INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Measurements of expired flow are commonly used to assess respiratory function among patients with obstructive lung disease. These measurements are governed by the principles of flow limitation during which maximal flow becomes independent of expiratory effort. Several models of flow limitation have been developed to allow physicians and physiologists to better understand clinical observations in patients with asthma and emphysema, and to assess the basis for responses to therapeutic interventions (1). One such model developed by Pride and Permutt (1), is described by the relationship

(1)

This expression states that flows (), and thus peak flow during a forced exhalation (max), are determined by three independent parameters: (1) lung elastic recoil (Pel), which varies as a function of volume; (2) conductance to flow upstream of the site of flow limitation (Gu) where dynamic collapse is occurring; and (3) the intrinsic ability of the airways to resist the tendency toward collapse during a forced exhalation, described in terms of the transmural pressure at collapse (Ptm'). Although Eq. (1), and the physiological concepts that it describes, are straightforward, the terms that influence expiratory flows appear as products, rather than sums, of one another. As a result, they contribute to improvements in max in a nonlinear fashion, and thus their individual contributions can be difficult to assess. Changes in max resulting from an intervention that affects flow limitation are determined not only by the magnitude of the change in each term, but also their absolute magnitude before change. For example, a patient with an initial conductance value of 0.1 L/s/cm H₂O who improves his/her recoil from 15 to 20 cm H₂O after lung volume reduction surgery (LVRS) would experience an increase in max of (0.1 L/s/cm H₂O × 5 cm H₂O) = 0.5 L/s. By contrast, a patient with an initial conductance of 0.2 L/s/cm H₂O who experiences an identical improvement in recoil pressures of 5 cm H₂O would experience an increase in max of 1.0 L/s.

In the present study, Eq. (1) is applied to patients undergoing LVRS in an attempt to better understand how changes in Pel, Gu, and Ptm' individually contribute to changes in lung function. Equation (1) has been expanded in a Taylor series expressed as follows:

(2)

Subscripts represent the evaluation of the derivative term with each of the subscripted parameters held constant. The partial derivatives can be expressed in terms of the independent parameters Pel, Gu, and Ptm' from Eq. (1) as follows:

Order of magnitude analysis (not presented) suggests that second-order terms are all smaller than first-order terms. Substituting each of the partial derivative expressions back into Eq. (2) while retaining only terms of first order renders the following expression for how max changes with respect to an intervention that can alter Pel, Gu, and Ptm' independently:

(3)

Equation (3) suggests that changes in max depend on both changes in each of the independent parameters Pel, Gu, and Ptm', as well as the preintervention (i.e., in this case preoperative) values of Pel, Gu, Ptm'. These concepts are embodied graphically in Figure 1. Both Eq. (3) and Figure 1 show that the absolute magnitude of the effect of changes in the independent parameters that influence max is "weighted" by either the preoperative conductance (for Pel and Ptm'), preoperative elastance (for Gu), or preoperative value of the critical transmural pressure at the site of flow limitation (for Gu). It has been argued that LVRS might improve lung function in patients with end-stage emphysema by increasing recoil (i.e., producing a positive Pel), by increasing airway tethering, and by reducing dynamic compression and gas trapping (i.e., producing a positive Gu) and collapse (i.e., producing a negative Ptm'). The present study utilizes the Taylor expansion model in Eq. (3) together with detailed pre- and postoperative lung function measurements to determine which of these potential mechanisms are most important in affecting lung function after LVRS.

View larger version (19K): [in this window] [in a new window]   Figure 1.   Pride-Permutt representation of maximal flow-static recoil pressure relationships, depicting how individual changes in PTLC, Gu, and Ptm' can each affect max. At baseline ( diamonds) max = 0.65 L/s, PTLC = 10 cm H2O, Ptm' = 3.5 cm H2O, and Gu = 0.1 L/s/cm H2O. An increase in only PTLC (dashed line) from 10 to 12 cm H2O (labeled 1) increases max to 0.85 L/s. An increase in only Gu ( triangles) from 0.1 to 0.2 L/s/cm H2O (labeled 2) increases max to 1.3 L/s. Finally, a decrease in only Ptm ' (circles) from 3.5 to 2.0 cm H2O (labeled 3) increases max to 0.85 L/s.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Protocol Summary

Spirometry, lung volumes, and pulmonary mechanics were measured after bronchodilator therapy preoperatively, and 4 to 6 mo post-LVRS.

