INTRODUCTION

TOP ABSTRACT INTRODUCTION DISCUSSION REFERENCES

Lung volume reduction surgery (LVRS), originally proposed by Brantigan and coworkers (1), has recently gained popularity for treatment of end-stage emphysema. LVRS has been shown to improve spirometric function as well as symptoms and exercise capacity in many patients (4). The mechanism of improvement has usually been attributed to an increase in elastic recoil leading to an increase in airway caliber, and to an improvement in respiratory muscle function from reduced chest wall volume (8, 9, 13). However, little consideration has been given to how LVRS could lead to an increase in vital capacity (VC); yet, such an increase has usually been observed (4).

In this report, we show how VC is determined by an interaction between the mechanical properties of the lungs and the chest wall. When the mechanical properties of the lungs and the chest wall are appropriately matched, VC is maximized. In diseases of airflow limitation, VC is often below its optimal level, but it can approach its maximum with removal of lung tissue. We propose that an increase in VC is a major mechanism of spirometric improvement after LVRS.

	MODEL

The analysis of LVRS is based on the relationship between the two static pressure-volume (P-V) curves shown in Figure 1: (1) lung volume (V) versus pleural pressure (Ppl) when alveolar pressure is atmospheric, and (2) V versus Ppl during maximal contraction of the inspiratory muscles when the air outlet is closed. The former curve is the mirror image of the static P-V curve of the lung where the elastic recoil pressure (Pel) = Ppl, and the slope is the negative value of the inspiratory compliance of the lung (CL). The second curve is the static P-V curve of the chest wall under conditions of maximal inspiratory muscle activity. We define its slope as the compliance of the chest wall during maximal inspiratory muscular activity (CW_max) and its position as the point of intersection with the volume axis (VW_max0). The analysis is based on the assumption of linearity of these two P-V relations. Although we concede that these actual relations are nonlinear, we shall show later that no analytic rigor is lost by these pragmatic simplifications.

View larger version (15K): [in this window] [in a new window]   Figure 1.   Graphic representation of the pressure-volume relationships used in the model. CWmax is the chest wall compliance during maximal inspiratory muscle contraction. CL is the linearized static lung compliance. RV, in the presence of airway smooth muscle tone (P'TM), may exceed RV0, the residual volume in the absence of tone. TLC is determined by the intersection of the curves representing the elastic properties of the lungs and of the chest wall during maximal inspiratory muscle contraction.

VC and TLC may be solved algebraically from the graphic representations in Figure 1. It is assumed that residual volume (RV) is determined by airway closure and is independent of chest wall properties. In the absence of airway tone, the transmural pressure of airway closure (P'TM) = 0, RV = RV₀, and alveolar pressure (PALV) = 0 (atmospheric) when the lungs begin to fill from RV. In the presence of airway tone, P'TM > 0, RV > RV₀, and PALV > 0 at RV. During inspiration from RV, V does not increase until Ppl = P'TM (Figure 1). With linear relations,

(1)

where

(2)

where P'TMCL = trapped volume from airway closure. Combining the linear P-V characteristics of the lungs and chest wall,

(3)

and

(4)

The Effect of LVRS on VC

The effects of LVRS are shown graphically in Figure 2 and algebraically below.

View larger version (14K): [in this window] [in a new window]   Figure 2.   Graphic depiction of the effects of LVRS on VC. Pressure-volume relations of the lung and chest wall are shown as in Figure 1, and are arbitrarily chosen for the purpose of illustration. (A) The effects of removal of pure bullae are shown by the dotted line. There is a parallel downward shift of the lung P-V relation (CL), the vertical extent of which is equal to the decrease in RV0. In this figure, removal of about one-third of lung volume ( = 0.66) is illustrated. (B) The effects of homogeneous LVRS with  = 0.66 are shown by the dotted line. For comparison, the postoperative VC in (A) is shown in grey. For these preoperative conditions and , VC improves slightly less after homogenous LVRS than after removal of bullae alone. (C ) The effects of homogenous LVRS with  = 0.66 from different starting conditions is shown by the dotted line. Preoperative lung compliance and RV/TLC were lower than in (B). LVRS now decreases VC; VC before is shown in grey next to VC after to facilitate comparison.

