Walter F. Boron
The complex anatomy of the pulmonary tree, the mechanics of the respiratory system, and the sophisticated carriage mechanisms for O2 and CO2 combine to serve two essential purposes: the ready diffusion of O2 from the alveoli to the pulmonary capillary blood and the movement of CO2 in the opposite direction. In this chapter, we consider principles that govern these diffusive events and factors that in certain diseases can limit gas exchange.
DIFFUSION OF GASES
Gas flow across a barrier is proportional to diffusing capacity (DL) and concentration gradient (Fick’s law)
Although, early on, physiologists thought that the lung actively secretes O2 into the blood, we now know that the movements of both O2 and CO2 across the alveolar blood-gas barrier occur by simple diffusion(see Chapter 5). 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 O2 and CO2 diffuse. Over short distances, diffusion can be highly effective.
Suppose that a barrier that is permeable to O2 separates two air-filled compartments (Fig. 30-1A). The partial pressures (see Chapter 26 for the box on partial pressures and Henry’s law) of O2 on the two sides are P1 and P2. The probability that an O2 molecule on side 1 will collide with the barrier and move to the opposite side is proportional to P1:
Figure 30-1 Diffusion of a gas across a barrier.
The unidirectional movement of O2 in the opposite direction, from side 2 to side 1, is proportional to the partial pressure of O2 on side 2:
The net movement of O2 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 P1 is 100 mm Hg (or torr) and P2 is 95 mm Hg (ratio of 1.05), the net flow is 5-fold greater than when P1 is 2 mm Hg and P2 is 1 mm Hg (ratio of 2).
The term flow describes the number of O2 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/(cm2·s)]. Respiratory physiologists usually measure the flow of a gas such as O2 as the volume of gas (measured at standard temperature and pressure/dry; see Chapter 26) 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, DL [units: mL/(min·mm Hg)]. Thus, the flow of gas becomes
This equation is a simplified version of Fick’s law (see Chapter 5), 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 (Fig. 30-1B). Now we can examine how the physical characteristics of the gas and the barrier contribute to DL.
Two properties of the gas contribute to DL—molecular weight and solubility in water. First, the mobility of the gas should decrease as its molecular weight (MW) increases. Indeed, Graham’s law states that diffusion is inversely proportional to the square root of MW. 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 Chapter 26 for the box on that topic), 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., N2, He) diffuse poorly across the alveolar wall.
Two properties of the barrier contribute to DL—area and thickness. First, the net flow of O2 is proportional to the area (A) of the barrier, describing the odds that an O2 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 O2 partial pressure gradient (ΔPO2/a) 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 endpoints of the journey are the same. However, the trip is much faster along the steeper trail!
Figure 30-2 Effect of barrier thickness.
Finally, a combined property of both the barrier and the gas also contributes to DL, a proportionality constant k that describes the interaction of the gas with the barrier.
Replacing DL in Equation 30-4 with an area, solubility, thickness, molecular weight, and the proportionality constant (k):
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 (net); the reciprocal of resistance (i.e., conductance) corresponds to diffusing capacity (DL); and the voltage difference (ΔV) that drives electrical current corresponds to the pressure difference (P1 − P2 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 O2 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 O2 (O2) from alveolar air to pulmonary capillary blood is
DLO2 is the diffusing capacity for O2, PAO2 is the O2 partial pressure in the alveolar air, and PcO2 is the comparable parameter in pulmonary capillary blood. Although Equation 30-7 may seem sophisticated, a closer examination reveals that DLO2, PAO2, and PcO2 are more complicated than they at first appear.
DLO2 Among the five terms that make up DLO2, 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. 30-3A). Because of these temporal differences, DLO2 should be maximal at the end of inspiration. However, even at one instant in time, barrier thickness—and the surface area of alveolar wall with this thickness—differs among pieces of alveolar wall. These spatial differences exist both at rest and during the respiratory cycle. (See Note: Spatial Differences in Alveolar Dimensions)
Figure 30-3 Complications of using Fick’s law.
PAO2 Like area and thickness, alveolar PO2 varies both temporally and spatially (Fig. 30-3B). In any given alveolus, PAO2 is greatest during inspiration (when O2-rich air enters the lungs) and least just before the initiation of the next inspiration (after perfusion has maximally drained O2 from the alveoli), as discussed in Chapter 31. These are temporal differences. We will see that when an individual is standing, PAO2 is greatest near the lung apex and least near the base (see Chapter 31). Moreover, mechanical variations in the resistance of conducting airways and the compliance of alveoli cause ventilation—and thus PO2—to vary among alveoli. These are spatial differences.
