Reciprocal Relationship between Alveolar Carbon Dioxide Pressure and Alveolar Oxygen Pressure Breathing Room Air

The V˙A/Q˙C line in Figure 12-3 is drawn as though the mixed venous blood gas composition does not change as V˙A/Q˙C changes. Although this statement is essentially true if the V˙/Q˙ of only one alveolus changes, it is not true if the collective V˙/Q˙ of all alveoli uniformly change. Chapter 4 explains that V˙A and P_ACO₂ are reciprocally related. For example, if V˙A decreases to half normal, P_ACO₂ increases from 40 mm Hg to 80 mm Hg. The corresponding P_AO₂ while breathing room air can be calculated with the alveolar air equation (see Chapter 7), yielding the following result:

PAO2=0.21(713)−80(1.2)PAO2=53.7or54mm Hg

Thus, the decrease in P_AO₂ is about the same as the increase in P_ACO₂ in uniform alveolar hypoventilation with room air (i.e., P_ACO₂ and P_AO₂ are reciprocally related).

This reciprocal relationship is not shown on the oxygen–carbon dioxide diagram in Figure 12-3 because this diagram represents a hypothetical change in the V˙/Q˙ of one alveolus out of millions of alveoli; a V˙/Q˙ change in one alveolus would not affect mixed venous blood composition. (The P_AO₂ of 54 mm Hg and P_ACO₂ of 80 mm Hg in the example do not define a point on the V˙/Q˙ curve.) In reality, mixed venous blood gases do change when the entire lung hypoventilates. For example, if all 300 million alveoli uniformly hypoventilate, the average P_ACO₂ increases, producing an equal increase in the average end-capillary PCO₂. As a result, arterial PCO₂ increases. When this arterial blood with an increased PCO₂ passes through tissue capillaries, tissue PCO₂ builds up until a diffusion gradient from tissues to blood is created; this increases mixed venous PCO₂. By increasing P_ACO₂, overall hypoventilation ultimately also increases the mixed venous PCO₂. The end result is a new P_ACO₂-P_AO₂ combination, identifying a point on a new V˙A/Q˙C line in the oxygen–carbon dioxide diagram. The important point illustrated by Figure 12-3 is that the gas composition of any alveolus is determined by its incoming venous gas composition and V˙/Q˙ ratio.

Normal Alveolar-Arterial Oxygen Pressure Difference

To understand how the lung’s normal V˙A/Q˙C imbalances contribute to the normal P(A-a)O₂, one must understand what determines alveolar and arterial oxygen compositions. (Recall from Chapter 1 that another source of the normal P(A-a)O₂ is anatomical shunting, in which bronchial venous blood mixes with freshly oxygenated pulmonary venous blood.) Arterial blood is a mixture of the end-capillary blood from all V˙A/Q˙C regions in the lungs. Alveolar gas, collected at the end of a tidal exhalation, is a mixture of alveolar gases from these same differing V˙A/Q˙C regions. Although alveolar gas is in equilibrium with end-capillary blood, the average P_AO₂ is not the same as the average end-capillary blood PO₂. The oxygen-hemoglobin equilibrium curve illustrates this point (Figure 12-5). For the sake of simplicity, this illustration assumes that equal volumes of end-capillary blood from apical and basal lung regions mix to form arterial blood. (This is not actually true because the lung’s bases receive more blood flow than the apices.) PaO₂ is not determined by an average of the mixed end-capillary PO₂ values; instead, PaO₂ is determined by an average of the mixed end-capillary oxygen contents.

For example, let us assume in Figure 12-5 that 100 mL of end-capillary blood from the lung apex is mixed with 100 mL of end-capillary blood from the lung base. Blood from the apex has a PO₂ equal to 130 mm Hg and an oxygen saturation (SaO₂) of 100%. Blood from the base has a PO₂ of 85 mm Hg and an SaO₂ of about 94%. With a hemoglobin concentration of 15 g/dL, the oxygen content in 100 mL of apical blood is as follows:

(15×1.34×1.0)+(130×0.003)=20.5mL

The oxygen content in 100 mL of basal blood is as follows:

(15×1.34×0.94)+(85×0.003)=19.1mL

Mixing these two samples produces 200 mL of blood containing 39.6 mL of oxygen, or 19.8 mL of oxygen per 100 mL of blood (19.8 mL/dL), corresponding to about 97% saturation on the oxyhemoglobin equilibrium curve (see Figure 12-5). This mixture produces a PaO₂ of about 96 to 97 mm Hg, which is obviously not the average of apical and basal PO₂ values. High V˙A/Q˙C apical units cannot negate the desaturating effect that low V˙A/Q˙C basal units have on mixed end-capillary blood. The desaturating effects of basal alveolar units are even more pronounced than illustrated in this example because basal regions actually receive more blood flow and contribute proportionally more to the arterial blood.

In contrast, mixed expired alveolar gas PO₂ is simply the average of the PO₂ values from all of the differing V˙A/Q˙C regions in the lungs because no hemoglobin is involved. In the example just discussed, the average P_AO₂ is (130 + 85)/2 = 108 mm Hg, producing a P(A-a)O₂ of 12 mm Hg (P_AO₂ of 108 mm Hg − PaO₂ of 96 mm Hg). The differing V˙A/Q˙C ratios in the lung create a normal P(A-a)O₂ of approximately 7 to 14 mm Hg, if room air is breathed (F_IO₂ = 0.21).³ Severely diseased lungs have many abnormally low V˙A/Q˙C regions; in such instances, the P(A-a)O₂ is even higher.

