Ventilation, Perfusion, and Ventilation/Perfusion Relationships

Learning Objectives

Upon completion of this chapter, the student should be able to answer the following questions:

1
What are the two types of dead space ventilation, and how does dead space ventilation change with changes in tidal volume?
2
What is the composition of gas in ambient air, the trachea, and the alveolus? How does this composition change when oxygen fraction (FiO ₂ ) is increased? How does a change in barometric pressure change gas composition?
3
How is the alveolar air equation, used to calculate the alveolar-arterial difference for oxygen (AaD o ₂ ), useful in the evaluation of hypoxemia?
4
What effect does a change in alveolar ventilation have on alveolar carbon dioxide?
5
At rest, how well does the distribution of pulmonary blood flow match the distribution of ventilation? What happens during exercise?
6
What are the four categories of hypoxia and the six causes of hypoxic hypoxia?
7
How does providing 100% inspired O ₂ help determine the cause of hypoxic hypoxia?
8
What are the two causes of hypercapnia, and how are they different from each other?

The major determinant of normal gas exchange and thus the level of P o ₂ and P co ₂ in blood is the relationship between ventilation ( $\dot{V}$ $\dot{V}$ ) and perfusion ( $\dot{Q}$ $\dot{Q}$ ). This relationship is called the ventilation/perfusion ( $\dot{V} / \dot{Q}$ $\dot{V} / \dot{Q}$ ) ratio.

Ventilation

Ventilation is the process by which air moves in to and out from the lungs. The incoming air is composed of a volume that fills the conducting airways (dead space ventilation) and a portion that fills the alveoli (alveolar ventilation). Minute (or total) ventilation ( ${\dot{V}}_{E}$ ${\dot{V}}_{E}$ ) is the volume of air that enters or leaves the lung per minute:

{\dot{V}}_{E} = f \times V_{T}

${\dot{V}}_{E} = f \times V_{T}$

where f is the frequency or number of breaths per minute and V _T (also known as TV) is the tidal volume, or volume of air inspired (or exhaled) per breath. Tidal volume varies with age, sex, body position, and metabolic activity. In an average-sized adult at rest, tidal volume is 500 mL. In children, it is 3 to 5 mL/kg. As metabolic activity increases, minute ventilation increases.

Dead Space Ventilation: Anatomical and Physiological

Anatomical Dead Space

Dead space ventilation is ventilation to airways that do not participate in gas exchange. There are two types of dead space: anatomical dead space and physiological dead space. Anatomical dead space (V _D ) is composed of the volume of gas that fills the conducting airways:

V_{T} = V_{D} + V_{A}

$V_{T} = V_{D} + V_{A}$

where V refers to volume and the subscripts T, D, and A refer to tidal, dead space, and alveolar. A “dot” above V denotes a volume per unit of time (n):

V_{T} \times n = (V_{D} \times n) + (V_{A} \times n)

$V_{T} \times n = (V_{D} \times n) + (V_{A} \times n)$

{\dot{V}}_{E} = {\dot{V}}_{D} + {\dot{V}}_{A}

${\dot{V}}_{E} = {\dot{V}}_{D} + {\dot{V}}_{A}$

where ${\dot{V}}_{E}$ ${\dot{V}}_{E}$ is the total volume of gas in liters expelled from the lungs per minute (also called exhaled minute volume), ${\dot{V}}_{D}$ ${\dot{V}}_{D}$ is the dead space ventilation per minute, and ${\dot{V}}_{A}$ ${\dot{V}}_{A}$ is alveolar ventilation per minute.