If we assume that the removal of lung does not alter the P-V characteristics of the chest wall or the intrinsic ability of the respiratory muscles to generate force at a given chest wall volume, then VW_max0 and CW_max should not change.* If we further assume that emphysematous blebs or bullae have little elastic recoil but contain gas with a volume that does not change with lung volume, the removal of the blebs or bullae alone would be equivalent to reducing RV₀. Thus, the removal of only blebs or bullae would be expected to cause an increase in Pel_TLC and VC (Equations 1 and 3) but reduce TLC (Equation 4). The increase in VC would be proportional to the decrease in RV₀ (assuming P'TM of blebs or bullae = 0) with the constant of proportionality = CL/(CW_max + CL) (Figure 2A).

If the emphysematous changes were uniformly distributed, LVRS would result in a proportional reduction in both RV and CL. We define this condition as homogeneous LVRS and will analyze its effect on VC, as an example of the minimum benefits that may be expected from LVRS. For homogeneous LVRS, the increase in VC is illustrated in Figure 2B and can be calculated as follows:

Let RV_B and CL_B = RV and CL before volume reduction, RV_A and CL_A, after volume reduction, and  = RV_A/RV_B = CL_A/CL_B · RV_B = RV_0B + P'TMCL_B and RV_A = RV_0B + P'TMCL_B where  = fraction of original lung remaining after volume reduction ( = 0.75 describes removal of 25% of the lung). Thus,

(5)

where VC_A = VC after making a proportional change in RV and CL equal to .

Maximal VC_A occurs when dVC/d = 0. Differentiating Equation 5 with respect to  and setting dVC_A/d = 0, rearranging, and simplifying yields

(6)

where

(7)

where  = 1 in absence of airway closure and increases with increases in P'TM. The positive root of this equation is:

(8)

When _max < 1, LVRS will always cause an increase in VC. This occurs when:

(9)

or, equivalently, when

(10)

Thus, based on a limited number of static mechanical factors, LVRS may increase (Figure 2A and B) or decrease (Figure 2C) VC. The factors favoring an increase in VC, high RV/TLC and CL, are factors typical of emphysema.

The Effect of LVRS on FEV₁

With linear relations between max and Pel (intercept P'TM; slope = 1/Ru) and between V and Pel (intercept = P'TM; slope = CL), the flow-volume curve is linear, and the relation between the volume expired and time during a forced expiration is exponential (17, 18). Thus,

(11)

(12)

where Ru = resistance upstream from the flow-limiting segment or choke point.

With removal of blebs or bullae alone, there is no change in RuCL. With homogeneous LVRS, Gu (1/Ru) and CL change proportionally so that RuCL remains constant. Thus, with removal of blebs or bullae alone or with homogeneous LVRS, FEV₁/FVC remains constant and FEV₁ increases in proportion to the increase in VC.

The equations of the model will first be applied to values measured in a 48-yr-old man 174 cm tall (Table 1, first column) (19). The linear inspiratory P-V curve was used. The value of CW_max was calculated from the data of DeTroyer and Yernault (20) from the upper 30% of TLC in normal men (Figure 3 in Reference 20). VW_max0 was calculated by assuming linear relations and using Equation 3. FEV₁ was calculated from the equation of Miller (21). Ru was calculated from Equation 12 using the normal values of FEV₁, VC, and CL.

View larger version (19K): [in this window] [in a new window]   Figure 3.   Effects of homogeneous LVRS on FEV1 when the latter has been reduced to 0.8 L by a single abnormal lung factor. Lung resection has substantial effects on FEV1 when its reduction is due to an elevated residual volume (either increased RV0 or P'TM). Lung resection has minimal effects on FEV1 when its abnormality is due to increased lung compliance or airway resistance. The percent LVRS when maximal improvement occurs is indicated by an arrow.

