The conducting airways from the mouth and nose down to and including terminal bronchioles constitute anatomical dead space (V_Danat). Ventilation of these airways is necessary to move gas to and from the alveoli, but no gas exchange occurs between blood and air across their walls. The fresh gas filling the conducting airways at the end of inspiration (see Figure 4-2, left) is exhaled and is sometimes called “wasted” ventilation because it takes no part in respiration. The term wasted ventilation is synonymous with dead space ventilation. Dead space is defined as airspaces that are ventilated but do not exchange gases with the pulmonary circulation.

The volume in the conducting airways (V_Danat) does not change unless surgery removes part of a lung or an artificial airway (endotracheal or tracheostomy tube) bypasses the upper airway dead space. Anatomical dead space increases slightly during a deep inspiration and with administration of drugs that relax smooth airway muscle because these factors increase the airway diameter. Diseases characterized by hyperinflation of the lungs (e.g., emphysema) increase V_Danat for the same reason. For clinical monitoring purposes, V_Danat is considered to be constant.

Gas Composition of Anatomical Dead Space

The composition of V_Danat gas is different at the end of expiration than at the end of inspiration (Figure 4-3). An inspired V_T of 500 mL completely flushes the normal 150 mL of V_Danat with atmospheric air, leaving behind a PCO₂ of 0 mm Hg and a PO₂ of 149 mm Hg (see Figure 4-3, left). Dead space gas is identical in composition to inspired air except that it is 100% humidified. After the 500 mL of V_T is completely exhaled, the 150 mL of V_Danat (see Figure 4-3, right) is wholly occupied by gas that came from the alveoli. The humidified atmospheric air that occupied the dead space at end-inspiration was exhaled ahead of the alveolar gas (i.e., this gas was wasted because it did not participate in respiration). At end-tidal expiration, dead space gas is identical in composition to the average alveolar gas composition. Under normal circumstances, end-tidal expiratory gas is assumed to be identical in composition to alveolar gas.

The alveolar gas residing in the dead space is reinspired with the next breath. Therefore, the first 150 mL of the inspired V_T does not change the alveolar gas composition.

The exhaled V_T is a mixture of dead space gas (identical to inspired gas—containing no CO₂) and alveolar gas (which contains CO₂). The PCO₂ of mixed exhaled gas is lower than alveolar PCO₂ (P_ACO₂) because dead space gas free of CO₂ is a component of exhaled gas. This fact is helpful in understanding the calculation of the dead space-to-tidal volume ratio (V_D/V_T) later in this chapter.

Measuring Anatomical Dead Space

V_Danat is related to lung size; in normal adults, anatomical dead space is approximately 1 mL per pound of ideal body weight.¹ The Fowler technique provides a more precise measurement of V_Danat (Figure 4-4).² In the Fowler technique, the subject first exhales maximally to residual volume (RV), then takes a maximal inhalation of 100% O₂ to total lung capacity, then exhales maximally to RV again. This technique is based on the fact that air is a mixture of N₂ and O₂. An N₂ analyzer is used to measure continuously the exhaled N₂ concentration at the mouth after the single maximal inspiration of 100% O₂. N₂ concentration measured at the mouth decreases abruptly to 0 during the 100% O₂ inspiration (see Figure 4-4). At the end of inspiration, V_Danat contains pure O₂, which is the first gas to be exhaled. This means that N₂ concentration remains at 0% for the first part of the expiration.

As expiration proceeds, alveolar gas (which still contains some N₂) moves up into the conducting airways, and dead space N₂% gradually increases to alveolar levels—note the S-shaped curve in Figure 4-4. The increase in N₂% would be sharp and abrupt if dead space and alveolar gas were completely separated, as illustrated by the hypothetical square front in Figure 4-5, A. If this were the case, N₂% would remain at 0% until all dead space gas was expired, and then it would abruptly increase to alveolar levels when alveolar gas suddenly appeared, as shown by the theoretical thin, solid vertical line in Figure 4-4. V_Danat would simply be the volume exhaled to the sharp increase in N₂%. However, alveolar gas moves through conducting airways in a conical rather than square front (see Figure 4-5, B), mixing with dead space gas. This movement makes it difficult to detect the exact point at which only the V_Danat has been expired. It is necessary to construct a line representing the theoretical square front that would be seen if all N₂-free dead space gas were expired first, followed by only N₂-containing alveolar gas. The hypothetical square front is constructed by placing a vertical line (see Figure 4-4) such that area A equals area B (i.e., in effect, the vertical line averages alveolar and dead space gas compositions). The dead space volume is the volume expired up to the hypothetically constructed square front.