PCO2 As discussed later, as the blood flows down the capillary, capillary PO2 rises to match PAO2 (Fig. 30-3C). Therefore, O2 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 O2 diffusion apply as well to CO2 diffusion. Of these complications, by far the most serious is the change in PcO2 with distance along the pulmonary capillary. How, then, can we use Fick’s law to understand the diffusion of O2 and CO2? Clearly, we cannot insert a single set of fixed values for DLO2, PAO2, and PcO2 into Equation 30-7 and hope to describe the overall flow of O2 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 O2:
For one piece of alveolar wall and at one instant in time, A and a (and thus DLO2) have well-defined values, as do PAO2 and PcO2. The total amount of O2 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, DLO2, PAO2, and PcO2 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 O2 diffusion from alveolar air to pulmonary capillary blood—and a comparable equation would do the same for CO2 diffusion in the opposite direction—it is not of much practical value for predicting O2 uptake. However, we can easily compute the uptake of O2 that has already taken place by use of the Fick principle (see Chapter 17). The rate of O2 uptake by the lungs is the difference between the rate at which O2 leaves the lungs through the pulmonary veins and the rate at which O2 enters the lungs through the pulmonary arteries. The rate of O2 departure from the lungs is the product of blood flow (i.e., cardiac output, ) and the O2 content of pulmonary venous blood, which is virtually the same as that of systemic arterial blood (CaO2). Remember that “content” (see Chapter 29) is the sum of dissolved O2 and O2 bound to hemoglobin (Hb). Similarly, the rate of O2 delivery to the lungs is the product of and the O2 content of pulmonary arterial blood, which is the same as that of the mixed-venous blood (CO2). Thus, the difference between the rates of O2 departure and O2 delivery is
For a cardiac output of 5 L/min, a CaO2 of 20 mL O2/dL blood, and a CO2 of 15 mL O2/dL blood, the rate of O2 uptake by the pulmonary capillary blood is
Obviously, the amount of O2 that the lungs take up must be the same regardless of whether we predict it by repeated application of Fick’s law of diffusion (Equation 30-9) or measure it by use of the Fick principle (Equation 30-10):
The flow of O2, CO, and CO2 between alveolar air and blood depends on the interaction of these gases with red blood cells
We have been treating O2 transport as if it involved only the diffusion of the gas across a homogeneous barrier. In fact, the barrier is a three-ply structure comprising an alveolar epithelial cell, a capillary endothelial cell, and the intervening interstitial space containing extracellular matrix. The barrier is remarkable not only for its impressive surface area (50 to 100 m2) and thinness (~0.6 μm) but also for its strength, which derives mainly from type IV collagen in the lamina densa of the basement membrane (often <50 nm) within the extracellular matrix. (See Note: Three-Ply Structure of the Alveolar Barrier)
One could imagine that as O2 diffuses from the alveolar air to the Hb inside an erythrocyte (red blood cell), the O2 must cross 12 discrete mini-barriers (Fig. 30-4). A mini-diffusing capacity (D1-D12) governs each of the 12 steps and contributes to a so-called membrane diffusing capacity (DM) because it primarily describes how O2 diffuses through various membranes. How do these mini-diffusing capacities contribute to DM? Returning to our electrical model (Equation 30-6), we recognize that D is analogous to the reciprocal of resistance. Therefore, we can represent the 12 diffusive steps by 12 resistors in series. Because the total resistance is the sum of the individual resistances, the reciprocal of DM is the sum of the reciprocals of the mini-diffusing capacities:
Figure 30-4 Transport of O2 from alveolar air to hemoglobin (Hb). The 12 diffusion constants (D1-D12) govern 12 diffusive steps across a series of 12 barriers: (1) the interface between the alveolar air and water layer; (2) the water layer itself; (3-5) the two membranes and cytoplasm of the type I alveolar pneumocyte (i.e., epithelial cell); (6) the interstitial space containing the extracellular matrix; (7-9) the two membranes and cytoplasm of the capillary endothelial cell; (10) a thin layer of blood plasma (<0.2 μm in mammals); and (11-12) the membrane and cytoplasm of the erythrocyte. θ·Vc describes how fast O2 binds to Hb.
Of course, these parameters vary with location in the lung and position in the respiratory cycle.
For most of the O2 entering the blood, the final step is binding to Hb (see Chapter 29), which occurs at a finite rate:
θ is a rate constant that describes how many milliliters of O2 gas bind to the Hb in 1 mL of blood each minute and for each millimeter of mercury (mm Hg) of partial pressure. Vc is the volume of blood in the pulmonary capillaries. The product θ·Vc has the same dimensions as DM [units: mL/(min · mm Hg)], and both contribute to the overall diffusing capacity:
Because O2 binds to Hb so rapidly, its “Hb” term 1/(θ·Vc) is probably only ~5% as large as its “membrane” term 1/DM.
For CO, which binds to Hb even more tightly than does O2 (see Chapter 29)—but far more slowly—θ·Vc is quantitatively far more important. The overall uptake of CO, which pulmonary specialists use to compute DL, seems to depend about equally on the DM and θ·Vc terms.
As far as the movement of CO2 is concerned, one might expect the DL for CO2 to be substantially higher than that for O2, inasmuch as the solubility of CO2 in water is ~23-fold higher than that of O2 (see Chapter 26). However, measurements show that DLCO2 is only 3-to 5-fold greater than DLO2. The likely explanation is that the interaction of CO2 with the red blood cell is more complicated than that for O2, involving interactions with Hb, carbonic anhydrase, and the Cl-HCO3 exchanger (see Chapter 29).
