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FIGURE 3 (A) Plastic cast of the lung airways showing extensive branching. (B) Diagram of terminal airway branches in an acinus, which is the functional unit of gas exchange in the lung. Pulmonary arterioles travel next to the bronchi to the level of respiratory bronchioles and branch extensively to cover the alveoli with pulmonary capillaries. Pulmonary veins are further from the bronchioles.

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FIGURE 3 (A) Plastic cast of the lung airways showing extensive branching. (B) Diagram of terminal airway branches in an acinus, which is the functional unit of gas exchange in the lung. Pulmonary arterioles travel next to the bronchi to the level of respiratory bronchioles and branch extensively to cover the alveoli with pulmonary capillaries. Pulmonary veins are further from the bronchioles.

Physical and Chemical Principles in Respiratory Physiology

Quantitative descriptions of gas exchange depend on relatively simple applications of the principle of conservation of mass (or mass balance) and the ideal gas law using the symbols defined in Table 1. The symbols may appear complicated at first, but they are based on a few simple conventions. Primary variables are symbolized with a capital letter, and a dot over the variable indicates the first derivative with respect to time (e.g., Q = blood flow, or quantity of blood per unit time in liters per minute). Modifiers are small capitals for the gas phase (e.g., Va= alveolar ventilation) and lowercase letters for liquid or tissues (e.g., Pa = partial pressure in arterial blood). Finally, a specific gas species is indicated with a subscript (eg, Cao2 = O2 concentration in arterial blood in mL O2/dL blood).

The principle of conservation of mass is simply that matter is neither created nor destroyed. This principle was applied to physiologic transport by the German physiologist Fick in the last century. The Fick principle states that the amount of a substance consumed or produced by an organ is the difference between the amount of the substance entering the organ and the amount leaving the organ. To calculate whole-body O2 consumption (Vo2 in milliliters per minute), one measures the difference between the amount of O2 inspired and the amount of O2 expired from the lungs per unit time. The amount of O2 inspired = V • Fio2, where V = ventilation (in liters per minute) and Fio2 = fractional concentration of O2 in inspired gas (0.21 for room air). The amount of O2 expired = V • Feo2, where Feo2 is the fractional concentration of O2 in mixed-expired gas. If inspired ventilation equals expired ventilation, then:

In a steady state, Vo2 is equal at each of the steps in the O2 cascade, so a similar equation can be written for the cardiovascular system. The amount of O2 consumed by the body equals the difference between arterial O2 delivery and venous O2 return:

V02 = Q (Cao2 — Cvo2 ), where Q = cardiac output (in liters per minute), Cao2 = 02 concentration in arterial blood (mL 02/dL blood), and Cvo2 = 02 concentration in mixed venous blood. The Fick principle can be used to calculate cardiac output (Q) from measurements of whole-body 02 consumption and arterial and venous 02 concentrations by rearranging the preceding equation.

Chapter 21 considers more applications of the Fick principle, which describes gas transport by convection, or bulk flow of air or blood. In contrast, diffusion is the mechanism of 02 transport across the blood-gas interface in the lungs and across systemic capillaries in metabolizing tissues. Fick also quantified diffusive gas transport with Fick's first law of diffusion:

V o2 = APo2D, where APo2 is the average 02 partial pressure gradient between two compartments, and D is a diffusing capacity, as defined in Chapter 21.

Note that the diffusive transport of respiratory gases occurs down a partial pressure gradient. Partial pressure of a gas is defined by Dalton's law, which states that the partial pressure of gas x in a mixture of gases is equal to the pressure that gas x would exert if the other gases were not present. Therefore:

Px — Fx(Ptot), where Fx is the fractional concentration of gas x in a dry gas sample. For example, PO2 in dry air at sea level is 160 mm Hg (= 0.21 • 760 mm Hg, where the O2 concentration is 21% in air and barometric pressure is 760 mm Hg at sea level). Partial pressure is also expressed in units of Torr (1 Torr = 1 mm Hg) or SI units of kilopascals (1 kPa = 7.5 mm Hg) in physiology.

For calculating partial pressure in the gas phase, it is important to specify the total dry gas pressure because of the effects of water vapor pressure in humidified gases. Water vapor pressure is determined only by the temperature and relative humidity of a gas, and it is independent of total pressure. Inside the lungs, temperature is generally 37°C and relative humidity is 100%. Saturated water vapor pressure at 37°C = 47 mm Hg, so the total gas pressure available for O2 and CO2 inside the body is reduced by this amount. Assuming barometric pressure equals 760 mm Hg:

Therefore, PO2 in inspired gas, which is saturated with water vapor at body temperature, is only 150 mm Hg (= 0.21 • 713 mm Hg) at sea level.

Gases dissolved in fluids also exert a partial pressure, and diffusion of gases also occurs down partial pressure gradients between fluids. For example, O2 diffuses from O2-rich blood in capillaries toward mitochondria where it is near zero. The partial pressure of gas x in solution equals Px in a gas mixture that would be in equilibrium with that solution. Henry's law describes the linear relationship between the concentration (C in mL/dL or mmol/L) and partial pressure (P in mm Hg) of gas x dissolved in solution:

where ax is the physical solubility of gas x in the solution. The relationship between O2 and CO2 concentration and partial pressure in blood is more complex because of chemical reactions between these physiologic gases and blood (Chapter 20).

The volume of a gas sample depends on temperature and pressure according to the ideal gas law:

Lung Airways and Ventilation where n is the number of moles, R is the universal gas constant, and T is temperature in degrees kelvins. Avogadro's law specifies that 1 mol of an ideal gas occupies 22.4 L at standard temperature (0°C) and standard pressure (760 mm Hg) when dry. Such volumes are called standard temperature and pressure dry (STPD), and can be used instead of moles to quantify the amount of a gas. For example, Vo2 and Vco2 are generally expressed as mLSTPD/min.

Ventilation and lung volumes are not usually dry gas volumes measured at 0°C and 760 mm Hg, however. Lung volumes occur at body temperature, actual barometric pressure, and saturated with water vapor. Such physiologic volumes are called body temperature and pressure saturated (BTPS) and they can be converted to STPD volumes as follows:

Vstpd = Vbtps (273 K/Tbody in K) (Pb/760) ([Pb - Ph2o]/Pb).

Vstpd = Vbtps (273°/310°) (713/760) Vstpd = Vbtps (0.826).

This equation derives from two special applications ofthe ideal gas law. Boyle's law states that volume is inversely proportional to pressure at constant temperature:

Charles' law states that volume is directly proportional to temperature at constant pressure:

Volumes are measured frequently at ambient temperature and pressure, or ambient temperature and pressure saturated (ATPS) conditions. For normal values of Pb = 760 mm Hg and T = 37°C, ATPS can be converted to STPD or BTPS by:

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