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# (p. 23) Gas Exchange

Gas Exchange
Chapter:
Gas Exchange
DOI:
10.1093/med/9780190670085.003.0002
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date: 13 July 2020

I use the term gas exchange to encompass several processes that allow the respiratory system to maintain a normal arterial partial pressure of O2 and CO2 (PaO2, PaCO2). Even though I separated ventilation and gas exchange in the introduction to Chapter 1, ventilation is actually an essential part of gas exchange because it delivers O2, eliminates CO2, and determines ventilation–perfusion ratios.

The components of normal gas exchange are:

• Delivery of oxygen

• Excretion of carbon dioxide

• Matching of ventilation and perfusion

• Gas diffusion

Before discussing each of these components, it’s important to review the concept of gas partial pressure.

## Partial Pressure

The total pressure (PT) produced by a gas mixture is equal to the sum of the pressures generated by each of its components.

$Display mathematics$
(2.1)

The pressure contributed by each gas is referred to as its partial pressure, which is equal to total pressure multiplied by the fractional concentration (F) of each gas in the mixture. For example, at sea level, the total pressure of the atmosphere (barometric pressure; PB) is 760 mmHg. Since the fractional concentration of O2 (FO2) in dry air is 0.21 (i.e., 21% of the gas molecules are O2), its partial pressure (PO2) is calculated as:

$Display mathematics$
(2.2)

Similarly, the partial pressure of nitrogen (PN2) is 760 mmHg x 0.79, or 600 mmHg.

Partial pressure is important because O2 and CO2 molecules diffuse between alveolar gas and pulmonary capillary blood and between systemic capillary blood and the tissues along their partial pressure gradients, and diffusion continues until the partial pressures are equal. Gas diffusion is discussed in much more detail later in this chapter.

## Delivery of Oxygen

Ventilation is responsible for delivering O2 molecules to the alveoli, and this is the first step in transferring O2 from outside the body to the arterial blood. As just mentioned, the PO2 of dry air at sea level is 160 mmHg. Once gas enters the upper and lower airways, it is heated and humidified. This introduces another gas into the mixture—water. Since the partial pressure of water (PH2O) at body temperature is 47 mmHg, the inspired partial pressure of oxygen (PIO2) becomes the product of FO2 and the difference between barometric and water pressure.

$Display mathematics$
(2.3)

Here, FIO2 is the fractional concentration of inspired oxygen.

When gas reaches the alveoli, the PO2 falls even further as O2 and CO2 molecules are exchanged across the alveolar–capillary interface. Although there’s no way to measure the mean PO2 of the gas in all the alveoli of the lungs $(PA¯O2)$, we can estimate it by using the alveolar gas equation.

$Display mathematics$
(2.4)

This equation has two components. The first part, within the brackets, is identical to the right side of Equation 2.3 and equals the PO2 of the gas within the conducting airways (i.e., the airways from the mouth to the terminal bronchioles). The second part equals the drop in PIO2 caused by the diffusion of O2 into the capillary blood. In this portion of the equation, $PA¯CO2$ is the mean alveolar PCO2, which is assumed to equal arterial PCO2, and R is the ratio of CO2 molecules entering to O2 molecules leaving the alveolar gas. Let’s assume for a moment that R is 1.0. In that case, $PA¯CO2$ would increase and $PA¯O2$ would fall by the same amount, and we could simply subtract PaCO2 from PIO2 to get the mean alveolar PO2. Normally, however, R is less than 1.0, and for the alveolar gas equation, it is assumed to equal 0.8. So, the decrease in PO2 between the conducting airways and the alveoli will be PaCO2 divided by 0.8 (or multiplied by 1.25). If PaCO2 is 40 mmHg, we get:

$Display mathematics$

As you can see, $PA¯O2$ varies directly with barometric pressure and FIO2 and inversely with PaCO2. The progressive fall in PO2 between the outside of the body and the alveoli is part of the oxygen cascade, which continues as O2 enters the arterial blood and the tissues (Figure 2.1).

You can think of the calculated $PA¯O2$ as being the highest possible PaO2 for a given PB, FIO2, and PaCO2. That’s because the alveolar gas equation tells us what the $PA¯O2$ and the PaO2 would be if the lungs were “perfect”—that is, if every alveolus had the same ratio of ventilation to perfusion. In fact, as you’ll soon learn, there’s no such thing as perfect lungs, and that’s why there’s always a difference between the calculated $PA¯O2$ and the measured PaO2.