In summary, the movement of O2, CO, and CO2 between the alveolus and the pulmonary capillary involves not only diffusion but also interactions with Hb. Although these interactions have only a minor effect on the diffusing capacity for O2, they are extremely important for CO and CO2. Although we will generally refer to “diffusing capacity” as if it represented only the diffusion across a homogeneous barrier, one must keep in mind its more complex nature.
DIFFUSION AND PERFUSION LIMITATIONS ON GAS TRANSPORT
The diffusing capacity normally limits the uptake of carbon monoxide from alveolar air to blood
Imagine that a subject breathes air containing a very low level of CO, say 0.1%, for a brief time. Breathing of higher levels of CO for longer periods could be fatal because CO, which binds to Hb with an affinity that is 200 to 300 times higher than that of O2, prevents Hb from releasing O2 to the tissues (see Chapter 29). If we assume that barometric pressure (PB) is 760 mm Hg and that PH2O is 47 mm Hg at 37°C, then we can compute the PCO of the wet inspired air entering the alveoli (see Chapter 26 for the box on wet gases):
If the subject smokes cigarettes or lives in a polluted environment, CO will be present in the mixed-venous blood—and therefore the alveolar air—even before our test begins. If not, the initial PCO of the mixed-venous blood entering the pulmonary capillaries will be ~0 mm Hg. Thus, a small gradient (~0.7 mm Hg) drives CO diffusion from alveolar air into blood plasma (Fig. 30-5A). As CO enters the blood plasma, it diffuses into the cytoplasm of red blood cells, where Hb binds it avidly. The flow of CO from alveolus to red blood cell is so slow, and the affinity and capacity of Hb to bind CO is so great, that Hb binds almost all incoming CO. Because only a small fraction of the total CO in the pulmonary capillary blood remains free in solution, the aqueous phase of the blood remains nearly a perfect sink for CO. That is, PCO in the capillary (PcCO), which is proportional to free [CO] in the capillary, rises only slightly above 0 mm Hg as the blood courses down the capillary (Fig. 30-5B). Thus, by the time the blood reaches the end of the capillary (~0.75 second later), PcCO is still far below alveolar PCO (PACO). In other words, CO fails to reach diffusion equilibrium between the alveolus and the blood. (See Note: An Analogy for the Diffusion-Limited Uptake of Carbon Monoxide)
Figure 30-5 Diffusion of CO. In A, ΔPCO is CO partial pressure gradient from alveolar air to pulmonary capillary blood. As the red blood cell (RBC) enters the capillary, O2 occupies three of the four sites on hemoglobin. In B, PACO is alveolar PCO. In C, the blood flow has a relative value of 1. In D, the diffusing capacity DL has a relative value of 1. Because PCO is very low in B-D, we are on the linear portion of the Hb-CO dissociation curve. Thus, the CO content at the end of the capillary is approximately proportional to the capillary PCO.
There are two reasons that PcCO rises so slowly as blood flows down the pulmonary capillary:
1. The CO flux (CO) is low. According to Fick’s law, CO = DLCO (PACO − PcCO). Because we chose to use an extremely low inspired PCO, the alveolar PCO driving CO diffusion was likewise extremely low, causing PcCO to rise slowly. In addition, the physiological DLCO is moderate.
2. Hb continuously traps incoming CO. Hb has a high affinity and high capacity for CO. Thus, for a low CO, PcCO—proportional to the free [CO]—rises very slowly.
We will now explore factors that influence how much CO the blood takes up as it flows down the capillary. The principles that we develop here apply equally well to O2 and CO2. First, we use the Fick principle (Equation 30-10) to quantitate, after the fact, how much CO has entered the blood:
Overall CO is the total flow of CO along the entire length of all capillaries throughout the lungs, is cardiac output, Cc′CO is the CO content of blood at the end of the pulmonary capillary (dissolved and bound to Hb), and CCO is the CO content of mixed-venous blood at the beginning of the capillary. If we assume that CCO is 0, then Equation 30-17 simplifies to
Of course, this overall CO, computed from the Fick principle, must be the same as the sum of the individual diffusion events, computed from Fick’s law (analogous to Equation 30-12):
How does CO uptake depend on DLCO and ? For basal conditions, we assume that DLCO and both have relative values of 1 and that the curve labeled DL = 1 in Figure 30-5C describes the trajectory of PcCO. As a result, Cc′COalso has a relative value of 1. According to the Fick principle, the total amount of CO moving into the blood along the capillary is
What would happen if we keep constant but double DLCO? Fick’s law (Equation 30-19) predicts that the flow of CO into the blood for each diffusion event along the capillary would double. Thus, along the entire capillary, PcCOwould rise twice as steeply (Fig. 30-5C, curve labeled DL = 2) as before. As a result, Cc′CO and thus CO would also double. (See Note: Assumptions Underlying Figure 30-5C)
Halving of DLCO would have the opposite effect: Cc′CO and thus CO would also halve (Fig. 30-5C, bottom curve). Therefore, CO uptake is proportional to DLCO over a wide range of DLCO values (Table 30-1, upper half). Of course, if it were possible to make DLCO extremely high, then capillary PCO would rise so fast that CO would equilibrate with the Hb before the end of the capillary, and capillary PCO would reach alveolar PCO (Fig. 30-5C, top curve). However, for realistic values of DLCO—as well as low alveolar PCO levels and normal Hb concentrations—CO would fail to reach equilibrium by the end of the capillary.
