## Ventilation‐Perfusion Relationships

### Abstract

1 Gas Exchange in a Single Alveolus
1.1 Oxygen and Carbon Dioxide
1.2 Nitrogen
1.3 Inert Gases
1.4 Review of Assumptions
1.5 Conclusions
2 Gas Exchange in the Whole Lung
2.1 Direct Measurement of Lobar Differences in Gas Exchange
2.2 Regional Differences in Gas Exchange in the Vertical Lung
2.3 Gas Exchange
3 Determination of V.A/Q. Distribution
3.1 Three‐Compartment Model
3.2 Two‐Compartment Model
3.3 Nitrogen Difference
3.5 Nitrogen‐Carbon Dioxide Relationship
3.6 Inert‐Gas Elimination
3.7 Gas Solubility, Dead Space, and Shunt
4 Alveolar‐Arterial Differences
5 Factors Affecting V.A/Q. Distribution
5.1 Posture
5.2 Gravity
5.3 Exercise
5.4 Altitude
5.5 Liquid Breathing
5.6 Compensatory Mechanisms
6 Ventilation, Perfusion, and Tissue Homeostasis
 Figure 1. Calculation of ventilation‐perfusion ratio () from CO2 exchange. Plot of CO2 concentration (Cco2) versus CO2 partial pressure () with a standard dissociation curve. Point , CO2 concentration in mixed venous blood. Any given point on the curve, e.g., A, can be joined to , providing a line in which the vertical distance between and A is given by − CA (where CA is the CO2 concentration in alveolar capillary blood), while the distance from A to the ordinate is by definition the alveolar partial pressure of CO2 (). Slope of the line is therefore or 1/863 x . Note that Cco2 must be in milliliters/milliliter and in torr. Figure 2. Alveolar and end‐capillary gas pressures as a function of . As increases, O2 partial pressure () and CO2 partial pressure () move toward inspired gas values; i.e., increases and decreases. Because the rate of change of these two pressures is not identical, N2 is concentrated at low values and diluted if the gas‐exchange ratio is >1. Figure 3. Calculation of from O2 exchange. Plot of O2 concentration () versus . To determine , apoint Cv is plotted at coordinates , . When this point is joined to point A (on the line that represents blood returning from a given alveolus) the A‐C slope is ( — )/( — ) and represents therefore 1/863 x . , inspired partial pressure of O2; , O2 concentration in mixed venous blood; , O2 concentration in arterial blood; , alveolar partial pressure of O2. Figure 4. Ventilation‐perfusion ratio plotted on O2‐CO2 diagram. Line is drawn for a resting subject, breathing air at sea level. Numbers above and to right of line indicate ; other numbers show gas‐exchange ratio (CO2 output/O2 uptake).From Farhi 11 Figure 5. Equilibrium pressures for elimination of inert gas from the lungs. Curves are normalized by showing alveolar pressure divided by pressure of the gas in the incoming mixed venous blood (P′A). O2 and CO2 are also shown to indicate that they behave appropriately if their dissociation curve is taken into account. O2 is normalized as ( — )/( — ), where is the mixed venous partial pressure of O2.From Farhi 12 Figure 6. Effect of solubility on inert‐gas elimination. Abscissa is pulmonary blood flow (), in liters/minute; ordinate is alveolar ventilation () in liters/minute. Isoclearance lines indicate virtual blood flow cleared of the inert gas for any combination of and , the two gases combined having a λ (partition coefficient) of ∼0.1 for xenon and 15 for ethyl ether. When exceeds 2 liters/min, ether clearance is perfusion dependent, while elimination of xenon is a function of .From Farhi 12 Figure 7. curves for various pairs of gases. P′1, P′A of gas 1; P′2, P′A of gas 2. Solid curves A‐D correspond to λ2/λ1 (ratio of partition coefficients of 2 gases) values shown and use the bottom and left scales. Although only the ratio λ2/λ1 (and not one of the specific partition coefficients) determines the shape of the curves, the value for any point on a curve is a function of the absolute λ. Dashed curve, curve for O2 and CO2, with appropriate pressures shown above and right. Dotted line, identity line.From Farhi and Yokoyama 17 Figure 8. Shaded area, area drawn assuming that alveoli rebreathe some gas from dead space. As opposed to the standard line, all points in shaded area can occur. Overall gas‐exchange ratio (R) is a combination of dead‐space R and alveolar R.From Ross and Farhi 53 Figure 9. curves for a subject breathing 21% O2 and various N2O fractions. Fraction of inspired N2O () is shown on each curve; remainder of inspired gas is N2. Mixed venous gas assumed to be free of N2O. When exceeds 0.7, will be higher than because of shrinkage in gas volume.From Farhi and Olszowka 15 Figure 10. curves during elimination of N2O on the O2‐CO2 diagram. Curves, curves of a subject who has previously breathed a mixture containing some N2O and is then suddenly switched to air breathing. Fraction of N2O in initial mixture is 0 (control, standard curve), 0.4, or 0.8. Curve area that lies near the = 0 area is expanded in the inset and shows that it is theoretically possible to have a lower than .From Farhi and Olszowka 15 Figure 11. curve on diagram. Inspired curve was presented by Canfield and Rahn 10. Curve shown here gives values for a resting subject breathing air at sea level, , Mixed venous.From Farhi 11 Figure 12. Principle used to determine distribution on the diagram. A: if two gases, L and M, are mixed in any proportion, yielding gas X, points L, M, and X must be on a straight line. B: if two secondary mixtures, X and Y, are plotted, the primary components must lie on the extrapolation of XY. , partial pressure of CO2 in gas M; , partial pressure of CO2 in gas X; , partial pressure of CO2 in gas L.From Farhi 11 Figure 13. Two‐compartment model of a lung on basis of arterial and alveolar and . With the idea elaborated in Figure 12, it is possible to determine 2 compartments on the line as the extension of the line joining the arterial and alveolar parts. I, inspired; A, alveolar; a, arterial; , mixed venous; L and M, gases.From Farhi 11 Figure 14. Relation between excess ventilation and dead‐space ventilation.From Farhi and Yokoyama 17 Figure 15. Relation between excess perfusion and shunt.From Farhi and Yokoyama 17 Figure 16. Contribution of various factors to arterial‐alveolar differences in and [(a–A)D] and alveolar‐arterial differences in [(A–a)D]. Contributions are shown as going from ○ (no effect of factor on the right on the difference shown above the symbol) to ++++. , Effect is too small to be measured accurately. , Differences that are specific to a certain factor.From Farhi 11 Figure 17. Control of local , assumed to be closely related to of the venous blood that has equilibrated with the tissue or organ. Because arterial O2 concentration () is not very responsive to changes in in the normal range, the main factor affecting (and hence ) is the local regulation of blood flow to match O2 needs. , O2 consumption. Figure 18. Control of local . Venous‐arterial CO2 difference ( — ) normally represents only ∼10% of ; is therefore the dominant factor in setting tissue , , CO2 output.