metabolic needs.

Figure 17-1 depicts the entire process in a homogeneousor “one-compartment” lung. The processes of ventilation,diffusion, and bloodflow are indicated, along with the nor-mal oxygen and carbon dioxide partial pressures in alveolargas 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 Hgas mentioned), and inspired air contains 21% oxygen at 150mm Hg. Thus, only about one-third of the inhaled oxygen isabsorbed, and considerable ventilatory effort is thereforewasted (compared with a hypothetically perfectly efficientlung, in which all of the inhaled oxygen would be taken up).Similarly, since blood returning from the tissues still hasa PO2 of 40 mm Hg (which corresponds to an oxygen–hemoglobin saturation of about 75%), only about 25% of theoxygen in each red blood cell is transferred to the tissues tosupport metabolism. Considerable cardiac contractile effortis therefore wasted as well.

In addition, the process of diffusion appears overendowed,when we consider that the transit time, at 0.75 seconds, isthree times as long as required. One could hypothetically sur-vive the removal of two-thirds of the lung tissue and still havesufficient time for diffusion equilibration (at rest).

There are reasons, however, why the body imposes these“taxes” on itself. First, maintaining alveolar PO2 at 100 mm Hgis important because when the arterial blood reaches thevarious tissue beds, the unloading of oxygen is, as in thelung, a process of passive diffusion. This requires a highincoming PO2 in the arterial blood to provide the diffusiongradient to the tissues. Thus, when arterial PO2 is reduced,such as at altitude, exercise capacity is also reduced, in largepart because of the reduction in the blood–tissue gradient ofoxygen driving diffusion. Second, the reserve capacity incapillary transit time seen at rest reflects the need for greatlyincreased oxygen uptake during exercise. If the lungs werenot “overbuilt” for resting conditions, little exercise could beaccomplished because during exercise oxygen would not beable to be transferred from alveolar gas to capillary bloodsufficiently quickly. Third, the low tissue extraction rate of25% noted above also reflects the need to be able to extractmore oxygen from each red cell during exercise to supportmuch higher metabolic rates.

CHALLENGES TO GAS EXCHANGE CAUSED BY THE STRUCTURE OF THE LUNGS

In the section above, I pointed out intrinsic inefficiencies,seen at rest, based on the need to provide the body with suf-ficient oxygen when metabolic needs increase. However, thefact that the lung accomplishes gas exchange by a processdependent on ventilation, passive diffusion, and bloodflowhas led to pulmonary structural characteristics that haveconsiderable potential to interfere with gas exchange, evenin the healthy lung. These potential problems are thus addi-tional to those described above. That such interferencesrarely seem to happen in health is remarkable. However,they collectively form the basis of why gas exchange canbe so severely compromised in pulmonary disease (seeChapter 18, “Ventilation–Perfusion Distributions in Disease”).

The potentially deleterious effects of lung structure ongas exchange include the following.

LUNG COLLAPSE: PNEUMOTHORAX

Because breathing is a tidal process, a mechanism is requiredfor alternately inflating and deflating the lungs with each

Ventilation

Conductingairways

Alveoli

Pulmonaryartery

PvO2 = 40PvCO2 = 45

PcO2 = 100PcCO2 = 40

PAO2 = 100PACO2 = 40

Diffusion

Capillaries

Bloodflow

Pulmonaryvein

FIGURE 17-1 The principal structures involved in pulmonary gas exchange and their functions. Gas exchange is an integratedprocess involving ventilation, bloodflow, and diffusion.

Ventilation–Perfusion Relationships 167

breath. The left and right lungs lie in physically separateparts of the thoracic cavity. The intrapleural space betweenthe surface of the lungs and the inner surface of the chestwall contains only a thin film of liquid. Since the lungs areelastic, they have a natural tendency to collapse away fromthe chest wall. The lungs are kept inflated and do not col-lapse, by virtue of the subatmospheric pressure in theintrapleural space. This pressure is below atmosphericbecause the lungs tend to collapse whereas the chest walltends to spring out. These opposing tendencies create a sta-ble state of lung inflation with a negative intrapleural pres-sure. If the integrity of the intrapleural space on either sideof the chest is violated (as may happen in chest wall traumaor with spontaneous pneumothorax), the lung on that sidewill collapse like a punctured balloon. In such a situation,breathing efforts will be ineffectual, and thus the lungwill remain unventilated, obviously compromising gasexchange, with potentially fatal consequences. The needfor sequential inflation and deflation in a system wheregas exchange occurs by diffusion through very thin alveolar–capillary membranes imposes constraints on lungstructure that result in a delicate tissue framework suscepti-ble to pneumothorax.

DEAD SPACE

Because gas exchange occurs by passive diffusion, a verylarge alveolar surface area is needed in order for sufficientoxygen to reach the pulmonary capillaries. Suppose that thelung, with a volume (V) at FRC of 4,000 mL, were a singlespherical large alveolus. Since volume is given by the for-mula V �(4/3) �x �r3, the radius, r, would be about 10 cm.Since the surface area (A) of this sphere is given by the formula A �4 �x �r2, total surface area would be about1,200 cm2. Given the thickness (about 0.3 �m) of theblood–gas barrier, it was noted above that an area of about80 m2 is required to enable the rates of oxygen uptakerequired for heavy exercise. This is 800,000 cm2. Thus, a sin-gle large alveolus would have more than 600-fold too smalla surface area to support gas exchange during exercise.

From the above area and volume formulae, it should beapparent that the surface area/volume ratio of a sphere (A/V)increases as its diameter is reduced. Thus, to achieve a suffi-cient surface area for gas exchange within a 4 L total volume,the lung must be constructed not as a single sphere butrather as a parallel collection of many smaller “spheres”—the alveoli. It turns out that to have an 80 m2 surface areawith a 4 L total volume, about 300 million spheres of diam-eter about 300 �m would be needed.

The consequence of this requirement is the herculeantask of ventilating each alveolus with relatively equalamounts of air on each breath. Much like a bunch of grapeson a branched stem, the alveoli (grapes) are connected to abranched system of conducting airways (stem). This tree-trunk-like system of airways has to branch some 23 times inorder to supply such a large number of alveoli.

The total volume of these conducting airways is consid-erable, and it should be clear that all inhaled air must nego-tiate these airways before it reaches the alveoli where gasexchange takes place. Down to about the sixteenth branch

point, the airways are constructed robustly only for deliveryof air, and no oxygen crosses the thick walls of these first 16branches to contribute to overall oxygen uptake. The totalvolume of these 16 generations of airways in the averageperson is about 150 mL5 and is called the anatomic deadspace.

Of every tidal breath taken, normally about 500 mL, only350 mL of fresh air will reach the alveoli and take part inoxygen uptake. If there are 15 breaths/min, total ventilationwill be 15 �500 mL /min, or 7.5 L /min. However, alveolarventilation (that amount of fresh air reaching the alveoli) isonly 15 �(500 �150) mL /min, or 5.3 L /min. The normaldead space is thus about 30% of the tidal volume, and theventilation associated with it (2.2 L /min in this example) istermed wasted ventilation.

One must ventilate some 40% more to achieve a givenlevel of oxygen uptake than if there were no conducting air-way system. This requirement may be problematic inpatients with severe lung disease and is the basis for the useof transtracheal catheter administration of air or oxygen topatients with impaired ventilation. Direct insufflation of airinto the trachea functionally eliminates that part of theanatomic dead space above the trachea (the larynx andoropharynx). This reduces the amount of ventilation neededto support a given metabolic rate.

AIRWAY INFECTION/INFLAMMATION

The progressive branching of the airways imposes not onlydead space but also ever-narrowing and increasing numbersof airways with each generation (or branching). In the smallbronchioles, because of their enormous number, the totalcross-sectional area is so high that the linear velocity of gasbecomes 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 inflamma-tion. Here, as elsewhere in the airways, edema and secre-tions can develop. In the small airways in particular, thelumen 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 progressivelybranching airway system is that the dimensions of all mem-bers of each generation cannot be identical. Since these air-ways are arranged in parallel with one another, those airwaysthat are for some reason longer and narrower than others willimpose higher resistance to airflow, and thus there may beinequality 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 toinequality in the distribution of alveolar bloodflow.

DYNAMIC COMPRESSION OF THE AIRWAYS

Yet another consequence of the branching airway system isthat smaller peripheral airways (which lack cartilage in theirwalls), in particular, become susceptible to compressionduring exhalation. During quiet breathing at rest this does notoccur, but during forceful exhalations, such as seen during


exercise, the resulting positive intrapleural pressure cancompress these airways, resulting in limitation of airflow.This problem is known as dynamic compression. To theextent that this phenomenon occurs unevenly throughoutthe lung, as a result of both gravitational and nongravita-tional influences, it will add to the possibility of inequalityof ventilation. In young healthy people, it is not of muchconcern. It is seen more with advancing age, as the elasticrecoil of the lungs diminishes,6 and is a hallmark of emphy-sema, where elastic recoil is greatly reduced. Reduced elasticrecoil is a factor because dynamic compression is to someextent counteracted by outward radial traction imposed onairways by alveoli connected to them, and the strength ofsuch 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 directcontact with air. This creates a (roughly spherical) air–liquidinterface, and surface tension must therefore exist. As withsoap bubbles, such surface tension acts to reduce the surfacearea of the interface, so that alveoli are intrinsically prone tocollapse. The law of LaPlace shows that the smaller the alve-olar radius, the greater will be the tendency for collapse tooccur because of this surface tension. Thus, having a greatmany small “bubbles” rather than fewer large ones mayserve gas exchange well but puts the lungs at risk of col-lapse. Without special molecules that greatly reduce the sur-face tension of the alveolar lining fluid (surfactant),widespread lung collapse would occur. This is indeed seenclinically in premature infants, whose surfactant system isimmature, and in acute lung injury at any age, when the sur-factant system malfunctions.

PULMONARY EDEMA

The balance of hydrostatic and osmotic forces between theblood in the pulmonary capillaries and the fluid in the inter-stitium around them is such that there is a net force drivingfluid out of the capillaries into the interstitium of theblood–gas barrier. Were this fluid to accumulate, the blood–gas barrier would thicken, and this would reduce the rate ofdiffusive equilibration for oxygen and carbon dioxidebetween the alveolar gas and capillary blood. It would alsomake affected alveolar walls stiffer and thus more difficult toinflate during inspiration. That such fluid does not normallyaccumulate is because of the pulmonary lymphatic system,which collects such fluid and facilitates its transport backinto the systemic venous system along a lymph vessel treethat follows the airway branching pattern centrally and endsin the superior vena cava.

Lymphatic obstruction or overwhelming the system withhigh rates of fluid transudation does, in fact, cause pulmonaryedema, 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 disruptionwhen stressed.7 This can result from high intracapillaryblood pressure (as happens frequently in race horses when

they are galloping, for example8). It could also possiblyresult from excessive stretch of the alveolar wall (as happensduring mechanical ventilation of ill patients when inflationpressures are excessive). Since the blood–gas barrier is pre-dominantly formed of capillary walls (mated to alveolarepithelium), its disruption leads to local inflammation,edema, and, when severe, even frank hemorrhage of bloodinto the alveoli. Any of these effects may impair gasexchange.