Table 30-1 Alveolar Transport of CO
How would alteration of blood flow affect CO? If were halved and the dimensions of the capillary remained constant, then the contact time of the blood with the alveolar capillary would double. Thus, at any distance down the capillary, twice as much cumulative time would be available for CO diffusion. The trajectory of capillary PCO versus distance would be twice as steep (Fig. 30-5D, curve labeled = 0.5) as in the basal state (curve labeled = 1), and Cc′CO would also be twice as great. However, because we achieved this increase in Cc′CO by cutting in half, the product ·Cc′CO =CO would be the same as that in the basal state (Table 30-1, lower half).
Doubling of blood flow would cause capillary PCO to rise only half as steeply (Fig. 30-5D, bottom curve) as in the basal state but still have no effect on CO. Thus, for the range of DL and values in this example, CO uptake is unaffected by changes in blood flow. Of course, if we were to reduce to extremely low values, then capillary PCO would reach alveolar PCO by the end of the capillary (Fig. 30-5D, top curve).
In our example, we have assumed that the PcCO profile along the capillary is linear and that changes in do not affect capillary dimensions. In fact, these assumptions are not entirely valid. Nevertheless, the uptake of CO is more or less proportional to the DL for CO and rather insensitive to perfusion. Therefore, we say that the uptake of CO is diffusion limited because it is the diffusing capacity that predominantly limits CO transport. We can judge whether the transport of a gas is predominantly diffusion limited by comparing the partial pressure of the gas at the end of the pulmonary capillary with the alveolar partial pressure. If the gas does not reach diffusion equilibrium (i.e., if the end-capillary partial pressure fails to reach the alveolar partial pressure), then transport is predominantly diffusion limited. However, if the gas does reach diffusion equilibrium, then its transport is perfusion limited, as discussed next. (See Note: Assumptions Underlying Figure 30-5D)
Perfusion normally limits the uptake of nitrous oxide from alveolar air to blood
Unlike CO, nitrous oxide (“laughing gas,” N2O) does not bind to Hb. Therefore, when a subject inhales N2O, the gas enters the blood plasma and the red blood cell cytoplasm but has nowhere else to go (Fig. 30-6A). Consequently, as blood courses down the pulmonary capillary, the concentration of free N2O—and thus capillary PN2O (PcN2O)—rises very rapidly (Fig. 30-6B). By the time the blood is ~10% of the way along the capillary, PcN2O has reached alveolar PN2O (PAN2O), and N2O is thus in diffusion equilibrium between alveolus and blood. The reason N2O reaches diffusion equilibrium—whereas CO does not—is not that its DLN2O is particularly high or that we chose a high inspired PN2O. The key difference is that Hb does not bind to N2O.
Figure 30-6 Diffusion of N2O. In B, PAN2O is alveolar PN2O and PcN2O is capillary PN2O. In C, the blood flow has a relative value of 1. In D, the diffusing capacity DL has a relative value of 1. The N2O content at the end of the capillary is proportional to PN2O.
How does N2O uptake by the lungs depend on DLN2O and ? If we assume that the N2O content of the mixed-venous blood entering the pulmonary capillary (CN2O) is 0:
Cc′N2O is the N2O content of the blood at the end of the pulmonary capillary and represents entirely N2O physically dissolved in blood, which according to Henry’s law (see Chapter 26 for the box on that topic) is proportional to PcN2O. The overall N2O computed from the Fick principle in Equation 30-21 is the sum of individual diffusion events along the capillary:
Because N2O reached diffusion equilibrium at ~10% of the way down the capillary (i.e., PcN2O = PAN2O), the individual diffusion terms in Equation 30-22 equate to 0 for the distal 90% of the capillary!
We can approach the uptake of N2O in the same way we did the uptake of CO. We begin, under basal conditions, with relative values of 1 for DLN2O, , and end-capillary N2O content. Thus, the initial N2O is × Cc′N2O = 1.
Figure 30-6C shows that doubling of DLN2O doubles the flow of N2O into the blood for each diffusion event, causing PCN2O to rise twice as steeply as before along the capillary. However, even though this doubling of DLN2O causes N2O to come into diffusion equilibrium twice as fast as before, it has no effect on either the N2O content of end-capillary blood or N2O, both of which remain at 1. Cutting DLN2O in half also would have no effect on N2O. Thus, N2O uptake is insensitive to changes in DLN2O at least over the range of values that we examined (Table 30-2, upper half). In other words, the uptake of N2O is not diffusion limited.