In a healthy adult, the volume of gas contained in the conducting airways at functional residual capacity (FRC) is approximately 100 to 200 mL, in comparison with the 3 L of gas in an entire lung. The ratio of the volume of the conducting airways (dead space) to tidal volume represents the fraction of each breath that is “wasted” in filling the conducting airways. This volume is related to tidal volume (V _T ) and to exhaled minute ventilation ${\dot{V}}_{E}$ ${\dot{V}}_{E}$ in the following way:

{\dot{V}}_{D} = \frac{V_{D}}{V_{T}} \times {\dot{V}}_{E}

${\dot{V}}_{D} = \frac{V_{D}}{V_{T}} \times {\dot{V}}_{E}$

IN THE CLINIC

If the dead space volume is 150 mL and tidal volume increases from 500 to 600 mL for the same exhaled minute ventilation, what is the effect on dead space ventilation?

\begin{matrix} V_{T} = 500 mL \\ V_{D} = (\frac{150 mL}{500 mL}) \times {\dot{V}}_{E} \\ V_{D} = 0.3 \times {\dot{V}}_{E} \end{matrix}

$\begin{matrix} V_{T} = 500 mL \\ V_{D} = (\frac{150 mL}{500 mL}) \times {\dot{V}}_{E} \\ V_{D} = 0.3 \times {\dot{V}}_{E} \end{matrix}$

and, similarly,

\begin{matrix} V_{T} = 600 mL \\ V_{D} = (\frac{150 mL}{600 mL}) \times {\dot{V}}_{E} \\ V_{D} = 0.25 \times {\dot{V}}_{E} \end{matrix}

$\begin{matrix} V_{T} = 600 mL \\ V_{D} = (\frac{150 mL}{600 mL}) \times {\dot{V}}_{E} \\ V_{D} = 0.25 \times {\dot{V}}_{E} \end{matrix}$

Increasing tidal volume is an effective way to increase alveolar ventilation. This might occur during exercise or periods of metabolic stress. As tidal volume increases, the fraction of the dead space ventilation decreases for the same exhaled minute ventilation.

Dead space ventilation (V _D ) varies inversely with tidal volume (V _T ). The larger the tidal volume, the smaller the proportion of dead space ventilation. Normally, V _D /V _T is 20% to 30% of exhaled minute ventilation. Changes in dead space are important contributors to work of breathing. If the dead space increases, the individual must inspire a larger tidal volume to maintain normal levels of alveolar ventilation. This adds to the work of breathing and can contribute to respiratory muscle fatigue and respiratory failure. If metabolic demands increase (e.g., during exercise or with fever), individuals with lung disease may not be able to increase tidal volume sufficiently. This can be observed at the beach when using a snorkel to extend the airway to the surface of the water, when swimming under water. This device increases “anatomic” dead space, such that increased tidal volume is needed to maintain adequate alveolar ventilation. Due to increased water pressure when under water, the mechanical work of breathing increases. Snorkel devices are manufactured with relatively short tubes to decrease the risk of underwater hypoventilation and CO ₂ accumulation.

Physiological Dead Space

The second type of dead space is physiological dead space. Often in diseased lungs, some alveoli are properly ventilated but poorly perfused, leading to increased physiological dead space. The total volume of gas in each breath that does not participate in gas exchange is called the physiological dead space. This volume includes the anatomical dead space and the dead space secondary to perfused but unventilated alveoli. The physiological dead space is always at least as large as the anatomical dead space, and in the presence of lung disease it may be considerably larger.

Both anatomical and physiological dead space can be measured, but they are not measured routinely in the course of patient care.

IN THE CLINIC

In individuals with certain types of chronic obstructive pulmonary disease (COPD), such as emphysema, physiological dead space is increased. If dead space doubles, tidal volume must increase in order to maintain the same level of alveolar ventilation. If tidal volume is 500 mL and V _D /V _T is 0.25, then:

\begin{matrix} V_{T} = V_{D} + V_{A} \\ 500 mL = 125 mL + 375 mL \end{matrix}

$\begin{matrix} V_{T} = V_{D} + V_{A} \\ 500 mL = 125 mL + 375 mL \end{matrix}$

If V _D increases from 125 mL to 250 mL in this example, tidal volume (V _T ) must increase to 625 mL to maintain a normal alveolar ventilation (i.e., V _A = 375 mL):