## Carbon Dioxide Excretion

Carbon dioxide is a normal byproduct of cellular metabolism and continuously diffuses from the tissues into the systemic capillary blood, and from the pulmonary capillary blood into the alveolar gas. The mean alveolar and arterial PCO2 are determined by the balance between the rates at which CO2 is produced by the tissues ($V˙PCO2$) and excreted by ventilation ($V˙ECO2$).

$Display mathematics$
(2.5)

If, for example, CO2 is produced faster than it’s eliminated, PaCO2 will rise. If CO2 is removed faster than it’s produced, PaCO2 will fall.

Although ventilation delivers O2 and removes CO2, not all of the gas entering and leaving the lungs takes part in this process. In fact, the tidal volume (VT) can be divided into two components. The first is the alveolar volume (VA), which is the portion that reaches optimally perfused alveoli and is responsible for the exchange of O2 and CO2. The second is referred to as the dead space volume (VD) because it does not participate in gas exchange.

$Display mathematics$
(2.6)

The total or physiologic dead space volume is divided into two components—airway and alveolar. The airway dead space is the volume of gas that remains in the conducting airways at the end of inspiration. Since this gas never reaches the alveoli, it cannot remove CO2. Alveolar dead space is the volume of gas that goes to non-perfused or under-perfused alveoli, and it will be discussed later in this chapter.

If each component of Equation 2.6 is multiplied by the respiratory rate, volume is converted to volume per minute, and the relationship between the gas leaving the lungs (minute ventilation; $V˙E$), optimally perfused alveoli (alveolar ventilation; $V˙A$), and the physiologic dead space (dead space ventilation; $V˙D$) can be expressed as:

$Display mathematics$
(2.7)

Carbon dioxide excretion is directly proportional to alveolar ventilation, and this allows us to rewrite Equation 2.5 as:

$Display mathematics$
(2.8)

which, according to Equation 2.7, can also be written as:

$Display mathematics$
(2.9)

Equation 2.9 tells us two important things. First, an increase in PaCO2 (hypercapnia) can result from a drop in $V˙E$, an increase in CO2 production, or a rise in $V˙D$. Second, any change in CO2 production or $V˙D$ must be matched by a change in $V˙E$ if PaCO2 is to remain constant.

The physiologic dead space is usually expressed as a fraction of the tidal volume (VD/VT). When VD/VT is high, VA is low, and each breath is relatively ineffective at eliminating CO2. When VD/VT is low, VA is high, and much more CO2 is excreted. The importance of VD/VT can be emphasized by rewriting Equation 2.9 as:

$Display mathematics$
(2.10)

This shows that $V˙E$ must increase and decrease with VD/VT if PaCO2 is to remain constant. Although VD/VT varies directly with the volume of physiologic dead space, clinically significant changes are more often due to variations in tidal volume. That is, a low VT increases the $V˙E$ needed to maintain a given PaCO2, whereas a high VT decreases the required $V˙E$.

## Matching of Ventilation and Perfusion

As shown in Figure 2.2, O2 is delivered by ventilation and removed by perfusion, and CO2 is delivered by perfusion and removed by ventilation. It follows that the partial pressure of oxygen and carbon dioxide in the gas of each alveolus (PAO2; PACO2) must be determined by its ratio of ventilation to perfusion ($V˙/Q˙$). It’s important to recognize that here PAO2 and PACO2 refer to the partial pressure of gas in individual alveoli, whereas $PA¯O2$ and $PA¯CO2$ refer to mean values of all alveolar gas.

Figure 2.2 Schematic representation of gas exchange. Oxygen (O2) is delivered to the gas–blood interface of the lungs by ventilation and transported to the tissues by perfusion. Carbon dioxide (CO2) is transported from the tissues by perfusion and removed from the body by ventilation.

Figure 2.3 illustrates the effect of three different ventilation–perfusion ratios. An “ideal” alveolus has a $V˙/Q˙$ that allows the ratio of CO2 to O2 exchange (R) to equal the ratio of total body CO2 production to O2 consumption (the respiratory quotient; RQ). If R and RQ are assumed to be 0.8, this ideal $V˙/Q˙$ is very close to 1.0, and PAO2 and PACO2 are approximately 100 mmHg and 40 mmHg, respectively. If an alveolus receives blood flow but no ventilation, $V˙/Q˙$ is zero, O2 cannot enter and CO2 cannot leave, and the PAO2 and PACO2 will be the same as in the mixed venous blood. If ventilation is intact but perfusion is absent, $V˙/Q˙$ is infinity, O2 is not removed and CO2 cannot enter, and the PAO2 and PACO2 will be the same as in the conducting airways.