Table 30-2 Alveolar Transport of N2O
What would be the effect of reducing by half while holding DLN2O constant? If we assume that capillary dimensions remain constant, then halving of would double the contact time of blood with the alveolus and make the PCN2O trajectory along the capillary twice as steep as before (Fig. 30-6D). Nevertheless Cc′N2O remains unchanged at 1. However, because we reduced by half, N2O also falls by half. Conversely, doubling of causes N2O to double. Thus, N2O uptake is more or less proportional to blood flow (i.e., perfusion) over a wide range of values (Table 30-2, lower half). For this reason, we say that N2O transport is predominantly perfusion limited. The transport of a gas is predominantly perfusion limited if the gas in the capillary comes into equilibrium with the gas in the alveolar air by the end of the capillary.
In principle, CO transport could become perfusion limited and N2O could become diffusion limited under special conditions
Although normally CO transport is diffusion limited and N2O transport is perfusion limited, changes in certain parameters could, at least in theory, make CO uptake perfusion limited or make N2O uptake diffusion limited. To illustrate, we introduce an analogy (Fig. 30-7): workers at a railroad siding trying to load boxes (transport gas at a rate ) onto the cars of a passing train. Each worker (the diffusive event) has a limited rate for putting boxes on the train, and the total rate is the sum for all the workers (DL). Each railway car (the red blood cell) has a limited capacity for holding boxes, and the total capacity is the sum for all cars (Hb concentration). Finally, because the train is moving (the perfusion rate, ), a limited time is available to load each railway car.
Figure 30-7 Railway car analogy. Workers represent the diffusion of O2 across the alveolar wall. Railway cars represent capacity of blood to carry O2. The speed of the train represents blood flow.
First imagine that the speed of the train perfectly matches the number of workers (Fig. 30-7A). Thus, all workers are always fully occupied, and the railway cars depart the siding fully loaded; the last box is put on each car just as the car leaves the siding. Any decrease in worker number, any increase in the carrying capacity of each car, or any increase in train speed causes the railway cars to leave the siding at least partially empty. Thus, if we fix train speed at “normal,” a decrease in the number of workers below “normal” (Fig. 30-7B) would cause a proportional decrease in the shipping rate—the number of boxes the train carries away per hour. In other words, when the number of workers is between 0 and normal, the shipping rate is worker (diffusion) limited.
Now return to the original “perfect-match” condition in which both worker number and train speed are normal. An increase in the worker number at constant train speed has no effect on either the number of boxes loaded onto each railway car (which remain filled to capacity) or the shipping rate (Fig. 30-7C). In this higher range of worker number, the shipping rate is no longer limited by the workers but by the speed of the train or by the carrying capacity of the railway cars. Thus, we could say that the shipping rate is speed (perfusion) limited, although it would be equally true to say that it is carrying capacity (Hb) limited.
Let us return again to the original condition in which worker number perfectly matches train speed. An increase in the train speed while the worker number is fixed at the normal value causes railway cars to leave the siding partially empty (Fig. 30-7D). However, shipping rate is unaffected because the normal number of boxes is simply distributed over a greater number of cars. Under these conditions, shipping rate is again worker (diffusion) limited because the increase in the number of workers would proportionally increase shipping rate. In fact, whenever you see cars leaving the siding only partially filled, you can conclude that shipping rate is worker (diffusion) limited, regardless of whether this situation arose because of a decrease in worker number, an increase in train speed, or an increase in car carrying capacity.
Finally, let us again return to the perfectly matched initial condition and now decrease train speed while holding worker number fixed at the normal value. As velocity decreases below normal, shipping rate decreases proportionally (Fig. 30-7E), even though the railway cars leave the siding fully loaded. Thus, shipping rate is speed (perfusion) limited. It would be equally true to characterize the system as being limited by carrying capacity (Hb). In fact, whenever you see cars leaving the siding fully filled, you can conclude that shipping rate is speed (perfusion) limited, regardless of whether this situation arose because of an increase in worker number, a decrease in train speed, or a decrease in car carrying capacity.
The reader is now in a position to consider factors that could render CO transport predominantly perfusion limited or N2O transport diffusion limited. Several changes to the system would cause CO transport to be no longer limited by DLCO. Conversely, several other changes would cause the transport of N2O to be no longer limited by . (See Note: Making CO Uptake Perfusion Limited, or Making N2O Uptake Diffusion Limited)
The uptake of carbon monoxide provides an estimate of DL
Because the pulmonary diffusing capacity plays such an important role in determining the partial pressure profile of a gas along the pulmonary capillary, being able to measure DL would be valuable. Moreover, an approach that is easily applicable to patients could be useful both as a diagnostic tool and to follow the progression of diseases affecting DL.
