Fig. 23.3 ). In the presence of increased resistance or increased compliance, however, volume equilibrium is not reached.
Adults with COPD have a very long time constant as a result when a person is supine rather than prone. This is because the diaphragm is pushed in a cephalad direction when a person is supine, and it affects the size of all of the alveoli.
In addition to gravitational effects on the distribution of ventilation, ventilation in alveoli is not uniform. The reason for this is variable airway resistance (R) or compliance (C), and it is described quantitatively by the time constant (τ):
Equation 23.17 of an increase in resistance and, in the case of individuals with emphysema, an increase in compliance. As a result, such affected adults tend to breathe at a low respiratory rate. Imagine now what happens when individuals with COPD climb a flight of stairs. The increase in respiratory rate does not allow sufficient time for a full exhalation, and a process called dynamic hyperinflation occurs (
Fig. 23.4 ); lung volumes, which are already increased, increase further, the lung becomes less compliant, and the work of breathing is very high.
CHAPTER 23 Ventilation, Perfusion, and Ventilation/Perfusion Relationships ˛=0.28 ˛=0.56 C=0.4 Decreased compliance C=0.8 Increased resistance R=0.7 R=1.4 R=0.7 ˛=1.12 • Fig. 23.4 Dynamic Hyperinflation. The total time for respiration (Ttot) is composed of the time for inspiration (Ti) and the time for exhalation (Te). When the respiratory rate increases (e.g., during exercise), Ttot decreases. In individuals with chronic obstructive pulmonary disease
C=0.8 Normal (COPD), the effect of the increase in Ttot on Te may not allow for complete emptying of the alveoli with a long time constant, and with each succeeding breath, there is an increase in the lung volume (air trapping). This increase in lung volume eventually results in such a degree of hyperinflation that the affected person is no longer able to do the work needed to overcome the decreased compliance of the lung at this high lung volume. In such individuals, it is a major cause of shortness of breath with activity. FRC, functional residual capacity.
• Fig. 23.3 Examples of Local Regulation of Ventilation as a Result of Variation in the Resistance (R) or Compliance (C) of Individual Lung Units. Top, The individual resistance and compliance values of three different lung units are illustrated. Bottom, The graph illustrates the volume of these three lung units as a function of time. In the upper schema, the normal lung has a time constant (τ) of 0.56 second. This lung unit reaches 97% of final volume equilibrium in 2 seconds, which is the normal inspiratory time. The lung unit at the right has a twofold increase in resistance; hence its time constant is doubled. That lung unit fills more slowly and reaches only 80% volume equilibrium during a normal inspiratory time (see graph); thus this lung unit is underventilated. The lung unit on the left has decreased compliance (is “stiff”), which acts to reduce its time constant. This lung unit fills quickly, reaching its maximum volume within 1 second, but receives only half the ventilation of a normal lung unit.
Blood flow in the pulmonary circulation is pulsatile and influenced by pulmonary vascular resistance (PVR), gravity, alveolar pressure, and the arterial-to-venous pressure gradient. PVR is calculated as the change in pressure from the pulmonary artery (PPA) to the left atrium (PLA), divided by the flow (QT), which is cardiac output:
Equation 23.18
Under normal circumstances,
Equation 23.19