Why Alveolar-Arterial Oxygen Pressure Difference Increases When Fractional Concentration of Oxygen in Inspired Gas Increases

P(A-a)O₂ increases from about 10 mm Hg when room air is breathed to greater than 50 mm Hg when 100% oxygen is breathed. The shape of the oxygen-hemoglobin equilibrium curve helps explain this phenomenon. Figure 12-6 shows the oxygen-hemoglobin curve extended to a PO₂ of 663 mm Hg, which compresses the sigmoid shape of the curve into the extreme left side of the diagram. At PO₂ values between 100 mm Hg and 663 mm Hg, the curve is practically flat because the hemoglobin is essentially saturated to capacity between these two points; the small increase in oxygen content is due to increased dissolved oxygen. The diagram of the lung indicates a small, normal amount of shunt—about 2% to 5% of the cardiac output does not perfuse ventilated alveoli. This shunted blood is venous in composition (PO₂ = 40 mm Hg; saturation = 75%; oxygen content = 15 mL/dL). Figure 12-6 shows the effects of adding this small, fixed amount of desaturated venous blood to arterial blood when 100% oxygen is breathed (P_AO₂ = 663 mm Hg, lower right of the graph) and while room air is breathed (P_AO₂ = 100 mm Hg, lower left of the graph). Because the amount of shunted blood is fixed, the same decrease in arterial oxygen content occurs whether room air or 100% oxygen is breathed. For the sake of illustration, let us assume this reduction in arterial oxygen content is 0.5 mL/dL in both instances (see Figure 12-6). As shown, this 0.5-mL/dL decrease produces a much greater decrease in PaO₂ when 100% oxygen compared to 21% oxygen is breathed because of the flatness of the curve at high PO₂ values. The breathing of 100% oxygen increases the P(A-a)O₂, not because it somehow impairs gas transfer from the alveolus to the blood, but simply because of the unique way hemoglobin binds to O₂ molecules.

Abnormal Gas Exchange

The small imbalance normally present between ventilation and perfusion is greatly exaggerated in various diseases affecting the lung. Low V˙A/Q˙C ratios produce hypoxemia. Carbon dioxide elimination may also be hindered, but the effect on oxygenation is usually much greater, as discussed later. The major V˙A/Q˙C imbalance mechanisms causing hypoxemia are (1) overall hypoventilation, (2) absolute shunt, and (3) V˙A/Q˙C mismatch. By convention, the term V˙A/Q˙C mismatch generally refers to a low V˙A/Q˙C ratio (<0.8). From this point on in this chapter, V˙A/Q˙C mismatch means a low V˙A/Q˙C ratio.

Hypoventilation

Overall hypoventilation increases P_ACO₂; P_AO₂ consequently decreases in a reciprocal fashion (Figure 12-7, A). This kind of hypoxemia points to a ventilation problem, not an oxygen transfer problem; in other words, if ventilation is restored to normal, hypoxemia resolves. Figure 12-7 shows that the P(A-a)O₂ is within normal limits when either room air or 30% oxygen is breathed, indicating normal oxygen transfer across the lung. (PaO₂ is less than PO₂ of the blood in either capillary in Figure 12-7 because a normal shunt of 2% to 5% [not illustrated] decreases arterial oxygen content and PO₂.) Causes of general hypoventilation include muscle paralysis or weakness and drug-induced respiratory center depression (Table 12-1).

TABLE 12-1

Respiratory Causes of a Low Arterial PO₂

Cause	Mechanism	P(A-a)O2	PaO2 Response to Oxygen	Examples
Hypoventilation	Decreased V˙A; increased PACO2	Normal	Good response	Drug overdoseMuscle paralysis
Shunt (intrapulmonary)	Venous blood mixing with arterial blood (venous admixture)	Increased	Extremely poor response	AtelectasisPneumonia
Ventilation-perfusion mismatch	Underoxygenated blood mixing with arterial blood (venous admixture)	Increased	Good response	Partial airway obstruction: asthma, obstructive lung diseases
				Nonuniform distribution of compliance

The logical corrective treatment for patients experiencing general hypoventilation and hypoxemia involves therapy that increases ventilation. At the extreme, intubation and mechanical ventilation may be needed. Hypoventilation-induced hypoxemia can be corrected with oxygen therapy (see Figure 12-7, B), but oxygen therapy does not correct the underlying cause of hypoxemia.

CONCEPT QUESTION 12-6

Why is P(A-a)O₂ essentially normal in overall hypoventilation?

Absolute Shunt

Absolute shunt occurs when deoxygenated mixed venous blood bypasses ventilated alveoli and mixes directly with oxygenated, ventilated arterial blood. For this reason, shunting is often called venous admixture. In absolute shunt, blood moves from the right, or venous, side of the circulation to the left, or arterial, side of the circulation without contacting alveolar gas; thus, shunts that produce arterial hypoxemia are called right-to-left shunts.

Right-to-left shunting occurs in three different conditions, two of which are anatomical shunts. Anatomical shunting occurs when mixed venous blood flows through a normal or abnormal anatomical channel, physically bypassing the alveoli and mixing with arterial blood. An example of a normal anatomical shunt is the bronchial systemic veins (carrying deoxygenated blood) emptying directly into the pulmonary veins (carrying freshly oxygenated blood). An abnormal anatomical shunt occurs in the heart if the septum separating the right and left ventricles has a large hole (ventricular septal defect), allowing deoxygenated right ventricular blood to mix with oxygenated left ventricular blood.

Physiological, or intrapulmonary, shunting occurs when mixed venous blood flows through the pulmonary capillaries of airless, unventilated alveoli (Figure 12-8, A). Venous blood does not physically bypass the lung, but the effect is the same; shunted blood can neither take up oxygen nor release carbon dioxide (i.e., the blood remains venous in composition). Any abnormal process that prevents alveolar ventilation produces physiological shunt (see Table 12-1). Examples include alveolar filling processes, such as pneumonia or pulmonary edema, and processes causing alveolar collapse, such as pulmonary surfactant abnormalities, pneumothorax, and major bronchial occlusion.