Patient Selection and Medical History

Fifty-two patients with end-stage emphysema underwent bilateral LVRS at our institution between October 1994 and May 1998. Of these, 19 men and 18 women (61 ± 7 yr) participated in this protocol. All displayed functional limitation (Karnofsky scale, 67 ± 7%), and had significant smoking histories (56 ± 22 pack-years). None had ₁-antiprotease deficiency. Three-quarters of participating patients (27 of 37) used oxygen continuously. All received inhaled -agonist, and the majority (33 of 37) received an inhaled anticholinergic and inhaled steroid (29 of 37). More than half were receiving theophylline (21 of 37), but only 6 patients were taking oral steroids at enrollment. Thirty-five completed pulmonary rehabilitation preoperatively.

"Responders" were defined by an increase in FEV₁ of  12%, and at least 150 ml after LVRS (5).

Pre- and Postoperative Pulmonary Mechanical Measurements

Expired flow was measured at the mouth during vital capacity and static deflation pressure-volume maneuvers were performed with a Fleisch no. 0 pneumotachometer. Expired volume was determined by integrating flow. To minimize errors in volume determinations from gas compression, we trained patients to breathe in maximally, to relax while initiating expiratory flow, and to continue to expire without forceful effort. Maximum errors from gas compression, calculated assuming idea gas behavior (Appendix ), were 351 ± 199 ml (5.5 ± 2.8%; range, 2.3 to 11.4%). Errors were similar in magnitude to intrasubject variation in lung volume determinations. Therefore, no corrections for gas compression were applied to our data.

Functional residual capacity, residual volume, and total lung capacity were measured in triplicate by plethysmography (P.K. Morgan, Haverhill, MA), and mean values reported.

Pleural pressures were estimated with an esophageal balloon positioned 40 cm from the nares. Balloon position was verified by demonstrating negligible fluctuations in transpulmonary pressure during panting against an occluded airway. Static deflation pressure-volume relationships were determined by measuring transpulmonary pressure and expired volume from total lung capacity, with intermittent airway occlusions held for sufficient time to ensure equilibration of airway opening pressure with alveolar pressure.

Maximal expiratory flow-static recoil pressure (MFSRP) curves were constructed by plotting expiratory airflow versus elastic recoil pressure, using lung volume as the common reference variable. The linear slope between 30 and 50% vital capacity was designated as Gu, airway conductance upstream of the flow-limiting site (1). The x axis (Pel axis) intercept was designated as Ptm'. max at TLC was determined through extrapolation, by dividing Pel at TLC by the Gu.

Method of Interpretation of Physiological Measurements, using Eq. (3)

max at TLC, Pel, Ptm', and Gu were determined pre- and postoperatively for all 37 participants. Lung compliance (CL) was calculated as the chord slope of the static pressure-volume curve between TLC and the volume at which Pel equals zero. Expiratory time constants (, seconds) were determined as CL/Gu. Values corresponding to changes () in parameters were expressed as 6-mo postoperative values minus preoperative values.

Statistical Analysis

Results are presented as means ± standard deviation. Significance of changes in physiology after LVRS was assessed by paired t test. Correlations were performed by least-squares linear regression analysis. Statistical significance was defined as p < 0.05.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Effects of LVRS on Spirometry and Lung Mechanics

Pre- and postoperative spirometry results are summarized in Table 1. Preoperative measurements for the entire cohort of 37 patients demonstrated evidence of severe obstruction with markedly reduced FEV₁ (0.69 ± 0.25 L; 24 ± 11% predicted), FVC (2.01 ± 0.64 L; 54 ± 21% predicted), and FEV₁/FVC ratio (0.35 ± 0.07). At 6-mo follow-up, FEV₁ (0.85 ± 0.35 L; %  = 28 ± 46%; p = 0.0018) and FVC (2.44 ± 0.89 L; %  = 18 ± 39%; p = 0.0003) improved significantly, whereas the FEV₁/FVC ratio (0.35 ± 0.06; %  = 0 ± 19%; p = 0.82) did not change.

