Ventilation (V), Perfusion (Q), and V/Q Relationships (2024)

Alveolar Gas Composition

When the inspired gas reaches the alveolus, O₂ is transported across the alveolar membrane, and CO₂ moves from the capillary bed into the alveolus. The process by which this occurs is described in Chapter 23. At the end of inspiration and with the glottis open, the total pressure in the alveolus is atmospheric; thus, the partial pressures of the gases in the alveolus must equal the total pressure, which in this case is atmospheric. The composition of the gas mixture, however, is changed and can be described as

Equation 22-8

N₂ and argon are inert gases, and therefore the fraction of these gases in the alveolus does not change over time. The fraction of water vapor also does not change because the gas is already fully saturated with water vapor and is at body temperature by the time that it reaches the trachea. As a consequence of gas exchange, the fraction of O₂ in the alveolus decreases and the fraction of CO₂ in the alveolus increases. Because of changes in the fractions of O₂ and CO₂, the partial pressure exerted by these gases also changes. The partial pressure of O₂ in the alveolus (PAO₂) is given by the alveolar gas equation, which is also called the ideal alveolar oxygen equation:

Equation 22-9

where PIO₂ is the inspired partial pressure of O₂, which is equal to the fraction (F) of inspired O₂ (FIO₂) times barometric pressure (P_b) minus water vapor pressure (PH₂O). PACO₂ is the CO₂ tension of alveolar gas, and R is the respiratory exchange ratio or respiratory quotient. The respiratory quotient is the ratio of CO₂ excreted (_CO2) to the O₂ taken up (_O2) by the lungs. This quotient is the amount of CO₂ produced relative to the amount of O₂ consumed by metabolism and is dependent on caloric intake. The respiratory quotient varies between 0.7 and 1.0 and is 0.7 in states of exclusive fatty acid metabolism and 1.0 in states of exclusive carbohydrate metabolism. Under normal dietary conditions, the respiratory quotient is assumed to be 0.8. Thus, the quantity of O₂ taken up exceeds the quantity of CO₂ that is released in the alveoli.

The partial pressures of O₂, CO₂, and N₂ from ambient air to the alveolus are shown in Table 22-1.

The fraction of CO₂ in the alveolus is a function of the rate of CO₂ production by the cells during metabolism and the rate at which the CO₂ is eliminated from the alveolus. This process of elimination of CO₂ is known as alveolar ventilation. The relationship between CO₂ production and alveolar ventilation is defined by the alveolar carbon dioxide equation,

Equation 22-10

where _CO2 is the rate of CO₂ production by the body, A is alveolar ventilation, and FACO₂ is the fraction of CO₂ in dry alveolar gas. This relationship demonstrates that the rate of elimination of CO₂ from the alveolus is related to alveolar ventilation and to the fraction of CO₂ in the alveolus. Alveolar PACO₂ is defined by the following:

Equation 22-11

Hence, we can substitute in the previous equation and demonstrate the following relationship:

Equation 22-12

This equation demonstrates several important relationships. First, there is an inverse relationship between the partial pressure of CO₂ in the alveolus (PACO₂) and alveolar ventilation (A), irrespective of the exhaled CO₂. Specifically, if ventilation is doubled, PACO₂ will decrease by 50%. Conversely, if ventilation is decreased by half, the partial pressure of CO₂ in the alveolus will double. Second, at a constant alveolar ventilation (A), doubling of the metabolic production of CO₂ (CO₂) will double the partial pressure of CO₂ in the alveolus. The relationship between alveolar ventilation and alveolar PCO₂ is shown in Figure 22-1.

Figure 22-1 Alveolar PCO₂ as a function of alveolar ventilation in the lung. Each line corresponds to a given metabolic rate associated with a constant production of CO₂ (V.CO₂ isometabolic line). Normally, alveolar ventilation is controlled to maintain an alveolar PCO₂ of about 40 torr. Thus, at rest, when V.CO₂ is approximately 250 mL/min, alveolar ventilation of 5 L/min will result in an alveolar PCO₂ of 40 mm Hg. A 50% decrease in ventilation at rest (i.e., from 5 to 2.5 L/min) results in doubling of alveolar PCO₂. During exercise, CO₂ production is increased (V.CO₂ = 750 mL/min), and to maintain a normal PCO₂, ventilation must increase (in this case to 15 L/min). Again, however, a 50% reduction in ventilation (15 to 7.5 L/min) will result in doubling of PCO₂.