An increase in the percentage of oxygen (the gas) breathed by patients with shunting disease does little to improve arterial oxygenation because shunted venous blood cannot contact inspired gas (see Figure 12-8, B). Thus, the hallmark of intrapulmonary shunting is hypoxemia that responds poorly to oxygen therapy (refractory hypoxemia). An increase in F_IO₂ can increase the PO₂ of only ventilated alveoli, but this adds little oxygen to the already saturated blood of these alveolar capillaries. (Compare capillary blood saturations in Figure 12-8, A and B.) Even increasing the F_IO₂ to 1.0 does not improve PaO₂ significantly because arterial oxygen content (CaO₂) or saturation

CLINICAL FOCUS 12-1   Hypoventilation as a Cause of Hypoxemia

A 61-year-old man with known myasthenia gravis (a disorder that causes muscular weakness and may reduce ventilatory capacity) was brought to the emergency department. The patient stated that he has become progressively weaker and short of breath. You obtain arterial blood gases and measure the vital capacity and maximum inspiratory force.

Arterial blood gas values (on room air; barometric pressure = 760 mm Hg) are as follows:

PaO₂ = 59 mm Hg

PaCO₂ = 63 mm Hg

pH = 7.22

HCO₃⁻ = 25 mEq/L

Vital capacity and maximum inspiratory force are below normal. From a previous hospitalization that year, you know his normal room air arterial blood gas values are as follows:

PaO₂ = 80 mm Hg

PaCO₂ = 40 mm Hg

pH = 7.39

HCO₃⁻ = 24 mEq/L

What is the reason for this patient’s hypoxemia? Is he having greater oxygen-transfer (lung to blood) problems compared with earlier normal blood gas values?

Discussion

This man is experiencing an acute respiratory acidosis (i.e., he is hypoventilating). PaCO₂ has increased about 23 mm Hg above his normal, stable value, and PaO₂ has decreased by about 21 mm Hg. This reciprocal relationship between PaCO₂ and PaO₂ indicates that the observed hypoxemia is a consequence of hypoventilation. If ventilation were restored to normal, the hypoxemia would be resolved. Is there a worsening oxygen-transfer problem? P(A-a)O₂ is a good indicator of oxygen-transfer efficiency. Using the alveolar air equation, calculate the P(A-a)O₂ for the stable, normal arterial blood gas values:

PAO2=FIO2(PB−47)−PaCO2×1.2PAO2=0.21(713)−40×1.2PAO2=102mm HgP(A−a)O2=102−80=22mm Hg

Calculate the P(A-a)O₂ for the current arterial blood gas values:

PAO2=0.21(713)−63×1.2PAO2=74mm HgP(A–a)O2=74−59=15mm Hg

Oxygen-transfer efficiency did not worsen. The origin of hypoxemia is hypoventilation. This is primarily a ventilation problem, not an oxygenation problem.

is determined by the mixed oxygen saturations of end-capillary blood. The resulting arterial oxygen saturation determines PaO₂ (see earlier discussion regarding Figure 12-5). The difference between P_AO₂ and PaO₂ values is increased in absolute shunt when either room air or 100% oxygen is breathed (see Figure 12-8). This alveolar-arterial difference indicates impaired oxygen transfer across the lung. The magnitude of P(A-a)O₂ is an indicator of the severity of shunt.

CONCEPT QUESTION 12-7

What is the basic defect of a disease that causes intrapulmonary shunting?

In Figure 12-8, PaCO₂ remains normal, around 40 mm Hg because arterial hypoxemia sensitizes the peripheral chemoreceptors, increasing the ventilation of normal alveoli such that the PCO₂ of their capillary blood is decreased to 35 mm Hg; this balances the PCO₂ of 45 mm Hg in the blood coming from the shunt unit, producing a final normal PaCO₂ of 40 mm Hg. Such an increase in ventilation of the normal alveoli cannot similarly create a normal PaO₂.¹ This phenomenon is explained later in this chapter.

The corrective treatment for intrapulmonary shunting is to restore ventilation to the airless alveoli. This procedure may involve special mechanical ventilatory support techniques that prevent alveolar pressure from decreasing to atmospheric pressure, even during expiration. These techniques include positive end expiratory pressure (PEEP) and continuous positive airway pressure (CPAP). If alveolar collapse is caused by pneumothorax, treatment may involve inserting a chest tube into the intrapleural space to evacuate pleural air and reexpand the lung.

Ventilation-Perfusion Mismatch

V˙A/Q˙C mismatch (V˙A/Q˙C <1 but >0) is the most common cause of hypoxemia.² Low V˙A/Q˙C ratios are sometimes called relative shunt because they produce a shuntlike effect. In other words, they produce hypoxemia and increase the P(A-a)O₂. As discussed previously, normal lungs have a small degree of V˙A/Q˙C mismatch, producing a normal P(A-a)O₂ gradient. However, this mismatch involves such a small number of alveoli that normal PaO₂ and PaCO₂ can easily be maintained.

Unlike intrapulmonary shunt, blood perfusing low V˙A/Q˙C alveoli is exposed to some ventilation. However, this blood receives inadequate ventilation, producing an increased end-capillary PCO₂ and decreased PO₂ (Figure 12-9, A). In contrast to overall hypoventilation, V˙A/Q˙C mismatch is a localized regional hypoventilation and does not usually produce an increased PaCO₂ (see Figure 12-9, A). V˙A/Q˙C mismatch must be quite extensive throughout the lungs before hypercapnia occurs (e.g., severe chronic obstructive pulmonary disease [COPD]). In most conditions involving V˙A/Q˙C mismatch, normally