Patients in the cohort were divided into two groups on the basis of their response to LVRS. Nineteen (11 males) of 37 experienced a 6-mo change in FEV₁  12% and 150 ml, and were designated as "responders." The remaining 18 patients (8 males) were designated as "nonresponders." Preoperative spirometry (Table 1) was similar in the two subgroups. Among responders, FEV₁ increased 58% (0.60 ± 0.24 vs. 0.95 ± 0.35 L, p < 0.0001), FVC 42% (1.86 ± 0.73 vs. 2.64 ± 1.05 L, p < 0.0001), and FEV₁/FVC ratio 13% (0.32 ± 0.06 vs. 0.36 ± 0.07, p = 0.05). Among nonresponders, FEV₁ decreased 8% (0.79 ± 0.21 vs. 0.73 ± 0.20 L, p = 0.06), FVC increased 2% (2.17 ± 0.51 vs. 2.22 ± 0.64 L, p = 0.54), and FEV₁/FVC ratio decreased 8% (0.37 ± 0.07 vs. 0.34 ± 0.07, p = 0.006).

Changes in FEV₁ measured 6 mo after LVRS correlated closely with changes in max determined from MFSRP relationships (r = 0.74, p < 0.001). Measurements of the physiological determinants of FEV₁ and max, which include PTLC, Gu, Ptm', , and CL, are summarized in Table 2 for the entire cohort, and for responders and nonresponders. Of these physiological parameters, only recoil pressure at total lung capacity increased significantly after LVRS in the cohort of 37 patients (9.2 ± 2.3 vs. 11.3 ± 3.8 cm H₂O, p = 0.0009). As depicted in Figure 2, virtually all the improvement in max was the result of an increase in recoil pressure. Overall, there were no consistent changes in Gu (0.12 ± 0.10 vs. 0.11 ± 0.07 L/s/cm H₂O, p = 0.83), Ptm' (2.3 ± 2.4 vs. 1.8 ± 1.7 cm H₂O, p = 0.31),  (2.5 ± 0.6 vs. 2.6 ± 0.6 s, p = 0.78), or CL (0.27 ± 0.19 vs. 0.26 ± 0.15 L/cm H₂O) after surgery.

View larger version (14K): [in this window] [in a new window]   Figure 2.   Pride-Permutt representation of mean response observed in the cohort of 37 patients presented in the current study. Preoperatively (diamonds) PTLC = 9.2 cm H2O, Ptm' = 2.3 cm H2O, and Gu = 0.12 L/s/cm H2O. After LVRS (squares), an increase in PTLC to 11.3 cm H2O accounted for virtually all of the increase in max, equivalent to mechanism 1 in Figure 1. There was no significant change observed in either Ptm ' or Gu in response to surgery.

Among responders, PTLC increased (8.8 ± 2.8 vs. 12.2 ± 4.7 cm H₂O, p = 0.0009) and  decreased (2.7 ± 0.6 vs. 2.3 ± 0.6 s, p = 0.009), but no significant changes were observed in any of the other parameters examined. Among nonresponders, only  (2.3 ± 0.6 vs. 2.6 ± 0.7 s, p = 0.0001) changed significantly, and in an adverse fashion. Figure 3 summarizes the mean MFSRP relationships for both responders (Figure 3A) and nonresponders (Figure 3B) pre- and post-LVRS.

