Chapter **5** Gas Exchange

# The Basis of Gas Exchange: Ventilation, Diffusion, and Perfusion

## Challenges to Lung Function Caused by its Structure

*Inequality of ventilation and blood flow*: Because the lungs are ventilated through a single main airway (trachea), yet air must reach all 300 million alveoli, there must be a substantial branching airway system. Indeed, some 23 orders of largely dichotomous branching are recognized, resulting in a very large number of very small airways arranged in parallel with each other—much like tree branches emanating and serially dividing from a single trunk. It is impossible to imagine that inhaled air can be distributed homogeneously to all 300 million alveoli, and nonuniform ventilation distribution is well known to occur. Similarly, blood flow reaches the lungs from the main pulmonary artery by a corresponding branching system, and it also is known that perfusion is nonuniform. Nonuniform distribution of ventilation and blood flow are important for gas exchange efficiency as will be shown later.

*Wasted ventilation (dead space)*: The first 17 or so generations of the airways are conducting airways—plumbing whose walls are unable to perform any gas exchange. Their total volume is about 150 mL. This means that with every single breath, 150 mL of inhaled air never reaches the alveoli yet must be moved by muscle contraction. Normally, each breath is about 500 mL in total volume, so about 30% of each breath represents wasted effort. This is not important in health, but in some lung diseases, the effort of breathing is so high that this wasted ventilation, called *dead space,* leads to insufficient ventilation of fresh gas to the alveoli.

*Alveolar collapse*: A very large number of very small collapsible structures is potentially physically unstable, due to surface tension forces. The laws of physics show that the pressure inside a soap bubble caused by surface tension is inversely proportional to the bubble radius. To the extent that the soap bubble analogy applies to the alveoli, which simply are not all exactly equal in size, surface tension forces will therefore tend to empty small alveoli into larger alveoli. Unchecked, this progression would lead to massive alveolar collapse with loss of gas exchange surface area and could prove fatal. In fact, the neonatal respiratory distress syndrome is considered to represent an example of just this phenomenon. The body has solved this problem by generating, in normal full-term newborns, a surfactant that lines each alveolus. It reduces surface tension by about an order of magnitude, greatly mitigating the risk of alveolar collapse. What also helps prevent collapse is the aforementioned interdependence whereby adjacent alveoli share common alveolar walls, creating a mesh or network that is inherently self-stabilizing.

*Particle deposition*: An array of about 20 orders of dichotomous branching leads to a very large (2^{20} in this case) number of small peripheral airways. Although individually each is very small, there are so many of them that their total cross-sectional area becomes very large. With this arrangement, the forward velocity of the air in each small airway is reduced as air is inhaled, which in turn increases the chance that an inhaled dust (or other) particle will settle out and deposit on the small airway wall (compared with larger, more proximal airways, in which the velocity of air flow is much greater). If such a particle is physically, chemically, or biologically dangerous, disease may result, often starting in those small peripheral airways—as is the case for emphysema caused by inhalation of tobacco smoke.

*Airway obstruction by mucus*: Although the airways have developed a sophisticated particle clearance mechanism using mucociliary transport, the mucus that traps the particles may itself occlude small airways, impairing distal ventilation of the alveoli.

*Capillary stress failure*: The pulmonary microcirculation is at risk from the inherent structure of the lungs. With capillaries poorly supported in very thin alveolar walls (good for diffusion), they risk rupture into the alveolar space when intravascular pressures rise even modestly. Such alveolar hemorrhage occurs in several conditions, and especially in racehorses, whose lungs are relatively small, leading to high vascular pressures, which in this setting can be fatal.

*Pulmonary hypertension*: Because all of the cardiac output has to pass through the lungs (compare the systemic circulation, for which flow is divided among all of the body’s other tissues and organs), the potential for high vascular pressures is considerable. The twin processes of capillary distention and recruitment mitigate increases in pressure when perfusion is increased, as in exercise.

## Gas Exchange in the Homogeneous Lung: Ventilation, Diffusion, and Perfusion

### Ventilation

where is the volume of O_{2} taken up into the blood per minute, and is the minute ventilation, both expressed in L/minute. FIO_{2} and FEO_{2} are, respectively, the inhaled and exhaled mean O_{2} fractional concentrations. commonly is about 7 L/minute. Because about 21 of every 100 molecules in air are O_{2} molecules (the rest being mostly nitrogen), FIO_{2} is 0.21. FE_{O}_{2} at rest is about 0.17; this difference shows that is about 0.3 L/minute. Because the conducting airways that feed the alveoli do not exchange O_{2} or CO_{2}, it has become conventional to subtract the volume of gas left in the conducting airways each breath—the so-called *anatomic dead space*—from the total breath volume before multiplying by respiratory frequency to calculate ventilation, resulting in a variable known as *alveolar ventilation* (). Equation 1 then becomes

The tendency is to use partial pressure (PI_{O}_{2}, inhaled; PAO_{2}, alveolar) rather than fractional concentration (FI_{O}_{2}, FAO_{2}) in describing these relationships: From Dalton’s law of partial pressure, PO_{2} = FO_{2} × (barometric pressure − water vapor pressure). Allowing for proper units, Equation 2 can then be rewritten as

is now expressed in mL/minute, in L/minute, and P in mm Hg.

is the whole-body metabolic rate and as such is dictated by the body tissues, not the lungs. Because PI_{O}_{2} is a constant, Equation 2 can be used to demonstrate the dependence of alveolar PO_{2} on alveolar ventilation for a given value of (**Figure 5-1**). The same concepts apply to CO_{2}, for which it is simpler, because CO_{2} is essentially absent from inhaled air. The corresponding equation is

Figure 5-1 Relationship between alveolar PO_{2}/PCO_{2} and alveolar ventilation when metabolic rate is held constant. *Dashed lines* indicate normal ventilation, PO_{2} and PCO_{2}. Note that as ventilation is reduced, even moderately, PO_{2} falls sharply and PCO_{2} rises similarly.

