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Pressure‐Flow Relationships in the Lungs

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Abstract

The sections in this article are:

1 Historical Perspectives
2 Physical Basis of Airway Resistance
2.1 General Principles
2.2 Predictions of Inspiratory Pressure Drop
2.3 Predictions of Expiratory Pressure Drop
2.4 Validity of the Quasi‐Steady Assumption for Pressure‐Flow Relationships for Oscillatory Flow
3 Resistance in Normal Subjects
3.1 Physiological Factors Influencing Measurements
3.2 Central Versus Peripheral Airway Contribution to Lower Pulmonary Resistance
3.3 Tissue Viscance
3.4 Inertance
3.5 Frequency Dependence
3.6 Techniques for Measuring Resistance
4 Concluding Remarks
Figure 1. Figure 1.

Measurement of pulmonary resistance showing airflow rate (P.T. denotes pneumotachograph) and both static (Pl.stat) and dynamic (Pl.dyn) components of pleural pressure during breathing. Zero pressure level for pleural pressure denoted by 0L; Ph. indicates pleural pressure points at instants of zero flow. Resistance is pressure difference between Pl.dyn and Pl.stat divided by simultaneous airflow rate.

From von Neergaard and Wirz
Figure 2. Figure 2.

Mouth pressure (dark line) with the zero pressure and airflow levels (OL) and airflow rate (lighter line, P. T. denotes pneumotachograph). V. Dr. indicates mouth pressure during occlusion. Note that during occlusion, airflow drops to zero and mouth pressure falls during inspiration or rises during expiration. Airway resistance was thought to be represented by ratio of mouth pressure to airflow rate either just before or after occlusion. See AIRWAY RESISTANCE, p. 289, for criticism of the authors' interpretation.

From von Neergaard and Wirz
Figure 3. Figure 3.

Idealized Moody diagram. Region 1 has a slope of −1 and indicates laminar flow. Region 2 has a slope of zero and represents fully turbulent flow. Region 3 has a variable slope between −1 and zero (average –½) representing transitional flow regimes.

From Drazen et al.
Figure 4. Figure 4.

Predicted variation of viscous flow resistance down the bronchial tree at airflow rates of 0.17 (□), 0.83 (▴), and 1.67 (▪) liters · s−1. Also shown on the same scale is the Poiseuille resistance (○).

From Pedley et al.
Figure 5. Figure 5.

Log‐log (Moody) plot of friction factor for the lower airways (CF) against tracheal Reynolds number (Re0). Solid curve: as predicted from theory of Pedley et al. ; broken line: straight line of slope −½; dashdot curve: theory modified according to proposals of Jaffrin and Kesic ; dotted curve: best fit according to Rohrer's equation; three lines marked S: results of Slutsky et al. . Experimental points: ○, adapted from Jaeger and Matthys ; ×, from Hyatt and Wilcox ; □, from Ferris et al. , corrected for tracheal diameter; Δ, from Vincent et al. ; ♦, from Blide et al. .

Figure 6. Figure 6.

Predicted variation of viscous pressure down different pathways of asymmetric model of bronchial tree given by Horsfield et al. . Viscous pressure drops were plotted at points representing downstream ends of all airways in model, and points joined by straight lines. Broken line is prediction for corresponding symmetric model. Flow rate = 1 liter · s−1; 100 N · m2 = 1 cmH2O.

From Pedley et al.
Figure 7. Figure 7.

Ratio × 100 of upper to lower airway resistance plotted against absolute values of lower airway resistance. Note that with increasing lower airway resistance there is decrease in relative contribution of upper airways to total resistance.

From Hyatt and Wilcox
Figure 8. Figure 8.

Schematic drawing showing how relative volume changes of volume‐pressure systems exposed to identical pressure cycles can be used to assess relative volume‐pressure hysteresis. V1, airway volume measured as anatomical dead space; V2, lung volume. Note in middle panel, for example, that airways are larger at same lung volume when volume is reached from deflation than when reached from inflation if airway hysteresis exceeds that of lung.

From Froeb and Mead
Figure 9. Figure 9.

