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Expiratory Flow Limitation

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Abstract

Expiratory flow limitation occurs when flow ceases to increase with increasing expiratory effort. The equal pressure point concept has been largely successful in providing intuitive understanding of the phenomenon, wherein maximal flows are determined by lung recoil and resistance upstream of the site where bronchial transmural pressure is zero (the EPP). Subsequent work on the fluid dynamical foundations led to the wave‐speed theory of flow limitation, where flow is limited at a site when the local gas velocity is equal to speed of propagation of pressure waves. Each is a local theory; full predictions require knowledge of both density‐dependent Bernoulli pressure drops and viscosity‐dependent pressure losses due to dissipation. The former is dominant at mid to high lung volumes, whereas the latter is more important at low lung volumes as the flow‐limiting site moves peripherally. The observation of relative effort independence of the maximal flow versus volume curves is important clinically insofar as such maneuvers, when carefully performed, offer a unique window into the mechanics of the lung itself, with little confounding effects. In particular, the important contributions of lung recoil and airways resistance can often be assessed, with implications and applications to diagnosis and management of pulmonary disease. © 2011 American Physiological Society. Compr Physiol 1:1861‐1882, 2011.

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Figure 1. Figure 1.

Left: Flow versus volume plot for normal subject. values are plotted against their corresponding volume at A, B, and C, and define the maximum expiratory flow versus volume (MEFV) curve (solid line). Right: Three isovolume pressure flow curves from the same subject. Curves A, B, and C were measured at volumes of 0.8, 2.3, and 3.0 liters from total lung capacity (TLC), respectively. Transpulmonary pressure is the difference between pleural pressure (estimated by an esophageal balloon) and mouth pressure. Adapted, with permission, from reference .

Figure 2. Figure 2.

Expiratory flow and alveolar pressure (Palv) versus expired box volume from TLC. Palv is calculated as the sum of the esophageal pressure measured during the maneuver and the static elastic recoil pressure measured immediately before. The alveolar pressure continues to increase after peak flow is reached. (Pompilio et al. unpublished observations).

Figure 3. Figure 3.

Graphical representation of the equal pressure point concept.

Figure 4. Figure 4.

Diagram linking together the pressures and pressure differences in the airway. It describes a monoalveolar lung with a Pitot‐static tube inserted in the airway.

Palv: Alveolar pressure.

Pca = Pressure used for convective acceleration .

Pel: Static elastic recoil pressure = PalvPpl.

Pfr: Frictional pressure loss from the alveoli to the flow‐limiting site (the choke point, CP) = PalvPtot.

Ppl: Pressure surrounding the lung and the airway.

J: Pressure head at the CP = PtotPpl.

Ptot: Impaction or stagnation pressure at the end hole of the Pitot‐static tube.

Plat: Pressure at the side hole of the probe.

Ptm: Transmural pressure = PlatPpl

Pd: Pressure drop from the side hole to the mouth (PlatPmouth).

: Expiratory flow.

: Gas density.

Figure 5. Figure 5.

Thin curves: Iso‐J flow versus transmural pressure (Ptm) curves for a mechanical model with a Pitot‐static probe at three different positions (A, B, and C) for J‐values ranging between 0.1 and −1.3 kPa. The iso‐J curves were calculated from the A versus Ptm curves, and based on Eqs. (5) or (9). Interrupted heavy curves: maximal flows calculated from the A versus Ptm curves [Eq. (8)]. They pass through the maxima of the iso‐J curves. Heavy continuous curves: actual flows. The same effort was applied at all positions. Panel A: The theoretical maximum flow calculated from Eq. (8), is considerably larger than the measured flow. The velocity is below wave‐speed (subcritical). The Pitot‐static probe is in the subcritical region upstream of the CP. Panel B: The actual flow follows closely the flow through the maxima of the iso‐J curves. Flows on the two flow versus Ptm curves are almost identical. The Pitot‐static probe is close to CP. Panel C: The flow is initially submaximal (measured flow is less than the calculated maximum), and the velocity subcritical. Flow then tracks the theoretical maximum over a region, but at lower transmural pressures, the actual flow is larger than the theoretical maximum. In this region, the velocity is supercritical (and the Pitot‐static probe is downstream of the CP); the observation that the volume flow exceeds the computed maximum implies the existence of important contributions to flow that have been neglected in the simple theory.