How ventilation affects PACO_{2} also is shown in Figure 5-1. It is evident that a relatively small reduction in ventilation will reduce PAO_{2} and increase PACO_{2}—both substantially.

Dividing Equation 4 by Equation 3 gives

which can be rearranged into what is called the *alveolar gas equation*:

### Diffusion

The laws of diffusion dictate that the rate at which a gas diffuses between two points is the product of the diffusion coefficient for the gas and the partial pressure difference between the two points. In the lungs, the diffusion coefficient, measured as the diffusing capacity, is determined by surface area and distance of the diffusion pathway (see earlier). When a red cell leaves the pulmonary arteries and enters the pulmonary capillary, it arrives with a reduced level of O_{2}, because the tissues visited by that red cell took O_{2} from the red cell for the tissue’s metabolic needs. The PO_{2} in the red cell in this blood commonly is about 40 mm Hg. Alveolar PO_{2}, on the other hand, usually is about 100 mm Hg. The large PO_{2} difference (“driving gradient”) of 60 mm Hg leads to rapid diffusion of O_{2} from the alveolar gas into the capillary blood. Consequently, however, the blood PO_{2} increases, reducing the driving gradient, and O_{2} diffusion slows down as the red cell progresses along the lung capillary network. With modeling of this process, again using mass conservation principles, PO_{2} is seen to rise approximately exponentially as the red cell moves along the lung capillary until PO_{2} in the red cell has reached the alveolar value, indicating that diffusion equilibration has occurred. This process is shown in **Figure 5-2**. Note that for O_{2}, equilibration occurred in about 0.25 second. On average, each red cell takes about 0.75 second to move through the alveolar capillary system, so that diffusion equilibration is complete already a third of the way along the capillary, and thus well before its end. As might be expected, during exercise, time available for a red cell to pick up O_{2} in the lung is reduced, because blood flow rate is increased, and at very high exercise intensity, there may not be sufficient time for PO_{2} in the red cell to reach the alveolar value. Accordingly, PO_{2} in the systemic arterial blood will be lower than that in the alveolus—a situation referred to as hypoxemia caused by diffusion limitation. This effect is seen commonly in exceptional athletes exercising heavily at sea level, and in all subjects exercising at altitude.

Figure 5-2 **A,** Rate of rise in gas partial pressure along the capillary. Inert gases equilibrate very rapidly, and O_{2} more slowly, but CO fails to equilibrate. **B,** Rate of fall in CO_{2} partial pressure along the capillary. CO_{2} equilibrates about twice as rapidly as does O_{2}.

While CO_{2} moves from blood to gas, the principle is the same as for O_{2}. Here, the red cell enters the alveolar capillary with a high PCO_{2} (because of addition of waste CO_{2} from tissues visited by the red cell), whereas alveolar PCO_{2} is lower. Thus, diffusion will move CO_{2} from red cell to alveolar gas, and red cell PCO_{2} will fall toward the alveolar value in mirror image to the rise in PO_{2} described earlier (see Figure 5-2). The speed of equilibration for CO_{2} is about twice that for O_{2}, so it takes about half the time to reach equilibration. In practice, CO_{2} is never diffusion-limited. Gases carried in blood only in physical solution (i.e., inert and anesthetic gases) equilibrate even faster—about 10 times as quickly as for O_{2} (see Figure 5-2). This rule holds true for gases of any solubility.

## Gas Exchange

Focusing on O_{2}, Equations 3 and 8 should now be considered together. They both embody mass conservation but express it differently, with Equation 3 reflecting alveolar loss of O_{2} into blood and Equation 8, red cell gain of O_{2} into blood. **Figure 5-3** shows how, for given constant values of and , and for designated values of inspired PO_{2} (PI_{O}_{2}) and inflowing pulmonary arterial O_{2} concentration (CvO_{2}), would have to vary with alveolar PO_{2} (to satisfy both these equations) when determined by each of the two equations independently. Because each molecule of O_{2} that leaves the alveolus by crossing the blood gas barrier appears in the capillary blood, the calculated from the two equations must be the same—again, conservation of mass. Thus, only a single value of PAO_{2} can exist—that at the point of intersection of the two relationships in Figure 5-3. If the calculations in Figure 5-3 were repeated for different values of , and thus (in this example, keeping the same), the lines and their point of intersection would change as in **Figure 5-4**. This figure shows that alveolar PO_{2} (x axis) and the amount of O_{2} that can be taken up (, y axis) both depend on and . Commonly, Equations 3 and 8 are combined, because must be the same when calculated from either equation. This yields the ventilation-perfusion equation: