Alveolar Air Equation

The sum of all gas pressures at any point in the lung must equal 760 mm Hg at sea level. When air—which is CO₂-free—is inspired and enters the alveoli, its PCO₂ immediately increases to 40 mm Hg as it mixes with the CO₂ present in the alveoli; because the sum of all alveolar gas pressures is constant (760 mm Hg), the inspired air PO₂ decreases by about 40 mm Hg. If the amount of O₂ diffusing out of alveoli into the blood each minute were exactly equal to the amount of CO₂ diffusing

from the blood into alveoli each minute, P_AO₂ would be calculated by simply subtracting alveolar PCO₂ (normally 40 mm Hg) from the result of equation 2. However, O₂ diffuses out of the alveolus at a greater rate than CO₂ diffuses into the alveolus. At rest, pulmonary capillary blood removes about 250 mL per minute of O₂ from the alveoli, replacing it with only 200 mL per minute of CO₂. The ratio of alveolar CO₂ excretion (V˙CO₂) to blood oxygen uptake (V˙O₂) is called the respiratory exchange ratio (R), and its value is normally about 0.8 (R=V˙CO2/V˙O2=200/250=0.8).

When R is equal to 0.8, the CO₂ diffusing into the alveolus replaces only 80% of the volume that O₂ vacated when it diffused out of the alveolus. This uneven exchange causes the alveolar gas volume to shrink slightly, but alveolar gas pressure remains constant at 760 mm Hg. The shrinkage in alveolar volume concentrates the alveolar nitrogen molecules, which the alveolar air equation takes into account. This equation is known as the ideal alveolar air equation because it assumes the ventilation-to-blood flow ratios of each alveolus in the lung are identical, as the following calculation shows:

In this equation P_IO₂ equals F_IO₂ (760 − 47). F_IO₂ represents inspired oxygen concentration expressed as a decimal fraction. The bracketed part of equation 3 is a correcting factor that considers the effect of R on P_AO₂. When R equals 1, the correction factor equals 1 and does not need to be applied.

The term 1 − F_IO₂ is equal to the inspired nitrogen concentration. When R is less than 1, the effect is to increase nitrogen concentration, causing the bracketed term to increase to values greater than 1. In equation 3, if R = 0.8 and F_IO₂ = 0.21 (room air), the bracketed factor is equal to 1.2.

Examination of equation 3 shows that higher F_IO₂ values require progressively smaller correction factors; at 100% inspired oxygen (F_IO₂ = 1.0), no correction is needed. A sufficiently accurate equation for clinical use is a simplified form of equation 3 for patients breathing an F_IO₂ of 0.60 or less. This is shown as follows:¹

For F_IO₂ values greater than 0.60, a sufficiently accurate clinical equation is as follows:¹

In equations 4 and 5, PaCO₂ is substituted for P_ACO₂ because these two values are generally equal, unless the lungs have a high degree of alveolar dead space.

A normal P_AO₂ for a person breathing room air at sea level, with a PaCO₂ equal to 40 mm Hg and an R equal to 0.8, is about 100 mm Hg (using equation 4). This is shown as follows:

PAO2=0.2093(760−47)−(40×1.2)

PAO2=149.2−48

PAO2=101.2

Table 7-1 summarizes respiratory gas partial pressures at sea level in dry inspired air, humidified (tracheal) air, alveolar air, and mixed expired air. Expired gas PO₂, PCO₂, and PN₂ differ from alveolar values because expired air contains dead space gas mixed with alveolar gas.