For analytic purposes, we shall first consider the effect of LVRS under the hypothetical conditions where FEV₁ has been reduced because of a single abnormal factor. Assuming no change in the chest wall (VW_max0 and CW_max remain normal), FEV₁ can be reduced by an increase in RV₀, an increase in P'TM, an increase in CL, or an increase in Ru (Equations 3 and 12). When FEV₁ has been reduced by a single such factor alone, it can be substantially improved by homogeneous LVRS only if the reduction is from an increase in RV₀ or in P'TM. There is essentially no improvement in FEV₁ if its reduction is solely from an increase in Ru or CL (Figure 3). Thus, LVRS will only increase FEV₁ when RV is increased: RV = RV₀ + P'TMCL, with P'TMCL being the component of the increase in RV caused by airway closure. Indeed, further analysis reveals that there are only two factors that determine the percentage increase in FEV₁ (%FEV₁) after homogeneous LVRS: RV/TLC and CW_max/CL:

(13)

where

This relationship between %FEV₁, RV/TLC, and CW_max/ CL after a homogeneous 25% reduction in lung volume ( = 0.75) is shown in Figure 4. When RV/TLC is within the normal range, there is a trivial increase in FEV₁ after LVRS. At levels of RV/TLC > 0.6, LVRS becomes increasingly effective. For the estimated normal value of CW_max/CL = 0.2, there is more than a 50% increase in FEV₁ at an RV/TLC = 0.75 and more than doubling of FEV₁ at an RV/TLC = 0.85. Assuming there is no impairment in the ability of the respiratory muscles to lower pleural pressure at a given lung volume in emphysema (15), an increase in CL in emphysema would shift this relationship to the left, and there would be an even greater increase in FEV₁ at a given RV/TLC than for the normal estimated value of CW_max/CL.

View larger version (17K): [in this window] [in a new window]   Figure 4.   Effects of homogeneous LVRS of 25% of the lung on FEV1 versus baseline RV/TLC, as isopleths of CWmax/CL. Increased baseline RV/TLC has the predominant effect on the percent improvement in FEV1. However, at any RV/TLC, decreased CWmax/CL also predicts greater benefit from LVRS, and the influence of CWmax/ CL becomes greater at higher RV/TLC.

Let us next consider the effects of LVRS for a hypothetical case of emphysema, in which two abnormal factors contribute to the decrease in FEV₁. In this example, RV is increased 3.2-fold, CL is increased 2.5-fold, but changes involve the lung parenchyma alone (Ru normal). The effects of these parenchymal changes can be seen in Table , second column. VC is reduced (Equation 3), FEV₁/FVC is reduced because of the increase in CL (Equation 11), TLC is increased (Equation 4), and FEV₁ is reduced to 0.8 L (Equation 12). With these changes in RV and CL sufficient to reduce FEV₁ to 0.8 L, LVRS causes a marked increase in FEV₁ (Figure 5). With the removal of blebs or bullae alone, the effect on VC is limited to a reduction in RV₀ (Equation 3). The effect of homogeneous LVRS on VC is determined from Equation 5. Homogeneous LVRS is nearly as effective as removal of blebs or bullae alone to approximately 25% reduction  = 0.75). With removal of larger amounts of lung, homogeneous LVRS becomes less effective than resection of blebs, and it reaches its maximal effect when 75% of the lung is removed (_max = 0.25) (Equation 8) for the conditions under consideration.

View larger version (24K): [in this window] [in a new window]   Figure 5.   Effects of homogeneous LVRS and resection of blebs and bullae for a hypothetical case of emphysema (Table , second column). Resection of blebs is considered as removal of lung with no elastic recoil, i.e., a reduction in RV0 alone. With resection of blebs/ bullae, FEV1 improves monotonically as more lung is removed. With homogenous LVRS, maximal improvement in FEV1 occurs when 75% of the lung is resected. Within the range of lung resection that is clinically feasible (20 to 30%), there is negligible difference in the improvement in FEV1 whether the resected lung is completely destroyed or identical to that left behind.