It is remarkable that in the face of all these challenges, gasexchange proceeds as smoothly as it does, even in health. Itis testament to the success of evolutionary countermeasuresto these problems—phenomena such as making the alveolisupport each other mechanically by being physically joinedtogether; reducing surface tension by surfactant production;clearing inhaled particles by means of scavenger cells(macrophages) and the mucociliary airway clearance sys-tem; and a pulmonary microvasculature that keeps bloodpressures low (when flow is increased) by mechanisms ofrecruitment and distention of blood vessels.

GRAVITATIONAL DETERMINANTS OF VENTILATION–PERFUSION DISTRIBUTION

As if these challenges were not enough, the presence of grav-ity imposes systematic gradients in the distribution of venti-lation and bloodflow in the lung. These gradients are in thesame direction but are unequal in magnitude. Thus, (1) bothbloodflow and ventilation are generally higher in dependentthan in nondependent regions, and (2) the inequality ofbloodflow considerably exceeds that of ventilation. As aresult, the ratio of ventilation to bloodflow, a critical deter-minant of gas exchange, is not uniform. In the upright lung,it is systematically higher at the apex than at the base.9 Thegradient in ventilation can be explained by the weight ofthe lung itself causing some “sagging” of the lung within thethorax. Thus, the nondependent alveoli will be moreexpanded than the dependent alveoli, much like a “slinky,”or coiled spring, hanging under its own weight: the uppercoils are further apart than the lower coils, due to its weight.This uneven expansion is considered in the context of thepressure–volume behavior of the lung. More expanded alve-oli, further up the pressure–volume curve, are stiffer thanless expanded alveoli. Thus, the larger, nondependent alve-oli expand less with each breath and thus receive less venti-lation than their dependent neighbors. As a result, theventilation of alveoli near the bottom of the upright humanlung is about twice the ventilation of alveoli near the top.

Gravity also explains the gradient in perfusion, whereinthe bloodflow in alveoli at the bottom of the upright humanlung is perhaps 10 times higher than at the top of the lung.This is explained in large part by the hydrostatic propertiesof a column of liquid and Ohm’s law. Ohm’s law states thatflow will vary directly with pressure (assuming constantresistance). Since pulmonary artery pressure falls by 1 cmH2O with each centimeter increase in height up the lung,because blood has a density of about 1 g/cm, bloodflow will fallwith increasing height up the lung. This concept suffices forthe general explanation of bloodflow variation with vertical


position throughout the lung, but the details are more com-plex because the blood vessels are exposed to alveolar gaspressure. Accordingly, as first described by West andDollery,10 lung perfusion is functionally described by rela-tionships among three pressures: pulmonary arterial, pul-monary 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 zonesfrom 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 dis-tance, drawn from the data of West.9 Figure 17-2 reminds usthat the systematic variation in ventilation and bloodflowimplies obligate variation in the ratio of ventilation (V̇A) tobloodflow (Q̇) with vertical distance, also shown in Figure17-2. This critical concept is discussed later.

NONGRAVITATIONAL DETERMINANTS OF V̇A/Q̇ DISTRIBUTION

It has been known for almost 40 years that gravity is not theonly factor responsible for uneven distribution of ventilationand bloodflow in the lungs. For example, ventilation andbloodflow fall off serially with distance along the airways,independently of gravity.11 Variation in ventilation andbloodflow at a given horizontal level also occurs because ofintrinsic anatomic variation in airway and vascular geome-try, and there may also be random or even systematic differ-ences in airway and vascular smooth muscle responses thatfurther modify distribution. Furthermore, the repeatedbranching pattern of the airways and blood vessels gives riseto fractal behavior in distribution, such that spatial correla-tion of both ventilation and bloodflow occurs.12 That is,there is clustering such that adjacent areas of the lung aregenerally more similar with regard to both ventilation andbloodflow than are distant areas. The degree of variationin both ventilation and bloodflow has been shown to be

substantial, and it has been claimed that, as a result, non-gravitational causes of both ventilation and perfusioninequality are more important than those based on gravity. Ifthat were true, it would imply that whereas ventilation andbloodflow were each nonuniform, variations in each mustcorrelate, such that the nonuniformity in their ratio (venti-lation/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 normalalveolar–arterial PO2 difference,9 leaving very little that canbe due to other, nongravitational causes.

PRINCIPLES OF PULMONARY GAS EXCHANGE

A central theme emerging from the preceding discussion isthe importance of the ratio of ventilation to bloodflow (theventilation/perfusion or V̇A/Q̇ ratio) in determining gasexchange. This section provides the quantitative basis forthis claim. It relies on a single, fundamental, yet simple prin-ciple: conservation of mass. The most well-known treatiseson the subject can be found in the literature of the immedi-ate post–World War II period. This is when Riley andCournand13 and Rahn and Fenn14 separately laid out theprinciples of gas exchange, converting them into useful rela-tionships that have given us our current understanding ofhow gas exchange takes place and what factors are involved.

The problem is approached by recognizing that oxygen istaken out of the respired air at a rate exactly equal to the rateof its uptake into the pulmonary capillary blood, so long asthe lung exchange process is in a steady state. With thisexplicit assumption, we can write one equation depictingthe removal of oxygen from respired gas and a seconddepicting its uptake into capillary blood, as follows:

V̇O2� V̇IFIO2� V̇AFAO2 (17-1)

V̇O2�Q̇CaO2�Q̇ CvO2 (17-2)

In these two equations, V̇O2 represents the rate of oxygenuptake, which is equal to the body metabolic rate, V̇I and V̇Aare, respectively, inspired and expired alveolar ventilation,and FIO2 and FAO2 are, respectively, inspired and expiredfractional alveolar oxygen concentrations. Equation 17-1thus states that the amount of oxygen taken out of respiredair per minute is the amount inhaled per minute (V̇IFIO2)minus the amount exhaled (V̇AFAO2). Equation 17-2 is verysimilar but refers to the blood. Thus, Q̇ is total pulmonarybloodflow (essentially equal to cardiac output), and CaO2

and CvO2 are, respectively, the oxygen concentrations inarterial and mixed venous blood. Here, oxygen taken intothe blood is the difference between the rate at which oxygenleaves the lungs (Q̇ CaO2) and the rate at which it enters (Q̇ CvO2). Because of the steady-state assumption, the V̇O2

values in the two equations are identical.Thus, Equations 17-1 and 17-2 can themselves be

equated:

V̇IFIO2� V̇AFAO2�Q̇CaO2�Q̇CvO2 (17-3)

If we assume for simplicity that V̇I and V̇A are numericallyidentical (and they normally differ by no more than 1%), we

Ven

tilat

ion

(L/m

in),

blo

odflo

w (

L/m

in)

and

vent

ilatio

n/bl

oodf

low

rat

io

Relative position from top to bottom of the lung

Ventilation/bloodflow ratio

Bloodflow

Ventilation

Top Bottom0.0

0.5

1.0

1.5

3.5

3.0

2.5

2.0

4.0

FIGURE 17-2 Data from West9 showing the systematic changes inventilation, bloodflow, and their ratio with distance up and downthe upright human lung. Whereas ventilation and bloodflow areboth lower at the top than the bottom, there is relatively more ven-tilation than bloodflow at the top and relatively more bloodflowthan ventilation at the bottom. As a result, ventilation/perfusionratios are higher at the top than at the bottom.


can replace V̇I with V̇A and simplify Equation 17-3 as follows:

V̇A(FIO2�FAO2) �Q̇ (CaO2�CvO2) (17-4)

This can be rearranged, yielding:

V̇A/Q̇�(CaO2�CvO2)/(FIO2�FAO2) (17-5)

It is more usual to convert the fractional concentrations FIO2

and FAO2 to their corresponding partial pressures PIO2 andPAO2 (using Dalton’s Law of Partial Pressures), which sim-ply involves a proportionality constant that we can call k,such that:

V̇A/Q̇�k(CaO2�CvO2)/(PIO2�PAO2) (17-6)

Exactly the same reasoning leads to a similar equation forcarbon dioxide:

V̇A/Q̇�k(CvCO2�CaCO2)/(PACO2�PICO2) (17-7)

Both the numerator and denominator terms are reversed forcarbon dioxide, simply reflecting the fact that whereas oxy-gen moves from air to blood, carbon dioxide moves fromblood to air. In addition, PICO2 is so low (air normally con-tains only 0.03% carbon dioxide) that it can be neglected.

Equations 17-6 and 17-7 describe the necessary quantita-tive relationships between V̇A/Q̇ ratio and gas concentrationsin the alveolar gas and capillary blood. It is critical to under-standing these equations to realize that they contain bothindependent and dependent variables. Most commonly, weuse Equation 17-6 to find, for given values of V̇A/Q̇ ratio andof mixed venous and inspired oxygen levels (the independ-ent variables), what the alveolar (and hence end-capillary)oxygen levels (the dependent variables) must be to satisfythe equation. The same applies for PACO2 in Equation 17-7.

The answer is given in Figure 17-3. Here, the numericalsolution to Equation 17-6 is presented for all possible valuesof V̇A/Q̇ , using normal values for inspired and mixed venousPO2. The lowest possible V̇A/Q̇ value is zero, correspondingto a perfused alveolus that has no ventilation (ie, a shunt).

Such a unit exchanges no gas, and so the end-capillary bloodleaving that unit has a PO2 equal to that of mixed venousblood (40 Torr in this example). The highest possible V̇A/Q̇value is infinite, representing a ventilated alveolus withoutany bloodflow (called alveolar dead space). This unit alsoexchanges no gas, and thus the alveolar PO2 equals that of the inspired gas (150 Torr in this case). Between theseextremes, there is a smooth relationship where PAO2

increases nonlinearly with increasing V̇A/Q̇ ratio as shown.A major assumption in solving Equation 17-6 is that the

alveolar and end-capillary PO2 values are the same. Thisimplies complete equilibration by diffusion for oxygenacross the blood–gas barrier. A justification for this assump-tion, at least at rest, was provided earlier. Identical assump-tions are used for carbon dioxide in solving Equation 17-7.

Figure 17-4 shows the solution to Equation 17-7 for car-bon dioxide in a manner similar to Figure 17-3 for oxygen.Again, the extremes of V̇A/Q̇ ratio produce PCO2 valuescorresponding to that of mixed venous blood when the V̇A/Q̇ratio is zero and to that of inspired gas (essentially zero)when the V̇A/Q̇ ratio is infinite, whereas between there is asmooth relationship, with PCO2 falling as V̇A/Q̇ is increased.