Alveolar and Physiological Dead Space

Alveolar dead space (V_DA) is the volume contained in nonperfused alveoli—that is, alveoli with no blood flow. The presence of V_DA is abnormal. Any factor decreasing pulmonary blood flow, such as extremely low cardiac output or a pulmonary embolus, increases V_DA. V_DA represents a decreased surface area for gas exchange and an increase in total wasted ventilation.

Physiological dead space (V_D) is the sum of V_Danat and V_DA (V_D = V_Danat + V_DA). Similarly, physiological dead space ventilation (V._D) per minute is as follows:

V.D=V.Danat+V.DA

V._D is increased not only by decreased pulmonary blood flow but also by an increased breathing rate. Doubling the breathing frequency doubles the number of times the V_T moves through the V_Danat, doubling the V._Danat.

Alveolar Ventilation

V._A is the amount of gas entering or leaving the alveoli per minute. It is the effective portion of the V._E in the sense that only V._A takes part in respiration. As shown previously, if V._D and V._E are known, V._A is easily calculated (V.A=V.E−V.D).

All CO₂ in exhaled gas comes from ventilated alveoli that have blood flowing through their capillaries. The source of this CO₂ is tissue metabolism. Normal aerobic metabolism produces CO₂, which is carried by venous blood to the lungs (see Figure 4-3). The mixed venous PCO₂ (Pv¯CO₂) approaching the alveoli is several millimeters of mercury higher than P_ACO₂. Thus, CO₂ diffuses into the alveoli.

Inspiration brings fresh CO₂-free gas into the alveoli, and expiration removes a portion of the CO₂-rich alveolar gas (see Figure 4-3). The balance between metabolic CO₂ production per minute (V.CO₂) and its rate of elimination (V._A) determines the PCO₂ of alveolar gas and the PCO₂ of the blood leaving the lung.

Alveolar Ventilation and P_ACO₂

P_ACO₂ is inversely related to PACO2×V.A=KV._A; if V._A is reduced by half, P_ACO₂ doubles. If V._A doubles, P_ACO₂ (and PaCO₂) is reduced by half. For example, if a V._A of 5 L per minute produces a P_ACO₂ of 40 mm Hg, a V._A of 10 L per minute produces a P_ACO₂ of 20 mm Hg. Similarly, a V._A of 2.5 L per minute produces a P_ACO₂ of 80 mm Hg. The V._A equation illustrates this relationship ().³ In this equation, K is a constant. (See Appendix III for the derivation of this equation.) This equation is based on the assumption that during a steady state of blood flow and ventilation, CO₂ production (V.CO₂) is constant and equal to CO₂ elimination. Normally, P_ACO₂ and PaCO₂ have almost identical values; as a rule, V._A has the same relationship with PaCO₂ as it has with P_ACO₂. Figure 4-6 illustrates the inverse relationship between P_aCO₂ and V._A

PCO₂ Equation

Because dead space does not participate in gas exchange, all CO₂ in exhaled gas comes from the alveoli. The amount of CO₂ the lungs exhale each minute (V.CO₂) equals the V._A multiplied by the concentration of CO₂ in the alveoli. This is shown as follows:

1. 

V.CO2=V.A×FACO2

In this equation, F_ACO₂ is the fractional concentration of CO₂ in the alveoli. The P_ACO₂ can be determined by multiplying F_ACO₂ by the total alveolar gas pressure. Therefore, equation 1 can be rewritten as follows:

2. 

V.CO2=V.A×PACO2×K

In this equation, K is a constant that reconciles the different measurement units; V.CO₂ is measured in milliliters per minute,

Clinical Focus 4-2   Predicting the Change in P_ACO₂ for a Given Change in Minute Ventilation

A mechanical ventilator is delivering 10 breaths per minute to your patient. The V_T is 700 mL, and the patient’s estimated V_Danat is 160 mL. Arterial blood gas results reveal a PaCO₂ of 40 mm Hg. What happens to V._A and PaCO₂ if the respiratory rate is increased to 16 breaths per minute but the V._E remains constant?