View larger version (16K): [in this window] [in a new window]   View larger version (15K): [in this window] [in a new window]   Figure 3.   Pride-Permutt MFSRP relationships are presented separately for responders and nonresponders. Among the 19 responders (A), small mean changes in Ptm' and Gu were observed in response to surgery, although these were not statistically significant. The large increase in max observed among this group of patients was largely accounted for by the increase in P TLC. Among the 18 nonresponders (B), Ptm' did not change, but a mean decrease in Gu was observed (23%), although this did not reach statistical significance (p = 0.18). On average, PTLC increased slightly, although this also was not statistically significant. max did not change in response to LVRS among this subgroup of patients.

To assess the self-consistency of our approach, estimates of FEV₁, FVC, and FEV₁/FVC ratio were calculated from measurements of PTLC, Ptm', Gu, and CL, and compared with independent spirometry measurements. This calculation provides an assessment of the accuracy of using the single-compartment model embodied in Eq. (1) for assessing expiratory dynamics. In Eq. (1), recoil pressure is first expressed in terms of lung volume and compliance (i.e., Pel = V/CL), and the resulting first-order differential equation is then integrated between volume end points of TLC and RV. The resulting expression, which is identical to that proposed by Fessler and Permutt (6), is

(4)

and each of the terms in these expressions is as defined previously. Calculated values and measured values of both FEV₁ (r = 0.70, p < 0.001) and FVC (r = 0.67, p < 0.001) correlated well, suggesting that the single-compartment model of flow limitation accurately describes many of the key physiological determinants of maximal expiratory flows in this cohort.

Application of Taylor Expansion Model for Interpreting Responses to LVRS

The Taylor expansion model was developed to provide additional insight into how changes in recoil pressures, airway conductance, and transmural pressures at the site of airway collapse after LVRS interact, and contribute to changes in lung function. The contribution of each term in Eq. (3) to max for the entire cohort, and for responders and nonresponder groups, is summarized in Figure 4. To determine which of the cross-product terms on the right-hand side of Eq. (3) were significantly correlated with the dependent variable max, a series of four univariate regression analyses were performed, one for each term. PelGu (r = 0.58, p < 0.001) and GuPel (r = 0.38, p = 0.015) correlated significantly with max for the entire cohort group of 37 patients, suggesting that changes in conductance (Gu) to airflow and changes in elastic recoil pressures (Pel) were responsible for the observed changes in max that occurred after LVRS.

View larger version (23K): [in this window] [in a new window]   Figure 4.   The contribution of each of the individual terms in the Taylor expansion model to overall changes in max is summarized for the entire cohort, and for responders and nonresponders. The stacked bar graph (right-hand graph for each pair) shows the degree and manner in which each cross-product term contributes to the overall change in max. A positive contribution to max is represented by a change above the x axis, and a negative contribution below the x axis. The net sum of the individual contributions is summarized in the solid bar graph (left-hand graph of each pair). Among responders, the largest contributor to max was the change in recoil pressure weighted by the preoperative conductance (Gu PTLC), which accounted for 72% of the overall increase. Among nonresponders, the largest single contributor to max had a detrimental effect on expiratory flows, and resulted from a decrease in conductance weighted by preoperative recoil pressure (Pel Gu).

An evaluation of responders and nonresponders demonstrates that different factors accounted for the increase in max observed among responders, and conversely, for the decrease observed among nonresponders. Multivariate regression analysis revealed that among responders, only GuPel correlated significantly (n = 19, r = 0.59, p = 0.0075) with observed changes in max. Normalizing Eq. (3) to max, results in the expression:

(5)

