Gas Exchange in the Lungs

Gas flow across a barrier is proportional to diffusing capacity and concentration gradient (Fick's law)

Although, early on, physiologists debated whether the lung actively secretes O ₂ into the blood, we now know that the movements of both O ₂ and CO ₂ across the alveolar blood-gas barrier occur by simple diffusion (see p. 108 ). Random motion alone causes a net movement of molecules from areas of high concentration to areas of low concentration. Although diffusion per se involves no expenditure of energy, the body must do work—in the form of ventilation and circulation—to create the concentration gradients down which O ₂ and CO ₂ diffuse. Over short distances, diffusion can be highly effective.

Suppose that a barrier that is permeable to O ₂ separates two air-filled compartments ( Fig. 30-1 A ). The partial pressures (see p. 593 ) of O ₂ on the two sides are P ₁ and P ₂ . The probability that an O ₂ molecule on side 1 will collide with the barrier and move to the opposite side is proportional to P ₁ :

The unidirectional movement of O ₂ in the opposite direction, from side 2 to side 1, is proportional to the partial pressure of O ₂ on side 2:

The net movement of O ₂ from side 1 to side 2 is the difference between the two unidirectional flows:

Note that net flow is proportional to the difference in partial pressures, not the ratio. Thus, when P ₁ is 100 mm Hg (or torr) and P ₂ is 95 mm Hg (ratio of 1.05), the net flow is 5-fold greater than when P ₁ is 2 mm Hg and P ₂ is 1 mm Hg (ratio of 2).

The term flow describes the number of O ₂ molecules moving across the entire area of the barrier per unit time ( units: moles/s). If we normalize flow for the area of the barrier, the result is a flux ( units: moles/[cm ² ⋅ s]). Respiratory physiologists usually measure the flow of a gas such as O ₂ as the volume of gas (measured at standard temperature and pressure/dry; see Box 26-3 ) moving per unit time. V refers to the volume and is its time derivative (volume of gas moving per unit time), or flow.

The proportionality constant in Equation 30-3 is the diffusing capacity for the lung, D _L ( units: mL/[min ⋅ mm Hg]). Thus, the flow of gas becomes

This equation is a simplified version of Fick's law (see p. 108 ), which states that net flow is proportional to the concen­tration gradient, expressed here as the partial-pressure gradient.

Applying Fick's law to the diffusion of gas across the alveolar wall requires that we extend our model somewhat. Rather than a simple barrier separating two compartments filled with dry gas, a wet barrier covered with a film of water on one side will separate a volume filled with moist air from a volume of blood plasma at 37°C (see Fig. 30-1 B ). Now we can examine how the physical characteristics of the gas and the barrier contribute to D _L .

Two properties of the gas contribute to D _L —molecular weight (MW) and solubility in water. First, the mobility of the gas should decrease as its molecular weight increases. Indeed, Graham's law states that diffusion is inversely proportional to the square root of molecular weight. Second, Fick's law states that the flow of the gas across the wet barrier is proportional to the concentration gradient of the gas dissolved in water. According to Henry's law (see Box 26-2 ), these concentrations are proportional to the respective partial pressures, and the proportionality constant is the solubility of the gas ( s ). Therefore, poorly soluble gases (e.g., N ₂ , He) diffuse poorly across the alveolar wall.

Two properties of the barrier contribute to D _L —area and thickness. First, the net flow of O ₂ is proportional to the area (A) of the barrier, describing the odds that an O ₂ molecule will collide with the barrier. Second, the net flow is inversely proportional to the thickness (a) of the barrier, including the water layer. The thicker the barrier, the smaller the O ₂ partial-pressure gradient ( ) through the barrier ( Fig. 30-2 ). An analogy is the slope of the trail that a skier takes from a mountain peak to the base. Whether the skier takes a steep “expert” trail or a shallow “beginner's” trail, the end points of the journey are the same. However, the trip is much faster along the steeper trail!

Finally, a combined property of both the barrier and the gas also contributes to D _L , a proportionality constant k that describes the interaction of the gas with the barrier.

Replacing D _L in Equation 30-4 with an area, solubility, thickness, molecular weight, and the proportionality constant yields

Equations 30-4 and 30-5 are analogous to Ohm's law for electricity:

Electrical current (I) in Ohm's law corresponds to the net flow of gas ( ); the reciprocal of resistance (i.e., conductance) corresponds to diffusing capacity (D _L ); and the voltage difference (ΔV) that drives electrical current corresponds to the pressure difference (P ₁ − P ₂ , or ΔP).

The total flux of a gas between alveolar air and blood is the summation of multiple diffusion events along each pulmonary capillary during the respiratory cycle

Equation 30-5 describes O ₂ diffusion between two compartments whose properties are uniform both spatially and temporally. Does this equation work for the lungs? If we assume that the alveolar air, blood-gas barrier, and pulmonary-capillary blood are uniform in space and time, then the net diffusion of O ₂ ( ) from alveolar air to pulmonary-capillary blood is

is the diffusing capacity for O ₂ ,
is the O ₂ partial pressure in the alveolar air, and
is the comparable parameter in pulmonary-capillary blood. Although Equation 30-7 may seem sophisticated enough, a closer examination reveals that
,
, and
are each even more complicated than they at first appear.