CLINICAL FOCUS 12-2   Treating Hypoxemia Caused by Intrapulmonary Shunt

A 28-year-old man in the intensive care unit is receiving mechanical ventilation. He sustained massive chest trauma in an automobile accident and now has acute respiratory distress syndrome (ARDS). ARDS is characterized by alveolar capillary membrane injury, leading to membrane hyperpermeability. The consequence is pulmonary edema, disruption of pulmonary surfactant, loss of alveolar stability, and widespread atelectasis. This patient’s current arterial blood gas values while breathing 50% oxygen are as follows:

PaO₂ = 45 mm Hg

PaCO₂ = 38 mm Hg

pH = 7.41

SaO₂ = 0.79

You adjust the ventilator to deliver 10 cm H₂O of PEEP. Alveolar pressure cannot decrease below 10 cm H₂O during the expiratory phase of the respiratory cycle. About 1 hour later, while the patient is still breathing 50% oxygen, arterial blood gas values are as follows:

PaO₂ = 65 mm Hg

PaCO₂ = 36 mm Hg

pH = 7.42

SaO₂ = 0.92

What accounts for the fact that PaO₂ increased after PEEP application, although F_IO₂ remained unchanged?

Discussion

ARDS is an example of a shunt-producing disease; pulmonary blood perfuses large numbers of nonventilated, collapsed alveoli and remains unoxygenated as it flows through the lung. The consequence is arterial hypoxemia, which is not very responsive to oxygen therapy; inspired oxygen cannot reach the blood perfusing collapsed alveoli.

By maintaining positive pressure in the airways during expiration, PEEP tends to prevent further alveolar collapse and may reopen already collapsed units. Depending on disease severity, 15 cm H₂O or more of PEEP may be required to reexpand collapsed alveoli. After they are reexpanded, these alveoli can again participate in gas exchange and oxygenate the blood perfusing them. PEEP can prevent or reduce shunting and increase PaO₂. Although F_IO₂ remained at 0.50, PaO₂ improved because previously unoxygenated, shunted blood became oxygenated. In other words, less unoxygenated, shunted blood mixed with oxygenated arterial blood. PEEP and similar techniques are the cornerstone of therapy in diseases characterized by widespread alveolar instability and atelectasis.

ventilated alveoli can easily compensate for the increased PCO₂ of underventilated alveoli and maintain a normal or even low PaCO₂. (Note the increased ventilation of normal units in Figure 12-9; PCO₂ is decreased enough to balance the increased PCO₂ of underventilated units.) The reason increased ventilation cannot do the same for oxygen is explained in detail in the next section.

As with shunting, V˙A/Q˙C mismatch increases the P(A-a)O₂, indicating impaired oxygen transfer across the lung (see Figure 12-9). In contrast to shunting, V˙A/Q˙C mismatch responds well to oxygen therapy because oxygen can enter underventilated units and increase the PO₂ values to near-maximum (see Figure 12-9, B). Blood perfusing these underventilated units is maximally oxygenated, and the effect of venous admixture disappears. As in overall hypoventilation, PaO₂ values in Figure 12-9 are lower than the values derived from averaging the saturations of end-capillary blood. The normal 2% to 5% shunt (which is not illustrated) accounts for this disparity.

Table 12-1 summarizes the mechanisms and effects of overall hypoventilation, absolute shunt, and V˙A/Q˙C mismatch on arterial blood. V˙A/Q˙C mismatch is the most common mechanism causing hypoxemia and is seen in all lung diseases characterized by low V˙/Q˙ ratios. These diseases include not only diseases involving partial airway obstruction but also those involving regional variations in lung compliance. For example, in emphysema and fibrotic lung diseases, compliance of all alveoli is not uniformly abnormal, and ventilation is not uniformly distributed.

CONCEPT QUESTION 12-8

Why do regional variations in lung compliance cause hypoxemia-producing V˙/ Q˙ mismatches?

Variable Effect of Q˙C Imbalance on Carbon Dioxide and Oxygen Exchange

Theoretically, low V˙A/Q˙C ratios (<1 and >0) should cause hypoxemia and hypercapnia. Consider a situation in which carbon dioxide production and oxygen consumption remain constant while overall V˙A/Q˙C decreases; if all other factors remain constant, this causes PaCO₂ to increase and PaO₂ to decrease. However, in the clinical setting, patients who are hypoxic because of V˙A/Q˙C mismatches or shunt often have a normal or low PaCO₂.¹ The reason is not, as some individuals erroneously suppose, that carbon dioxide is more diffusible than oxygen. Rather, when the medullary chemoreceptors sense even a slight increase in PaCO₂, they increase the ventilatory drive¹; this increases the ventilation of normal V˙A/Q˙C units enough to offset the effects of low V˙A/Q˙C units, keeping PaCO₂ in the normal range. A normal PaCO₂ can be maintained in this situation only by increasing total minute ventilation (V˙E) above that which would normally be required. If a low V˙A/Q˙C ratio causes significant hypoxemia, PaCO₂ may actually be lower than normal. That is, hypoxemia sufficient to activate the peripheral chemoreceptors may increase the ventilation of normal V˙A/Q˙C units enough to produce overall hyperventilation and respiratory alkalosis.

How can an increased V˙E effectively decrease PaCO₂ without significantly increasing PaO₂? The differences in the shapes of the carbon dioxide and oxygen equilibrium curves answer this question. Figure 12-10 shows that the carbon dioxide equilibrium curve is almost a straight diagonal line in the physiological range, whereas the oxygen equilibrium curve is almost horizontal. Oxygen or carbon dioxide content is plotted on the vertical axis, and the partial pressure of either gas in arterial blood is plotted on the horizontal axis. The lung model to the right

illustrates low and high V˙A/Q˙C ratios. These V˙A/Q˙C ratios are plotted on both equilibrium curves, showing their respective contents and partial pressures. Point a on each curve represents normal arterial contents and partial pressures. (Low V˙A/Q˙C ratios produce high carbon dioxide contents and PCO₂ values but low oxygen contents and PO₂ values.)