We have already seen (Equation 30-9) that we can use Fick’s law to compute the overall uptake of a gas if we summate many individual diffusion events for all pieces of alveolar wall and all times in the respiratory cycle:
If we could ignore spatial and temporal nonuniformities, then we could eliminate the two troublesome Σ symbols and compute an overall Dlgas from the overall gas. We could accommodate modest spatial and temporal variations in PAgas by computing an average alveolar partial pressure (Agas). Furthermore, if the partial pressure profile of the gas along the capillary were linear, we could use an average capillary partial pressure (cgas) as well. If we could identify a gas for which these assumptions are reasonable, we could simplify Equation 30-23 to an expression that is similar to the version of Fick’s law with which we started this chapter (Equation 30-7):
Which gas could we use to estimate DL? We certainly do not want to use N2O, whose uptake is perfusion limited. After all, N2O is more or less proportional to changes in but virtually insensitive to changes in DL (Table 30-2). Viewed differently, the driving pressure between alveolus and capillary (PAN2O − PCN2O) is high at the beginning of the capillary but soon falls to zero (Fig. 30-6B). Thus, it would be very difficult to pick a reasonable value for the average capillary PN2O to insert into Equation 30-24. However, CO is an excellent choice because its uptake is diffusion limited, so that changes in the parameter of interest (i.e., DL) have nearly a proportionate effect on CO. Viewed differently, the driving pressure between alveolus and capillary (PACO − PcCO) is nearly ideal because it falls more or less linearly as blood courses down the pulmonary capillary (Fig. 30-5B). Thus, we might solve Equation 30-24 for DLCO:
Note that DLCO and CO are average values that reflect properties of all alveoli throughout both lungs at all times in the respiratory cycle. ACO reflects minor changes during the respiratory cycle as well as more substantial variations in PACO from alveolus to alveolus due to local differences in ventilation and perfusion (see Chapter 31). Finally, cCO reflects not only the small increase in PcCO as blood flows down the capillary but also any CO that may be present in the mixed-venous blood that enters the pulmonary capillary. For nonsmokers who live in a nonpolluted environment, PCO is nearly zero and thus we often can ignore cCO.
We will discuss two general methods for estimation of DLCO, the steady-state technique and the single-breath test. These tests, both using CO, are useful for estimation of pulmonary diffusing capacity in a clinical setting, even among very ill patients in the intensive care unit.
In the steady-state technique (Fig. 30-8), the subject breathes a low CO/air mixture (e.g., 0.1% to 0.2%) for approximately a dozen breaths to allow PACO to stabilize. Calculation of DLCO requires at least two measurements: COand ACO. We compute the rate of CO uptake from the difference between the amounts of CO in inspired air versus expired air over time. We can directly measure ACO in an alveolar air sample (see Chapter 31). DL is then CO/ACO. If the subject happens to be a smoker or to live in a polluted environment, an accurate measurement of DL requires a venous blood sample to estimate the mixed-venous PCO. In this case, we calculate DL from the more complete expression in Equation 30-25.
Figure 30-8 Steady-state method for estimating DLCO.
In the single-breath technique (Fig. 30-9), the subject makes a maximal expiratory effort to residual volume (see Chapter 27) and then makes a maximal inspiration of air containing CO and holds the breath for 10 seconds. The inhaled air is a mixture of dilute CO (e.g., 0.3%) plus a gas such as helium, which has a low water solubility and thus a negligible transport across the blood-gas barrier (see Equation 30-5). We can use helium to compute the extent to which the inhaled CO/He mixture becomes diluted as it first enters the alveoli and also to calculate the alveolar volume into which the CO/He mixture distributes (see Chapter 27). This information allows us to calculate two crucial parameters at the beginning of the breath-holding period: (1) PACO and (2) the amount of CO in the alveoli. During the 10 seconds of breath-holding, some of the inhaled CO diffuses into the blood. The greater the DLCO, the greater the diffusion of CO, and the more PACO falls. As the subject exhales, we obtain a sample of alveolar air and use it to determine two crucial parameters at the end of the breath-holding period: (1) PACO and (2) the amount of CO in the alveoli. The initial and final PACO values allow us to compute ACO. The initial and final alveolar CO amounts allow us to compute CO during the 10-second breath-holding period.
Figure 30-9 Single-breath method for estimating DLCO.
Bear in mind that the value of DLCO determined by use of either of these methods is an average pulmonary diffusing capacity. As discussed in Chapter 31, pulmonary disease can cause ventilation to become nonuniform, making it difficult to obtain alveolar air samples that are representative of the entire lung. A normal value for DLCO is ~25 mL CO taken up per minute for each millimeter of mercury of partial pressure driving CO diffusion and for each milliliter of blood having a normal Hb content. This value of DLCO depends not only on DM (i.e., the “membrane” or truly diffusive component of DL) in Equation 30-15 but also on θ·Vc. For CO transport, DM and θ·Vc are each ~50 mL CO/(min·mL blood): (See Note: Effect of Nonuniformity of Ventilation on Alveolar Air Samples)
Thus, 1/(θ·Vc) makes a major contribution to the final DLCO. Because Vc is proportional to the Hb content of the blood, and because Hb content is decreased in anemia, a subject can have a reduced DLCO even though the diffusion pathways in the lung (i.e., DM) are perfectly normal. Recall that 1/(θ·Vc) makes an insignificant contribution to the DL for O2. Nevertheless, it is the DL for CO—and not that for O2—that one uses for a clinical index of diffusing capacity. Table 30-3 summarizes several factors that can affect the calculated DLCO.