Equations 17-6 and 17-7 are very useful. Under the pre-vailing major assumptions (steady-state conditions andcomplete diffusion equilibration), they show that alveolar(and thus end-capillary) PO2 and PCO2 values are deter-mined by three interacting factors. These are (1) the V̇A/Q̇ratio, (2) the so-called “boundary” conditions—mixedvenous and inspired oxygen and carbon dioxide levels, and(3) the oxygen–hemoglobin and carbon dioxide dissociationcurves because they determine the relationships betweenoxygen and carbon dioxide concentrations (numerator ofEquations 17-6 and 17-7) and partial pressures (denomina-tor of Equations 17-6 and 17-7). Alterations in any one ofthese three factors thus have the potential to affect alveolarand hence arterial PO2. Figures 17-3 and 17-4 showed howthe first of these three (V̇A/Q̇ ratio) affects PO2 and PCO2.Figure 17-5 shows how changes in mixed venous PO2 and

Inspired PO2

Alv

eola

r P

O2

(Tor

r)

Mixed venous PO2

80

120

160

100

140

60

40

20

0

Ventilation/perfusion ratio

0.001 0.01 0.1 1 10 100

FIGURE 17-3 Dependence of alveolar PO2 on ventilation/perfusion(V̇A/Q̇) ratio. At low V̇A/Q̇, alveolar PO2 is close to mixed venousPO2; at high V̇A/Q̇ , it is close to inspired PO2. Alveolar PO2 is mostsensitive to V̇A/Q̇ in the normal range (V̇A/Q̇ of about 1).

Alv

eola

r P

CO

2 (T

orr)

Inspired PCO2

Mixed venous PCO2


0.001 0.01 0.1 1 10 1000

10

40

20

30

50

FIGURE 17-4 Dependence of alveolar PCO2 on ventilation/ perfusion (V̇A/Q̇ ) ratio. At low V̇A/Q̇, alveolar PCO2 is close tomixed venous PCO2; at high V̇A/Q̇, it is close to inspired PCO2.Alveolar PO2 is most sensitive to V̇A/Q̇ in the above-normal range(V̇A/Q̇ of about 1 to 10).


inspired PO2 affect PO2. A fall in mixed venous PO2 reducesalveolar PO2 in all alveoli, but much more so in alveoliwhose V̇A/Q̇ ratio is low. Such units have their PO2 “tied to”that of mixed venous blood, as shown. Correspondingly, afall in inspired PO2 also reduces alveolar PO2, but more sowhen V̇A/Q̇ ratio is high. The curve for carbon dioxidebehaves correspondingly when venous or inspired PCO2 ischanged. Figure 17-6 shows how changes in the PO2

corresponding to hemoglobin oxygen saturation of 50%(P50) affect alveolar PO2 when mixed venous and inspiredPO2 are maintained at normal values. Thus, a fall in P50

leads to a higher alveolar PO2 at any V̇A/Q̇ ratio, and viceversa. The effects are clearly greatest in the normal rangeof V̇A/Q̇ and are negligible when V̇A/Q̇ is either very low orvery high.

Solving Equations 17-6 and 17-7 by hand or graphically,as done originally,14 is very laborious, due mostly to the non-linear and interdependent nature of the oxygen and carbondioxide dissociation curves. Today, these equations are eas-ily solved by computer, and the necessary algorithms arewell established15,16 and available.

GAS EXCHANGE IN THE PERFECTLY HOMOGENEOUS LUNG

To apply these concepts to the lungs, it is useful to beginwith an ideal lung that is completely homogeneous. Eventhough the lungs of young healthy subjects contain V̇A/Q̇inequality from several sources, as discussed above, thedegree of inequality normally present has very little detri-mental effect on arterial PO2 and PCO2. Commonly, arterialPO2 is only about 5 to 10 Torr below alveolar PO2; this hasnegligible effects on arterial oxygen saturation and concen-tration and no measurable effect on arterial PCO2. Thus, thenormal lung is not far from being homogeneous in terms ofoverall gas exchange, and the following analysis thereforecan be used with little error.

Once again, it is the concept of which variables in the sys-tem are independent and which are dependent that shouldfirst be considered when applying Equations 17-1 through17-7. Restating Equations 17-1 and 17-2, we have:

V̇O2 � V̇IFIO2 � V̇AFAO2 �kV̇A(PIO2 �PAO2) (17-8)

(remember that taking V̇I � V̇A is reasonable; k converts frac-tional concentration F to partial pressure P) and

V̇O2�Q̇(CaO2�CvO2) (17-9)

When considering Equation 17-8, recall that the lungremains the “servant of the body,” such that the body, notthe lung, sets V̇O2 as an independent variable in the currentcontext. Likewise, PIO2 is set by the environmental condi-tions, and V̇A is determined by the integrated respiratorycontrol system and mechanical properties of the lungs andchest wall. Thus, the single dependent variable is alveolarPO2 (PAO2). What Equation 17-8 tells us is as follows: giventhe V̇O2, PIO2, and amount of alveolar ventilation (V̇A), thealveolar PO2 takes a unique, dependent value that mustsatisfy Equation 17-8. These are the only determinants ofalveolar PO2 in a homogeneous lung.

Let us now proceed to Equation 17-9. The same value ofV̇O2 must exist as for Equation 17-8. Total pulmonary blood-flow will also be determined, like ventilation, by complex

Alv

eola

r P

O2

(Tor

r)


Inspired PO2:

0.001 0.01 0.1 1 10 1000

20

140

80

60

40

120

100

160

140130

150

B

Alv

eola

r P

O2

(Tor

r)


Mixed venous PO2:

0.001 0.01 0.1 1 10 1000

20

140

80

60

40

120

100

160

403020

A

FIGURE 17-5 Relationship of alveolar PO2 to V̇A/Q̇ depends onboth mixed venous PO2 (A) and inspired PO2 (B). In particular,PO2 in areas of low V̇A/Q̇ reflects mixed venous PO2, whereas areasof high V̇A/Q̇ reflect inspired PO2.

Alv

eola

r P

O2

(Tor

r)


Hemoglobin P50:

20

27

34

0.001 0.01 0.1 1 10 1000

20

140

80

60

40

120

100

160

FIGURE 17-6 Dependence of alveolar PO2 on hemoglobin P50. AsP50 varies, alveolar PO2 changes (at given mixed venous andinspired PO2). Changes in P50 affect alveolar PO2 mostly in thenormal range of V̇A/Q̇ , around 1.


control systems external to the lungs. Given that alveolarand end-capillary (here �arterial) PO2 are equal in thishomogeneous lung, arterial oxygen concentration (CaO2)must be that value read off the oxygen–hemoglobin dis-sociation curve for the value of alveolar PO2 determinedfrom Equation 17-8. Hence, the remaining unknown, mixedvenous oxygen concentration must be that value thatsatisfies Equation 17-9.

In sum, Equation 17-8 shows that it is only metabolic rate,ventilation, and inspired PO2 that together influence arterialPO2 when the lungs are completely homogeneous. Cardiacoutput does not influence arterial PO2 under such circum-stances but does affect mixed venous PO2. Again, these con-clusions pertain only to steady-state conditions and whenthere is complete diffusion equilibration across the blood–gasbarrier. Although this is strictly true only for a homogeneouslung, these conclusions are also approximately correct for thenormal human lung, as discussed above.

When this approach is taken, and as can be inferred fromFigures 17-3 and 17-4, we can see that normal arterial PO2

is about 100 Torr, and arterial PCO2 is about 40 Torr. This isbased on (1) alveolar ventilation at 5 to 6 L/min and cardiacoutput at 5 to 6 L /min, such that overall V̇A/Q̇ ratio isclose to 1, and (2) a metabolic rate resulting in a V̇O2 of 300 mL/min and a V̇CO2 of 240 mL/min.

GAS EXCHANGE IN THE PRESENCE OF V̇A/Q̇ INEQUALITY

V̇A/Q̇ inequality is defined as the state wherein not all alve-oli enjoy the same V̇A/Q̇ ratio. However, all of the principleslaid out in Equations 17-1 to 17-7 apply when V̇A/Q̇ inequal-ity develops, just as in the homogeneous lung. In the pres-ence of V̇A/Q̇ inequality, these equations can be applied inturn to each different V̇A/Q̇ ratio unit in the lung. The per-formance of the whole lung is then found simply by sum-ming 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 toeach other, it is thought that many adjacent alveoli togetherform a functional unit of gas exchange. Evidence points tothe acinus (all alveoli distal to the last terminal bronchiole)as the anatomic basis of a functional unit,17 and there areabout 100,000 such acini in the lung, consistent with about17 generations18 of dichotomously branching airways up tothe last terminal bronchiole (217�131,072). Although thisnumber is very much lower than 300 million, it is still fartoo high to deal with experimentally. Since each unit is char-acterized by two independent variables (ventilation andbloodflow), it would take some 260,000 measurements tofully describe the functional V̇A/Q̇ distribution! We have nei-ther the technology nor the resources to do this, and thank-fully it turns out not to be necessary to understand V̇A/Q̇inequality in the lung. In fact, the simplest model of inequal-ity, the two-compartment model, is quite adequate for illus-tration of how V̇A/Q̇ inequality affects gas exchange. I showthis below.

To work through this more difficult analysis, it is mostinstructive to use particular examples. It is easiest to start

from the homogeneous lung and then use the above equa-tions to determine how a two-compartment model with adefined degree of V̇A/Q̇ mismatch affects gas exchange. Whatwill be found is that V̇A/Q̇ inequality causes hypoxemia,hypercapnia, and reductions in the rates of both oxygenuptake and carbon dioxide elimination. Such a result is notcompatible with life in the long term because the lung can-not supply enough oxygen for the metabolic needs of thebody or keep up with the associated rate of carbon dioxideelimination. Usually, the body employs one or more com-pensatory mechanisms (discussed below), which can returnV̇O2 and V̇CO2 to levels matching the tissue metabolic rate.However, sometimes this does not happen. And, occasion-ally, the degree of inequality may be too severe for availablecompensatory mechanisms to cope with. In either case,death will ensue.

I will begin with a homogeneous lung, using values forthe variables that correspond to those of a typical normalresting adult breathing air at sea level. I will stipulate thefollowing independent variables: FIO2�0.21; FICO2�0;barometric pressure �760 Torr; V̇O2�300 mL/min;V̇CO2�240 mL/min; alveolar ventilation �5.2 L/min; car-diac output �6.0 L/min. Additional secondary informationrequired includes hemoglobin concentration (taken to benormal, 15 g/dL), hemoglobin P50 (normal at 27 Torr), andacid–base status, which will also be taken to be normal. Thatis, there is no metabolic acidosis or alkalosis.