Discussion

Initial V._E and V._A are calculated as follows:

V.E=700×10=7000mL/min

V.A=(700−160)×10=5400mL/min

With a V._A of 5400 mL/min, PaCO₂ is normal at 40 mm Hg. If V._E stays the same while you increase the respiratory rate to 16 breaths per minute, V_T must decrease (i.e., the ventilatory pattern is changed to a rapid, shallow pattern). This is shown as follows:

7000=VT×16

VT=7000/16=437.5mL

Because V_Danat remains the same at 160 mL, V._A must decrease. This is shown as follows:

V.A=(437.5−160)×16=4440mL/min

After the change in respiratory rate, arterial blood gases reveal a PaCO₂ increase from 40 mm Hg to 49 mm Hg (see Clinical Focus 4-4). CO₂ production remained the same, and the reduced V._A resulted in a decreased removal of CO₂ from the body, creating a state of hypoventilation.

V._A is measured in liters per minute, and P_ACO₂ is measured in millimeters of mercury (see Appendix III for the derivation of K). Equation 2 can be solved for P_ACO₂ as follows:

3. 

PACO2=V.CO2V.A×K=V.CO2V.A×1K

In this equation, 1/K is equal to 0.863. The classic PCO₂ equation is written as follows:

4. 

PACO2=V.CO2×0.863V.A

Because P_ACO₂ is usually equal to PaCO₂ in the absence of lung disease, PaCO₂ can be substituted for P_ACO₂. This is shown as follows:

5. 

PaCO2=V.CO2×0.863V.A

Equation 5 means that the balance between the rate of CO₂ elimination (V._A) and the rate of CO₂ production (V.CO₂) determines the PaCO₂. For example, under normal resting conditions, the body produces about 200 mL of CO₂ each minute, and alveolar ventilation is about 4 L per minute; using equation 5, PaCO₂ is calculated to be about 43 mm Hg. If V._A decreases to 3 L per minute while V.CO₂ stays the same, PaCO₂, as calculated with equation 5, would increase to about 58 mm Hg, indicating the presence of hypoventilation. If instead the metabolic rate increases, increasing CO₂ production to 300 mL per minute, but V._A stays at 4 L per minute, PaCO₂ increases to 65 mm Hg, again indicating hypoventilation. In the latter example, the lungs fail to increase V._A to meet the increased need for CO₂ elimination. (See Appendix III for the complete derivation of equation 5 and the 0.863 factor.) Equation 5 also can be solved for V._A; if the PaCO₂ and V.CO₂ are known, V._A can be calculated as follows:

6. 

V.A=V.CO2×0.863PaCO2

Modern CO₂ measuring devices called capnometers make it feasible to measure V.CO₂ in the clinical setting. This information, coupled with arterial blood PaCO₂ analysis, allows V._A to be precisely quantified.

Ratio of Dead Space to Tidal Volume

V._A can be calculated if the fraction of V_T that is dead space (V_D/V_T) is known. Normally, about 30% to 40% of the inspired V_T remains in conducting airways, never reaching alveoli (see Figure 4-2, left), which means V._D constitutes about 30% to 40% of V._E.³ It follows that about 60% to 70% of the V._E is V._A. Shallow tidal volumes increase V_D/V_T because conducting airway volume (V_Danat) remains constant (see Figure 4-2, right). Deep breaths decrease V_D/V_T for the same reason, causing a larger percentage of the inspired volume to reach the alveoli.

With the basic relationship (V_T = V_D + V_A), V_A can be expressed in terms of V_D/V_T and V_T. This is shown as follows:

VA=VT(1−[VD/VT])

This formula is useful if V_D is unknown but V_D/V_T is known. For example, if a normal adult weighing 150 lb has a V_T of 500 mL and V_D/V_T equals 0.33, 33% of the V_T is dead space; the remaining 67% of the V_T must be V_A. This is shown as follows:

VA=500(1−0.33)

VA=500(0.67)

VA=335mL

The V_D/V_T can be clinically calculated if the mixed exhaled carbon dioxide (PE¯CO2) and PaCO₂ partial pressures are known. The physiological dead space equation, known as the Bohr equation, allows the V_D/V_T to be calculated in the following manner:

VD/VT=PaCO2−PE¯CO2PaCO2

In this equation, PE¯CO2 is the mean carbon dioxide pressure of mixed-expired gas (dead space plus alveolar gas). (See Appendix III for the derivation of the Bohr equation.)

The Bohr equation is based on the premise that all CO₂ in mixed-expired gas originates from the alveoli and not the dead space. Figure 4-7 illustrates this point; the lightly shaded blocks represent CO₂-free inspired air, and the darkly shaded blocks represent CO₂-containing alveolar gas. The CO₂ in exhaled gas (two dark blocks) comes from the alveoli; dead space gas, which contains no CO₂ (one light block), makes up the rest of the exhaled volume.