Figure 6. Figure 6.

Calculation of the relationship between the A versus Ptm curve on the one hand and the versus J curve (MFJ curve) on the other. If Pfr is zero, then the MFJ curve becomes the maximum flow versus static recoil curve (MFSR curve). Caw is the slope of the A versus Ptm curve, G is the slope of the MFJ curve.

Figure 7. Figure 7.

Pressure (top) and area (bottom) as functions of axial position in a compliant tube for each flow rate. For limiting or critical flow (), two branches of the solution of the governing equations are shown downstream of the critical point. The branch is determined by the level of effort, here equivalent to pressure boundary condition at the downstream outlet. At high efforts, the lower branch obtains, and a region of supercritical flow ends with a dissipative hydraulic jump to subcritical flow. Adapted, with permission, from reference .

Figure 8. Figure 8.

Schematic drawing, adapted with permission, from Wiggs et al. showing buckling of a two‐layer tube with a thin (A) and a thick (B) layer. Because of the lesser fold patterns in B, the tube can narrow to a greater extent than in A before folds push against one another, causing an increase in airway stiffness. In the extreme case shown, tube in B narrows to zero luminal area (LA) at a load corresponding to maximum effective pressure exerted by smooth muscle (P*). P, smooth muscle pressure.

Figure 9. Figure 9.

Panel A: A versus Ptm curves for bronchial generations (z = 1‐16) were calculated from data of Lambert et al. , and were transformed into versus J curves by the equations given in Figure . Pfr was assumed to be zero. The CP is in the airway which, at the given value of J, gives the smallest maximal flow. It is seen that the CP moves toward the periphery with decreasing J. Panel B: The upper curve taken from Lambert et al. shows which airway generation contains the choke point at different elastic recoil pressures when viscous pressure loss and viscous flow limitation is taken into account. The lower curve is in accordance with panel A, where Pfr is assumed to be zero and Pel = J.

Figure 10. Figure 10.

Previously unpublished flow versus volume curves with reproducible configuration findings (the arrows) in a healthy subject.

Figure 11. Figure 11.

The first figure describes maximum flow versus static recoil (MFSR) curves on air and He/O2. If density dependence is less than , density corrected flows on He/O2 will be smaller than on air, as shown in the second figure. If the A versus Ptm curve is not affected by the gas, the two points in the second figure will now be on the same curve, as in the third figure, but separated due to Pfr. Because there is a unique relationship between the MFcJ curve describing density corrected versus J and the A versus Ptm curve, two separate points on the MFcJ curve will also give two separate points on the single valued A versus Ptm curve, as in the fourth figure.

Figure 12. Figure 12.

Maximum expiratory flow versus volume curves with different efforts. Three of the peaks reach wave speed (the heavy curves), but at different thoracic gas volumes. For the broken curve, the peak is not at wave‐speed flow. Modified, with permission, from reference .

Figure 13. Figure 13.

Lung resistance at three different lung volumes. Rapid, shallow respirations were produced (1) near maximum inspiration; (2) at normal resting mid position; and (3) near maximal expiration. At the lowest lung volume, the expiratory part of the resistance curve forms a loop. The maximum expiratory flow decreases, while the expiratory pressure continues to increase. This suggests flow is limited near RV. Adapted, with permission, from Mead and Whittenberger .

Figure 14. Figure 14.

Panel A: A tidal flow volume loop during which negative pressure negative expiratory pressure (NEP) was applied over the middle part of the expiration (between 2 arrows) in a seated chronic obstructive pulmonary disease (COPD) patient at rest together with preceding control loops. Note the sustained increase of flow during NEP, indicating that flow was not limited during the control expiration. Panel B: Similar loops in another seated COPD patient at rest. Application of a NEP pulse caused only a transient increase of flow during NEP, indicating flow limitation during control.

Reproduced, with permission, from reference .
Figure 15. Figure 15.