Applying first Equations 17-1 and 17-2 for oxygen andusing the corresponding approach simultaneously for car-bon dioxide, we find that, for the given V̇A/Q̇ ratio of 5.2/6.0,or 0.87, PAO2�100 Torr and PACO2�40 Torr. This is com-patible with Figures 17-3 and 17-4. Mixed venous PO2 isabout 40 Torr, and mixed venous PCO2 is 46 Torr. Theseunique values (here rounded to the nearest integer) fit theequations and allow for the requisite V̇O2 and V̇CO2

specified above.Figure 17-7 shows these results in diagrammatic form,

where the lung is drawn as two “alveoli” that are equallyperfused and equally ventilated. Thus, although two “alve-oli” are drawn, they have the same V̇A/Q̇ ratio, and thus thesystem is really a homogeneous lung. The “trachea” is rep-resented by the single vertical line at the top of the figure. Itdivides into two “bronchi” that connect the “trachea” to thetwo circular “alveoli.” Beneath each alveolus is its vascula-ture, drawn as a curved “vessel” on each side that touches itsalveolus, forming the “blood–gas barrier” at the points ofcontact. Blood flows from the outside inwards for each“alveolus,” and the two “blood vessels” join at the foot of thefigure to form the “left atrial” and hence “systemic arterial”bloodstreams.

Suppose we now suddenly create severe airway obstruc-tion in the “bronchus” of the left-hand “alveolus.” Thiscould, in fact, happen, for example, from inhalation of a for-eign body into a main bronchus, and is depicted in Figure17-8. If we analyze the effects of this inequality, assumingfirst that the mixed venous blood oxygen and carbon diox-ide levels remain normal, the results are as shown in Figure17-8A. The large black dot indicates the obstruction, whichhas reduced ventilation on the left side from 2.6 to just


10040

2.6 2.6

3.0 3.0

0.9 0.9

10040

.

.

PVO2 40PVCO2 46

PAO2

PACO2

Ventilation L/min

Perfusion L/min


Arterial PO2 100 Torr

Arterial PCO2 40 Torr

Normal lungs

VO2 300VCO2 240

FIGURE 17-7 Gas exchange function in a homogeneous lung thatis normally perfused and ventilated. Arterial PO2 and PCO2 are 100and 40 Torr, respectively, and the lung is able to take up the normalamount of oxygen (300 mL/min) and eliminate the normal amountof carbon dioxide (240 mL/min). These results all come from solv-ing the mass conservation equations (Equations 17-1 and 17-2 foroxygen and the corresponding equations for carbon dioxide).

0.3 L /min. As a result, the rest of the ventilation is divertedto the right side, keeping total ventilation constant. In real-ity, both ventilation and mixed venous gas levels wouldchange, as too may cardiac output, and these changes arediscussed below. However, to understand the effects of V̇A/Q̇inequality on gas exchange, we will first assume no changesin any of these variables.

The redistribution of ventilation gives rise to two differ-ent V̇A/Q̇ ratios, as Figure 17-8 shows: 0.1 on the left and 1.6on the right. Since overall ventilation and bloodflow areunchanged, the overall V̇A/Q̇ ratio remains at 5.2/6.0, or0.87. Note that the V̇A/Q̇ ratio of the left side is lower, andthat of the right side is higher, than this overall value. At firstsight, one might think that, for this reason, the two wouldoffset one another, and overall gas exchange would be unaf-fected. This is not the case, as the following analysis demon-strates.

When Equations 17-1 and 17-2 are applied separately toboth “alveoli,” the resulting alveolar PO2 values are, asshown, 47 and 119 Torr (see Figure 17-3). Similar calcula-tions for carbon dioxide reveal that alveolar PCO2 values are46 and 35 Torr, respectively (see Figure 17-4). The bloodflowremains equally distributed between the alveoli (3 L/mineach), and so the mixed arterial blood is a 50:50 mixture ofthe bloodstreams from the two alveoli. Because the oxygendissociation curve is so nonlinear, this mixture does not pro-duce a PO2 halfway between the two alveolar PO2 values of47 and 119 (which would be 83) but gives rise to a muchlower PO2, 58 Torr.

Similar calculations for carbon dioxide give a rather dif-ferent result: because the carbon dioxide dissociation curveis nearly linear, the PCO2 of mixed arterial blood is essen-tially the average of the two alveolar PCO2 values, at 41 Torr.Although this is a small absolute increase from normal (ofonly about 1 Torr), even a 1-Torr increase is a significantpercentage (about 20%) of the mixed venous–arterial PCO2

difference, suggesting that carbon dioxide elimination isindeed compromised, even though the change in arterialPCO2 seems trivial.

Thus, in this particular model, where the primary lesioncorresponds to areas of greatly reduced V̇A/Q̇ ratio, theeffects on arterial PO2 are shown to be far greater than thoseon arterial PCO2. These results also imply that total oxygenuptake must have been reduced (same mixed venous PO2

but lower than normal arterial PO2), and Figure 17-8Aindicates this, with V̇O2 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 asimplied above, from 240 mL/min in the normal lung to 210 mL/min here, but the interference is less than foroxygen, a reduction of only 13%.

The next step in the analysis is to determine the effectof this hypoxic and (slightly) hypercapnic blood onoxygen transport to (and carbon dioxide transport from) theperipheral tissues. Since tissue metabolic rate continuesunchanged, the tissues will attempt to extract sufficientoxygen from the blood for their metabolic needs. Extractingthe same amount of oxygen from arterial blood with a lowerPO2 must result in a fall in venous PO2 draining the tissues.This must cause a fall in mixed venous PO2 in the pul-monary artery. Returning to Figure 17-5A, it becomes clearthat this fall in mixed venous PO2 must reduce alveolar PO2,especially in the low-V̇A/Q̇ “alveolus,” which will furtherlower systemic arterial PO2 as well. However, this strategydoes enable restoration of V̇O2 to normal. Figure 17-8Bshows the result of this process, and it can be seen that V̇O2

is indeed restored to 300 mL/min, but the penalty is a fall inboth mixed venous and arterial PO2 (to 33 and 48 Torr,respectively). In a similar manner, because arterial PCO2 wasincreased by V̇A/Q̇ inequality, adding all the metabolicallyproduced carbon dioxide to tissue blood raises mixedvenous PCO2, which will lead to a further increase in arte-rial PCO2. Arterial PCO2 is now 45 Torr, up from 41 Torr.However, as for oxygen, the lungs are again able to eliminateall of the carbon dioxide produced (240 mL/min). Figure17-8B shows this as well.

We thus have what at first sight appears to be a paradox:overall lung function (ie, V̇O2 and V̇CO2) has been restored,but the hypoxemia and hypercapnia are both worse thanbefore the changes in venous PO2 and PCO2 that allowedV̇O2 and V̇CO2 to be normalized. Actually, this is typical ofother functional systems in the body and is not a paradox.For example, in stable chronic renal failure, the totalamount of urea excreted in the urine per unit time exactlymatches tissue urea production, but this can happen only inthe case of a higher than normal blood urea level when somenephrons are diseased and functionally compromised.

To this point, the body tissues have been protected (V̇O2

and V̇CO2 normalized), but hypoxemia and hypercapnia areboth significant. The next likely response is therefore anincrease in ventilation resulting from chemoreceptor activa-tion in response to the low PO2 and high PCO2. Figure 17-8Cshows that if the normal (right-hand) alveolus has its venti-lation increased by just 0.6 L/min (ie, by just 12%), arterialPCO2 is returned to the normal value of 40 Torr, even if the


obstruction on the left side is unaltered. This is a trivialincrease in ventilation, and thus in respiratory effort, andnormally will take place rapidly. However, note that thisincrease in ventilation has no significant effect on arterialPO2, as Figure 17-8 indicates. Improving alveolar PO2 on theright side increases oxygen concentration in the blood neg-ligibly because the oxygen dissociation curve is flat in thisregion. PO2 on the left side is essentially unchanged becausethere has been no relief of the airway obstruction. Thus,there is little effect on arterial PO2. In fact, PO2 in this exam-ple has actually fallen (even if by only 1 Torr), despite theincrease in ventilation. This is explained by the Bohr effectof carbon dioxide on the oxygen dissociation curve. In thisparticular model, further increases in ventilation on theright side are futile. Even reducing arterial PCO2 to 30 Torrby increasing ventilation on the right side to 7.7 L/min(Figure 17-8D) fails to improve arterial PO2. The patient cansurvive the obstruction in terms of overall gas exchange and

can overcome the initial hypercapnia quite easily. However,hypoxemia remains severe and refractory to increases inventilation.

It is very instructive to contrast the behavior of this par-ticular model (severe airway obstruction) with its symmet-ric counterpart of severe vascular obstruction, as mightoccur as a result of pulmonary thromboembolism. Figure17-9 shows such a two-compartment model, with the sameoverall ventilation and cardiac output as in the normal lung.In this case, bloodflow on the left-hand side is impaired,essentially as severely as was ventilation in the prior modelof airway obstruction (see Figure 17-8). We can applyexactly the same principles to calculate how oxygen and car-bon dioxide exchange will be affected, using the relation-ships in Figures 17-3 and 17-4 and the particular values forV̇A/Q̇ shown in Figure 17-9A. At this point, the assumptionof unchanged mixed venous PO2 and PCO2 will again bemade, as in Figure 17-8A. Note again that in this example,

3646

0.3 5.5

3.0 3.0

0.1 1.8

11035

.

.

PVO2 32PVCO2 46

PAO2

PACO2

Ventilation L/min

Perfusion L/min




Normocapnia restored by increased ventilation

VO2 300VCO2 240

C

3435

0.3 7.7

3.0 3.0

0.1 2.6

12126

.

.

PVO2 30PVCO2 35

PAO2

PACO2

Ventilation L/min

Perfusion L/min




Hypocapnia caused by further hyperventilation

VO2 300VCO2 240

D

4746

0.3 4.9

3.0 3.0

0.1 1.6

11935

.

.

PVO2 40PVCO2 46

PAO2

PACO2

Ventilation L/min

Perfusion L/min




Effect of VA/Q inequality alone. . ..

VO2 200VCO2 210

A

3751

0.3 4.9

3.0 3.0

0.1 1.6

10540

.

.

PVO2 33PVCO2 51

PAO2

PACO2

Ventilation L/min

Perfusion L/min




VO2 and VCO2 restored by mixed venous changes

VO2 300VCO2 240

B

FIGURE 17-8 Effect on gas exchange of severe unilateral airway obstruction causing inequality of ventilation distribution. A, Withoutchange in total ventilation, bloodflow, or inspired/mixed venous composition, there is moderate hypoxemia, slight hypercapnia, and dimin-ished oxygen uptake and carbon dioxide elimination. B, There will be an immediate fall in mixed venous PO2 and rise in PCO2. This allowsnormalization of V̇O2 and V̇CO2, but at a cost of further hypoxemia and hypercapnia. C, Hypercapnia and hypoxemia will stimulate respi-ration, normalizing arterial PCO2. Hypoxemia is not corrected, however. D, With arterial PO2 still low after ventilation has increased, theremay be a further increase in ventilation, now leading to hypocapnia but still not alleviating hypoxemia.


one side has a V̇A/Q̇ ratio lower than normal, and the otherhas a V̇A/Q̇ ratio higher than normal—just as for the airwayobstruction model. The different values result in differentnumbers, and in this case, whereas arterial PO2 has been lessaffected than in the case of airway obstruction, arterial PCO2

has increased twice as much as in the prior model—by 2 Torr. V̇O2 has fallen from 300 mL/min to 260 mL/min, areduction of only 13%, whereas V̇CO2 has fallen from 240 to180 mL/min, or by 25%. Thus, carbon dioxide has beenaffected more than oxygen in this analog of pulmonaryembolism.