The Role of RV/TLC in Airflow Limitation

Because substantial improvement with LVRS will occur only when there has been an increase in RV/TLC, we will next examine the contribution of RV/TLC to diseases of airflow limitation.

FEV₁ may be expressed as the product of three factors: FEV₁/VC, 1-RV/TLC, and TLC (the product of the second and third factors = VC and the product of VC and the first factor = FEV₁). Thus,

(14)

This equation shows that the volume that leaves the lung in the first second of a forced expiration is equal to the total volume of the lungs (TLC) as modified by two fractions: (1) the fraction of TLC that is capable of leaving the lungs (1-RV/ TLC) and (2) the fraction of the volume that leaves within the first second to the total volume that is capable of leaving (FEV₁/VC). This latter fraction is a function of the product of Ru and CL (Equation 11). An increase in either Ru or CL causes a decrease in FEV₁/VC. In the linear model, RuCL is the time constant of forced expiration, the time required for 63% of the VC to be expired. Thus, with either an increase in Ru or CL, FEV₁/VC decreases, and the time taken to expire VC increases. This equation will now be applied to data obtained from patients with ₁-antitrypsin deficiency, asthma, and "chronic obstructive pulmonary disease."

Airflow Limitation in ₁-Antitrypsin Deficiency

Findings in 10 patients with homozygous ₁-antitrypsin deficiency studied at the Mayo Clinic by Black and coworkers (22) are shown in Table 2, ranked in order of RV/TLC. Of the three determinants of FEV₁ from Equation 14, there was a highly significant correlation between FEV₁ and 1-RV/TLC (Figure 6) (r = 0.88, p < 0.001), but not between FEV₁ and either TLC or FEV₁/VC (r = 0.08 and 0.23, respectively). There was also no significant correlation between FEV₁ and Pel_TLC (r = 0.045). CL and Ru changed in opposite directions with FEV₁ (r = 0.81, p = 0.005 for CL and 0.76, p = 0.01 for Ru), which contributed to the lack of correlation between FEV₁/ VC and FEV₁. Thus, contrary to intuition, neither the degree of hyperinflation (TLC), nor the loss of recoil (Pel_TLC), nor the time constant of emptying (proportional to FEV₁/FVC) were predictive of FEV₁, whereas RV/TLC was strongly predictive.

View larger version (12K): [in this window] [in a new window]   Figure 6.   Regression of FEV1 against (1-RV/TLC) from the data of Black and coworkers (22). FEV1 = [4.9 × (1-RV/TLC) + 0.004; r = 0.88, p < 0.001. There was no significant relationship between FEV1 and either TLC or FEV1/VC, its other determinants from Equation 14.

Because RV/TLC is a strong correlate of FEV₁, what then determines RV/TLC? By multiple regression, nearly all of the large variance in RV/TLC (range: 0.32 to 0.87) was attributable to the combined effect of age and pack-years of smoking, r² = 0.79, p < 0.005) (Table 3). Thus, the relatively young, nonsmoking patients with homozygous ₁-antitrypsin deficiency had lung parenchymal changes that decreased elastic recoil and increased TLC, but these changes alone did not significantly limit airflow. Without an increase in RV/TLC, FEV₁ was only minimally reduced. The lungs took a longer time to empty as reflected by the subnormal FEV₁/VC, but this was largely overcome by the increase in TLC (Equation 14). With age and years of smoking, we suggest that the marked increase in RV/TLC and RV was due to the destruction of lung tissue and the development of space-filling holes within the lungs.