Table 30-3 Factors That Affect the Diffusing Capacity for CO
↑Size → ↑DLCO
With ↑ in lung size, diffusion area (A) and volume of pulmonary capillary blood (Vc) both ↑.
↑Age → ↓DLCO
DLCO decreases by ~2% per year after the age of 20 years.
Male → ↑DLCO
Corrected for age and body size, DLCO is about 10% greater in men than in women.
↑Volume → ↑DLCO
In an individual, ↑ in lung volume causes an ↑ in volume of pulmonary capillary blood (Vc), an ↑ in diffusion area (A), and a ↓ in diffusion distance (a).
Exercise → ↑DLCO
An ↑ in causes dilation of pulmonary capillaries, which in turn causes an ↑ in area for diffusion (A) and volume of pulmonary capillary blood (Vc).
DLCO: supine > sitting > standing
Changes in posture presumably ↑ volume of pulmonary capillary blood (Vc).
O2 lowers the rate at which CO combines with hemoglobin.
CO2 causes an ↑ in volume of pulmonary capillary blood (Vc).
DLCO, diffusion capacity of CO; PAO2, partial pressure of O2 in alveolar blood; PACO2, partial pressure CO2 in alveolar air. (See Note: Capillary Reserve in Renal Glomerulus)
For both O2 and CO2, transport is normally perfusion limited
Uptake of O2 Blood enters the pulmonary capillaries (Fig. 30-10A) with the PO2 of mixed-venous blood, typically 40 mm Hg. Capillary PO2 reaches the alveolar PO2 of ~100 mm Hg about one third of the way along the capillary (Fig. 30-10B, black curve). This PO2 profile along the pulmonary capillary is intermediate between that of CO in Figure 30-5B (where CO fails to reach diffusion equilibrium) and N2O in Figure 30-6B (where N2O reaches diffusion equilibrium ~10% of the way along the capillary). The transport of O2 is similar to that of CO in that both molecules bind to Hb. Why, then, does O2 reach diffusion equilibrium, whereas CO does not?
Figure 30-10 Diffusion of O2. In A, as the red blood cell (RBC) enters the capillary, O2 occupies three of the four sites on hemoglobin. In B-D, PAO2 is alveolar PO2. In B and D, is constant.
The uptake of O2 differs from that of CO in three important respects. First, Hb that enters the pulmonary capillary is already heavily preloaded with O2. Because Hb in the mixed-venous blood is ~75% saturated with O2 (see Chapter 29)—versus ~0% for CO—the available O2-binding capacity of Hb is relatively low. Second, because the alveolar PO2 is rather high (i.e., ~100 mm Hg)—versus <1 mm Hg for CO—the alveolar blood PO2 gradient is large (i.e., ~60 mm Hg) and the initial rate of O2 diffusion from the alveolus into pulmonary capillary blood is immense. Third, DL for O2 is higher than that for CO owing to a greater θ·Vc. As a result of these three factors, Hb in pulmonary capillary blood rapidly approaches its equilibrium carrying capacity for O2 along the first third of the capillary. Because capillary PO2reaches alveolar PO2, O2 transport is perfusion limited, as is the case for N2O. Because O2 normally reaches diffusion equilibrium so soon along the capillary, the lung has a tremendous DL reserve for O2 uptake. Even if we reduce DLO2 by half, O2 still reaches diffusion equilibrium about two thirds of the way along the capillary (Fig. 30-10B, blue curve). If we could double DLO2, O2 would reach diffusion equilibrium much earlier than usual (Fig. 30-10B, red curve). However, neither change in DLO2 would affect O2 uptake, which is not diffusion limited. (See Note: Effect of CO2 on the Diffusing Capacity (DL))
The DL reserve for O2 uptake is extremely important during exercise, when cardiac output can increase by up to a factor of 5 (see Chapter 17), substantially decreasing the contact time of the blood with the pulmonary capillaries. The contact time appears not to decrease by more than a factor of ~3, probably because the slightly increased pressure recruits and distends the pulmonary vessels (see Chapter 31). As a result, even with vigorous exercise, PCO2reaches virtual equilibrium with the alveolar air by the end of the capillary (Fig. 30-10C, green curve)—except in some elite athletes. Thus, the increase in during exercise leads to a corresponding increase in O2, which carries obvious survival benefits. In patients with pulmonary disease, thickening of the alveolar blood-gas barrier can reduce DLO2 sufficiently that equilibration of PO2 fails to occur by capillary’s end during exercise (Fig. 30-10C, brown curve). In this case, O2 transport becomes diffusion limited. (See Note: Exercise-Induced Arterial Hypoxemia in Females)
Like exercise, high altitude stretches out the PO2 profile along the capillary (Fig. 30-10D, red curve). At altitude, barometric pressure and ambient PO2 decrease proportionally (see Chapter 61), leading to a fall in alveolar PO2. Because of O2 extraction by the systemic tissues, PO2 also is lower in the mixed-venous blood entering the pulmonary capillaries. This lower PO2 has two consequences. First, the alveolar capillary PO2 gradient at the beginning of the capillary is low, reducing the absolute O2 transport rate. Second, because at altitude the mixed-venous PO2 is lower, we now operate on a steeper part of the Hb-O2dissociation curve (see Fig. 29-3). Thus, a given increment in the O2content of the pulmonary capillary blood causes a smaller increase in PO2.