As with the prior model, the tissues will extract the nec-essary oxygen from the venous blood and add all of the car-bon dioxide produced, causing venous PO2 to fall and PCO2

to rise. As before, this will cause arterial PO2 to fall furtherand PCO2 to rise further, but this will again allow normal-ization of V̇O2 and V̇CO2, as shown in Figure 17-9B. Notehere that arterial hypercapnia is severe, whereas hypoxemia

is relatively mild, consistent with the greater effects of sucha V̇A/Q̇ pattern on carbon dioxide than on oxygen.

Stimulation of the chemoreceptors will thus occur andlead to an increase in ventilation. Figure 17-9C shows that asmall increase in ventilation of just over 2 L/min (from 5.2to 7.4 L/min) will suffice to completely normalize arterialPCO2. In stark contrast to the airway obstruction model, inwhich half the lung (in terms of bloodflow) could not beventilated and was very hypoxic, almost all of the lung(again in terms of bloodflow) is well ventilated. Thus, arte-rial PO2 is essentially normalized (to 89 Torr) by this mod-est level of increased ventilation. In fact, a small furtherincrease in ventilation to just 10 L/min would produce anabove-normal arterial PO2 of over 100 Torr (Figure 17-9D),along with an arterial PCO2 of 30 Torr.

These two models illustrate the spectrum of gas exchangedisturbances. They show that, based on straightforwardprinciples of mass balance, it is possible to understand how

14314

3.7 3.7

0.3 ?.7

12.3 0.7

8842

.

.

PVO2 41PVCO2 45

PAO2

PACO2

Ventilation L/min

Perfusion L/min




Normocapnia restored by increased ventilation

VO2 300VCO2 240

C

14510

5.0 5.0

0.3 5.7

16.7 0.9

10432

.

.

PVO2 39PVCO2 35

PAO2

PACO2

Ventilation L/min

Perfusion L/min




Hypocapnia caused by further hyperventilation

VO2 300VCO2 240

D

14117

2.6 2.6

0.3 5.7

8.5 0.5

7444

.

.

PVO2 40PVCO2 46

PAO2

PACO2

Ventilation L/min

Perfusion L/min




Effect of VA/Q inequality alone. . ..

VO2 260VCO2 180

A

13921

2.6 2.6

0.3 5.7

8.5 0.5

6259

.

.

PVO2 33PVCO2 63

PAO2

PACO2

Ventilation L/min

Perfusion L/min




VO2 and VCO2 restored by mixed venous changes

VO2 300VCO2 240

B

FIGURE 17-9 Effect on gas exchange of severe unilateral vascular obstruction causing inequality of bloodflow distribution. A, Withoutchange in total ventilation, bloodflow, or inspired/mixed venous composition, there is mild hypoxemia, slightly more hypercapnia than inthe airway obstruction model, and diminished oxygen uptake and carbon dioxide elimination. In this model, the effects on carbon diox-ide are more prominent than for airway obstruction. B, As in Figure 17-8, there will be an immediate fall in mixed venous PO2 and a risein PCO2. This normalizes V̇O2 and V̇CO2, but at the cost of further hypoxemia and, especially, hypercapnia. C, Hypercapnia (in particu-lar) and hypoxemia will stimulate respiration, which normalizes arterial PCO2. Hypoxemia is essentially corrected. D, Any further increasein ventilation, were it to occur, would be able to raise arterial PO2 above normal.


V̇A/Q̇ inequality affects the ability of the lungs to exchangethe required amounts of oxygen and carbon dioxide and thepenalties that must be paid in terms of arterial blood gasaberrations to achieve this. They also illustrate the impor-tant concept that the degree to which oxygen and carbondioxide are differently affected by V̇A/Q̇ inequality dependson the pattern of that inequality.

METHODS FOR QUANTIFYING GAS EXCHANGE ABNORMALITIES

To this point, the focus has been on understanding how gasexchange takes place and how V̇A/Q̇ inequality perturbs gasexchange. This is necessary for learning about the process,but simply understanding the concepts is not sufficientwhen one wishes to approach altered gas exchange inpatients with lung disease. Accordingly, much work over thelast half century has dealt with attempts to measure alteredgas exchange and abnormal ventilation–perfusion relation-ships in particular. The most common approaches are nowdescribed, in order of increasing complexity.

ARTERIAL PO22, ARTERIAL PCO22, AND THE

PaO22/FIO22 RATIO

The simplest parameters of gas exchange are the arterial PO2

and PCO2 themselves. Normal values have been establishedby sampling arterial blood from large numbers of normalsubjects.19–21 The results are consistent with all of the abovetheory. Arterial PO2 is normally greater than 90 Torr (at sealevel), and arterial PCO2 is normally 40 Torr (also at sealevel). There is variability in both PO2 and PCO2. This is dueto both biologic and instrumental variance. A commoncause of biologic variance is hyperventilation during thesampling procedure as a result of the anxiety-provokingarterial puncture itself. Reasonable values for total variancewith well-functioning blood gas electrodes are about 3 to 5 Torr (1 SD) for PO2 and 1 to 2 Torr for PCO2.

Both arterial PO2 and PCO2 fall with altitude,22 due to thereduction in inspired PO2 and its concomitant effect ofincreasing ventilation. Thus, the altitude at which blood issampled is important for interpretation of the data. Anotherfactor is age since PO2 falls gradually (if slightly) with age.The changes in healthy nonsmokers are small, and octo-genarians typically have a PO2 in the range of 80 to85 Torr.19–21 PCO2, on the other hand, appears to remainconstant with age.

Measuring arterial PO2 and PCO2 is simple and is verycommonly done, but these variables represent the entire inte-grated result of all gas exchange processes in the lung (V̇A/Q̇relationships, shunting, diffusion limitation) and the above-mentioned compensatory responses in mixed venous blood,in ventilation, and in cardiac output. Thus, the informationobtained, although clinically very useful, is limited in termsof the insights provided into the alterations in physiology.

In situations where inspired oxygen levels may vary, suchas in the intensive care unit, an extensively used alternativeto the direct use of arterial PO2 is the ratio of arterial toinspired PO2 (or arterial PO2 to FIO2). This ratio is intendedto allow comparisons of arterial PO2 even as FIO2 is

therapeutically altered. It represents an attempt to controlfor the expected changes in arterial PO2 when FIO2 ischanged, so that the lungs can be compared irrespective ofFIO2. The physiologic basis of this is reasonable under somebut not all conditions, as Figure 17-10 shows.

Figure 17-10A shows arterial PO2 itself as a function ofFIO2, over the range from air (FIO2�0.21) to pure oxygen(FIO2�1.0) in three theoretical models of the lung. Theyreflect a normal lung, a lung containing a 20% shunt but noV̇A/Q̇ inequality, and a lung with severe V̇A/Q̇ inequality butno shunt. Arterial PO2 changes with FIO2 substantially in allthree examples, but at different rates.

Figure 17-10 shows the same arterial PO2 values nowdivided by FIO2. The normal lung and the lung with only ashunt show quite different ratios that are roughly constant

PaO

2 / F

IO2

ratio

FIO2

Normal

VA/QInequality

20% shunt

0.0 0.2 0.4 0.6 0.8 1.00

100

200

300

700

600

500

400

800

B

PaO

2 (T

orr)

FIO2

Normal

VA/QInequality

. .

. .

20% shunt

0.0 0.2 0.4 0.6 0.8 1.00

100

200

300

700

600

500

400

800

A

FIGURE 17-10 Response of arterial PO2 (A) and the ratio of arte-rial PO2 to FIO2 (B) to increases in FIO2 in three different lungs.Closed circles indicate a normal lung, triangles indicate a lung witha 20% shunt but no V̇A/Q̇ inequality, and open circles indicate a lung with severe V̇A/Q̇ inequality but no shunt.The normal lungand the lung with a pure shunt show essentially constant but verydifferent PaO2/FIO2 ratios, providing a rationale for the use of thisratio in assessing gas exchange when FIO2 is subject to change (asin critically ill patients). However, the response in the third lung,which has V̇A/Q̇ inequality rather than shunt, is very different. Thislung looks like the lung with a shunt at lower FIO2 but like the nor-mal lung at high FIO2. This points out the limitations in the use ofthis ratio.


over a wide FIO2 range. Certainly, the mean values of about600 (normal) and 200 (20% shunt) are very different, andthe variability, especially above an FIO2 of 0.3 to 0.4, is mod-est. The problem with the PaO2/FIO2 ratio is seen in lungswith V̇A/Q̇ inequality but no shunt, where between room airand 40% inspired oxygen, the PaO2/FIO2 ratio is about 200,similar to that of the lung with a 20% shunt. However, athigh FIO2 values, the PaO2/FIO2 ratio rises rapidly and is notdifferent from normal above about 90% inspired oxygen.Consequently, the PaO2/FIO2 ratio must be used with carewhen significant V̇A/Q̇ inequality is present.

ALVEOLAR–ARTERIAL PO2 DIFFERENCE

The alveolar–arterial PO2 difference (PA–aO2) is the calcu-lated difference between the “ideal” (essentially, the mean)alveolar PO2

13 and the measured arterial PO2. The PA–aO2 ismore informative than just PO2 and PCO2 alone for morethan one reason. First, it accounts for hyperventilation andhypoventilation because these processes affect both PO2 andPCO2 in a well-defined manner, such that PA–aO2 does notchange much. In other words, an increase or decrease inventilation will not per se affect PA–aO2 significantly, eventhough PO2 and PCO2 will each change. Thus, PA–aO2

reflects the integrated effects of ventilation–perfusioninequality, shunting, and diffusion limitation. As a result, itmarks the degree of pulmonary dysfunction better than do absolute values of PO2 and PCO2. Second, it allows forchanges in inspired PO2 because that variable is explicitly apart of the formula.