Physical Gas Characteristics and Diffusion

O₂ and CO₂ diffuse through gaseous and liquid phases in the lung; the alveolar capillary membrane (see Figure 7-1) is a liquid barrier. Light gases diffuse more rapidly than heavier gases, and highly soluble gases diffuse through liquids more rapidly than less soluble gases. The rate of gas diffusion in the lung is inversely proportional to its molecular weight and directly proportional to its solubility; the diffusion coefficient in Fick’s law is derived from these two factors. Specifically, the gas diffusion rate is inversely proportional to the square root of its gram molecular weight (gmw) (Graham’s law). Relative rates of diffusion for O₂ (molecular weight = 32) and CO₂ (molecular weight = 44) in a gaseous medium are as follows:

O2 rateCO2 rate=gmwCO2gmwO2=4432=6.635.66=1.171.0

Because O₂ is a lighter molecule, it diffuses through a gas medium 1.17 times faster than CO₂.

Conversely, CO₂ is much more soluble in water than O₂Henry’s law states that the amount of gas dissolving in a liquid is directly proportional to the gas partial pressure. At body temperature (37° C) and 760 mm Hg pressure, 0.592 mL of CO₂ and 0.0244 mL of O₂ dissolve in 1 mL of water. CO₂ is about 24 times more soluble than O₂, as the following equation shows:

CO2 solO2 sol=0.5920.0244=24.31.0

Combining Graham’s law and Henry’s law, CO₂ diffuses across the alveolar capillary membrane about 20 times faster than O₂. This is shown as follows:

CO2 rateO2 rate=3244×0.5920.0244=3.350.16=20.7

For this reason, alveolar capillary membrane defects limit O₂ diffusion long before they limit CO₂ diffusion. In a practical clinical sense, the alveolar capillary membrane never limits outward diffusion of CO₂ from blood to alveoli. Discussion of diffusion in this chapter is therefore primarily focused on O₂ diffusion.

Effects of the Partial Pressure Gradient and Capillary Blood Transit Time on Gas Equilibrium

At a resting cardiac output, a red blood cell spends about 0.75 second traveling through the pulmonary capillary. Normally, the equilibrium between alveolar gas and capillary blood PO₂ occurs within 0.25 second, or about one third of the distance through the capillary (Figure 7-4, dark curved line). The time to reach equilibrium may be prolonged if alveolar capillary membranes are thickened (light curved line in Figure 7-4). Even so, equilibrium is virtually always achieved at rest. The rate of diffusion is rapid at first when the partial pressure gradient across the alveolar capillary membrane is greatest. The diffusion rate continuously slows as the partial pressure gradient diminishes (notice the shape of the PO₂ curve [dark line] in Figure 7-4) until diffusion completely ceases at equilibrium. Thus, during the last two thirds of travel through the pulmonary capillary, no diffusion normally occurs.

Even when capillary transit time is shortened to 0.25 second by a high blood flow rate during exercise, complete O₂ equilibrium normally occurs between alveolar gas and end-capillary blood; it simply occurs at some point farther along the capillary path. In such a situation, the number of O₂ molecules transferred into the blood each minute is greatly increased because the greater rate of blood flow takes up more O₂ molecules from the alveoli each minute. Another reason exercise increases the number of O₂ molecules transferred each minute is that previously nonperfused capillaries are recruited, which increases the surface area for diffusion.

If a healthy person exercises vigorously at a high altitude, where atmospheric PO₂ is very low, the O₂ diffusion gradient may be so low that O₂ cannot diffuse across the alveolar capillary membrane fast enough to establish equilibrium during the shortened capillary transit time. Alternatively, if disease thickens the alveolar capillary membrane, the diffusion rate across the membrane may be slowed enough to prevent complete O₂ equilibrium by the time blood leaves the capillary. In the clinical setting, this situation rarely occurs at rest, even in severe lung disease.² However, exercise immediately exposes the diffusion abnormality problem because it shortens the blood’s transit time through the capillary, making it likely that alveolar and capillary O₂ equilibrium never occurs (Figure 7-5). Patients with thickened alveolar capillary membranes are most likely to show evidence of O₂ diffusion impairment during exercise.³