Of the four terms on the right-hand side of Eq. (5), GuPel/ max was the only term in this normalized expression that was significantly different from 0 (0.71 ± 0.99, p = 0.006). This finding demonstrates that the majority of the increase (72%) in max was accounted for by an increase in elastic recoil "weighted," or multiplied by, the preoperative value of Gu. By contrast, multivariate regression analysis revealed that among nonresponders, only PelGu (n = 18, r = 0.76, p < 0.001) correlated significantly with changes in max. Applying Eq. (5) to the nonresponders, virtually all of the decrease in max (99%) was accounted for by a decrease in conductance "weighted" by the preoperative value of Pel.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Results presented here using a model based on a Taylor expansion of the Pride and Permutt equation of flow limitation demonstrate that, in a cohort of patients with severe emphysema, expiratory flows after lung volume reduction change by one of two distinct mechanisms. Among patients who improve their expiratory flows in response to surgery, designated as responders, changes in max can be accounted for almost entirely by an increase in elastic recoil pressure weighted by the preoperative value of conductance upstream of the site of flow limitation (GuPel). In this group of patients, elastic recoil and the time constant for expiration were the only parameters that increased significantly in response to surgery. These changes resulted in a significant increase in FEV₁, FVC, and the FEV₁/ FVC ratio. Conductance, transmural pressure airway pressure at the site of flow limitation, and lung compliance did not change in response to surgery. Among patients who failed to improve, or who experienced a decline in function after LVRS, designated as nonresponders, changes in max correlated with a change in conductance weighted by preoperative elastic recoil (PelGu). In this group, the expiratory time constant increased significantly, whereas recoil pressure, conductance, lung compliance, and transmural pressure at the site of flow limitation did not change. This increase in expiratory time constant corresponded with a significant decline in the FEV₁/FVC ratio and a reduction in FEV₁ (8%; p = 0.06), but surgery in this group had no effect on the FVC. These observations suggest that two potential mechanisms of improvement previously hypothesized to account for changes in lung function after LVRS(1) an increase in airway tethering with a resultant change in Gu, or (2) a decrease in Ptm', which would result in a decrease in dynamic gas trappingare in fact not important in the majority of responders. Thus our analysis, while phenomenological rather than mechanistic, provides new insights into how volume reduction surgery affects expiratory flow dynamics both among patients who have improved after surgery, and among those who have not.

The cohort included in the present study is similar demographically and physiologically to those described by previous investigators reporting on the effects of LVRS in emphysema (7). All patients had extensive smoking histories, had severe obstruction as assessed by spirometry, and were markedly limited by their disease (Karnofsky functional status of 67%). After LVRS, FEV₁ improved 28%, and FVC improved 18% for the entire cohort, comparable to results in prior studies (7, 9). Slightly more than half the patients experienced a substantial improvement in response to LVRS. Although this response rate is lower than that reported by several groups (7- 9, 13), the present cohort was not screened so as to exclude patients with homogeneously distributed disease, and thus our group includes patients who are known to respond less favorably to surgical therapy. Among the responder group, overall changes in lung function were greater than for the cohort as a whole: FEV₁ increased 58%, FVC 42%, and FEV₁/FVC ratio 13%. Interestingly, the FEV₁/FVC ratio changed to a much lesser extent than either FEV₁ or FVC, an observation that, in retrospect, is also similar to most prior studies (7). It has consistently been reported that FEV₁ and FVC tend to change in parallel after LVRS. This observation suggests that the primary determinant of improved lung function (FEV₁) among responders is an increase in vital capacity due to a beneficial effect of surgery on the amount of functioning lung, rather than a beneficial effect on airway dimensions at a given lung volume, which would produce a change in the expiratory time constant. This notion, similar to that previously proposed by Hoppin (14), is summarized schematically in Figure 5. Response 1 shows an expiratory flow-volume relationship that would be expected if LVRS altered either Gu and/or CL so as to decrease the expiratory time constant, but produced identical reductions in TLC and RV such that postoperative vital capacity was identical to preoperative vital capacity. Relative to the preoperative profile, the Response 1 profile shows a reduction in the convex shape of the flow-volume loop, but no change in overall expired volume. Alternatively, Response 2 depicts the opposite extreme. LVRS is shown to have no effect on the expiratory time constant (i.e., the convexity of the flow-volume loop), but rather increases isovolume expiratory flows through a selective reduction in RV relative to TLC. The result is a significant increase in vital capacity. This type of response can occur only through resection of regions with markedly elevated RV/TLC ratios, leaving behind lung with a decreased overall RV/TLC ratio.

