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Pittman RN. Regulation of Tissue Oxygenation. San Rafael (CA): Morgan & Claypool Life Sciences; 2011.

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# Chapter 3The Respiratory System and Oxygen Transport

Before describing the regulation of tissue oxygenation, it is instructive to consider the respiratory system and how blood flowing through the pulmonary capillaries is oxygenated. Prior to that discussion, it is necessary to review the physical chemical basis by which oxygen is carried in the blood and how it moves between the air spaces and the blood.

## PHYSICAL CHEMISTRY OF RESPIRATORY GASES

### Gas Laws

The quantitative relationship among the pertinent variables in a gas confined to a volume, V, is given by the Ideal Gas Law:

3.1
where P is the pressure due to gas molecules in the volume, V; n is the number of moles of gas in the volume; R is the molar gas constant (= 0.082 atm l K−1 mol−1); and T is the absolute temperature (K). For the respiratory gases at normal physiological pressures and temperatures, the Ideal Gas Law adequately describes the relationship among P, V, n and T. The Ideal Gas Law is a combination of Boyle's law (1622, PV = constant) and Charles' (1678) and Gay-Lussac's laws (1809) to represent the relation among the pressure, volume and temperature of a given mass of ideal gas. A related and useful relationship is Avogadro's law (1811) which states that equal volumes of different gases at the same temperature and pressure contain the same number of molecules. At one atmosphere pressure (760 mm Hg at sea level) and a temperature of 0 °C (273 K), the volume of 1 mole of an ideal gas is 22.4 l.

Dalton's law of partial pressures defines the partial pressure of a gas in a gas mixture as the pressure that the gas would exert if it occupied the total volume of the mixture in the absence of the other components (i.e., no interactions between gas molecules). Dalton's law follows directly from the Ideal Gas Law since it states that the pressure exerted by a gas is proportional to the number of moles of that gas. Thus,

3.2
where Pi is the partial pressure of gas component i, Fi is the mole fraction of component i (or ni/ntotal, where ni is the number of moles of component i among the total number of moles of all gases in the mixture, ntotal) and PB is the ambient barometric pressure. The total pressure of a gas mixture is thus the sum of the partial pressures of all the components. For the four gases normally found in the alveoli, we have:
3.3
since, by definition, PB is the total pressure of all gases in a mixture in contact with the atmospheric pressure. For instance, at sea level, barometric pressure is 760 mm Hg, and oxygen makes up 21% of dry air. Thus, the partial pressure of oxygen in dry air is PO2 = 0.21 × 760 mm Hg = 160 mm Hg.

It is useful to consider a few additional definitions and conventions related to respiratory gases. Pressure (P) is generally expressed in atmospheres (atm) or mm Hg. At sea level, 1 atm is equivalent to 760 mm Hg. The unit “mm Hg” is sometimes referred to as “torr.” Barometric pressure decreases at higher altitudes (e.g., at 5,000 ft, PB is 632 mm Hg). The absolute (Kelvin) scale is generally assumed in all equations involving temperature (T). To convert °C to K, add 273 to the Celsius reading.

Since respiratory gases are typically in a humidified environment, the vapor pressure of water, PH2O, deserves special consideration. For a volume of water at temperature, T, there will be some water molecules in the gas phase above those in the liquid phase due to evaporation. When equilibrium is reached between the gas and liquid phases (i.e., rate of evaporation = rate of condensation or return of gaseous water molecules to the liquid phase), the partial pressure due to the water molecules in the gas phase is defined to be the vapor pressure of water and its value depends on the temperature; values for different temperatures have been tabulated. For instance, PH2O (20°C) equals 17.5 mm Hg and PH2O (37°C) equals 47.0 mm Hg; PH2O increases with increasing temperature. Tracheal air is 100% humidified so that PH2O = 47 mm Hg in the trachea and beyond (i.e., alveolar gas, blood) at normal body temperature.