\begin{matrix} V_{T} = 250 mL + 375 mL \\ V_{T} = 625 mL \end{matrix}

$\begin{matrix} V_{T} = 250 mL + 375 mL \\ V_{T} = 625 mL \end{matrix}$

Alveolar Ventilation

Composition of Air

Inspiration brings ambient or atmospheric air to the alveoli, where O ₂ is taken up and CO ₂ is removed. Ambient air is a gas mixture composed of N ₂ and O ₂ , with minute quantities of CO ₂ , argon, and inert gases. The composition of this gas mixture can be described in terms of either gas fractions or the corresponding partial pressure.

Ambient air is a gas, so gas laws can be applied. This provides two important principles. First when the components of a gas mixture are viewed in terms of gas fractions (F), the sum of the individual gas fractions must equal one.

1.0 = F N_{2} = F O_{2} + F_{argon and other gases}

$1.0 = F N_{2} = F O_{2} + F_{argon and other gases}$

The sum of the partial pressures (in millimeters of mercury) of individual gas components in a mixture, also known as the gas tension (in torr), must be equal to the total pressure of the entire gas mixture. Thus at sea level, where atmospheric pressure (also known as barometric pressure [P _b ]) is 760 mm Hg, the partial pressures of the gases in air are as follows:

P_{b} = P N_{2} + P O_{2} + P C O_{2} + P H_{2} O + P (O T H E R G L A S E S)

$P_{b} = P N_{2} + P O_{2} + P C O_{2} + P H_{2} O + P (O T H E R G L A S E S)$

Three important gas laws govern ambient air and alveolar ventilation. According to Boyle’s law, when temperature is constant, pressure (P) and volume (V) are inversely related; that is, P ₁ V ₁ = P ₂ V ₂ . Boyle’s law is used in the measurement of lung volumes (see Fig. 21.4 ). Dalton’s law is that the partial pressure of a gas in a gas mixture is the pressure that the gas would exert if it occupied the total volume of the mixture in the absence of the other components. Eq. 23.7 is an example of how Dalton’s law is used in the lung. According to Henry’s law, the concentration of a gas dissolved in a liquid is proportional to its partial pressure.

The second important principle is that the partial pressure of a gas (P _gas ) is equal to the fraction of that gas in the gas mixture (F _gas ) multiplied by the atmospheric (barometric) pressure:

P_{g a s} = F_{g a s} \times P_{b}

$P_{g a s} = F_{g a s} \times P_{b}$

Ambient air is composed of approximately 21% O ₂ and 79% N ₂ . (The contribution of CO ₂ , <0.01%, is typically excluded.) Therefore, the partial pressure of O ₂ in inspired ambient air (P o ₂ ) is calculated as follows:

\begin{matrix} P o_{2} =Fi o_{2} \times P_{b} \\ P o_{2} =0 . 21 \times 760 mm Hg \\ P o_{2} =159 mm Hg or 159 torr \end{matrix}

$\begin{matrix} P o_{2} =Fi o_{2} \times P_{b} \\ P o_{2} =0 . 21 \times 760 mm Hg \\ P o_{2} =159 mm Hg or 159 torr \end{matrix}$

where (Fi o ₂ ) is the fraction of oxygen in inspired air. The partial pressure of O ₂ , or oxygen tension, in ambient air at the mouth at the start of inspiration is therefore 159 mm Hg, or 159 torr. The O ₂ tension at the mouth can be altered in one of two ways: by changing the fraction of O ₂ in inspired air (Fi o ₂ ) or by changing barometric pressure. Thus ambient O ₂ tension can be increased through the administration of supplemental O ₂ or by increasing air pressure. At high altitude, the FiO ₂ is unchanged, but atmospheric pressure is decreased and as a result, the partial pressure of oxygen is decreased.

