Appendix 2. Basic physical properties applied to the respiratory system Fluid is a general definition of a state of matter characterized by a weak intermolecular connection (Van der Waal's cohesive forces), with molecules relatively free to change their respective positions. Hence, a fluid is unable to resist even the slightest shearing force, as opposed to a solid, which retains its original shape, or, if deformed, regains it when the force is eliminated. Both a gas and a liquid are fluids. In the former, the intermolecular connections are so weak that the matter does not have its own defined shape and volume. In the latter, the cohesive forces are sufficiently strong for the matter to retain its own volume; in fact, to a large extent, the volume (V) of a liquid cannot change irrespective of the pressure (P) applied. On the other hand, in the case of a gas, V is undefined, depending upon the pressure (P, Boyle's law) and the temperature (T, Charles' law) applied to it: P · V = n · R · T [eq.1] n being the number of molecules and R the gas constant. If P is measured in mm Hg, T in oK, and V in liters, R=62.4*; [*at standard T (273oK) R approximates 543 calories/mol] in standard Temperature, Pressure, Dry (STPD) conditions (T=273oK, P=760 mm Hg, dry) 1 mole of gas occupies a volume of approximately 22.4 liters. The cohesive forces are T dependent, becoming weaker when T increases. In fact, an increase in T implies that thermal energy has been added to the kinetic energy of the molecules. Hence, at any given P, T dictates whether a fluid is in a liquid or gaseous state. At standard P, the liquid- o o gas transitional T (boiling T) for H2O is at about 100 C, for O2 is -183 C. CO2 is somewhat special, in that it does not retain a liquid state, subliming directly from the solid to the gaseous o form at -42 C, i.e. melting and boiling T coincide. N2 retains the liquid form only between -210 (melting T) and -196oC (boiling T). These values would differ if P changed. For example, a reduction in P, as at high altitude, reduces the boiling T of water; on the highest Tibetan mountains, above 8,000 m, P is less than 240 mm Hg, and water vaporizes at T=-70oC. Sudden exposure to very low P, as in extra- atmospheric spaces, would imply the instantaneous boiling of all body fluids. Gas in a gas mixture When several gases are mixed together, as it is the case of air, gas law [eq.1] still applies, with P indicating Ptotal, i.e. the sum of the individual partial pressures, and N the sum of the total molecules (Dalton's Law: the total pressure of a gas mixture equals the sum of the pressure of each of the components). It follows that the partial pressure Px of a gas x can be easily calculated from its concentration n(x)/N and Ptotal, since Px is n(x)/N of Ptotal. For example, O2 is 20.95% of the total dry air; therefore, at Ptotal=760 mm Hg, its partial pressure PO2 is 20.95% of 760 mmHg, or 159 mm Hg. At Ptotal=240 mm Hg, PO2 is 50 mm Hg. Gas in a liquid In a condition of perfect equilibrium, by definition, there is no net flow of molecules in any direction. This would apply not only to the gas mixture of which the gas x is part, but also to the liquid in which it is dissolved. In other words, in a two-phase system in which a liquid and a gas are in contact with each other, once equilibrium is reached, Px is the same in the gas and in the liquid, i.e. Px(gas) = Px(liquid). If it was not so, a flow of molecules would be generated by the Px difference, negating the assumption of equilibrium. 1 However, Px(gas) = Px(liquid) does not necessarily mean that the molar concentration of the gas x is the same in the two media; most often is not. In fact, as stated above, in the gas medium the concentration of x [n(x)/N] simply equals Px/Ptotal. Differently, in the liquid medium the quantity of x, n(x), depends not only on Px but also on its solubility a n(x) = Px · a (eq.2) where a is the solubility coefficient expressed as volume of gas contained in a unitary volume of liquid, at STPD, per unit pressure (e.g., ml gas STPD · ml liquid-1 · mm Hg-1). Its value depends not only on the specific gas and liquid, but also on the ionic strength and T of the liquid, both o factors being inversely related to a . For example, at 37 C, the solubility of O2 in salty water and in distilled water is, respectively, 1.17 and 1.41 µmole · liter-1 · mm Hg-1 (or approximately 26 and 32 µl STPD · liter water-1· mm Hg-1). Neither the nature of the liquid electrolytes nor the presence of other gases in solution has an appreciable effect on a . o In water at 20 C, relative to that of O2, a of CO2 is almost 30 times greater, whereas a of N2 is