PA–aO2 is calculated from a formula derived fromEquation 17-8 and the corresponding equation for carbondioxide. Recall that Equation 17-8 was given as:

V̇O2 � V̇ IFIO2� V̇AFAO2 �kV̇A(PIO2�PAO2)

The corresponding equation for carbon dioxide, assumingno significant carbon dioxide in inspired gas, is:

V̇CO2 � V̇AFACO2 �kV̇A(PACO2) (17-10)

If we now simply divide Equation 17-10 by Equation 17-8and define the ratio of carbon dioxide eliminated (V̇CO2) tooxygen taken up (V̇O2) as the respiratory exchange ratio, R,we have:

R �PACO2/(PIO2�PAO2) (17-11)

This is rearranged to define alveolar PO2:

PAO2 �PIO2�PACO2/R (17-12)

PA–aO2 is now just the difference between PAO2 fromEquation 17-12 and arterial PO2 (PaO2):

PA–aO2 �PIO2�PACO2/R�PaO2 (17-13)

This is called the alveolar gas equation. Because we used theapproximation that V̇I� V̇A in developing Equation 17-8,Equation 17-13 is also based on that assumption. We cantake account of the fact that, in general, V̇I and V̇A are slightlydifferent. When this is done, Equation 17-13 becomes:

PA–aO2�PIO2 �PACO2/R �PaO2 �PACO2FIO2(1 �R)/R(17-14)

If normal values for all of the variables are inserted intoEquation 17-14, we can calculate that the additional term inEquation 17-14 is very small, usually about 2 Torr. For clin-ical purposes, it can be neglected, and the simpler form,Equation 17-13, is used. For research purposes, however,Equation 17-14 is preferred.

Three important limitations should be kept in mind whenusing either form of the alveolar gas equation. The first isthat the equation applies only when gas exchange is in asteady state. The second is that R needs to be known ifPA–aO2 is to be accurate. Measuring R in clinical circum-stances is uncommon. It is found by determining V̇O2 andV̇CO2 from analysis of expired gas. Under most circum-stances, assuming R�0.85 is reasonable. The third limita-tion is that alveolar PCO2 (PACO2 in Equations 17-13 and17-14) is taken to be the same as arterial PCO2. This is rea-sonable under many conditions, especially when areas oflow, but not high, V̇A/Q̇ ratio are prominent. However, whenhigh V̇A/Q̇ ratio regions are significant, alveolar PCO2 can beconsiderably lower than arterial PCO2, causing an underes-timation of PA–aO2. The two examples discussed above inthe two-compartment analysis of V̇A/Q̇ inequality are consis-tent with this conclusion.

PA–aO2 is thus a compromise parameter, balancing sim-plicity against both limitations resulting from the requiredassumptions and the depth of information revealed. Hypo-ventilation (or hyperventilation) alone will not increasePA–aO2, but whether an abnormal PA–aO2 is caused by V̇A/Q̇inequality, shunting, or diffusion limitation alone or in com-bination cannot be determined.

Normally, PA–aO2 is 5 to 10 Torr in young healthy sub-jects. Because it is the difference between two large numbers(alveolar PO2, about 100 Torr, and arterial PO2, about 90 to95 Torr), the variance in PA–aO2 resulting from measurementerrors is quite large. Negative values are not uncommonlyfound but should not be considered intrinsically problem-atic because of the large variance.

TWO- AND THREE-COMPARTMENT MODELS

OF V̇A/Q̇ INEQUALITY

Given the limitations of the PA–aO2, efforts have been madeto find more informative ways of quantifying gas exchange.Some 50 years ago, Riley and Cournand13 devised a three-compartment model that is still clinically useful today, espe-cially in critically ill patients. The lungs are imagined asconsisting of just three alveoli. One alveolus is unventilatedbut is perfused, and thus is a shunt. A second alveolus isventilated but unperfused and is therefore a dead space. Thethird, normal, compartment is both ventilated and perfusedand is responsible for all of the oxygen uptake and carbondioxide elimination by the patient. These three alveolitogether account for all of the ventilation and all of thebloodflow, and the model is applied by using measured arte-rial and mixed venous oxygen concentration data to dividethe total bloodflow into two fractions—that in the shunt and that in the normal compartment. In a correspondingmanner, the arterial and mixed expired PCO2 values are thenused to divide the total ventilation into two fractions—thatin the dead space and that in the normal compartment. The


Riley three-compartment model is thus really a pair of two-compartment models in which the normal compartmentis shared. The bloodflow fraction in the shunt compartmentis called physiologic shunt (or, equivalently, venous admix-ture), and the ventilation fraction in the dead space iscalled physiologic dead space (or, equivalently, wastedventilation).

The calculations of physiologic shunt and dead space arebased on mass conservation principles (as was all of the pre-ceding discussion on gas exchange), as follows.

Arterial oxygen concentration, CaO2, must be the blood-flow-weighted average of the concentrations of oxygen inthe normal (called “ideal,” i) alveolus, CiO2, and that ofmixed venous blood passing through the shunt, CvO2, as fol-lows, where S is fractional perfusion in the shunt compart-ment:

CaO2 �(1�S)CiO2 �SCvO2 (17-15)

If arterial and mixed venous oxygen levels are measured,and CiO2 is calculated from the oxygen dissociation curvewith knowledge of PiO2 (the PO2 of the normal alveolus cal-culated using the alveolar gas equation), S can be computedby rearranging Equation 17-15:

S �(CiO2 �CaO2)/(CiO2 �CvO2) (17-16)

In normal lungs, S should be very close to zero and not more than 0.01 to 0.02. This is because there are essentiallyno unventilated alveoli in normal lungs. Thus, any valuegreater than about 0.02 would be interpreted as abnormal.

There is a very important limitation to the use ofEquation 17-16. It explicitly requires knowledge of themixed venous oxygen concentration. As the preceding dis-cussion of two-compartment models of V̇A/Q̇ inequality hasshown, mixed venous PO2 can vary considerably, so thatassuming any particular value may be problematic. Thus,unless CvO2 is measured, S may contain substantial errors.

From principles similar to those underlying calculationof physiologic shunt, mixed expired PCO2 (PexpCO2) mustbe the weighted average of the PCO2 in the normal (ideal)alveolus (PiCO2) and zero (which is the PCO2 of the venti-lated but unperfused, dead space alveolus; see Figure 17-3).If VD is the fraction of the total ventilation in the dead-spacealveolus, we have:

PexpCO2�(VD �0) �(1 �VD)PiCO2 (17-17)

On rearrangement, this becomes:

VD �(PiCO2�PexpCO2)/PiCO2 (17-18)

As with the alveolar gas equation above, it is common prac-tice to assume that the ideal PCO2 is equal to the arterialvalue (PaCO2), such that Equation 17-18 now becomes:

VD�(PaCO2�PexpCO2)/PaCO2 (17-19)

In Equation 17-19, VD is often called “VD/VT” or dead-space/tidal volume ratio. Note that to measure mixedexpired PCO2, we must collect several entire exhalationsand measure mean PCO2 in that mixed, exhaled gas. Theconducting airways will clearly contribute to the dilution ofcarbon dioxide in mixed expired gas because the mixed

expirate contains gas that filled the conducting airways atthe end of inspiration—that is, inspired gas, normallydevoid of carbon dioxide. Thus, the normal value of VD isabout 0.3 because conducting airway volume is about 30%of the total tidal volume under normal conditions. Anincrease above 0.3 therefore marks abnormal exchange. Thiswarning sign requires further consideration because thenormal value of VD can vary greatly as tidal volume varies.Thus, with a constant conducting airway volume of 150 mL,a fall in tidal volume from 500 to 300 mL /breath wouldincrease VD from 0.3 to 0.5. Thus, in applying Equation 17-19,it is critical to know actual tidal volume. We can assume thatconducting airway volume is about 1 mL per pound of bodyweight (in a nonobese patient). Once tidal volume is known,the fraction of VD that should be attributable to conductingairway volume can be easily computed, and what is left isthen the measure of the ventilation of unperfused alveoli.

In applying both Equation 17-16 for physiologic shuntand Equation 17-19 for physiologic dead space, the lungshave been modeled by Riley as a three-compartment struc-ture. This is a gross oversimplication in many if not mostcases. Of course, if there actually is only a true shunt pres-ent (as, for example, in atelectasis, or via a right-to-leftintracardiac shunt), the calculated physiologic shunt will beaccurate. The same holds true for physiologic dead space—it will be accurate if the actual situation is one of completelyunperfused alveoli. However, in most patients, there is a dis-tribution of V̇A/Q̇ ratios present—low but greater than zeroand/or high but less than infinite. In such circumstances,S from Equation 17-16 and VD from Equation 17-19 willsystematically underestimate the fractions of bloodflowand ventilation (respectively) associated with these low- andhigh-V̇A/Q̇ regions. Nevertheless, these are very usefulindices of abnormal gas exchange that have withstood thetests of time. They represent the equivalent fractional shuntand dead space necessary to explain arterial and expired gasconcentrations and as such are useful measures of the degreeof pulmonary abnormality.

DISTRIBUTION OF VENTILATION/PERFUSION RATIOS

Theoretical Basis The limitations of the PA–aO2, thePaO2/FIO2 ratio, and the Riley three-compartment model dis-cussed above have led workers to search for better methodsfor assessing gas exchange. Just as Riley and Cournand usedmeasurements of arterial and expired oxygen and carbondioxide levels to determine parameters of simple three-compartment models of ventilation and bloodflow, it hasbeen shown that measurements of arterial and expired levelsof foreign inert gases can also be used to determine parame-ters of the ventilation/perfusion ratio distribution. The prin-ciples of such inert gas methods are identical to those usedby Riley and Cournand, but by simultaneously exposing thelungs to a mixture of many inert gases, one can go from sim-ple three-compartment models to a smooth approximationof the entire V̇A/Q̇ distribution.

The difference between Riley’s three-compartment modeland the V̇A/Q̇ distribution derived from inert gases is essentiallyonly quantitative; the basis is the same. Riley used oxygento determine the division of bloodflow between two


compartments and carbon dioxide to divide ventilationbetween two compartments. Using a mixture of several inertgases allows one to divide both ventilation and bloodflowamong the entire possible spectrum of V̇A/Q̇ units. The onlyother differences are that (1) changes in the levels of FIO2,total ventilation, and cardiac output affect the parametersobtained in the Riley analysis for the same actual V̇A/Q̇ dis-tribution, and (2) the level of oxygen (and possibly also ofcarbon dioxide) can affect how ventilation and bloodfloware distributed, thus making the three-compartment modelsensitive to values of the variables used to measure it. If inertgases are applied at trace (parts per million) levels, they donot affect the distribution and thus provide a more reliablepicture of V̇A/Q̇ relationships.

To understand inert gas methods, one needs to under-stand the objective of using them: to describe the way inwhich V̇A/Q̇ ratios are distributed within the lung. The imageis one of a lung that consists of a spectrum of gas exchangeunits, each of which is a homogeneous unit with a particu-lar V̇A/Q̇ ratio. These particular V̇A/Q̇ ratios are selectedobjectively to adequately represent the whole possible V̇A/Q̇range (from zero to infinity), just as in a human populationsurvey only a small fraction of the actual population is usedto represent the whole population. The question thenbecomes how bloodflow (and, separately, how ventilation) isdistributed among these many V̇A/Q̇ units.

An analogy would be the distribution of weight /heightratios in a group of people. One would take the members ofthe group and measure their weight and height. One wouldthen aggregate members into small weight /height ranges(such as 30 to 32 kg/m or 32 to 34 kg/m) and plot thenumber of members in each such range (y-axis) againstweight /height group ratio midpoint on the x-axis. With alarge enough number of subjects, one would probably endup with a smooth, bell-shaped curve, with most subjectsnear the mean and the numbers decreasing on either sidewith increasing distance from the mean. This kind of plot iscalled a frequency distribution and is the most succinctand complete description of the population of height /weight ratios.

