## Alveolar Ventilation

Ventilation is the first step in the O2 cascade, and the level of alveolar ventilation (Va) is the most important physiologic factor determining arterial Po2 for any given inspired Po2 and level of O2 demand (Vo2) in healthy lungs. As described in Chapter 18, anatomic dead space reduces the fraction of the tidal volume that reaches the alveoli:

Va = fR(VT - Vd), where Va is alveolar ventilation, fR is respiratory frequency, VT is tidal volume, and VD is anatomic dead space. Anatomic dead space can be measured with the single breath method (see Chapter 18, Fig. 10) but gas exchange principles can be used to obtain a more direct measure of the effective, or functional, alveolar ventilation.

Alveolar Ventilation Equation Predicts Paco2

The Fick equation (see Chapter 18) defines CO2 elimination from the lungs (Vco2) as:

(V co2) = (V aFaco2)-(V iFico2), where Vco2 is the difference between the CO2 expired from the alveoli and the amount of CO2 inspired to the alveoli. Fico2 is nearly zero, so the inspired terms can be dropped.

The alveolar ventilation equation is obtained by substituting Paco2 for Faco2 and rearranging the Fick equation:

Va = (Vco2/Paco2 )K, where K is a constant (= 0.863) to convert Fco2 to Pco2 in mm Hg, and Vco2 in mLsTPD/min to Va in LBTPs/min. In practice, arterial Pco2 is substituted for alveolar Pco2 because the two values are equal in normal lungs and an arterial blood sample is usually taken to measure arterial Po2 for evaluating gas exchange.

The most important thing to remember about the alveolar ventilation equation is that Va and Paco2 (or Paco2) are inversely related for any given metabolic rate. For example, if Va is doubled, Paco2 is halved, regardless of the exact values for either variable. Therefore, the effectiveness of ventilation can be judged by the Paco2 at any given metabolic rate. Hyperventilation is defined by a decrease in Paco2 from the normal value, implying excess Va for the given Vco2. Increased ventilation does not always mean hyperventilation. For example, Va must increase to maintain normal Paco2 when Vco2 increases during exercise. Hypoventilation is defined by an increase in Paco2 and this occurs when Va is lower than normal for a given Vco2.

### Physiologic Dead Space

Physiologic dead space is a functional measure of "wasted ventilation," and it is always greater than anatomic dead space. Physiologic dead space is defined from another rearrangement of the Fick principle applied to CO2 elimination by the lungs. In a steady state, Vco2 measured in mixed-expired gas must equal Vco2 measured from alveolar gas:

(V eFEo2) — (V iFico2) = (V aFaco2 ) — (V iFico2).

The inspired terms can be subtracted from both sides, and ventilation is converted to volume by dividing both sides by respiratory frequency. This yields:

VtFE co2(Vt — Vd)Faco2, where Vt — Vd = Va. As illustrated in Fig. 2, mixed-expired Fco2, which can be measured by collecting all inspired gas in a bag or a spirometer, includes gas exhaled from the alveoli and dead space. Therefore, physiologic dead space can be defined as a ratio of mixed expired and alveolar gas CO2 levels:

End inspiration

Equilibrate

FIGURE 2 Not all of the tidal volume (Vt) is effective at bringing fresh gas into the alveoli during inspiration because of dead space (Vd). CO2 in the mixed expired gas (Fe) is a mixture of dead space (inspired gas that has not undergone exchange, FI) and alveolar gas (Fa). The equation can be rearranged to calculate Vd/Vt as described in the text.

End inspiration

Equilibrate

FIGURE 2 Not all of the tidal volume (Vt) is effective at bringing fresh gas into the alveoli during inspiration because of dead space (Vd). CO2 in the mixed expired gas (Fe) is a mixture of dead space (inspired gas that has not undergone exchange, FI) and alveolar gas (Fa). The equation can be rearranged to calculate Vd/Vt as described in the text.

This measure of physiologic dead space is also called Bohr's dead space after the Danish physiologist who developed the method. In practice, Pco2 is substituted for FCO2 so measured PaCO2 can be substituted for alveolar PCO2 as follows:

Factors that may increase physiologic dead space relative to anatomic dead space are considered in detail later (see Va/Q Mismatching between Different Alveoli section).

The respiratory exchange ratio (R) is the ratio of O2 uptake by the lungs to CO2 elimination by the lungs:

Under steady-state conditions, R equals the respiratory quotient (RQ), which is the ratio of CO2 production to O2 consumption in metabolizing tissues. RQ averages 0.8 but can range from 0.67 to 1, depending on the relative amounts of fat, protein, and carbohydrate being metabolized. However, R can exceed this range in nonsteady states, for example when R exceeds 1 during hyperventilation or at the onset of exercise. CO2 stores in the body are much greater than O2 stores because of bicarbonate in blood and tissues. R can increase because it takes longer to wash out the CO2 stores than it does to charge up the much smaller O2 stores in the body.

Substituting normal values predicts that Pao2 =100 mm Hg in normal individuals breathing room air (PAO2 = 150 — 40/0.8). Increases in Va (hyperventilation) increase PAO2 by decreasing PACO2, whereas decreases in Va (hypoventilation) decrease Pao2. The alveolar gas equation calculates ideal alveolar PO2, which is greater than measured arterial PO2 (Fig. 1). Reasons for this difference are explained later.

Alveolar Gas Equation Predicts Pao2

Alveolar Po2 (Pao2) can be predicted from inspired Po2 (Pio2) and alveolar Pco2 (Paco2) by the alveolar gas equation:

Pao2 = Pio2 — (Pao2/R)+ F, where R is the respiratory exchange ratio (see below), and F = [Paco2 • Fio2 (1 — R)/R]. Note that F increases Pao2 about 2 mm Hg under normal conditions (Fio2 = 0.21 and Paco2 = 40 mm Hg), so F can be neglected under normal conditions. The alveolar gas equation is only valid if inspired Pco2 = 0, which is a reasonable assumption for room air breathing (Fico2 = 0.0003). Alveolar ventilation is a major determinant of Pao2 because Va determines Paco2, according to the alveolar ventilation equation described earlier.

Pio2 is less than ambient Po2 because air is warmed and humidified in the respiratory system. The vapor pressure of water = 47 mm Hg at 37°C, and the total pressure available for o2 is decreased by this amount, whereas the fractional concentration of o2 in dry gas remains constant (Chapter 18). Ambient Po2 =160 mm Hg (0.21 • 760 mm Hg) but inspired Po2 = 150 mm Hg [0.21 • (760 — 47)= 0.21 • 713 mm Hg].

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