IN THE CLINIC

The partial pressure of O ₂ in ambient air varies with altitude. The highest and lowest points in the contiguous United States are Mount Whitney in Sequoia National Park/Inyo National Forest (14,505 feet above sea level; barometric pressure, 437 mm Hg) and Badwater Basin in Death Valley National Park (282 feet below sea level; barometric pressure, 768 mm Hg). On Mount Whitney, the partial pressure of O ₂ in ambient air is calculated as follows:

{Po}_{2} = 0.21 \times 437 mm Hg = 92 mm Hg

${Po}_{2} = 0.21 \times 437 mm Hg = 92 mm Hg$

whereas in Death Valley Badwater Basin, the partial pressure of oxygen is calculated as follows:

{Po}_{2} = 0.21 \times 768 mm Hg = 161 mm Hg

${Po}_{2} = 0.21 \times 768 mm Hg = 161 mm Hg$

If supplemental oxygen were used on Mount Whitney to bring Fi o ₂ from 0.21 to 0.40, P o ₂ = 0.40 × 437 mm Hg = 175 mm Hg. Note that the Fi o ₂ does not vary at different altitudes; only the barometric pressure varies. These differences in oxygen tension have profound effects on arterial blood gas values.

As inspiration begins, ambient air is brought into the nasopharynx and laryngopharynx, where it becomes warmed to body temperature and humidified. Inspired air becomes saturated with water vapor by the time it reaches the glottis. Water vapor exerts a partial pressure and dilutes the total pressure in which the other gases are distributed. Water vapor pressure at body temperature is 47 mm Hg. To calculate the partial pressures of O ₂ and N ₂ in a humidified mixture, the water vapor partial pressure must be subtracted from the total barometric pressure. Thus in the conducting airways, which begin in the trachea, the partial pressure of O ₂ is calculated as follows

\begin{matrix} P_{trachea} o_{2} = (P_{b} - {PH}_{2} o) \times {Fio}_{2} \\ = (760 mm Hg - 47 mm Hg) \times 0.21 \\ = 150 mm Hg \end{matrix}

$\begin{matrix} P_{trachea} o_{2} = (P_{b} - {PH}_{2} o) \times {Fio}_{2} \\ = (760 mm Hg - 47 mm Hg) \times 0.21 \\ = 150 mm Hg \end{matrix}$

and the partial pressure of N ₂ is calculated similarly

\begin{matrix} P_{trachea} N_{2} = (P_{b} - {PH}_{2} O) \times {FiN}_{2} \\ = (760 mm Hg - 47 mm Hg) \times 0.79 \\ = 563 mm Hg \end{matrix}

$\begin{matrix} P_{trachea} N_{2} = (P_{b} - {PH}_{2} O) \times {FiN}_{2} \\ = (760 mm Hg - 47 mm Hg) \times 0.79 \\ = 563 mm Hg \end{matrix}$

Note that the total pressure remains constant at 760 mm Hg (150 + 563 + 47 mm Hg) and that the fractions of O ₂ and N ₂ are unchanged. Water vapor pressure, however, reduces the partial pressures of O ₂ and N ₂ . Note also that in the calculation of the partial pressure of ambient air ( Eq. 23.9 ), water vapor is ignored, and ambient air is considered “dry.” The conducting airways do not participate in gas exchange. The partial pressures of O ₂ , N ₂ , and water vapor remain unchanged in the airways until the air reaches the alveolus.

Alveolar Gas Composition

When the inspired air reaches the alveolus, O ₂ diffuses across the alveolar membrane into the capillary bed, and CO ₂ diffuses from the capillary bed into the alveolus. The process by which this occurs is described in Chapter 24 . At the end of inspiration and with the glottis open, the total pressure in the alveolus is atmospheric. The sum of 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 follows:

1.0 = {FO}_{2} + {FN}_{2} + {FH}_{2} O + F_{argon} + F other gases

$1.0 = {FO}_{2} + {FN}_{2} + {FH}_{2} O + F_{argon} + F other gases$

where N ₂ and argon are inert gases; the fraction of these gases in the alveolus does not change from ambient fractions. The fraction of water vapor also does not change because the inspired gas is already fully saturated with water vapor and is at body temperature. As a consequence of gas exchange, however, the fraction of O ₂ in the alveolus decreases, and the fraction of CO ₂ in the alveolus increases. Because of changes in the fractions of O ₂ and CO ₂ , the partial pressures exerted by these gases also change. The partial pressure of O ₂ in the alveolus (PA o ₂ ) is given by the alveolar gas equation, which is also called the ideal alveolar oxygen equation:

\begin{matrix} {PAO}_{2} = {PiO}_{2} - \frac{{PACO}_{2}}{R} \\ = [{FiO}_{2} \times (P_{b} - {PH}_{2} O)] - \frac{{PACO}_{2}}{R} \end{matrix}

$\begin{matrix} {PAO}_{2} = {PiO}_{2} - \frac{{PACO}_{2}}{R} \\ = [{FiO}_{2} \times (P_{b} - {PH}_{2} O)] - \frac{{PACO}_{2}}{R} \end{matrix}$

where Pi o ₂ is the partial pressure of inspired O ₂ , which is equal to the fraction of O ₂ (Fi o ₂ ) multiplied by the barometric pressure (P _b ) minus water vapor pressure (P h ₂ o ); PA co ₂ is the partial pressure of alveolar CO ₂ ; and R is the respiratory exchange ratio, or respiratory quotient. The respiratory quotient is the ratio of the amount of CO ₂ excreted ( V ̇ co ₂ ) to the amount of O ₂ taken up ( V ̇ o ₂ ) by the lungs. This quotient is the amount of CO ₂ produced in relation to the amount of O ₂ consumed by metabolism, and is to some extent dependent on the metabolic calorie source. The respiratory quotient varies between 0.7 and 1.0; it 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 O ₂ taken up exceeds the quantity of CO ₂ that is released in the alveoli. The partial pressures of O ₂ , CO ₂ , and N ₂ from ambient air to the alveolus at sea level are shown in Table 23.1 .

TABLE 23.1

Total and Partial Pressure Kres of Respiratory Gases in Ideal Alveolar Gas and Blood at Sea Level (760 mm Hg)

Parameter	Ambient Air (Dry)	Moist Tracheal Air	Alveolar Gas (R = 0.8)	Systemic Arterial Blood	Mixed Venous Blood
P o ₂	159	150	102	90	40
P co ₂	0	0	40	40	46
P h ₂ o , 37°C	0	47	47	47	47
P n ₂	601	563	571 ^a	571	571
P _total	760	760	760	748	704 ^b

a P n ₂ is increased in alveolar gas by 1% because R is normally less than 1.

b P _total is less in venous than in arterial blood because P o ₂ has decreased more than P co ₂ has increased. Pco ₂ , Partial pressure of carbon dioxide; Ph ₂ o , partial pressure of water; Pn ₂ , partial pressure of nitrogen; Po ₂ , partial pressure of oxygen; P _total , partial pressure of all parameters; R , respiratory quotient.

A similar approach can be used to calculate the estimated PA co ₂ . The fraction of CO ₂ in the alveolus is a function of the rate of CO ₂ production by the cells during metabolism and the rate at which the CO ₂ is eliminated from the alveolus. This process of elimination of CO ₂ is known as alveolar ventilation. The relationship between CO ₂ production and alveolar ventilation is defined by the alveolar carbon dioxide equation:

\begin{matrix} \dot{V} {CO}_{2} = {\dot{V}}_{A} \times {FACO}_{2} \\ or \\ {FACO}_{2} = \dot{V} {CO}_{2} / {\dot{V}}_{A} \end{matrix}