Mead and Whittenberger graphs (A and C) obtained by plotting airway opening flow versus the resistive pressure drop (Pfr) during a single breath. Data from a non flow‐limited COPD patient (A and B) and a flow‐limited patient (C and D). The lower graphs (B and D) show the time course of resistive pressure (Pfr) and reactance Xrs for the two subjects. In patient AB, there is no open respiratory loop, and the reactance is almost the same during in and expiration. In patient CD, there is evidence of flow limitation in the resistance loop (see Figure ), and expiratory reactance is considerably more negative than inspiratory reactance. Modified, with permission, from reference .



Figure 1.

Left: Flow versus volume plot for normal subject. values are plotted against their corresponding volume at A, B, and C, and define the maximum expiratory flow versus volume (MEFV) curve (solid line). Right: Three isovolume pressure flow curves from the same subject. Curves A, B, and C were measured at volumes of 0.8, 2.3, and 3.0 liters from total lung capacity (TLC), respectively. Transpulmonary pressure is the difference between pleural pressure (estimated by an esophageal balloon) and mouth pressure. Adapted, with permission, from reference .



Figure 2.

Expiratory flow and alveolar pressure (Palv) versus expired box volume from TLC. Palv is calculated as the sum of the esophageal pressure measured during the maneuver and the static elastic recoil pressure measured immediately before. The alveolar pressure continues to increase after peak flow is reached. (Pompilio et al. unpublished observations).



Figure 3.

Graphical representation of the equal pressure point concept.



Figure 4.

Diagram linking together the pressures and pressure differences in the airway. It describes a monoalveolar lung with a Pitot‐static tube inserted in the airway.

Palv: Alveolar pressure.

Pca = Pressure used for convective acceleration .

Pel: Static elastic recoil pressure = PalvPpl.

Pfr: Frictional pressure loss from the alveoli to the flow‐limiting site (the choke point, CP) = PalvPtot.

Ppl: Pressure surrounding the lung and the airway.

J: Pressure head at the CP = PtotPpl.

Ptot: Impaction or stagnation pressure at the end hole of the Pitot‐static tube.

Plat: Pressure at the side hole of the probe.

Ptm: Transmural pressure = PlatPpl

Pd: Pressure drop from the side hole to the mouth (PlatPmouth).

: Expiratory flow.

: Gas density.



Figure 5.

Thin curves: Iso‐J flow versus transmural pressure (Ptm) curves for a mechanical model with a Pitot‐static probe at three different positions (A, B, and C) for J‐values ranging between 0.1 and −1.3 kPa. The iso‐J curves were calculated from the A versus Ptm curves, and based on Eqs. (5) or (9). Interrupted heavy curves: maximal flows calculated from the A versus Ptm curves [Eq. (8)]. They pass through the maxima of the iso‐J curves. Heavy continuous curves: actual flows. The same effort was applied at all positions. Panel A: The theoretical maximum flow calculated from Eq. (8), is considerably larger than the measured flow. The velocity is below wave‐speed (subcritical). The Pitot‐static probe is in the subcritical region upstream of the CP. Panel B: The actual flow follows closely the flow through the maxima of the iso‐J curves. Flows on the two flow versus Ptm curves are almost identical. The Pitot‐static probe is close to CP. Panel C: The flow is initially submaximal (measured flow is less than the calculated maximum), and the velocity subcritical. Flow then tracks the theoretical maximum over a region, but at lower transmural pressures, the actual flow is larger than the theoretical maximum. In this region, the velocity is supercritical (and the Pitot‐static probe is downstream of the CP); the observation that the volume flow exceeds the computed maximum implies the existence of important contributions to flow that have been neglected in the simple theory.



Figure 6.

Calculation of the relationship between the A versus Ptm curve on the one hand and the versus J curve (MFJ curve) on the other. If Pfr is zero, then the MFJ curve becomes the maximum flow versus static recoil curve (MFSR curve). Caw is the slope of the A versus Ptm curve, G is the slope of the MFJ curve.



Figure 7.