Among the five terms that make up , two vary both temporally (during the respiratory cycle) and spatially (from one piece of alveolar wall to another). During inspiration, lung expansion causes the surface area (A) available for diffusion to increase and the thickness of the barrier (a) to decrease ( Fig. 30-3 A ). Because of these temporal differences, should be maximal at the end of inspiration. However, even at one instant in time, barrier thickness and the surface area of alveolar wall differ among pieces of alveolar wall. These spatial differences exist both at rest and during the respiratory cycle. N30-1

N30-1

Spatial Differences in Alveolar Dimensions

The total area of the lungs is not distributed evenly among all alveoli. First, all else being equal, some alveoli are “naturally” larger than others. Thus, some have a greater area for diffusion than do others, and some have a thinner wall than do others.

Second, the position of an alveolus in the lung can affect its size. As we saw in Chapter 27 , when a person is positioned vertically, the effects of gravity cause the intrapleural pressure to be more negative near the apex of the lung than near the base (see Fig. 27-2 ). Thus, other things being equal, alveoli near the apex of the lung tend to be more inflated, so that they have a greater area and smaller thickness compared to alveoli near the base of the lung.

Third, during inspiration, alveoli undergo an increase in volume that causes their surface area to increase and their wall thickness to decrease. However, these changes are not uniform among alveoli. Again, the differences can be purely anatomical: all other things being equal, some alveoli “naturally” have a greater static compliance (see p. 610 ) than others. Thus, during inspiration, their area will increase more, and their wall thickness will decrease more. However, other things being equal, the compliance of an alveolus also depends on its position in the lung. We will see in Chapter 31 that the relatively overinflated alveoli near the apex of the lung (in an upright individual) have a relatively low compliance. In other words, during inspiration these apical alveoli have a smaller volume increase (see Fig. 31-5 D ). Thus, their area for diffusion undergoes a relatively smaller increase, and their wall thickness undergoes a relatively smaller decrease, than alveoli near the base of the lung.

In summary, for all of the reasons we have discussed, the area and thickness parameters vary widely among alveoli at the end of a quiet inspiration, and the relation among these differences changes dynamically during a respiratory cycle.

As discussed below, as the blood flows down the capillary, capillary rises to match (see Fig. 30-3 C ). Therefore, O ₂ diffusion is maximal at the beginning of the pulmonary capillary and gradually falls to zero farther along the capillary. Moreover, this profile varies during the respiratory cycle.

The complications that we have raised for O ₂ diffusion apply as well to CO ₂ diffusion. Of these complications, by far the most serious is the change in with distance along the pulmonary capillary. How, then, can we use Fick's law to understand the diffusion of O ₂ and CO ₂ ? Clearly, we cannot insert a single set of fixed values for , , and into Equation 30-7 and hope to describe the overall flow of O ₂ between all alveoli and their pulmonary capillaries throughout the entire respiratory cycle. However, Fick's law does describe gas flow between air and blood for a single piece of alveolar wall (and its apposed capillary wall) at a single time during the respiratory cycle. For O ₂ ,

For one piece of alveolar wall and at one instant in time, A and a (and thus ) have well defined values, as do and . The total amount of O ₂ flowing from all alveoli to all pulmonary capillaries throughout the entire respiratory cycle is simply the sum of all individual diffusion events, added up over all pieces of alveolar wall (and their apposed pieces of capillary wall) and over all times in the respiratory cycle:

Here,
,
, and
are the “microscopic” values for one piece of alveolar wall, at one instant in time.

Even though the version of Fick's law in Equation 30-9 does indeed describe O ₂ diffusion from alveolar air to pulmonary-capillary blood—and a comparable equation would do the same for CO ₂ diffusion in the opposite direction—it is not of much practical value for predicting O ₂ uptake. However, we can easily compute the uptake of O ₂ that has already taken place by use of the Fick principle (see p. 423 ). The rate of O ₂ uptake by the lungs is the difference between the rate at which O ₂ leaves the lungs via the pulmonary veins and the rate at which O ₂ enters the lungs via the pulmonary arteries. The rate of O ₂ departure from the lungs is the product of blood flow (i.e., cardiac output, ) and the O ₂ content of pulmonary venous blood, which is virtually the same as that of systemic arterial blood ( ). Remember that “content” (see p. 650 ) is the sum of dissolved O ₂ and O ₂ bound to hemoglobin (Hb). Similarly, the rate of O ₂ delivery to the lungs is the product of and the O ₂ content of pulmonary arterial blood, which is the same as that of the mixed-venous blood ( ). Thus, the difference between the rates of O ₂ departure and O ₂ delivery is

For a cardiac output of 5 L/min, a of 20 mL O ₂ /dL blood, and a of 15 mL O ₂ /dL blood, the rate of O ₂ uptake by the pulmonary-capillary blood is

Obviously, the amount of O ₂ that the lungs take up must be the same regardless of whether we predict it by repeated application of Fick's law of diffusion (see Equation 30-9 ) or measure it by use of the Fick principle (see Equation 30-10 ):