$\begin{matrix} \dot{V} {CO}_{2} = {\dot{V}}_{A} \times {FACO}_{2} \\ or \\ {FACO}_{2} = \dot{V} {CO}_{2} / {\dot{V}}_{A} \end{matrix}$

where V ̇ co ₂ is the rate of CO ₂ production by the body, V ̇ _A is alveolar ventilation per minute, and FA co ₂ is the fraction of CO ₂ in dry alveolar gas. This relationship demonstrates that the rate of elimination of CO ₂ from the alveolus is related to alveolar ventilation and to the fraction of CO ₂ in the alveolus. Like the partial pressure of any other gas (see Eq. 23.8 ), PA co ₂ is defined by the following:

{PACO}_{2} {=FACO}_{2} \times (P_{b} - {PH}_{2} O)

${PACO}_{2} {=FACO}_{2} \times (P_{b} - {PH}_{2} O)$

Substituting for FA co ₂ in the previous equation yields the following relationship:

{PACO}_{2} = \frac{[\dot{V} {CO}_{2} \times (P_{b} - {PH}_{2} O)]}{{\dot{V}}_{A}}

${PACO}_{2} = \frac{[\dot{V} {CO}_{2} \times (P_{b} - {PH}_{2} O)]}{{\dot{V}}_{A}}$

This equation demonstrates several important relationships. First, there is an inverse relationship between the partial pressure of CO ₂ in the alveolus (PA co ₂ ) and alveolar ventilation per minute ( V ̇ _A ), regardless of the exhaled CO ₂ . Specifically, if ventilation is doubled, PA co ₂ decreases by 50%. Conversely, if ventilation is decreased by half, the PA co ₂ doubles. Second, at a constant alveolar ventilation per minute ( V ̇ _A ), doubling of the metabolic production of CO ₂ ( V ̇ co ₂ ) causes the PA co ₂ to double. The relationship between V ̇ _A and PA co ₂ is depicted in Fig. 23.1 .

Fig. 23.1, The alveolar partial pressure of carbon dioxide (P co 2 ; y-axis ) as a function of alveolar ventilation per minute ( V ̇ A ; x-axis ) in the lung. Each line corresponds to a given metabolic rate associated with a constant production of CO 2 ( V ̇co 2 isometabolic line ). Normally, alveolar ventilation is controlled to maintain an alveolar P co 2 of approximately 40 mm Hg. Thus at rest, when V ̇ co 2 is approximately 250 mL/minute, alveolar ventilation of 5 L/minute results in an alveolar P co 2 of 40 mm Hg. A 50% decrease in ventilation at rest (i.e., from 5 to 2.5 L/minute) results in doubling of alveolar P co 2 . During exercise, CO 2 production is increased ( V ̇ co 2 = 750 mL/minute), and to maintain normal alveolar P co 2 , ventilation must increase (in this case, to 15 L/minute). Again, however, a 50% reduction in ventilation (from 15 to 7.5 L/minute) results in doubling of the alveolar P co 2 .

Arterial Gas Composition

In normal lungs, Pa co ₂ is tightly regulated by the brain stem respiratory center, and maintained at 40 ± 2 mm Hg. Increases or decreases in Pa co ₂ , particularly when associated with changes in arterial pH, have profound effects on cell function, including enzyme and protein activity. Specialized chemoreceptors monitor Pa co ₂ in the brainstem ( Chapter 25 ), and exhaled minute ventilation ( Eq. 23.1 ) varies in accordance with the level of Pa co ₂ .

An acute increase in Pa co ₂ results in respiratory acidosis (pH < 7.35), whereas an acute decrease in Pa co ₂ results in respiratory alkalosis (pH > 7.45). Hypercapnia is defined as an elevation in Pa co ₂ , and it occurs when CO ₂ production exceeds alveolar ventilation (hypoventilation). Conversely, hyperventilation occurs when alveolar ventilation exceeds CO ₂ production, and it decreases Paco ₂ (hypocapnia).

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Learning Objectives

Ventilation

Dead Space Ventilation: Anatomical and Physiological

Anatomical Dead Space

Physiological Dead Space

Alveolar Ventilation

Composition of Air

Alveolar Gas Composition

Arterial Gas Composition

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