The spaces resulting from destruction of the parenchyma do not contribute significantly to the elastic recoil. This inference is supported by the findings of Hogg and coworkers (23) who found that "centrilobular emphysematous spaces have a high residual volume, are less compliant than the normal lung, and are much less compliant than the emphysematous lungs which contain them." If the increasing proportion of the lung occupied by the noncompliant spaces is indeed due to parenchymal destruction, all of the significant associations between FEV₁, CL, Ru, and RV/TLC would be explained. As the lung parenchyma is destroyed and replaced by noncompliant spaces, CL decreases because fewer air spaces capable of expansion are left behind. With progressive destruction, there is a decrease in the number of small airways; thus, an increase in Ru in association with the decrease in CL. The noncompliant spaces become a greater fraction of the TLC; thus, the decrease in 1-RV/TLC and the progressive decrease in VC and FEV₁.

In our review of the literature, we find little consideration given to the role of RV and RV/TLC in airflow limitation, which has been conventionally expressed as follows: "Either a reduced elastic recoil (from damage to alveolar tissue) or compromise of the conducting air passages producing airflow resistance or both may limit airflow and reduce the FEV₁" (24). Macklem and Eidelman (25) reexamined the elastic properties of emphysematous lungs and concluded: "It would seem that in emphysema the abnormalities of the ability to blow air rapidly from the lungs are not primarily due to the abnormalities in lung elastic properties. Thus, small airway obstruction may be the principal cause of abnormal expiratory flow limitation as well as abnormalities in gas exchange." Macklem and Eidelman proposed that the elastic abnormalities of lung parenchyma in emphysema were twofold: an increase in resting length of alveolar wall accounting for hyperinflation and a decrease in extensibility of the walls once they became stressed. Although this was in keeping with the elastic properties of the centrilobular emphysematous space described by Hogg and coworkers (23), they completely failed to consider the implications of an increase in resting length and hyperinflation on FEV₁.

Despite much study, the relationship between morphometric parenchymal changes of emphysema and pulmonary function remains unclear (26). We propose that this is so because the parenchymal changes affect FEV₁ to a great extent only indirectly, through a mismatch of the size of the lungs and chest wall as reflected by the level of RV/TLC. This is strikingly revealed by considering what would have happened to the normal values of pulmonary function shown in Table , first column, if the properties of the chest wall remained unchanged, but a pair of normal lungs exactly three times the normal size was transplanted within that chest wall. RV₀ would have increased threefold, as would have both the conductance (Ru reduced to one-third) and the compliance, but FEV₁/VC would have remained normal. There would have been a marked increase in RV/TLC responsible for the decrease in VC and FEV₁. Most of the changes would be those of severe emphysema: an increase in TLC and compliance and a marked reduction in the elastic recoil pressure at TLC (Table , third column).

The Role of RV/TLC in Conventional Chronic Airflow Limitation

Eidelman and coworkers (27) carried out extensive measurements of pulmonary function, including P-V relations, in 39 patients referred to the pulmonary function laboratories of the Royal Victoria and Montreal Chest Hospitals (27). They were considered by the investigators to be "reasonably representative of smokers with respiratory symptoms." Of these patients, 26 had values of Pel at 90% TLC that were less than 80% predicted. Our reanalysis of their published data of the 26 patients with a low Pel reveals striking similarities between the role of RV/TLC in airflow limitation in these patients and those with ₁-antitrypsin deficiency studied by Black and coworkers (22). Of the three determinants of FEV₁ from Equation 14, there was a highly significant correlation between FEV₁ and 1-RV/TLC (r = 0.64, p < 0.0005), but not for TLC.* As in the patients with homozygous ₁-antitrypsin deficiency, CL and Ru changed in opposite directions with FEV₁ (r = 0.48, p < 0.01 for CL and 0.83, p < 0.00001 for Ru). In contrast to the 10 patients with homozygous ₁-antitrypsin deficiency, there was a highly significant correlation between FEV₁ and FEV₁/VC (r = 0.74, p < 0.00002). This is compatible with small airways disease contributing to the airflow limitation above and beyond destruction of lung tissue from emphysematous changes.