View larger version (18K): [in this window] [in a new window]   View larger version (13K): [in this window] [in a new window]   Figure 5.   (A) Flow-volume representation of the two types of potential responses that can occur after LVRS. The baseline flow-volume loop is shown as a solid black line. Response 1 (solid gray line) reflects a situation in which expiratory flows improve as a result of an increase in Gu and/or decrease in CL. This produces a change in the expiratory time constant, an increase in peak expiratory flow, and an increase in the FEV1/FVC ratio, but FVC does not increase because RV and TLC decrease by identical amounts. Response 2 (dashed black line) reflects a situation in which expiratory flows improve through "resizing" of the lung to chest wall. Gu and CL do not change, and thus the expiratory time constant and FEV1/FVC ratio are identical to the preoperative flow-volume loop. However, RV decreases to a much greater extent than TLC, and thus peak flows and FVC increase significantly. (B) Each of these situations is depicted, using the model of Fessler and Permutt. In response 1, CL decreases, and recoil pressure increases, but RV and TLC change in identical fashion. In response 2, CL does not change, but recoil pressure increases significantly as a result of lung-chest wall "resizing." RV decreases to a greater extent than TLC, resulting in a significant increase in vital capacity.

Changes in lung volumes corresponding to each of these response patterns are shown in Figure 5B, using the approach described by Fessler and Permutt (6). In Response 1, recoil pressure increases, lung compliance decreases, and RV and TLC decrease postoperatively, but vital capacity, equivalent to TLC  RV, does not change because the reductions in TLC and RV are identical. In Response 2, recoil pressure increases, lung compliance does not change, and RV and TLC decrease post-operatively in such a way that vital capacity increases significantly because the reduction in RV is greater than that which occurs in TLC.

The Taylor expansion model implicitly suggests the same conclusion, although it is expressed in a different manner, one that provides insight with respect to identifying patients who are likely to benefit most from LVRS, as determined on the basis of preoperative physiology. Changes in max and FEV₁ correlated significantly with the term GuPel, the change in recoil pressure "weighted" by the presurgical conductance to airflow. Lung "resizing" results both in the increase in FVC and the increase in Pel that occur among patients who respond favorably to LVRS, as suggested by the Fessler-Permutt analysis (6). The Taylor expansion model suggests that, for an equivalent change in recoil pressure, patients with larger preoperative values of Gu increase their expiratory flows, and their FEV₁ values, to a greater extent than patients with lower preoperative values of Gu (see Figure 1). Although this observation does not provide any specific new insight into how LVRS works mechanistically to improve lung function, it provides a simple method for assessing which patients are likely to benefit most from LVRS: those with reduced preoperative recoil pressures, but larger preoperative conductance values. This observation is of particular interest to our group, given previously observed correlations between preoperative inspiratory conductance (GLI) and improvement in FEV₁ after LVRS (7). Gu, in theory, provides an assessment of flow conductance that is similar to GLI. Gu represents the conductance upstream of the collapsible segment, and GLI, measured during inspiration when dynamic collapse does not occur, should largely reflect the characteristics of this same population of peripheral airways. The present analysis provides a physiological rationale for our prior observations regarding the predictive clinical utility of GLI. In our current cohort, GLI again correlated closely with improvement in FEV₁ (n = 37, r = 0.50, p < 0.001). If this physiologically based argument is, indeed, correct, it would suggest that, within a given cohort, a close relationship between these two measures of conductance should exist. GLI and Gu did, in fact, correlate significantly with one another in the present study (n = 37, r = 0.77, p < 0.001). These findings suggest that patients with higher inspiratory conductance also have better preoperative Gu values, and are more likely to benefit from changes in elastic recoil pressure after LVRS than patients with lower preoperative GLI (and Gu) values. These quantitative expressions, in essence, embody a simple concept originally proposed by Brantigan and coworkers (15) when this therapy was first conceived: that patients with "pure" emphysema, those with normal airflow conductance but reduced elastic recoil, benefit most from LVRS.