To apply this to the lung, we need such frequency distri-butions: one for ventilation and the other for bloodflow.Figure 17-11A illustrates the principle. Two curves areshown for a hypothetical V̇A/Q̇ distribution, one for howventilation is distributed among units of varying V̇A/Q̇ ratioand the other for bloodflow. The x-axis depicts the V̇A/Q̇ratio, which in this example runs from 0.001 to 1,000. Notethat units with V̇A/Q̇ of zero [a shunt: perfused (Q̇ � 0) butnot ventilated (V̇A�0)] are absent in this case; units with aninfinite V̇A/Q̇ ratio [dead space: ventilated (V̇A � 0) butunperfused (Q̇�0)] are also not present. However, bothshunt and dead space could be placed on Figure 17-11A,were they present. Figure 17-11A indicates the pattern ofventilation and bloodflow across the range of V̇A/Q̇ ratios,and the key point is that real lungs will have units with anyor all V̇A/Q̇ ratios in between the extremes, as shown by thecurves. A special feature of the V̇A/Q̇ distribution is thatbecause the V̇A/Q̇ ratio is defined as the ratio of ventilationto bloodflow, any points on the ventilation and bloodflow

curves at the same x-axis value of V̇A/Q̇ are numericallyrelated:

V̇A � QV̇A/Q̇ (17-20)

Thus, if we know the bloodflow distribution (Q̇ vs. V̇A/Q̇ ),we also know the ventilation distribution (V̇A vs. V̇A/Q̇), andvice versa.

In Figure 17-11B, the Riley three-compartment modelobtained from the same distribution shown in Figure 17-11Ais projected onto this platform. Figure 17-11B shows threevirtual compartments with V̇A/Q̇ ratios of 0, the ideal value(about 1.2 in this case), and infinity, with the bloodflow splitbetween the first two and the ventilation split between thelatter two. Physiologic shunt and dead space are each a littleless than 2 L /min. It is evident how the Riley model,although clinically useful, greatly oversimplifies the actuallungs by representing a broad distribution as a three-compartment equivalent.

FIGURE 17-11 Concept of the distribution of ventilation/perfusionratios. A shows a continuous distribution of both ventilation andbloodflow. It succinctly describes the relative amounts of ventila-tion and bloodflow associated with lung regions of different V̇A/Q̇ratio from 0.001 to 1,000. This is the information necessary toexplain how well or poorly the lung exchanges oxygen and carbondioxide. B shows the Riley three-compartment equivalent of thisparticular distribution and indicates how this model, althoughclinically useful, greatly oversimplifies the actual situation.


Figure 17-11A depicts ventilation and bloodflow, respec-tively, at a series of 20 equally spaced V̇A/Q̇ ratios (equallyspaced on a logarithmic scale, which is more useful than alinear scale for a distribution of ratios). Using a discrete setof V̇A/Q̇ ratios (be it 20 or 50 or some other number) is a veryconvenient way to describe the distribution and turns out to be both simpler and more flexible than trying to workwith a truly continuous mathematical function. What is keyis to select the V̇A/Q̇ ratios evenly across the V̇A/Q̇ scale, ashas been done in Figure 17-11A.

Based on this concept of the V̇A/Q̇ distribution, we cannow proceed to examine the behavior of a single inert gas inany one of the V̇A/Q̇ compartments and then in the distribu-tion as a whole, as in Figure 17-11A. Going back toEquations 17-1 and 17-2, which described mass conserva-tion for the uptake of oxygen by the lungs, we can apply thesame principles to an inert gas of solubility �. Since inertgases obey Henry’s law, the concentration in blood (Cig) isdirectly proportional to partial pressure (Pig):

Cig ��Pig (17-21)

The constant of proportionality is the solubility, �, and sinceinert gases equilibrate very rapidly across the blood–gas bar-rier, alveolar (PAig) and end-capillary (Pcig) inert gas partialpressures are identical. Equations 17-1 and 17-2 thenbecome:

V̇ig � V̇IPIig � V̇APAig (17-22)

and

V̇ig �Q̇(Ccig �Cvig) �Q�(PAig �Pvig) (17-23)

The inert gases are presented to the lungs dissolved in salineor dextrose by way of constant intravenous infusion. In thisway, they are being eliminated by the lungs, just as for car-bon dioxide. PIig is therefore zero by design, simplifying theequations. Equating Equations 17-22 and 17-23 and drop-ping the subscript “ig” for simplicity, we have:

V̇APA �Q̇�(Pv �PA) (17-24)

Isolating PA and dividing by both Q̇ and Pv yields:

PA/Pv �Pc/Pv ��/(�� V̇A/Q̇) (17-25)

The units for � are such that it becomes what is called theblood/gas partition coefficient of the gas. The partition coef-ficient is the ratio of the equilibrium concentrations of theinert gas in the blood and gas phases and describes the sol-ubility of the gas in blood. Remember that PA is alveolar, Pcis end-capillary, and Pv is mixed venous partial pressure ofthe inert gas.

Equation 17-25 is very useful. The ratio Pc/Pv for a gasbeing eliminated by the lungs is its fractional retention.Thus, if 100 molecules were infused and 80 were eliminatedby ventilation, retention would be 0.2 (or 20%). Equation17-25 shows that retention is a simple function of only thepartition coefficient and the V̇A/Q̇ ratio. Retention falls withincreasing V̇A/Q̇ ratio for a given value of �; it also falls as �is reduced for a given value of V̇A/Q̇. This equation can beapplied to each V̇A/Q̇ ratio unit in the entire V̇A/Q̇ distribu-tion. Suppose that we simultaneously infused six inert gases

and wished to use the retention data to construct the V̇A/Q̇distribution. We could set up a lung having six predeter-mined (ie, known) V̇A/Q̇ ratios (equally spaced across theV̇A/Q̇ range in Figure 17-11A). The task would be to deter-mine how total pulmonary bloodflow is distributed amongthe six compartments. We apply the same mass conservationlogic as for physiologic shunt (Equation 17-15). That logicmeans that, for any one inert gas, its retention fraction meas-ured in mixed systemic arterial blood must be a bloodflow-weighted average of the six compartmental retentions. IfR�Pc/Pv, we can write for any one gas:

Rj (retention in V̇A/Q̇ compartment j) ��/(� � V̇A/Q̇ j)(17-26)

Then, systemic arterial R would be:

R �Q̇ 1R1 �Q̇ 2R2 �Q̇ 3R3 �Q̇ 4R4 �Q̇ 5R5 �Q̇ 6R6

(17-27)

Here the six values of Q̇ j are fractional bloodflow values thatsum to 1.0. It is these values that are unknown and thatwe need to determine, given the measured value of R and thecalculated values of all Rj. If six different gases weresimultaneously infused and their systemic arterial retentions(R values on the left side of Equation 17-27) were measured,each of the six gases would generate one equation similar toEquation 17-27. In each of these six equations, we alreadyknow � as the measured partition coefficient and have spec-ified the six values of V̇A/Q̇. Thus, each value of Rj for eachgas can be calculated. What we now have is a set of sixsimultaneous linear equations in six unknowns—the sixcompartmental bloodflow fractions. Such an equation sys-tem is easily and uniquely solved—there is only one set ofsix values of fractional Q̇ that satisfies all six equations. It isno accident that in this example there is the same number ofgases as V̇A/Q̇ compartments. That is required for a conven-tional solution to such a set of equations.

We now can plot the paired values of bloodflow and V̇A/Q̇ratio compartment by compartment, as in Figure 17-11A,and we have found the distribution of V̇A/Q̇ ratios, at least asa six-compartment model.

This process has been described to give a feel for the basicprinciples. However, there are three major limitations to theuse in practice of such a simple system:

1. In being limited to the same number of V̇A/Q̇ compart-ments as we have gases, six in this example, we mayhave a too coarse sampling of the V̇A/Q̇ axis to prop-erly fit the results. Six gases are about all that can bemeasured simultaneously in a reasonable time frame.Modeling research has shown that the V̇A/Q̇ domainneeds to be divided into at least 20 compartments(plus shunt and dead space) to overcome thislimitation in practice. It would be infeasible inpractice to expose the lungs to 20 different gases toenable a 20-compartment analysis.

2. There is no guarantee that the six compartments willend up having positive values for bloodflow when theequations are solved. However, negative bloodflow hasno physiologic meaning, and therefore bloodflow in


every compartment must be constrained to be non-negative (ie, greater than or equal to zero).

3. Such a system, in which the number of compartmentsand the number of gases are equal, turns out to bequite sensitive to inevitable random experimentalerrors. Thus, the allocation of bloodflow among thesix compartments may jump around between dupli-cate samples, due to experimental error. It would bedesirable to be able to solve the equations in such away as to return a stable set of compartmental blood-flows from duplicate data sets that differed because ofrandom error only. This would reduce concern thattwo apparently different results from two data setsreflected a real difference in the lungs and at the sametime increase confidence that an observed differencein results was a true biologic change.

Fortunately, mathematical methods exist that can overcomethese limitations.23,24 The present formulation of the multi-ple inert gas elimination technique (MIGET) uses an infu-sion of six inert gases whose partition coefficients (�) spanthe range from very low (sulfur hexafluoride [SF6],��0.005) to very high (acetone, ��300). The four inter-vening gases are ethane (��0.1), cyclopropane (��0.5),enflurane (��2.5), and ether (��12). A 50 V̇A/Q̇ compart-mental discretization of the V̇A/Q̇ axis is used with this set ofsix gases. Although the number of compartments (50)exceeds the number of gases (6), by incorporation of asmoothing constraint on the process for solving the equa-tions, the V̇A/Q̇ distribution can be found in a manner that isstable to normal levels of experimental error. It limits theresults to smooth frequency distributions, thereby acknowl-edging that fine resolution in the shape of the V̇A/Q̇ distribu-tion cannot be determined. Given the likelihood that thereare some 100,000 individual acini (essentially the unit of gasexchange) in a lung, it is highly unlikely that actual V̇A/Q̇distributions are ragged or jagged. Imagine the frequencydistribution of height in a population of 100,000 people.With this many points, it would be a smooth curve. Thus,limiting the outcome to smooth curves is unlikely to imposea significant constraint.

To understand the concept of smoothing, a good analogyis the task of mapping the location of, say, 50 tennis ballsthrown randomly onto a tennis court. It would take pre-cisely 50 independent measurements to locate all 50 balls.However, if the 50 balls were first threaded onto a rope, eachball separated by, say, no more than 12 inches from its neigh-bor, and the rope of balls was thrown randomly onto thecourt, the task of mapping the location of all 50 balls wouldbe far easier. Mapping every, say, eighth ball would allow theapproximate locations of the remainder to be identifiedwithout further measurements. This is because the string of50 balls would have to form a relatively smooth line becauseof the short distances between adjacent balls.