PE¯CO2 is always less than P_ACO₂ because the exhaled V_T consists of V_Danat gas, which has a PCO₂ of 0 mm Hg, mixed with alveolar gas (Figure 4-8). The degree to which V_Danat gas reduces the PCO₂ of mixed expired gas is reflected by the size of the difference between P_ACO₂ and PE¯CO2. This difference is proportional (∝) to V_Danat (see Figure 4-8), shown as follows:

VDanat∝(PACO2−PE¯CO2)

In Figure 4-8, two thirds of the exhaled V_T originates from alveoli (P_ACO₂ of 40 mm Hg), and one third originates from V_Danat (PCO₂ of 0), yielding a mixed-expired PCO₂ of 26.7 mm Hg. The Bohr equation confirms that V_D/V_T is 0.33 (i.e., that V_Danat is one third of V_T). The PACO2−PE¯CO2 difference in the numerator of the Bohr equation reflects only the presence of V_Danat. It does not accurately reflect the presence of V_DA. As illustrated in Figure 4-9, if some alveoli lose their blood flow, the PCO₂ values hypothetically decrease to 0, causing average P_ACO₂ to decrease also. (Average P_ACO₂ is measured through an analysis of the gas stream at end-expiration.) Mixed-expired gas in Figure 4-9 contains anatomical plus alveolar dead space gas, causing PE¯CO2 to decrease to 13.3 mm Hg. (Compare Figures 4-8 and 4-9.) If alveolar dead space is present, and the PACO2−PE¯CO2 difference is improperly used in the numerator of the Bohr equation, the calculated V_D/V_T is 0.34 (see Figure 4-9), essentially the same as in Figure 4-8, where no V_DA is present. However, if the PACO2−PE¯CO2 difference is used in the Bohr equation, the physiological, or total, dead space can be calculated. This form of the Bohr equation takes into account both V_DA and V_Danat⁴ The term (PACO2−PE¯CO2) should be used with the Bohr equation in the clinical setting because the size of this difference is directly proportional to the total V_D. This is shown as follows:

VD∝(PaCO2−PE¯CO2)

Changes in alveolar blood flow commonly occur in critically ill patients and are of great clinical interest. Conducting airway volume is not subject to periodic changes. Therefore, measuring V_Danat is not of great clinical importance. Rapid breathing increases V_Danat ventilation simply because it increases the number of times the V_T moves through the conducting airways each minute. Clinical physical assessment (counting the respiratory rate) easily detects this condition. However, placing a tracheostomy tube in the trachea below the larynx reduces the V_Danat because it bypasses all upper airways. Thus, for a given V_T, the alveoli would receive more ventilation than if the patient breathed normally through the upper airways. Endotracheal intubation also reduces V_Danat because the volume of the tube is much less than the volume of the upper airways.

Figure 4-9 illustrates the Douglas bag method for clinically measuring the mixed-expired gas in determining V_D/V_T. The person’s expired gas is collected over several minutes in a large, previously airless balloon (Douglas bag). An arterial blood sample is obtained at the same time. Mixed-expired and PaCO₂ values are used in the Bohr dead space equation. (The Douglas bag is no longer used clinically, but it is used in this example to illustrate the concept.)

A capnometer is a device used in the clinical setting to analyze exhaled CO₂. These instruments respond instantaneously to PCO₂ changes. Capnography refers to the PCO₂ changes of exhaled tidal volumes graphically displayed as a waveform (capnogram). A capnogram allows the PCO₂ to be identified at the end of a tidal exhalation (P_ETCO₂), which corresponds to average P_ACO₂ (P_ACO₂ = P_ETCO₂). (P_ETCO₂ reflects alveolar gas composition and is not equal to mixed expired PCO₂, which reflects the composition of a mixture of dead space and alveolar gases; i.e., PETCO2≠PE¯CO2.) A microprocessor can determine the average PCO₂ over the entire exhaled V_T (PE¯CO2).

Successive measurements over time are useful for following trends and assessing the effects of therapeutic interventions on pulmonary blood flow. V_D/V_T is a measure of ventilatory efficiency. A high V_D/V_T means much of the V._E is wasted in ventilating nonperfused alveoli, requiring high-energy expenditure to accomplish a relatively small amount of V._A