The mixing of equal blood volumes from high and low V˙A/Q˙C units produces a final carbon dioxide content determined by averaging high and low V˙A/Q˙C points, represented by point a on the carbon dioxide curve. (Point a denotes a PCO₂ of about 35 mm Hg.) Using the same method, the averaging of high and low V˙A/Q˙C points on the much flatter oxygen curve (half the vertical distance between these two points) produces a final oxygen content, denoted by point X. The corresponding PO₂ is slightly less than 60 mm Hg, well below the normal arterial point designated by a on the oxygen curve.

The shapes of the oxygen and carbon dioxide equilibrium curves dictate that high V˙A/Q˙C units can effectively decrease the end-capillary carbon dioxide contents and PCO₂ values but cannot significantly increase the end-capillary oxygen contents (i.e., end-capillary oxygen contents are already maximal). Overventilated alveoli can compensate for the increased PCO₂ values produced by underventilated areas, but overventilated alveoli cannot compensate for the decreased PO₂ values of underventilated regions.

If ventilation-perfusion mismatch involves a large number of the lung’s alveoli, as it does in advanced COPD, patients may be unable to increase their overall alveolar ventilation enough to sustain a normal PaCO₂. These patients cannot ventilate their small amount of normal lung tissues enough to compensate for the high PCO₂ values in their diseased lung tissue. Consequently, these patients must adapt to less ventilation and allow PaCO₂ values to increase. Thus, V˙A/Q˙C imbalance is not only the most common cause of hypoxemia but also the most common cause of chronic hypercapnia.

The discussion so far has focused mainly on the effect of low V˙A/Q˙C ratios on gas exchange. It was briefly mentioned that high V˙A/Q˙C ratios are produced in the normal alveoli of lungs with shunt and V˙A/Q˙C mismatch (see Figures 12-8 and 12-9). However, these units do not produce hypoxemia or hypercapnia in the end-capillary blood; instead, they increase P_AO₂ and decrease P_ACO₂ because their ventilation is high with respect to their blood flow. These units constitute relative dead space, or a dead space effect. Overall ventilation must increase in the lung to maintain a normal PaCO₂, which is a hallmark of dead space. In this situation, increased dead space ventilation occurs because ventilation is increased out of proportion to blood flow. Generally, however, dead space–producing diseases are diseases in which reduced blood flow is the primary defect.

Effect of High V˙A/Q˙C on Arterial PCO₂ and Arterial PO₂

Figure 12-11, A, illustrates the effect of cutting off blood flow to one lung while the lung continues to ventilate. Assuming both lungs had originally received equal blood flows, blood is redirected to the normal lung, doubling its flow. If ventilation of the normal lung remains constant, a low V˙A/Q˙C ratio is created (i.e., perfusion increases while ventilation stays the same). Such conditions would produce increased PaCO₂ and decreased PaO₂ (see Figure 12-11, A).

However, ventilation normally does not remain constant when dead space develops. At the same instant PaCO₂ increases, medullary chemoreceptors stimulate an increase in V˙E (see Figure 12-11, B). Ventilation increases as much as necessary to maintain normal PaCO₂. Figure 12-11, B, represents the usual response to alveolar dead space; ventilation of the perfused lung increases to match its increased blood flow, preserving normal blood gases at the expense of greatly increased V˙E and work of breathing.

Arterial hypoxemia is not an inherent feature of dead space disease unless the ability to increase overall ventilation is impaired, as might be the case in patients with severe obstructive lung disease. Also, P_ACO₂ of mixed alveolar gases is decreased because the nonperfused lung has a P_ACO₂ of 0 mm Hg. This situation creates an alveolar-to-arterial carbon dioxide pressure difference (P[a-A]CO₂) which is a diagnostic indicator of increased dead space. Alveolar dead space also creates an increased difference between PaCO₂ and mixed expired PCO₂ (PE¯CO2). This difference is the basis for the Bohr dead space equation explained in Chapter 4. The Bohr equation is used to calculate the dead space-to-tidal volume ratio (V_D/V_T). If V_D/V_T is known and V˙E is measured, V˙A can be calculated.

Physiological Compensatory Responses to Dead Space and Shunt

The lung has two compensatory responses that help restore abnormal V˙A/Q˙C ratios toward normal. Figures 12-8, 12-9, and 12-11 are oversimplified because they do not take these responses into account. In shunt, the decreased PO₂ of blood passing through unventilated alveoli causes localized hypoxic pulmonary vasoconstriction (see Chapter 6). This vasoconstriction redistributes blood flow to well-ventilated alveoli. Poorly ventilated units receive less blood flow, which improves their V˙A/Q˙C ratios and reduces their effect on arterial blood. With regard to alveolar dead space, the low PCO₂ values of alveoli with little or no blood flow cause local alveolar duct constriction, increasing airways resistance and decreasing ventilation in these regions; this helps create a better match between ventilation and blood flow, reducing the adverse blood gas effects of the V˙A/Q˙C imbalance.

Alveolar-Arterial Oxygen Pressure Difference

P(A-a)O₂ has been discussed extensively in earlier sections. P(A-a)O₂, often called the A-a gradient, is probably the best-known index of oxygen-transfer efficiency. In the complete absence of shunt, no difference would exist between P_AO₂ and PaO₂ values (see Figure 12-6); arterial blood would be identical to end-capillary blood of the ventilated alveolus. Thus, an increased P(A-a)O₂ indicates increased physiological shunting. The normal P(A-a)O₂ is about 7 to 14 mm Hg during breathing of room air and 50 to 60 mm Hg when breathing 100% oxygen.³ These normal values increase with age as the lung becomes more inefficient. The variability of P(A-a)O₂ with F_IO₂ limits its usefulness as a shunt indicator when F_IO₂ is changed.