about half. A somewhat more comprehensive concept of solubility is the physiological concept of capacitance coefficient b. It includes not only the solubility coefficient a , but also any possible chemical binding of the gas to any molecule in the liquid. This is of major physiological importance, since in the blood both O2 and CO2 bind to hemoglobin, greatly increasing the capacitance of the blood for these gases. Hence, b has the same units of a , but depends on the concentration of hemoglobin; at full hemoglobin saturation (arterial PO2=100 mm Hg), 1 liter of -1 -1 blood contains approximately 200 ml O2; hence, b(O2) is 89 µmole · liter blood · mm Hg , i.e. more than 70 times the a (O2) of salty water. From the above, several aspects need to be emphasized. a. Given Ptotal and Px, it is easy to know the concentration of the gas x in the gas mixture, whereas its concentration in the liquid medium cannot be known, unless a is specified. b. Because a varies among liquids, the content of the gas x also changes among different liquids, even if Px remains the same. c. Because gas diffusion depends on difference in Px, and not on the difference in concentration, a gas can diffuse from one liquid to another (with higher a ) against its concentration gradient. Conversely, at equilibrium (i.e. same Px), liquids in contact can have different concentrations of the gas x. d. Because gas volumes depend on T and P, the conditions of the measurements need to be specified. Respiratory volumes (i.e. pulmonary ventilation, tidal volume, vital capacity) are usually reported at the temperature and pressure of the body (Body Temperature and Water vapour-Saturated Pressure, BTPS). On the other hand, moles of gas (i.e. oxygen consumption, carbon dioxide production) are commonly reported at Standard Temperature (273oK) and Pressure Dry (760 mm Hg) condition (STPD). In many cases volume measurements are performed neither at STPD nor at BTPS, but at ATPS (Ambient Temperature Pressure Saturation). Conversion among these conditions can be easily performed by applying the general law for ideal gases, with volume proportional to absolute temperature, and inversely proportional to pressure. As an example, if a spirometer is used to measure the tidal volume (VT) of a subject in a mountain region where barometric pressure P=450 mm Hg, and the spirometer is at 23oC (knowing that the pressure of water vapour at saturation at 23oC is 21 mm Hg, and that at the body temperature of 37oC is 47 mm Hg) VBTPS/VATPS = (TBTPS ·PATPS) / (T ATPS · PBTPS) = [ (273+37) · (450-21) ] / [273+23) · (450-47)] 2 hence, VT, BTPS = 1.1149 VT, ATPS Similar computations are applied to convert volumes into STPD conditions (in which case water vapour pressure is nil). An STPD volume is about 83% of the value at 37oC, 1 saturated atmosphere. Tables of conversion factors between ATPS, BTPS and STPD are available. e. One important implication of the temperature-sensitivity of a (and b) is the change in blood gas partial pressure with changes in blood temperature. A lower blood temperature (e.g. in the peripheral circulation during exposure to cold, or during hibernation) increases the O2 and CO2 solubility, therefore reducing the corresponding partial pressures. Values of pH also depend on temperature, since water dissociation is temperature dependent. This needs to be kept in mind in a number of occasions, of which probably the most frequent is blood gas analysis in the clinical setting. Because the PO2, PCO2 and pH electrodes are usually maintained at a fixed temperature (37oC in most analysers), values need to be corrected to the body temperature of the patient [Fig.1]. 3 Fig.1. Effect of changes in temperature on PO2, PCO2 and pH of human blood. 4 Diffusion In absence of equilibrium, molecules of a gas x 'diffuse', i.e. 'move' from a region of high Px to a region of low Px, until equilibrium is reached. Once more, it is important to stress that diffusion is determined by differences in Px, not differences in concentration. The diffusion equatio n defining the magnitude of gas diffusion is essentially equivalent to the familiar flow= pressure/resistance (V=P/R), where flow is the quantity of gas diffusing per unit time (V), pressure indicates the difference in Px, and R is the diffusional resistance; the latter is a term which includes the diffusional area A, the diffusional distance d, and the diffusion coefficient D (Fick’s law of diffusion) Vx = D Px · [(A/d) · D] [eq.3] The value of the diffusion coefficient D depends on the atomic mass of x (the rate of diffusion of a gas is inversely proportional to its mass) and the strength of its cohesive forces.