Four plethysmographic methods for measuring airway resistance. Pmouth, mouth pressure; Pbox, pressure within plethysmograph; , airflow rate at mouth. A: most commonly used technique. [Adapted from DuBois et al. .] B: bag contains air at BTPS conditions to avoid thermal effects. [Adapted from Jaeger and Otis .] C: ΔVpump is volume change of pump at mouth. [Adapted from Finucane et al. .] D: barospirator technique.

Adapted from Schwaber and Mead


Figure 1.

Measurement of pulmonary resistance showing airflow rate (P.T. denotes pneumotachograph) and both static (Pl.stat) and dynamic (Pl.dyn) components of pleural pressure during breathing. Zero pressure level for pleural pressure denoted by 0L; Ph. indicates pleural pressure points at instants of zero flow. Resistance is pressure difference between Pl.dyn and Pl.stat divided by simultaneous airflow rate.

From von Neergaard and Wirz


Figure 2.

Mouth pressure (dark line) with the zero pressure and airflow levels (OL) and airflow rate (lighter line, P. T. denotes pneumotachograph). V. Dr. indicates mouth pressure during occlusion. Note that during occlusion, airflow drops to zero and mouth pressure falls during inspiration or rises during expiration. Airway resistance was thought to be represented by ratio of mouth pressure to airflow rate either just before or after occlusion. See AIRWAY RESISTANCE, p. 289, for criticism of the authors' interpretation.

From von Neergaard and Wirz


Figure 3.

Idealized Moody diagram. Region 1 has a slope of −1 and indicates laminar flow. Region 2 has a slope of zero and represents fully turbulent flow. Region 3 has a variable slope between −1 and zero (average –½) representing transitional flow regimes.

From Drazen et al.


Figure 4.

Predicted variation of viscous flow resistance down the bronchial tree at airflow rates of 0.17 (□), 0.83 (▴), and 1.67 (▪) liters · s−1. Also shown on the same scale is the Poiseuille resistance (○).

From Pedley et al.


Figure 5.

Log‐log (Moody) plot of friction factor for the lower airways (CF) against tracheal Reynolds number (Re0). Solid curve: as predicted from theory of Pedley et al. ; broken line: straight line of slope −½; dashdot curve: theory modified according to proposals of Jaffrin and Kesic ; dotted curve: best fit according to Rohrer's equation; three lines marked S: results of Slutsky et al. . Experimental points: ○, adapted from Jaeger and Matthys ; ×, from Hyatt and Wilcox ; □, from Ferris et al. , corrected for tracheal diameter; Δ, from Vincent et al. ; ♦, from Blide et al. .



Figure 6.

Predicted variation of viscous pressure down different pathways of asymmetric model of bronchial tree given by Horsfield et al. . Viscous pressure drops were plotted at points representing downstream ends of all airways in model, and points joined by straight lines. Broken line is prediction for corresponding symmetric model. Flow rate = 1 liter · s−1; 100 N · m2 = 1 cmH2O.

From Pedley et al.


Figure 7.

Ratio × 100 of upper to lower airway resistance plotted against absolute values of lower airway resistance. Note that with increasing lower airway resistance there is decrease in relative contribution of upper airways to total resistance.

From Hyatt and Wilcox


Figure 8.

Schematic drawing showing how relative volume changes of volume‐pressure systems exposed to identical pressure cycles can be used to assess relative volume‐pressure hysteresis. V1, airway volume measured as anatomical dead space; V2, lung volume. Note in middle panel, for example, that airways are larger at same lung volume when volume is reached from deflation than when reached from inflation if airway hysteresis exceeds that of lung.

From Froeb and Mead


Figure 9.

Four plethysmographic methods for measuring airway resistance. Pmouth, mouth pressure; Pbox, pressure within plethysmograph; , airflow rate at mouth. A: most commonly used technique. [Adapted from DuBois et al. .] B: bag contains air at BTPS conditions to avoid thermal effects. [Adapted from Jaeger and Otis .] C: ΔVpump is volume change of pump at mouth. [Adapted from Finucane et al. .] D: barospirator technique.

Adapted from Schwaber and Mead
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Roland H. Ingram, T. J. Pedley. Pressure‐Flow Relationships in the Lungs. Compr Physiol 2011, Supplement 12: Handbook of Physiology, The Respiratory System, Mechanics of Breathing: 277-293. First published in print 1986. doi: 10.1002/cphy.cp030318