Whereas the analyses of Pride and coworkers (1) and Fessler and Permutt (6) provide a means for understanding what determines improvement in lung function after LVRS, the failure of patients to improve lung function after LVRS (i.e., the nonresponders) is less well understood, and perhaps of greater interest. Nonresponders have all undergone surgical procedures like those in the responder group, and should, in theory, have experienced similar lung "resizing." Despite this, no improvement in expiratory flows was observed. Among the nonresponders, FEV₁ and FCV were not significantly different after LVRS, whereas FEV₁/FVC decreased on average 8% (p = 0.006). Detailed lung function measurements suggest that recoil pressures, lung compliance, and Ptm' had not varied in nonresponders at the time of follow-up. The implication of this observation is that neither TLC nor RV changed significantly in response to surgery despite the removal of lung tissue, because a change in lung volumes is not possible without changing at least one of these parameters. This seemingly paradoxical outcome, wherein patients who have undergone lung reduction show no evidence of a decrease in lung volumes, could result from any one of several scenarios. One possibility would be that despite resection of 30-40% of a markedly compliant lung, as is conventionally done during LVRS, the lung remaining within the chest might be nearly equally compliant and, before resection, not fully inflated. Given more room to expand, this hypercompliant lung could rapidly fill the void left by the resected tissue without changing overall compliance, TLC, or RV. Such a patient would be left with no decrease in lung volumes, and no improvement in either FVC or FEV₁ despite having undergone "technically successful" surgery. A second scenario might be that nonresponders actually do experience an initial response to LVRS similar to responders, but then experience rapid "stress relaxation" resulting from an initial increase in recoil pressures within a very diseased lung. At the 6-mo follow-up time point, much of the improvement may have been lost as a result of this relaxation process, which could represent an accelerated form of the functional loss that has been reported in most patients post-LVRS.

Application of the Taylor expansion model to nonresponder patients was less helpful for identifying preoperative profiles that might predict unfavorable responses to LVRS beyond that corresponding to physiological profiles opposite to those of responders. Decreases in FEV₁ among nonresponders correlated significantly with PelGu, the change in conductance "weighted" by the preoperative recoil pressure. In the nonresponder group, declines in function resulted from decreases in lung conductance that by themselves were not significant, but when multiplied by preoperative values of elastic recoil were significant. None of the other cross-product terms in the Taylor expansion model changed appreciably.

Although the approach applied here provides some new information about how patients respond to LVRS, and which patients are likely to respond best, our approach has several important limitations. First, it must be noted that this analysis does not provide new insights into how LVRS works to improve lung function. Rather, it applies existing paradigms to understand how those parameters that can theoretically affect expiratory flows actually do change, and through the use of the Taylor expansion model, how they tend to interact. Second, the analysis assumes that a one-compartment model that can be described by a single conductance value and single compliance value adequately represents expiratory flow dynamics. Visual inspection of the expiratory flow-volume relationships of many of our patients suggests that this is not the case. Nevertheless, the strong correlations between measured FEV₁ values, and those calculated assuming a single-compartment model, suggest that this simple approach embodies most of the characteristics that account for changes in expiratory flows in this patient population.

Despite these important limitations, the present study does provide some new insights into how LVRS affects lung function in patients with emphysema. Our results suggest that improvement in expiratory flows after LVRS can be largely accounted for by increases in vital capacity without significant changes in the FEV₁/FVC ratio. As proposed by Fessler and Permutt, the increase in FVC appears to result from resizing of the lung to the chest wall, which in turn causes an increase in recoil pressure at any given lung volume, without producing changes in either Gu, Ptm', or CL. The failure of LVRS to significantly affect Gu or Ptm' in patients who manifest a favorable response to surgical therapy suggests that this procedure does not work through changing tethering of airways, as has been previously suggested. Among patients who fail to improve after LVRS, FVC did not increase, and PTLC, Ptm', and CL did not change significantly, suggesting that LVRS had little effect on TLC or RV. The Taylor expansion model developed here suggests that the best candidates for LVRS are those with reduced PTLC and preserved Gu preoperative values. This model also provides physiological justification for prior observations showing that conductance to airflow measured during inspiration is a useful preoperative predictor of potential responsiveness to LVRS.