Figure 2.3 Illustration of the effect of three different ventilation–perfusion ratios $(V˙/Q˙)$. An “ideal” alveolus has a $V˙$/$Q˙$ of about 1.0, and the alveolar gas has a partial pressure of oxygen (PAO2) and carbon dioxide (PACO2) of approximately 100 mmHg and 40 mmHg, respectively. An alveolus with no ventilation has a $V˙$/$Q˙$ of zero, and the PAO2 and PACO2 are the same as in the mixed venous blood. An alveolus with no perfusion has a $V˙$/$Q˙$ of infinity, and PAO2 and PACO2 are the same as in the conducting airways.

In fact, as shown in Figure 2.4, there is an infinite number of ventilation–perfusion ratios that may exist within individual alveoli, and every $V˙/Q˙$ between zero and infinity produces a unique PAO2 and PACO2. As $V˙/Q˙$ increases, PAO2 rises and PACO2 falls as ventilation delivers more O2 and removes more CO2. As $V˙/Q˙$ decreases, the opposite occurs; PAO2 falls and PACO2 rises.

Figure 2.4 The O2-CO2 diagram. The line represents the PO2 and PCO2 of all possible ventilation–perfusion ratios ($V˙$/$Q˙$) between zero and infinity. The points representing a $V˙$/$Q˙$ of 0, 1, and infinity are shown.

In a theoretical perfect lung, every alveolus has the same $V˙/Q˙$ and the same PAO2 and PACO2. Normal lungs are not perfect, because they have a distribution of ratios representing both high and low $V˙/Q˙$ alveoli. This modest degree of $V˙/Q˙$ mismatching occurs because ventilation and perfusion increase at different rates from the less to the more dependent regions of the lungs. All lung diseases, regardless of whether the airways, parenchyma, or vasculature are primarily affected, generate both abnormally high and low $V˙/Q˙$ regions. This is because reduced ventilation or perfusion to some alveoli must be accompanied by increased ventilation or perfusion to others if total ventilation and perfusion are unchanged.

Mismatching of ventilation and perfusion is important because it interferes with the ability of the respiratory system to maintain a normal PaO2 and PaCO2. You can see how and why this occurs by studying Figures 2.5 and 2.6, which show lung models that consist of two “compartments.” Each compartment could represent an individual alveolus or a region of a lung that contains any number of alveoli, but for our purposes, let’s assume that each is an entire lung (pretend that you’re looking at a chest X-ray). The blood leaving each lung, which we’ll call the pulmonary venous blood, combines to form the arterial blood.

Figure 2.5 Two-compartment model of the respiratory system. Since the lungs have identical $V˙$/$Q˙$ ratios, the arterial blood has the same PO2 and PCO2 as the blood leaving each lung, and the A–a gradient is zero. PV = partial pressure of pulmonary venous blood; SVO2 = hemoglobin saturation of pulmonary venous blood; SaO2 = saturation of arterial blood; CVO2 = O2 content of pulmonary venous blood; CaO2 = O2 content of arterial blood.

Figure 2.6 Two-compartment model of the respiratory system. Ventilation has been diverted from the left lung to the right lung, and this has produced both low and high $V˙$/$Q˙$ ratios. Compared to Figure 2.5, the PaO2 has fallen and the PaCO2 and the A–a gradient have increased. The combined PAO2 and PACO2 are weighted averages.

In Figure 2.5, both lungs receive the same amount of ventilation and perfusion, so their $V˙/Q˙$ ratios are identical (in this case, $V˙/Q˙=1.0$). Notice that under these conditions both lungs have the same PAO2 and pulmonary venous PO2 (PVO2), and that the PO2 and hemoglobin saturation (SO2) of the mixed (arterial) blood are identical to those of the blood leaving each lung. Because these lungs are “perfect,” the averaged alveolar and arterial PO2 are equal, and the difference between them (the A–a gradient) is zero.

In Figure 2.6, total ventilation and perfusion are unchanged, but narrowing of the airway to the left lung has altered the $V˙/Q˙$ ratios. Now, the right lung receives more ventilation than perfusion $(V˙/Q˙= 1.5)$, and the left lung has more perfusion than ventilation $(V˙/Q˙= 0.5)$. As you would expect, when compared to the values in Figure 2.5, the high $V˙/Q˙$ of the right lung has increased PAO2 and PVO2 and lowered PACO2 and pulmonary venous PCO2 (PVCO2). The low $V˙/Q˙$ of the left lung has had the opposite effect.

Now things really get interesting. When we combine the blood from the two lungs, we find that the PaO2 has fallen from 100 mmHg in Figure 2.5 to 60 mmHg, and the A–a gradient has gone from 0 to 42.5. Why did this happen? To answer this question, you first need to understand that the PO2 of a blood mixture is determined by the average oxygen content, not the average PO2.