Perfusion and Diffusion Limitations to Oxygen Transfer

Figure 7-4 shows that diffusion normally stops when O₂ equilibrium is reached between the alveolus and capillary, which occurs long before the blood travels the length of the capillary. If blood flow (perfusion) increases, more O₂ leaves the lung each minute because the O₂-saturated blood moves out of the capillary more quickly, which means deoxygenated blood enters more quickly to take up more O₂. Therefore the O₂ diffusion rate through the alveolar-capillary membrane is normally perfusion limited (see Figure 7-4); that is, a change in blood flow rate alters the number of O₂ molecules that cross the alveolar-capillary membrane each minute. If O₂ equilibrium between the alveolus and capillary never occurs because of thickened membranes, O₂ transfer is truly diffusion limited. In such an instance, it is the alveolar capillary membrane, not blood flow rate, that influences the O₂ transfer rate (see Figure 7-5).

CONCEPT QUESTION 7-5

In what way would changes in pulmonary blood flow interfere with the measurement of diffusion capacity of the lung for O₂ (as opposed to carbon monoxide)?

If one wishes to evaluate the extent to which the alveolar capillary membrane itself impedes the diffusion rate (milliliters per minute of O₂ transfer per millimeters of mercury pressure gradient), one should not measure the O₂ diffusion rate because it is affected by blood flow rate. Instead, one should measure the diffusion rate of a gas that never reaches equilibrium between alveolar gas and capillary blood, even in resting conditions. In other words, the blood’s capacity for this gas should be so great that the gas cannot diffuse across the membrane fast enough to saturate the blood to capacity before it leaves the capillary. For such a gas, the only factor that limits diffusion is the resistance of the alveolar capillary membrane itself. Carbon monoxide (CO) is the ideal gas for this kind of measurement because blood can absorb it at a greater rate than CO can diffuse across the alveolar capillary membrane, even under resting conditions. For this reason, CO is always diffusion limited. Figure 7-6 illustrates the diffusion-limited characteristics of CO. All events that are illustrated in Figure 7-6 occur at rest; increased blood flow cannot result in greater CO uptake because CO is already diffusing through the alveolar-capillary membrane at its maximum rate. For this reason, CO is commonly used in pulmonary function laboratories to evaluate the lung’s true diffusion capacity.

CONCEPT QUESTION 7-6

What is the main reason CO₂ diffuses across the alveolar capillary membrane so much more rapidly than O₂?

Hemoglobin in the blood makes O₂ and CO much more soluble in whole blood than they are in the alveolar-capillary membrane fluid or the blood plasma. In contrast, a gas such as nitrous oxide (N₂O), highly soluble in the alveolar-capillary membrane and plasma, does not chemically bind with hemoglobin; its solubility in whole blood is much less than that of CO or O₂. If N₂O is inhaled, the pulmonary capillary blood reaches its maximum capacity for N₂O almost instantly (Figure 7-7). N₂O partial pressures across the alveolar capillary membrane reach equilibrium in the first one twentieth of the distance along the capillary.

Increased blood flow causes N₂O-saturated blood to exit the capillary sooner, allowing more mixed venous blood to enter and take up alveolar N₂O. Thus, diffusion of N₂O in the lung is strictly perfusion limited. This characteristic makes N₂O an ideal test gas to measure pulmonary blood flow.

O₂ diffusion is normally perfusion limited because it equilibrates across the alveolar capillary membrane long before blood leaves the capillary; increased blood flow increases the amount of O₂ taken up from the alveolus. Exercise increases blood flow and may cause O₂ to become diffusion limited if the alveolar capillary membrane is thickened.

Diffusion Path Length

The distance for diffusion includes the entire path length from alveolar gas to the hemoglobin in the red blood cell. It was originally thought that the alveolar capillary membrane was the only important rate-limiting barrier to diffusion; it is now known that the red blood cell membrane and rate of O₂ combined with hemoglobin limit the lung’s O₂ uptake to the same extent as the alveolar-capillary membrane.⁴ The total diffusion path distance is normally less than 0.1 µ and includes the following (see Figure 7-1): (1) surfactant layer that is lining the alveolar surface, (2) alveolar epithelium, (3) basement membrane of the alveolar epithelium, (4) extremely thin interstitial space, (5) basement membrane of the capillary endothelium, (6) capillary endothelium, (7) plasma, (8) red blood cell membrane, and (9) intracellular fluid bathing the hemoglobin molecule.