Kesten and Rebuck (28) analyzed pulmonary function tests from outpatients in whom an unambiguous diagnosis of either asthma or COPD could be made. Plethysmographic lung volume measurements were made in 268 patients with the diagnosis of asthma and 93 patients with the diagnosis of COPD. There were very good correlations in both groups of patients between FEV₁ and RV/TLC: (asthma, r = 0.72; COPD, r = 0.78). Thus, pathologically dissimilar diseases share striking relationships between FEV₁ and RV/TLC.

Justification of Linear Model

Use of linear relations simplifies the formulae we have presented. Although these linear relations are only estimates, their use is supported by their correlation with other, more precisely measured, values. The calculation of Ru assumes a linear relation between Pel and flow and between Pel and V. This generates an exponential relation between volume expired and time during a forced expiration (Equation 13). The validity of the linear analysis of the data of Black and coworkers (22) is supported by the strong correlation between the calculated Ru and two direct measurements of resistance made by Black and coworkers. From the measurement of FEV₁/VC and CL, Ru can be estimated from Equation 13. In the study of Black and coworkers (22), pulmonary resistance (Rp) was measured during tidal breathing from the relations between esophageal pressure and flow. In addition, Ru was estimated by the slope of the relation between max and Pel for each of the 10 subjects. These slopes were arranged in rank order (RO) 1 to 10 from the steepest (low Ru) to the most shallow (high Ru) (Figure 3 in reference 22). The greater the rank, the greater the resistance between the alveoli and the choke point. Each of the three measurements of resistance were significantly correlated to the other two (Table 4). The strongest correlation was between the slope measurement of Ru by Black and coworkers and the estimation of Ru from the linear model (r = 0.82).

From the data of Eidelman and coworkers (27) on the 26 subjects with low elastic recoil, the validity of the linear model is given further support by the good correlation between CL (VC/Pel_TLC) and the direct measurement of compliance, CST (the slope of the relation between V and Pel during deflation from TLC between FRC and FRC + 0.5 L). Regression of CST against CL was highly significant with a slope close to 1 and an intercept close to 0. [CST = (1.200 × CL) 0.064, r = 0.834, p < 0.0001], and their means were not significantly different (CST 0.427 ± 0.19 SD versus CL 0.409 ± 0.13 SD L/cm H₂O).

The use of linear model leads to the prediction that LVRS would not improve FEV₁/FVC. In contrast, some investigators have found greater improvements in FEV₁ than in FVC (4, 9). There are two reasons for this discrepancy. First, we have defined homogeneous LVRS as removal of lung identical to that left behind, with proportional reductions in CL and 1/Ru. In practice, resection of peripheral lung parenchyma would spare larger airways, and CL could be reduced proportionally more than Ru increased. It would be expected, then, that FEV₁ would increase more than would VC. Second, and perhaps more importantly, it is known that FEV₁/FVC of an expiration from a volume less than TLC is lower than that of an expiration from TLC (29). Because LVRS increases VC, the comparison of FEV₁/VC before and after surgery may be likened to comparison of a partial and full expiration. Thus, this difference between predicted and observed effects of LVRS does not invalidate our simplifying assumptions of linearity. Rather, it emphasizes that we have made a conservative estimate of the effect of LVRS.

	DISCUSSION

TOP ABSTRACT INTRODUCTION DISCUSSION REFERENCES

This model clearly indicates that when LVRS improves airflow limitation, it does so primarily by improving the fit between lungs and chest wall, decreasing RV more than TLC. TLC is reached when the force generated by maximal contraction of the inspiratory muscles balances the elastic recoil of the lungs and chest wall. This balance of the forces must occur at a lower TLC when lung volume is reduced. The ability of the inspiratory muscles to generate force would be increased at this lower volume, and the elastic recoil pressure would be greater. It is these two features of LVRS, increased elastic recoil at TLC and increased ability of the inspiratory muscles to generate force, that are often invoked to explain the beneficial effects of LVRS (1, 8, 9, 13). However, neither of these factors would necessarily increase VC. Indeed, LVRS in a patient with interstitial pulmonary fibrosis would also be accompanied by a decrease in TLC, increased elastic recoil pressure at TLC, and greater inspiratory muscle force at TLC. Nevertheless, it is nearly a certainty that VC would decrease. The model presents an analytical solution of the conditions necessary for LVRS to be accompanied by an increase in VC instead of a decrease (Equations 9 and 10). The effect of LVRS on the direction and magnitude of the change in VC is dominated by RV/TLC (Equations 10 and 13).