Calculation of P(A-a)O₂ is straightforward. The ideal alveolar gas equation is used to compute P_AO₂, and arterial blood gas analysis provides PaO₂. At F_IO₂ values ≤0.60, P_AO₂ is calculated as follows (see Chapter 7):

PAO2=FIO2(PB−47)−PaCO2×1.2

At F_IO₂ values > 0.60, the factor 1.2 is eliminated, as the following equation shows:

PAO2=FIO2(PB−47)−PaCO2

Arterial PO₂/Alveolar PO₂

The PaO₂/P_AO₂ index (a-A ratio) represents the percentage of the alveolar PO₂ that is transferred to the arterial blood. In theory, the percentage of P_AO₂ transferred across the lung stays constant as long as lung function (whether normal or abnormal)

CLINICAL FOCUS 12-5   Using the Bohr Dead Space Equation to Determine Dead Space and Alveolar Ventilation

You are conducting tests to determine whether your patient receiving mechanical ventilation is ready to be removed from the ventilator and breathe spontaneously. In addition to performing various other tests, you wish to evaluate the efficiency of your patient’s ventilation. To do this, you need to know the amount of your patient’s total ventilation that does not participate in gas exchange. You can then calculate the degree to which ventilation participates in gas exchange. You have the following information:

V˙E = 10 L/min

pH = 7.39

PaCO₂ = 43 mm Hg

HCO₃⁻ = 25 mEq/L

PE¯CO2 = 17 mm Hg

PaO₂ = 70 mm Hg

F_IO₂ = 0.35

Discussion

The Bohr dead space equation calculates V_D/V_T, which is the fraction of the tidal volume used to ventilate nonperfused airspace, as the following shows:

VD/VT=PaCO2−PE¯CO2PaCO2

V˙D/V˙E can be substituted for V_D/V_T to calculate the fraction of total V˙E that is devoted to dead space ventilation. Using the appropriate data as provided, you can determine the following:

V˙D/V˙E=43−1743V˙D/V˙E=2643V˙D/V˙E=0.6

This means 0.6, or 60%, of the V˙E is dead space ventilation, leaving 40% for V˙A. Specifically, the following equation is true:

V˙D=0.6(10L/min)=6L/minV˙A=0.4(10L/min)=4L/min

A normal V_D/V_T or V˙D/V˙E is about 0.25 to 0.40. An abnormally high amount of this patient’s V˙E is used to ventilate nonperfused dead space. Ventilation is relatively inefficient; a high V˙E is required to maintain a normal PaCO₂ of 43 mm Hg (see previous patient data). The patient may have difficulty breathing spontaneously because the work of breathing required to sustain a normal PaCO₂ is abnormally high.

stays constant. Thus, PaO₂/P_AO₂ is more stable than P(A-a)O₂ when F_IO₂ changes.³ The lower normal limit for PaO₂/P_AO₂ is about 0.75. That is, at least 75% of P_AO₂ is normally transferred to the arterial blood. Because there is always some degree of P(A-a)O₂ present, PaO₂/P_AO₂ can never be 1.0.

Because of its stability, PaO₂/P_AO₂ is useful in following a patient’s lung function as F_IO₂ is changed. Its stability also means PaO₂/P_AO₂ can be used to predict the F_IO₂ required to achieve a desired PaO₂.

Arterial PO₂/Fractional Concentration of Inspired Oxygen

The PaO₂/F_IO₂ ratio is another measure of oxygenation efficiency. A normal range is about 380 to 475 (i.e., when PaO₂ is 80 to 100 mm Hg on F_IO₂ of 0.21). PaO₂/F_IO₂ is easy to calculate because it does not require calculation of P_AO₂. However, its usefulness as a shunt indicator is limited. A major problem with PaO₂/F_IO₂ is that changes in PaCO₂ affect it. For example, if PaCO₂ increases from 40 mm Hg to 80 mm Hg during general hypoventilation, PaO₂ decreases by about the same amount (i.e., from 90 mm Hg to 50 mm Hg). If the patient is breathing room air, PaO₂/F_IO₂ is 50/0.21 = 238. This low value implies that oxygen-transfer efficiency is impaired when it is not; P(A-a)O₂ does not change in this situation. For this reason, PaO₂/F_IO₂ is the least accurate indicator of shunt, especially at low F_IO₂ values when the effect of PaCO₂ is greatest.

Comparison of P(A-a)O₂, PaO₂/P_AO₂, and PaO₂/F_IO₂

None of the indicators discussed previously consider the fact that in abnormally high shunt conditions mixed venous oxygen content (Cv¯O₂) affects CaO₂ and PaO₂. This is true because shunted blood is composed of mixed venous blood, which eventually becomes part of the arterial blood. As was explained in Chapter 8, a decrease in cardiac output can decrease Cv¯O₂. Thus, a nonpulmonary factor (cardiac output) can decrease PaO₂. In this respect, shunt indicators sensitive to only pulmonary factors are inaccurate in reflecting the efficiency of the lung’s oxygen-transfer ability.

Consider a patient in whom 20% of the cardiac output (venous blood) is shunted through capillaries of nonventilated alveoli; this produces abnormal P(A-a)O₂, PaO₂/P_AO₂, and PaO₂/F_IO₂ values because the shunted venous blood reduces the PaO₂. Now assume that the cardiac output decreases to half normal, decreasing Cv¯O₂ significantly. The same 20% shunted blood is now more profoundly deoxygenated, and further decreases CaO₂ and PaO₂. In this situation, each shunt indicator would show a greater degree of abnormality, although the percentage of shunted cardiac output and oxygen-transfer efficiency did not change. Therefore, these shunt indicators must be cautiously interpreted in patients with cardiovascular instability.

