## Ventilation and Perfusion

Gaseous exchange is mediated by the combination of ventilation of the alveoli with inspired air and the perfusion of the capillaries with blood. It is the balance of these two that determines the gas content of the lungs and of the recharged blood.

To see how this balance is maintained, suppose that V is the volume flow rate of air that participates in the exchange of the alveolar content. Not all inspired air participates in this exchange, because some inspired air never reaches the terminal bronchioles. The parts of the lung that are ventilated but do not participate in gaseous exchange are called the anatomical dead space. In normal breathing, the total amount of inspired air is about 500 ml per breath (men 630 ml; women 390 ml). Of this, 150 ml is anatomical dead space, so only 350 ml participates in alveolar gaseous exchange. With 15 breaths per minute, V is about 5250 ml/min.

Now suppose that Q is the volume flow rate of blood into and out of the alveolar capillaries. Cardiac output is about 70 ml per beat, so at 72 beats per minute, Q is about 5000 ml/min. The ratio V/Q is called the ventilation-perfusion ratio, and it is the most important determinant of lung-blood gas content.

If ci and ca are the concentrations of a gas in the inspired air and in the alveolar air, respectively, then the flow of the gas is

Similarly, the flow of the gas into the blood is given by

where c0 and cL are the input and output capillary gas concentrations. The fact that these two must be in balance leads to the equation

From the previous section we learned that the two most important respiratory gases, carbon dioxide and oxygen, are equilibrated when they leave the alveolus in the capillaries. In other words, the partial pressures of carbon dioxide and oxygen in the alveolus and in the blood leaving the pulmonary capillary are the same. Of course, this is not true at high perfusion rates, but it is a satisfactory assumption at normal physiological flow rates.

Because carbon dioxide is quickly converted to bicarbonate, the total blood carbon dioxide (i.e., both free and converted) is given by

This implies that for carbon dioxide, the ventilation-perfusion ratio must satisfy

Q Pa where P0 and Pa are the inflow and alveolar carbon dioxide partial pressures. Note that we have taken the carbon dioxide partial pressure in the inspired air to be zero, we have assumed that PL = Pa, and we have used the ideal gas law to express the atmospheric carbon dioxide concentrations in terms of pressures.

For oxygen, the relationship between partial pressure and total blood oxygen (both free and bound to hemoglobin) is determined from the hemoglobin saturation function f (W) as

where Z0 is the total hemoglobin concentration, as in the previous section. In these terms the ventilation-perfusion ratio must be

V RT

where the subscripts a, i, and 0 have the same interpretations as above. Here, as with carbon dioxide, we assume that the partial pressure of oxygen in the alveolar air is the same as the partial pressure in the blood leaving the alveolus, so that Wa = aOlPa.

A plot of the alveolar partial pressures of carbon dioxide and oxygen as a function of ventilation-perfusion ratio is shown in Fig. 17.7. This figure was determined as follows. First, using Wa as a parameter and keeping W0 = 40ctQ2 mm Hg fixed, the ventilation-perfusion curve for oxygen was found using (17.45). For this curve we used m X

J9 o

60 H 40

60 H 40 Ventilation-perfusion ratio

Figure 17.7 Alveolar partial pressure as a function of ventilation-perfusion ratio.

Ventilation-perfusion ratio

Figure 17.7 Alveolar partial pressure as a function of ventilation-perfusion ratio.

f (W) = -W^ with KO2 = 30a mm Hg, and Z0 = 2.2mM (RT = 1.7 x 104 mm Hg/M).

Then, we used (17.43) to find the carbon dioxide partial pressure as a function of ventilation-perfusion. For this plot, PCO2 = 45 mm Hg, and we chose Kc = 12 because it gives a reasonable fit of the available data.

From this figure we see that the alveolar oxygen partial pressure is an increasing function of V/Q, while the alveolar carbon dioxide partial pressure is a decreasing function thereof. In normal situations, the ventilation-perfusion ratio is about 1. An increase in this ratio is called hyperventilation, and a decrease is called hypoventilation. During hyperventilation, there is rapid removal of carbon dioxide, and the partial pressure of carbon dioxide in the arterial blood drops below the normal level of 40 mm Hg. This results in less carbon dioxide available for carbonic acid formation, and consequently blood pH rises above the normal level, resulting in respiratory alkalosis. In hyperventilation there is no substantial change in oxygen concentration because the hemoglobin is fully saturated.

The opposite situation, in which the ventilation-perfusion ratio drops, increases carbon dioxide content and decreases oxygen content of the arterial blood. The increase of carbon dioxide increases carbonic acid formation and decreases blood pH, a condition referred to as respiratory acidosis. To compensate for these changes, the blood gas concentration stimulates the carotid and aortic chemoreceptors to increase the rate of ventilation.

In Fig. 17.8 is shown the volume fraction of gaseous exchange as a function of ventilation-perfusion ratio. (Volume fraction of a gas is the fraction of gas in a given volume, found as the ratio ofpartial pressure to total pressure.) Typical partial pressures of the respiratory gases are shown in Table 17.1.

The oxygen that is taken in by the blood is consumed by metabolic processes to produce carbon dioxide. However, the amount of carbon dioxide produced is generally

Table 17.1 Partial pressures (in mm Hg) of respiratory gases as they enter and leave the lungs.

 Substance Atmospheric air Humidified air Alveolar air Expired air n2 597.9 563.5 569.0 566.0 O2 159.0 149.3 104.0 120.0 CO2 0.3 0.3 40.0 27.0 H2O 3.7 47.0 47.0 47.0

less than the amount of oxygen consumed. The respiratory exchange rate R is the ratio of carbon dioxide output to oxygen uptake, and is rarely more than one. When a person is using carbohydrates for body metabolism, R is 1.0 because one molecule of carbon dioxide is formed for every molecule of oxygen consumed. On the other hand, when oxygen reacts with fats, a large share of the oxygen combines with hydrogen to form water instead of carbon dioxide. In this mode, R falls to as low as 0.7. For a normal person with a normal diet, R = 0.825 is considered normal.

Since the respiratory exchange rate is just the ratio of the two curves shown in Fig. 17.8, one can use that figure to determine the ventilation-perfusion ratio as a function of the respiratory exchange rate, which is, in turn, determined by the metabolism.

For these figures, the inflow carbon dioxide and oxygen partial pressures were fixed at 45 and 40 mm Hg, respectively. If, however, the metabolic rate and the type of metabolism are taken into account, the inflow partial pressures are determined by those rates and are not fixed. For example, during strenuous exercise, the partial pressure of oxygen in the tissue can drop to as low as 15 mm Hg. However, the general result is the same, namely that alveolar carbon dioxide partial pressure decreases with increasing V/Q and alveolar oxygen partial pressure increases. Ventilation-perfusion ratio

Figure 17.8 Volume fraction of gaseous exchange as a function of ventilation-perfusion ratio.

Ventilation-perfusion ratio

Figure 17.8 Volume fraction of gaseous exchange as a function of ventilation-perfusion ratio. Figure 17.9 Effects of increased arterial PCO2 and decreased arterial pH on the alveolar ventilation rate. (Guyton and Hall, 1996, Fig. 4^, p. 528.)