The combination of exercise and high altitude can cause O2 transport to become diffusion limited even in healthy individuals (Fig. 30-10D, green curve). If the subject also has a pathological condition that lowers DLO2, then transport may become diffusion limited even more readily at altitude. Obviously, any combination of exercise, high altitude, and reduced DLO2 compounds the problems for O2 transport.
Escape of CO2 Mixed-venous blood entering the pulmonary capillary has a PCO2 of ~46 mm Hg, whereas the alveolar PCO2 is ~40 mm Hg (Fig. 30-11A). Thus, CO2 diffuses in the opposite direction of O2—from blood to alveolus—and PCO2 falls along the pulmonary capillary (Fig. 30-11B, black curve), reaching diffusion equilibrium. Compared with O2, one factor that tends to speed CO2 equilibration is that the DL for CO2 is 3-fold to 5-fold greater than that for O2. However, two factors tend to slow the equilibration of CO2. First, the initial PCO2 gradient across the blood-gas barrier is only ~6 mm Hg at the beginning of the capillary, ~10% as large as the initial PO2 gradient. Second, in their physiological ranges, the CO2 dissociation curve (see Fig. 29-10) is far steeper than the Hb-O2 dissociation curve (see Fig. 29-3). Thus, a decrement in the CO2 content of the pulmonary capillary blood causes a relatively small decrease in PCO2. Thus, a smaller gradient and a steeper dissociation curve counteract the larger DL. Many authors believe that as indicated by the black curve in Figure 30-11B, capillary PCO2 reaches alveolar PCO2 about one third of the way along the pulmonary capillary (as is the case for O2). Others have suggested that CO2 equilibration is slower, occurring just before the end of the pulmonary capillary. In either case, a decrease in DL in certain lung diseases (see next section) or heavy exercise (Fig. 30-11B, red and blue curves) may cause the transport of CO2 to become diffusion limited.
Figure 30-11 Diffusion of CO2. In B, PACO2 is alveolar PCO2.
Pathological changes that reduce DL do not necessarily produce hypoxia
The measured pulmonary diffusing capacity for CO falls in disease states accompanied by a thickening of the alveolar blood-gas barrier, a reduction in the surface area (i.e., capillaries) available for diffusion, or a decrease in the amount of Hb in the pulmonary capillaries. Examples of pathological processes accompanied by a decrease in DL include the following:
Diffuse interstitial pulmonary fibrosis, which is a fibrotic process causing a thickening of the interstitium, thickening of alveolar walls, and destruction of capillaries—sometimes with marked decreases in DL. In some cases, the cause is unknown (i.e., idiopathic); in others, it is secondary to such disorders as sarcoidosis, scleroderma, and exposure to occupational agents (e.g., asbestos).
Chronic obstructive pulmonary disease (COPD), which not only increases the resistance of conducting airways but can lead to a destruction of pulmonary capillaries and thus a reduction in both (1) surface area available for diffusion and (2) total pulmonary capillary Hb content (see Chapter 27)
Loss of functional lung tissue, as caused by either a tumor or surgery. Surgical removal of lung tissue reduces DL because of a decrease in both (1) surface area and (2) total pulmonary capillary Hb content.
Anemia, in which the fall in total Hb content decreases the θ·Vc component of DLCO.
Although pulmonary diseases can cause both a decrease in DL and hypoxemia (i.e., a decrease in arterial PO2), it is not necessarily true that the decrease in DL is the sole or even the major cause of the hypoxemia. The same diseases that lower DL also upset the distribution of ventilation and perfusion throughout the lung. As discussed in Chapter 31, mismatching of ventilation to perfusion among various regions of the lungs can be a powerful influence leading to hypoxemia. Furthermore, because the lung has a sizeable DL reserve for O2 (and perhaps for CO2 as well), DL would have to decrease to about one third of its normal value for O2 transport to become diffusion limited. Thus, in a disease causing both a decrease in DL and disturbances in the distribution of ventilation and perfusion, it is difficult to determine the extent to which an accompanying reduction of DL is responsible for the resulting hypoxemia.
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