The two symbols BTPS and STPD represent two conventional conditions used when discussing respiratory gases. BTPS stands for body temperature (37°C), ambient pressure and gas saturated with water vapor, whereas STPD stands for standard temperature (0°C or 273 K) and pressure (760 mm Hg) and dry (no water vapor). Pulmonary ventilation (1/min) is usually measured at BTPS, whereas gas volumes in blood are usually expressed at STPD. To convert a gas volume at BTPS to one at STPD, one needs to multiply the former volume by (273/310) (PB − 47) / 760.

Finally, a few words about gas mixtures are in order. Consider a dry gas mixture containing the following fractional amounts of O2, CO2 and N2: FO2, FCO2 and FN2, respectively. If barometric pressure is PB, then the partial pressure of oxygen is PO2 = FO2 PB. Similar expressions hold for the other gases. If this same gas mixture is placed in a humidified volume (i.e., saturated with water vapor), then PO2 = FO2 (PBPH2O), where FO2 is the fraction of the gas that is oxygen in a dry mixture. The partial pressures of all the gases in the mixture must add up to PB, but PH2O is already set by the ambient temperature. One can think of the other gases as being diluted by the presence of water vapor.

### Properties of Gases in Liquids: Henry's Law

Gases are soluble to varying degrees in liquids and, as a general rule, the solubility decreases with increasing temperature. Henry's law (1803) relates the amount of gas dissolved in a liquid to the partial pressure (P) of the gas: C = α P, where C is the concentration of the gas in solution, and a is the Bunsen solubility coefficient, which is specific for a given gas and liquid.

When a liquid is put in contact with a gas phase of partial pressure, Pgas, gas will dissolve in the liquid until equilibrium is reached between the two phases. The condition for equilibrium of a gas between a gas phase and a liquid phase is that the partial pressures of the gas are equal in the two phases, not the concentrations, as is the more familiar case for non-gaseous solutes. Thus, at equilibrium, Pliquid = Pgas rather than Cliquid = Cgas. This is an important principle in understanding gas exchange between the alveolar space (gas phase) and the pulmonary capillary blood (liquid phase). In general, gases diffuse between sites where there is a difference in partial pressure (e.g., red blood cell and plasma, ISF and cell cytoplasm), not in concentration. Thus, gas exchange takes place between the two phases as long as there is a partial pressure difference between them. Once equilibrium is reached, net gas exchange ceases.

Table 1 gives Henry's law solubility coefficients for several common gases in four different media.

#### Table 1

Solubilities of some common gases.

Except for CO2, these gases are quite insoluble in aqueous media. The partial pressure used above in Henry's law is the pressure in the gas phase above a solution in equilibrium with that gas. Dissolved gas concentrations are often expressed as “volume percent (vol% = ml gas/100 ml liquid).” Thus, 10 ml of O2 dissolved in 100 ml of water would yield a concentration of 10 vol%. Key assumptions for Henry's law are that (1) the gas does not chemically react with the solvent and (2) the gas does not bind to other molecules in the solution.

### Forms in Which Gases Are Carried

All gases are carried in solutions in the dissolved form, and Henry's law describes the relationship between gas content or concentration, [X], and the partial pressure of the gas, PX:

3.4
where aX is the solubility coefficient of gas X. It is important to remember that only free gas molecules (those that are physically dissolved) contribute to the partial pressure of a gas in solution. Gases bound to proteins (e.g., O2, CO2, CO) or present in a chemically modified form (e.g., CO2 as HCO3) do not contribute to the partial pressure of the gas and hence are not “seen” by regulatory mechanisms that rely upon free gas molecules.

Gases can be bound to protein molecules, such as hemoglobin or plasma proteins. Examples of this form of gas carriage are oxygen or carbon monoxide bound to the heme groups of the hemoglobin molecule or carbon dioxide bound to the terminal amino groups of hemoglobin or plasma proteins.

Some gases can be carried in a chemically modified form. For instance, most (∼90%) of the CO2 in blood is carried as HCO3. Carbon dioxide taken up by the blood is converted to bicarbonate in the red blood cells (with the help of the enzyme carbonic anhydrase) and plasma as blood passes through the tissues, and the process is reversed when the blood passes through the pulmonary circulation.

The total concentration of a gas in a liquid is the sum of the concentrations of the various forms in which it is carried and is given by the expression:

3.5

Bookshelf ID: NBK54114