The oxygen content of blood (CxO2) is determined by its hemoglobin concentration (Hb) and saturation (SO2) and is expressed as milliliters of O2 per deciliter of blood (ml/dl).

$Display mathematics$
(2.11)

In this equation, 1.34 is the milliliters of O2 carried by one gram of completely saturated hemoglobin (ml/g), and Hb is expressed in grams per deciliter of blood (g/dl). When we average the O2 contents of the blood leaving the two lungs (CVO2) in Figure 2.6 and solve Equation 2.11 for SO2, we find that the saturation of the arterial blood is 90%, which, based on the normal hemoglobin dissociation curve, corresponds to a PaO2 of 60 mmHg. Since the hemoglobin concentration of the blood coming from both lungs is the same, we can actually take a shortcut and simply average the saturations rather than the O2 contents of the pulmonary venous blood. Try it and see.

Okay, but how did $V˙/Q˙$ mismatching produce such a dramatic drop in the PaO2? The explanation lies in the nonlinear shape of the hemoglobin dissociation curve. Look at Figure 2.7. If we combine two blood samples, each with a PO2 of 80 mmHg and an SO2 of 95%, the PO2 and SO2 will be unchanged in the mixture. But what if we were to decrease the PO2 in one sample by 30 mmHg and increase it by the same amount in the other? As you can see, hemoglobin saturation (and O2 content) is affected much more by a fall in PO2 than by an equivalent increase. So, when we combine these blood samples, the average SO2 is 84%, which corresponds to a PO2 of 55 mmHg. Figure 2.7 demonstrates an essential concept: Blood from high $V˙/Q˙$ alveoli can never compensate for the drop in SO2 and O2 content caused by low $V˙/Q˙$ regions.

Figure 2.7 The oxygen–hemoglobin dissociation curve. When two blood samples ( ) with a PO2 of 80 mmHg and a SO2 of 95% are mixed together, there is no change in the combined PO2 or SO2. When the PO2 of one sample is reduced by 30 mmHg ( ) and the other is increased by the same amount ( ), the average SO2 of the mixture ( ) is only 84%, which corresponds to a PO2 of 55 mmHg.

Figure 2.8 shows what happens when one lung receives no ventilation $(V˙/Q˙= 0)$. Since no O2 or CO2 exchange can occur, the left lung becomes a right-to-left shunt, and mixed venous blood enters the arterial circulation. This causes an even greater fall in PaO2 despite the higher PO2 of the blood leaving the right lung.

Figure 2.8 Two-compartment model of the respiratory system. The left lung receives no ventilation, and blood passes through it unchanged. This creates a large right-to-left intra-pulmonary shunt.

What about the PaCO2 in Figures 2.6 and 2.8? Just like the PaO2, the PaCO2 is determined by the average CO2 content of the blood coming from the two lungs. But notice that the PaCO2 is actually very close to the mean PCO2 of the pulmonary venous blood. That’s because the relationship between CO2 content and PCO2 is nearly linear in the physiological range. This means that high $V˙/Q˙$ alveoli can (almost) compensate for the high CO2 content of blood coming from low $V˙/Q˙$ alveoli.

So, alveoli with low $V˙/Q˙$ reduce the PaO2, increase the A–a gradient, and increase the PaCO2. But what about high $V˙/Q˙$ alveoli? They, too, interfere with gas exchange because they create alveolar dead space. Figure 2.9 shows an extreme example in which the left lung receives ventilation but no perfusion $(V˙/Q˙= ∞)$. Clearly, the gas entering and leaving the alveoli of this lung cannot assist with CO2 excretion and is functionally no different from the gas that fills the conducting airways.

Figure 2.9 Two-compartment model of the respiratory system. The left lung receives no perfusion, so the ventilation reaching the alveoli cannot remove CO2. This creates alveolar dead space or “wasted ventilation.”

Although it may not be nearly as obvious, alveolar dead space is also produced whenever alveoli receive too little blood flow for their amount of ventilation (i.e., whenever $V˙/Q˙>1$). It may help you to think of these alveoli as having wasted ventilation rather than dead space. For example, when an alveolus receives 10 times as much ventilation as perfusion $(V˙/Q˙=10)$, only 10% of the ventilation is needed to excrete CO2, and the other 90% is wasted. Similarly, the right lung in Figures 2.6 and 2.8 also generates excess alveolar dead space.