The details of the mathematical process (including thenon-negativity requirement, which involves a differentprocess from that of smoothing) used for the MIGET can be found in a series of publications23,24 and are not fur-ther presented here. Papers analyzing the limits on the

information that the method provides have also beenpublished.25–27 Many published studies show the findingsin a variety of cardiopulmonary diseases and are discussedin Chapter 18, “Ventilation–Perfusion Distributions inDisease.”

V̇A/Q̇ Distribution in Health The first question onemight have concerning the MIGET is what is found in nor-mal young adult subjects. Figure 17-12 shows the V̇A/Q̇ dis-tribution typically found in such a subject.28 It is symmetricabout its mean V̇A/Q̇ (which is very close to 1.0). It is nar-row, with almost all ventilation and bloodflow confined to asingle V̇A/Q̇ decade (between about 0.3 and 3.0), as Figure17-12 shows. Thus, there are no regions of very low or veryhigh V̇A/Q̇ ratio. There is no shunt, and dead space is about30% (of total ventilation). It is interesting that when thispattern is compared with that reconstructed from topo-graphic measurements made with radioactive tracers (seeFigure 17-2), there is little difference. Thus, most of thefunctional V̇A/Q̇ inequality in the young, normal lung can beexplained by gravitational variance in V̇A/Q̇ ratios. Althoughventilation and bloodflow are both apparently nonuniformin a given horizontal plane, there must be considerablecovariance between them. Otherwise, this nonuniformitywould add considerably to the functional V̇A/Q̇ inequalityobserved with the MIGET.

Whereas the curves shown in Figure 17-12 represent thefull picture of how ventilation and bloodflow are distributedfunctionally, summary parameters of this distribution arefrequently used, just as for any group of observations. Thefirst three moments of the distribution are most commonlyused for this. The first moment is the mean V̇A/Q̇ ratio; thesecond moment (about the mean) reflects dispersion. For aperfectly symmetric, logarithmically normal curve similar tothat in Figure 17-12, the second moment yields the standarddeviation, such that about 68% of the total ventilation andbloodflow falls between the mean �1 SD and the mean �1SD. For nonsymmetric curves, the second moment gives a

FIGURE 17-12 V̇A/Q̇ distribution typical of a young, normal,upright human subject. The distribution is narrow, symmetric, andconfined to the V̇A/Q̇ decade between about 0.3 and 3. There is noshunt or dead space. See text for further analysis.


useful quantitative index of dispersion, but it should notstrictly be called the standard deviation. The third moment(about the mean) depicts the curves’ symmetry. A thirdmoment equal to zero indicates a symmetric distribution;skewing to the left or right is manifested by a third momentdifferent from zero.

A large body of work over the years has established thatthe second moment has a normal range that runs from about0.3 to 0.6 (95% confidence limits).19,29–31 A completelyhomogeneous lung (which does not exist) would have avalue of zero. A patient with severe lung disease in an inten-sive care unit on a ventilator might have a second momentof 2 to 2.5. Thus, mildly abnormal values run from 0.6 toabout 0.8. Moderately abnormal values run from 0.8 toabout 1.2, and severe V̇A/Q̇ inequality produces a secondmoment above 1.2. The highest values seen are about 2.5.

The distribution shown in Figure 17-11A has a secondmoment of 1.25, whereas that of the normal subject inFigure 17-12 has a second moment of 0.40.

Note that neither shunt nor dead space, which are explic-itly recovered by the MIGET, along with the rest of the dis-tribution, is included in the second moment calculationbecause the formula requires taking the logarithm of theV̇A/Q̇ ratio of each compartment in the distribution. The log-arithms of zero and of infinity are not definable, so shuntand dead space are excluded and reported separately asfractions of total pulmonary bloodflow and ventilationrespectively.

ADDITIONAL INFORMATION AVAILABLE

FROM THE MIGETDetermination of the frequency distribution of ventilationand bloodflow with use of the MIGET allows the analysis ofgas exchange in considerable detail. The very shape of thedistribution can yield mechanistic insights into how gasexchange is regulated and affected as conditions change.Changes in the degree of inequality with interventions areuseful in assessing their mechanisms. However, two addi-tional categories of information can be obtained when themethod is used: (1) determining the role, if any, of diffusionlimitation in oxygen uptake and (2) determining the modi-fying roles of any “extrapulmonary” influences on gasexchange.32

ASSESSMENT OF DIFFUSION LIMITATION

OF OXYGEN UPTAKE

Diffusion limitation is inferred as follows. All nonreactiveinert gases are essentially invulnerable to reduced elimina-tion by limited diffusion across the blood–gas barrier, nomatter what conditions prevail.4 Oxygen, however, can bediffusion limited, especially during exercise and at alti-tude.30,33,34 This means that if diffusion limitation for oxy-gen exists, there will be more severe hypoxemia thanexpected from the degree of V̇A/Q̇ inequality alone as deter-mined by the MIGET. Comparison of the actual with theexpected arterial PO2 reflects the extent of diffusion limita-tion for oxygen.

The expected arterial PO2 is determined with the use ofprinciples already described. First, Equations 17-1 and 17-2

are used to find alveolar PO2 and the corresponding end-capillary oxygen concentration for each V̇A/Q̇ ratio unit inthe V̇A/Q̇ distribution. This computation is performed withthe explicit assumption that oxygen exchange across theblood–gas barrier is not diffusion limited. Then, mass con-servation rules are used to compute the mixed arterial oxy-gen concentration as a bloodflow-weighted average ofoxygen concentrations from all units in the particular V̇A/Q̇distribution under consideration. Mixed arterial PO2 is thendetermined from the arterial oxygen concentration with useof the hemoglobin dissociation curve. If there is no diffusionlimitation for oxygen, the arterial PO2 calculated in this waywill agree with the arterial PO2 that was actually measured.However, if oxygen is, in fact, diffusion limited, the actualarterial PO2 will be lower than that predicted by the MIGET.The difference between the actual and the predicted arterialPO2 values then can be used to calculate the oxygen-diffusing capacity of the lungs necessary to explain thedifference.35

With this approach, diffusion limitation of oxygen uptakeis rarely seen, even in lung disease—measured and expectedarterial PO2 values are in agreement. The only condition inwhich diffusion limitation is seen consistently in lung dis-ease is pulmonary fibrosis during exercise.36 Diffusion limi-tation is actually more commonly observed in health, butonly during the heaviest of exercise, especially in athletes,where pulmonary capillary red cell transit time is presumedto be reduced to the point of causing diffusion limitation.Exercise at altitude accentuates diffusion limitation for oxy-gen, so that it is seen in essentially all normal subjects, notjust athletes.30,33 At altitude, it can have an enormous nega-tive impact on arterial oxygenation and thus tissue oxygenavailability.37

ROLE OF EXTRAPULMONARY FACTORS

IN MODULATING ARTERIAL PO22

Returning to the basic principles of pulmonary gas exchangediscussed above, it should be clear that, in addition to theintrapulmonary factors (V̇A/Q̇ inequality, shunts, and diffu-sion limitation), additional factors can influence arterialPO2. These are the so-called “extrapulmonary” factors. Theyinclude the inspired oxygen level, metabolic rate, total ven-tilation, cardiac output, features of the hemoglobin dissoci-ation curve (total hemoglobin concentration and P50), bodytemperature, and acid–base state. All of these factors influ-ence local alveolar PO2 through the way in which they affectthe solutions to the basic equations for gas exchange(Equations 17-1 and 17-2).

The MIGET is well suited to elucidating the quantitativeroles of such factors, especially when more than one maychange at a time in a given patient. Many examples can beimagined. One of the earliest applications was explaininghow the bronchodilator isoproterenol affected gas exchangein patients with asthma.38 It was shown that the drug causedpreferential vasodilatation in areas of reduced V̇A/Q̇ ratio(presumably by releasing prior hypoxic vasoconstriction),such that V̇A/Q̇ inequality was actually made acutely worseby the increased bloodflow through these poorly ventilatedregions. However, the expected fall in arterial PO2 was


attenuated by the concomitant increase in cardiac outputbecause of an increase in mixed venous PO2 (see Figure 17-5A). Another example is reconciling the mild hypoxemiausually seen in asthmatic patients with the much moresevere hypoxemia seen in patients with large myocardialinfarcts and pulmonary edema resulting from associatedheart failure.39 With use of the MIGET, the actual fractionalperfusion of poorly ventilated regions is often greater inasthmatic patients than in patients with heart failure. Thisapparent paradox is explained by the fact that cardiac out-put is often above normal in asthmatic patients, whereas itis considerably reduced in patients with heart failure, withconsequent effects on mixed venous PO2. Thus, maintaininga high mixed venous PO2 is effective in preventing severehypoxemia in asthma, whereas failure to keep mixed venousPO2 levels normal leads to substantial hypoxemia even whenV̇A/Q̇ inequality is not that severe. Further situations inwhich extrapulmonary factors may change arterial oxygena-tion can be imagined. A simple case is when inspired oxygenlevels are changed. Arterial PO2 will change as a result, andthe MIGET allows one to answer the question of whether ornot the change in PO2 is as expected for the particularchange in FIO2. One needs to know the distribution of V̇A/Q̇ratios for this, because the expected change is very depend-ent on the underlying pattern of V̇A/Q̇ inequality. One usesthe method much as described above in the context ofassessing diffusion limitation. If the change in PO2 is not asexpected, the MIGET will identify the reason, be it a changein V̇A/Q̇ relationships or something else.

SUMMARY

This chapter has focused on how ventilation and bloodfloware distributed to the very large number of alveoli in the lungand laid out the structural basis of why these distributions arenot uniform, even in health. What is remarkable is that,despite the great potential for severe maldistribution of bothventilation and bloodflow, the overall amount of V̇A/Q̇inequality is very small and has a negligible impact on gasexchange and arterial PO2 and PCO2. The relationshipbetween how much oxygen (and carbon dioxide) isexchanged in a unit of lung and the V̇A/Q̇ ratio of that unit isdeveloped with the use of basic principles of mass conserva-tion. This is then used to explain how nonuniformity in thedistribution of either ventilation or bloodflow in diseaseimpairs gas exchange and how the body adjusts to maintainoverall oxygen and carbon dioxide transport between theenvironment and the tissues. These same relationships arethen used in reverse as tools to characterize the degree of V̇A/Q̇inequality on the basis of simple two- and three-compartmentmodels. This is done by taking measurements of oxygen andcarbon dioxide exchange and using them to partition blood-flow and ventilation among the compartments. Finally,because of the limitations of these models, the MIGET is pre-sented in some depth. This method is a tool for determiningnot only the distribution of ventilation/perfusion ratios butalso the roles of diffusion limitation of oxygen uptake and ofpotential extrapulmonary factors that can significantly modu-late arterial PO2 and PCO2 when V̇A/Q̇ inequality is present.

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