Assuming that cardiovascular function is constant, PaO₂/P_AO₂ is the most reliable shunt indicator.³ It varies least with

CLINICAL FOCUS 12-6   Calculation of Fractional Concentration of Inspired Oxygen Required to Achieve Acceptable Arterial PO₂

A 29-year-old woman has been admitted to the hospital. She complains of severe shortness of breath. Her room air arterial blood gas values are as follows:

PaO₂ = 65 mm Hg

PaCO₂ = 30 mm Hg

pH = 7.45

HCO₃⁻ = 20 mEq/L

F_IO₂ = 0.21

P_B = 760 mm Hg

How much oxygen is needed to achieve a PaO₂ of 90 mm Hg? What F_IO₂ should be used?

Discussion

The equation used to calculate a F_IO₂ required for a desired PaO₂ is as follows:

FIO2required=[Desired PaO2/([PaO2/PAO2])]+PaCO2×1.2(PB−47)

This equation is a rearrangement of the alveolar air equation. The following shows the alveolar air equation solved for F_IO₂:

PAO2=FIO2(PB−47)−PaCO2×1.2 1

1

FIO2(PB−47)=PAO2+PaCO2×1.2 2

2

FIO2=PAO2+PaCO2×1.2/PB−47 3

3

Equation 3 is similar to the “F_IO₂ required” equation. In fact, equation 3 can be used to calculate the F_IO₂ required. The P_AO₂ in the numerator of equation 3 is the P_AO₂ needed to produce the desired PaO₂. This needed P_AO₂ can be calculated as follows if the original PaO₂/P_AO₂ ratio is known:

NeededPAO2=Desired PaO2/(PaO2/PAO2)

The term “desired PaO₂/(PaO₂/P_AO₂)” in the numerator of the “F_IO₂ required” equation is merely a way to calculate the P_AO₂ needed to achieve the PaO₂ desired. The PaO₂/P_AO₂ ratio can be calculated from the current measured PaO₂, and the P_AO₂ can be calculated from the current F_IO₂.

First, the patient’s PaO₂/P_AO₂ ratio is calculated from current data. This ratio indicates the fraction of the P_AO₂ that entered the arterial blood. Dividing the desired PaO₂ by this fraction provides the P_AO₂ that must exist in the alveoli to produce the desired PaO₂ in the arterial blood. Using the patient’s current data, you can determine the following:

CurrentPAO2=0.21(760−47)−(30×1.2)=113.73mm HgCurrentPaO2=65mm HgPaO2/PAO2=65/113.73=0.57

This means 0.57, or 57%, of the P_AO₂ enters the blood. Therefore, the desired PaO₂ of 90 mm Hg must be 0.57 of the needed P_AO₂, as the following shows:

90mm Hg=0.57×neededPAO290mm Hg/0.57=157.9mm Hg=neededPAO2to achieve PaO2 of90mm Hg

Referring to the “F_IO₂ required” equation at the beginning, the appropriate numbers are inserted to arrive at the following solution:

FIO2required=Desired PaO2/(PaO2/PAO2)+PaCO2×1.2PB−47              FIO2=157.8+(30×1.2)(760−47)              FIO2=193.8713              FIO2=0.27

An F_IO₂ of 0.27 should produce a PaO₂ of about 90 mm Hg.

changes in F_IO₂, is not affected by PaCO₂, and can be used to compute the F_IO₂ necessary to achieve a desired PaO₂.

Physiological Shunt Equation

The physiological shunt equation takes into account the effects of both pulmonary and nonpulmonary factors (e.g., cardiac output) that influence arterial oxygenation. With this equation, the true fraction of cardiac output that is shunted through nonventilated airspace can be calculated. The shunt equation takes both anatomical and intrapulmonary shunting into account (i.e., physiological shunt [Q˙s]). Shunt calculated by this method is the only accurate way to measure physiological shunting when cardiac output is unstable and is the most reliable method to assess oxygen-transfer efficiency. Q˙s is calculated as a fraction of the total cardiac output (Q˙T), or the shunt fraction, as the following shows:

Q˙sQ˙T=CćO2−CaO2CćO2−Cv¯O2

In this equation, Q˙s/Q˙T represents the physiological shunt fraction, Cc′O₂ represents the end-capillary oxygen content from ideal alveoli, CaO₂ represents the arterial oxygen content, and Cv¯O₂ represents the mixed venous oxygen content.

Figure 12-12 helps illustrate the rationale for the shunt equation. The (Cc′O₂ − Cv¯O₂) is equal to the total oxygen uptake by the capillary blood. The (Cc′O₂ − CaO₂) is the amount of oxygen lost from the Cc′O₂ as a result of mixing with poorly oxygenated Q˙s. In other words, the greater the amount of shunted blood (Q˙s), the greater the amount of oxygen lost from the Cc′O₂ when it mixes with Q˙s. The shunt equation expresses this oxygen loss as a fraction of the total oxygen uptake:

(CćO2−CaO2)(CćO2−Cv¯O2)=Oxygen lost from mixing withQs=Total amount of oxygen uptake

It should be apparent that this fraction is equal to the shunt fraction (Q˙s/Q˙T).

A mixed venous blood sample must be available to use the shunt equation in the clinical setting. Mixed venous blood is available only when a pulmonary artery catheter is in place (see Chapter 6). In addition, because end-capillary blood cannot be directly sampled, the Cc′O₂ is calculated as follows:

CćO2=(Hb×1.34g/dL×SćO2+(PAO2×0.003mL/dL)

In reference to Figure 12-12, the Pc′O₂ is of necessity equal to P_AO₂ because alveolar gas and end-capillary blood are in equilibrium. Pc′O₂ is calculated from the alveolar air equation.

Virtually all patients requiring shunt measurements breathe supplementary oxygen. Because even low concentrations of inspired oxygen result in P_AO₂ values greater than 150 mm Hg, the assumption is that capillary blood oxygen saturation is 1.0 when the patient breathes any amount of supplementary oxygen. The Sc′O₂ term of the shunt equation is generally ignored in calculating Cc′O₂

Clinical Significance

The periodic assessment of Q˙s in patients with oxygenation difficulties is clinically important. Increased shunting indicates an increase in nonventilated alveoli.