So what is the clinical effect of high $V˙/Q˙$ alveoli? Remember from Equations 2.8 and 2.9 that PaCO2 is inversely related to alveolar ventilation, which is the difference between minute and dead space ventilation. By creating alveolar dead space, high $V˙/Q˙$ alveoli increase dead space ventilation and reduce alveolar ventilation, which, according to our equations, leads to an increase in PaCO2.

At this point, it would seem that both high and low $V˙/Q˙$ alveoli can increase PaCO2; but let’s take a closer look. Although it may be conceptually useful to think that high $V˙/Q˙$ alveoli increase PaCO2 through their effect on dead space ventilation, that’s not really what happens. As shown in our two-compartment models, it is the alveoli with low$V˙/Q˙$ ratios that reduce CO2 excretion and are actually responsible for any rise in the PaCO2. In fact, as shown in Figures 2.6 and 2.8, blood from high $V˙/Q˙$ alveoli has a low PCO2, and alveoli with no perfusion (Figure 2.9) contribute no blood at all to the systemic circulation.

In “real life,” any rise in PaCO2 resulting from $V˙/Q˙$ mismatching is quickly detected by central and peripheral chemoreceptors, which increase respiratory drive and minute ventilation. This is the increase in ventilation that, according to Equation 2.9, compensates for the rise in dead space ventilation and normalizes the PaCO2. But, as you can see, it is triggered by the impaired CO2 excretion of low $V˙/Q˙$ alveoli and actually has nothing to do with increased dead space. Furthermore, it is primarily the increase in ventilation to low $V˙/Q˙$ alveoli that augments CO2 excretion (by increasing $V˙/Q˙$ ratios) and returns the PaCO2 to normal.

Of course, our two-compartment models are a gross oversimplification. In reality, there are hundreds of millions of compartments (alveoli), each of which contributes blood with a specific content of O2 and CO2 that is determined by its ratio of ventilation to perfusion. The final result is the same, though. High $V˙/Q˙$ alveoli increase alveolar dead space and dead space ventilation, whereas low $V˙/Q˙$ alveoli cause a drop in the PaO2, increase the A–a gradient, impair CO2 excretion, and stimulate a compensatory rise in minute ventilation.

## Gas Diffusion

The final component of gas exchange is the diffusion of O2 and CO2 molecules between alveolar gas and pulmonary capillary blood. During this journey, O2 moves through the alveolar epithelium, the capillary endothelium, both basement membranes, and the plasma (where some dissolves) before entering the erythrocyte and combining with hemoglobin. Carbon dioxide molecules, of course, move in the opposite direction.

The factors that determine the rate at which gas molecules cross the alveolar–capillary interface ($V˙$) are shown by this modification of Fick’s law for diffusion:

$Display mathematics$
(2.12)

In this equation, A is the total area of contact between gas and blood in the lungs, (P1 – P2) is the difference between the partial pressure of the gas in the alveolus and the blood, and D is the distance that the molecules must travel.

Oxygen moves from a mean PAO2 of around 100 mmHg to a mixed venous PO2 of about 40 mmHg. Carbon dioxide diffuses from a mixed venous PCO2 of about 46 mmHg to a PACO2 of approximately 40 mmHg. Remember, though, that the actual PO2 and PCO2 of the gas in each alveolus are determined by its $V˙/Q˙$ ratio.

The lungs have an enormous gas–blood interface of approximately 100 square meters, and the alveolar-capillary membrane is incredibly thin at 0.2–0.5 μ‎m. So it’s not surprising that O2 and CO2 normally equilibrate very rapidly between alveolar gas and capillary blood. It’s estimated that blood normally spends about 0.75 second in each alveolar capillary. But, as shown in Figure 2.10A, it normally takes only about one-third of this time for the alveolar and capillary PO2 and PCO2 to equilibrate. Even during exercise, when transit time is reduced by the increase in cardiac output, equilibration occurs before blood leaves the alveoli.

Figure 2.10 (A) The partial pressure of O2 and CO2 in the capillary blood entering an alveolus (PcO2, PcCO2) normally equilibrates with alveolar gas (PAO2, PACO2) within the first third of its transit time. (B) When there is a loss of blood–gas interface or an increase in the diffusion distance (represented by the thick line), there may be insufficient time for equilibration to occur.

Diseases that decrease the area of the gas–blood interface or increase diffusion distance, however, slow the rate of diffusion. If diffusion impairment is severe (Figure 2.10B), there may be insufficient time for equilibration to occur, and this will produce a gradient between alveolar and end-capillary PO2 and PCO2. As you can see from Figure 2.10, because of the larger partial pressure gradient, the PaO2 will be affected much more than the PaCO2. If diffusion impairment does cause the PaCO2 to rise, a compensatory increase in minute ventilation will be needed to return it to normal.