Various abnormal conditions can increase the diffusion path length, including the following: (1) fibrotic thickening of alveolar and capillary walls; (2) interstitial edema fluid, separating alveolar and capillary membranes; (3) fluid in the alveoli; (4) interstitial fibrotic processes that thicken the interstitial space; and (5) dilated, engorged capillaries, which allow red blood cells to flow side by side. Abnormalities that increase the distance for diffusion are rarely the cause of decreased end-capillary or arterial PO₂ at rest. The major cause of resting hypoxemia in these patients is a mismatch between ventilation and blood flow.² That is, the processes that increase diffusion distance generally decrease lung compliance, which decreases ventilation in these areas. Blood perfusing these underventilated areas tends to be inadequately oxygenated.

Diffusion Surface Area

Diffusion surface area is the total area of contact between ventilated alveoli and perfused capillaries. A decrease in the number of open, perfused capillaries or in the number of open, ventilated alveoli decreases the diffusion surface area and the lung’s diffusion capacity. In such instances, diffusion capacity is decreased, although the diffusion path length may be normal at all points. For example, emphysema destroys alveolar walls and their associated capillaries, which decreases the diffusion surface area. Although the diffusion path length is not thickened at any point, overall diffusion rate is decreased because much of the functional gas-exchange surface area is lost.

Normal Values

Normal D_LCO values in healthy individuals vary considerably depending on age, body size, and body position as explained in subsequent sections. A large cross-sectional study of healthy, never-smoking adult men and women in the United States yielded a mean D_LCO of 26.4 mL/min/mm Hg (single breath testing method).⁵ The mean D_LCO was about 33 mL/min/mm Hg in men and about 24 mL/min/mm Hg in women. The diffusion capacity of the lung for oxygen (D_LO₂) is obtained by multiplying D_LCO by 1.23. A mean D_LCO of 26 mL/min/mm Hg yields a normal D_LO₂ of about 32 mL/min/mm Hg. It may seem odd that D_LO₂ is greater than D_LCO, considering the much greater affinity of hemoglobin for CO than O₂. This peculiarity is explained by the fact that O₂ is more soluble than CO in the alveolar capillary membrane and the plasma and diffuses more rapidly. The fact that hemoglobin has 210 times greater affinity for CO than O₂ simply means that at a given partial pressure (PCO or PO₂), the hemoglobin carries more CO than O₂. This fact is unrelated to O₂ and CO diffusion rate across the alveolar capillary membrane, which is determined by molecular weight and solubility coefficients.

D_LCO increases with body size. Larger lungs have a greater absolute D_LCO than smaller lungs because they have a greater gas-exchange surface area.

Clinical Use of Carbon Monoxide Diffusion in the Lung

The D_LCO test assesses the extent to which the alveolar capillary membrane is a barrier to gas diffusion. Because O₂ equilibrium normally occurs before blood traverses one third of the

pulmonary capillary distance, a 50% reduction in D_LCO can exist without affecting end-capillary and arterial PO₂. In this sense, the D_LCO test is more sensitive than the PaO₂ to potential O₂ transfer problems (i.e., as disease progresses, D_LCO becomes abnormal before PaO₂). Impairment of diffusion across the alveolar capillary membrane is only one mechanism that can cause arterial hypoxemia. Many factors decrease PaO₂ without affecting the diffusion path length or membrane surface area, such as ventilation–blood flow mismatches. The D_LCO test can help clarify the mechanism of arterial hypoxemia; if D_LCO is normal, diffusion impairment cannot be a contributing factor.