Pressure (top) and area (bottom) as functions of axial position in a compliant tube for each flow rate. For limiting or critical flow (), two branches of the solution of the governing equations are shown downstream of the critical point. The branch is determined by the level of effort, here equivalent to pressure boundary condition at the downstream outlet. At high efforts, the lower branch obtains, and a region of supercritical flow ends with a dissipative hydraulic jump to subcritical flow. Adapted, with permission, from reference .



Figure 8.

Schematic drawing, adapted with permission, from Wiggs et al. showing buckling of a two‐layer tube with a thin (A) and a thick (B) layer. Because of the lesser fold patterns in B, the tube can narrow to a greater extent than in A before folds push against one another, causing an increase in airway stiffness. In the extreme case shown, tube in B narrows to zero luminal area (LA) at a load corresponding to maximum effective pressure exerted by smooth muscle (P*). P, smooth muscle pressure.



Figure 9.

Panel A: A versus Ptm curves for bronchial generations (z = 1‐16) were calculated from data of Lambert et al. , and were transformed into versus J curves by the equations given in Figure . Pfr was assumed to be zero. The CP is in the airway which, at the given value of J, gives the smallest maximal flow. It is seen that the CP moves toward the periphery with decreasing J. Panel B: The upper curve taken from Lambert et al. shows which airway generation contains the choke point at different elastic recoil pressures when viscous pressure loss and viscous flow limitation is taken into account. The lower curve is in accordance with panel A, where Pfr is assumed to be zero and Pel = J.



Figure 10.

Previously unpublished flow versus volume curves with reproducible configuration findings (the arrows) in a healthy subject.



Figure 11.

The first figure describes maximum flow versus static recoil (MFSR) curves on air and He/O2. If density dependence is less than , density corrected flows on He/O2 will be smaller than on air, as shown in the second figure. If the A versus Ptm curve is not affected by the gas, the two points in the second figure will now be on the same curve, as in the third figure, but separated due to Pfr. Because there is a unique relationship between the MFcJ curve describing density corrected versus J and the A versus Ptm curve, two separate points on the MFcJ curve will also give two separate points on the single valued A versus Ptm curve, as in the fourth figure.



Figure 12.

Maximum expiratory flow versus volume curves with different efforts. Three of the peaks reach wave speed (the heavy curves), but at different thoracic gas volumes. For the broken curve, the peak is not at wave‐speed flow. Modified, with permission, from reference .



Figure 13.

Lung resistance at three different lung volumes. Rapid, shallow respirations were produced (1) near maximum inspiration; (2) at normal resting mid position; and (3) near maximal expiration. At the lowest lung volume, the expiratory part of the resistance curve forms a loop. The maximum expiratory flow decreases, while the expiratory pressure continues to increase. This suggests flow is limited near RV. Adapted, with permission, from Mead and Whittenberger .



Figure 14.

Panel A: A tidal flow volume loop during which negative pressure negative expiratory pressure (NEP) was applied over the middle part of the expiration (between 2 arrows) in a seated chronic obstructive pulmonary disease (COPD) patient at rest together with preceding control loops. Note the sustained increase of flow during NEP, indicating that flow was not limited during the control expiration. Panel B: Similar loops in another seated COPD patient at rest. Application of a NEP pulse caused only a transient increase of flow during NEP, indicating flow limitation during control.

Reproduced, with permission, from reference .


Figure 15.

Mead and Whittenberger graphs (A and C) obtained by plotting airway opening flow versus the resistive pressure drop (Pfr) during a single breath. Data from a non flow‐limited COPD patient (A and B) and a flow‐limited patient (C and D). The lower graphs (B and D) show the time course of resistive pressure (Pfr) and reactance Xrs for the two subjects. In patient AB, there is no open respiratory loop, and the reactance is almost the same during in and expiration. In patient CD, there is evidence of flow limitation in the resistance loop (see Figure ), and expiratory reactance is considerably more negative than inspiratory reactance. Modified, with permission, from reference .

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Ole F. Pedersen, James P. Butler. Expiratory Flow Limitation. Compr Physiol 2011, 1: 1861-1882. doi: 10.1002/cphy.c100025