The effect of increased shunt on CaO₂ is magnified by a low cardiac output. As discussed previously, low cardiac output decreases Cv¯O₂, exaggerating the desaturating effect of shunted venous blood on CaO₂. A low cardiac output and decreased Cv¯O₂ do not affect arterial oxygenation in people with normal shunt because shunt units contribute very little desaturated blood to the arterial stream.

Calculated shunt fractions of 10% or less have no significant clinical effect. Table 12-2 summarizes the clinical significance of shunting.⁴

TABLE 12-2

Clinical Significance of Shunt

Shunt Fraction Percentage	Clinical Significance
<10%	Clinically compatible with normal lungs
10-19%	Intrapulmonary abnormality; seldom requires significant ventilatory support
20-29%	Significant abnormality; requires ventilatory assistance with PEEP or CPAP
≥30%	Severe disease; life threatening; requires aggressive mechanical support with PEEP

CPAP, Continuous positive airway pressure; PEEP, positive end expiratory pressure.

Because shunting involves loss of airspace in the lung (i.e., alveolar collapse or fluid-filled alveoli), it is associated with decreased lung compliance, which increases the work of breathing. The severe hypoxemia of shunting combined with associated low lung compliance may place such high work demands on the respiratory system that mechanical ventilation is required.

CLINICAL FOCUS 12-7   Calculating Physiological Shunt Using Classic Shunt Equation

A 36-year-old woman is admitted to the intensive care unit with diffuse bilateral pneumonia. Because of severe hypoxia (PaO₂ = 40 mm Hg), the patient is intubated and placed on a mechanical ventilator with an F_IO₂ of 1.0. Arterial blood gases are drawn 1 hour later and show the following:

PaO₂ = 145 mm Hg

PaCO₂ = 42 mm Hg

pH = 7.39

SaO₂ = 1.0

Hb = 13 g/dL

A catheter is placed into the patient’s pulmonary artery, and the following blood gas values are obtained:

Pv¯O₂ = 34 mm Hg

Sv¯O₂ = 0.63

Using the classic shunt equation, calculate this patient’s Q˙s fraction.

Discussion

Q˙sQ˙T=Cc′O2−CaO2Cc′O2−Cv¯O2

To calculate shunt, first calculate Cc′O₂, CaO₂, and Cv¯ O₂:

CćO2=(Hb×1.34×SćO2)+(PAO2×0.003)CćO2=(13×1.34×1.0)+(PAO2−0.003)

PAO2=PIO2−PaCO2PAO2=FIO2(760−47)−PaCO2PAO2=1.0(713)−42PAO2=671mm Hg (thisPO2yields ScO2=1.0)

CćO2=(13×1.34×1.0)+(671×0.003)CćO2=17.42+2.013CćO2=19.43mL/dL

CaO2=(Hb×1.34×SaO2)+(PaO2×0.003)CaO2=(13×1.34×1.0)+(145×0.003)CaO2=17.42+0.435CaO2=17.855mL/dL

Cv¯O2=(Hb×1.34×Sv¯O2)+(Pv¯O2×0.003)Cv¯O2=(13×1.34×0.63)+(34×0.003)Cv¯O2=10.9746+0.102Cv¯O2=11.08mL/dL

The following calculations are made:

Q˙sQ˙T=19.43−17.85519.43−11.08Q˙sQ˙T=1.5758.35Q˙sQ˙T= 0.19 or 19% shunt

This means 19% of the cardiac output flows through nonventilated alveoli and receives no oxygen from the lungs. Normal Q˙s is less than 5%. This patient’s severe pneumonia fills many alveoli with inflammatory debris, rendering them airless. Venous blood perfusing these alveoli cannot take up oxygen and ultimately mixes with arterial blood. To correct the resulting arterial hypoxemia, you must find ways to re-aerate the diseased alveoli; possible measures include secretion mobilization and removal techniques or PEEP with mechanical ventilation.

CLINICAL FOCUS 12-8   Effect of Low Cardiac Output on Arterial Oxygenation When Shunt Is High

Consider again the case presented in Clinical Focus 12-7. The patient is a 36-year-old woman with severe bilateral pneumonia, which fills many alveoli with fluid, creating a Q˙s of 21%. Her cardiac output decreases from 6.0 L per minute to 3.0 L per minute. Arterial blood gases are drawn and reveal the following:

	Cardiac Output 6.0 L/min	Cardiac Output 3.0 L/min
FIO2 =	1.0	1.0
PaO2 =	145 mm Hg	82 mm Hg
PaCO2 =	42 mm Hg	45 mm Hg
pH =	7.39	7.34

Examine the effect that decreased cardiac output had on this patient’s arterial oxygenation.

Discussion

Arterial oxygenation worsened with a decrease in cardiac output because low cardiac output results in low Cv¯O₂. Blood that moves more slowly spends more time giving up oxygen to the tissues, decreasing Cv¯O₂. Blood perfusing nonventilated alveoli is now even more hypoxic than before, and when mixed with arterialized blood, it decreases the PaO₂ and arterial oxygen content even more. If you estimated this patient’s shunt by examining the P(A-a)O₂, PaO₂/P_AO₂ ratio, or PaO₂/F_IO₂ ratio, you would incorrectly assume that PaO₂ is decreased because of increased shunting. In other words, these estimators do not consider the effect of Cv¯O₂ on PaO₂. The classic shunt equation reflects the effect of pulmonary and cardiac factors on PaO₂ and is the most accurate way to estimate Q˙s in patients with unstable cardiac output. This case illustrates that cardiac output changes can affect PaO₂, although F_IO₂ remains unchanged.