Because the model predicts that an increase in RV/TLC is the best predictor of the improvement that can be obtained by LVRS, we analyzed the role of such an increase in chronic airflow limitation. We were surprised that it was the best correlate of the FEV₁ in previously published data on patients with ₁-antitrypsin deficiency (22), conventional forms of COPD (27, 28), and asthma (28). Thus, regardless of the cause of the increase in RV, whether from emphysema, an increase in airway closing pressure, or even a completely normal lung that is too large for the chest wall within which it is contained (Table , third column), there will be a decrease in FEV₁ that may be restored by LVRS. The level of RV/TLC is of greater importance than the specific cause of the increase. Although one would certainly not advocate LVRS when RV could be reduced pharmacologically, in theory the improvement in FEV₁ would be the same for a patient with an RV/TLC of 0.9 whether produced by long-standing emphysema or by status asthmaticus.

Another important implication of this model is the modest effect of homogeneity in predicting the benefit of LVRS. The model indicates that up to 25% reduction in lung volume, there is little difference in the improvement in FEV₁ whether completely nonfunctioning lung tissue is removed or whether the tissue removed is exactly the same as the lung tissue left behind.

The implications of these findings for patient selection are clear. If one considers improvement in FEV₁ as the goal of LVRS (conceding its imperfect relationship to dyspnea, exercise tolerance, and survival), the optimal candidates will be those with the highest RV/TLC. The increase in TLC is of importance only to the extent that it is a marker for an even greater abnormality of RV. A normal relationship between max and Pel has been suggested as a selection criteria (30). Our findings suggest that an abnormality of this relationship should not exclude patients who also have an elevated RV/ TLC. Indeed, both theoretically and supported by the data from Black and coworkers there is a significant correlation between resistance and RV/TLC. Likewise, the measurement of elastic recoil pressure determines neither the best candidates nor the mechanism of their improvement (8), and lung compliance measurements or detailed radiologic measures of inhomogeneity add little predictive value to noninvasive lung volume measurements (although they may serve to confirm the presence of emphysema). If "target regions" can be radiographically identified, it is logical that these be resected. It does not logically follow that patients with homogenous emphysema be excluded from surgery.

Our analysis is focused on the mechanical properties of lung and chest wall, and does not consider circulatory or gas exchange functions that may limit the amount of resectable lung. The optimal improvement from consideration of mechanics alone is likely to occur with removal of more lung than would be compatible with adequate pulmonary circulation and gas exchange, for example, 75% removal of lung (Figure 5). However, in patients with elevated RV/TLC, the model predicts continued improvement in FEV₁ extending well beyond the usual goal of 20 to 30% resection. This is consistent with the findings at several centers, in which techniques that remove more lung produce more benefit (10). It suggests that, were it possible to demonstrate sufficient vascular reserve, even more aggressive resection might be reasonable.

It also follows that a critical factor in comparing outcomes between patients, different procedures, or centers is the amount of lung removed. This fraction is generally only roughly estimated from inspection of the partially atelectatic lung at the time of surgery. Weighing the resected specimens is of no benefit since the volume and density of resected and nonresected lung in situ is unknown. We propose that the best measurement of the fraction of lung resected be derived from the ratio of residual volumes (1-RV_A/RV_B). This value best reflects the fractional change in lung volume in situ, independent of potential changes in respiratory muscle function or chest wall remodeling. Such a measure is essential to allow meaningful comparisons between the physiologic outcomes of varied procedures that all attempt to remove lung.

Finally, although this analysis provides insight into both the determinants of airflow limitation and of the effects of LVRS, we stress that its greatest utility is for hypothesis generation. The implications outlined above should be subjected to retrospective and prospective validation.