Article Text

## Abstract

Previous work has shown that area under the expiratory flow–volume curve (AEX) performs well in diagnosing and stratifying respiratory physiologic impairment, thereby lessening the need to measure lung volumes. Extending this prior work, the current study assesses the accuracy and utility of several geometric approximations of AEX based on standard instantaneous flows. These approximations can be used in spirometry interpretation when actual AEX measurements are not available. We analysed 15 308 spirometry tests performed on subjects who underwent same-day lung volume assessments in the Pulmonary Function Laboratory. Diagnostic performance of four AEX approximations (AEX_{1–4}) was compared with that of actual AEX. All four computations included forced vital capacity (FVC) and various instantaneous flows: AEX_{1} was derived from peak expiratoryflow (PEF); AEX_{2} from PEF and forced expiratoryflow at 50% FVC (FEF_{50}); AEX_{3} from FVC, PEF, FEF at 25% FVC (FEF_{25}) and at 75% FVC (FEF_{75}), while AEX_{4} was computed from all four flows, PEF, FEF_{25}, FEF_{50} and FEF_{75}. Mean AEX, AEX_{1}, AEX_{2}, AEX_{3} and AEX_{4} were 6.6, 8.3, 6.7, 6.3 and 6.1 L^{2}/s, respectively. All four approximations had strong correlations with AEX, that is, 0.95–0.99. Differences were the smallest for AEX–AEX_{4}, with a mean of 0.52 (95% CI 0.51 to 0.54) and a SD of 0.75 (95% CI 0.74 to 0.76) L^{2}/s. In the absence of AEX and in addition to the usual spirometric variables used for assessing functional impairments, parameters such as AEX_{4} can provide reasonable approximations of AEX and become useful new tools in future interpretative strategies.

- lung function
- spirometry
- lung volumes
- area under flow-volume curve
- decision trees
- forest bootstrap models

## Statistics from Altmetric.com

- lung function
- spirometry
- lung volumes
- area under flow-volume curve
- decision trees
- forest bootstrap models

### Significance of this study

#### What is already known about this subject?

Usual pulmonary function testing consists of spirometry and several, more advanced lung volume assessments, such as body plethysmography, gas dilution or diffusion measurements.

Area under expiratory flow–volume loop (AEX) is a spirometric measurement computed as the integral function of respiratory flow versus volume during a forced exhalation maneuver.

We have shown before that the AEX has good discriminating capacity between different functional impairments and patterns (eg, obstruction, restriction, mixed defects and small airway disease) and may lessen the need to use lung volume testing.

Only a minority of pulmonary function testing platforms compute and make available AEX measurements.

#### What are the new findings?

We derived four different AEX approximations, AEX

_{1}to AEX_{4}, and compared them with the actual AEX.AEX approximations based on instantaneous flows at different volumes are good surrogate measurements of AEX.

The AEX

_{4,}derived from four instantaneous flows measured during spirometry, seems to be a good approximation or surrogate measurement for AEX.

#### How might these results change the focus of research or clinical practice?

Whenever AEX is not available, the use of AEX

_{4}could provide additional value in the diagnosis and the severity stratification of respiratory function impairment.The use of such measurements could avoid the need to use more laborious, complex and expensive methods of respiratory function assessment.

## Introduction

Central to spirometry interpretation is the process of comparing measured flows and volumes with reference values obtained from predictive equations that are derived from healthy subjects from similar, relevant populations.1–3 Forced vital capacity (FVC), forced expiratory volume in 1 s (FEV_{1}), FEV_{1}/FVC ratio and ‘mid’ or ‘distal’ flows represent the main parameters used to investigate the presence and severity of lung function impairment by spirometry. Measurements for total lung capacity, residual volume and functional residual capacity are the gold standards of pulmonary function testing (PFT) for diagnosing hyperinflation with air trapping, thoracic overdistension or restriction. Yet, these measurements add to the testing burden and may be technically challenging, thus limiting their use in clinical practice. Nevertheless, in specific clinical situations, the availability of these measurements becomes essential for unequivocal diagnosis of a physiological state or impairment.4 Furthermore, predicted ‘mid’ and ‘distal’ flows tend to have wide CIs, limiting their diagnostic utility.

Previous work described the diagnostic utility of a novel spirometric parameter called area under expiratory flow–volume curve (AEX) (Ioachimescu OC, An alternative spirometric measurement: area under the expiratory flow-volume curve (AEX). Unpublished data, 2019).5 as an alternative measure for categorizing and estimating the severity of PFT impairments, thereby lessening the need to assess lung volumes in a large percentage of subjects. The AEX is the actual integral function of the variable flow (on the Y axis) versus expiratory volume (on the X axis) during a forced exhalation maneuver from TLC (figure 1). AEX is expressed in L^{2}/s and can be computed by any PFT digital programme but appears currently to be made available on only a minority of PFT equipment manufacturers’ platforms.

The current study extends our prior work by assessing the utility of several approximations of AEX derived from FVC and available instantaneous flows (AEX_{1}, AEX_{2}, AEX_{3} and AEX_{4}; figure 2A–D). Deriving approximated values of the area under the flow–volume loop from widely available spirometric parameters may eliminate the need for actual AEX availability from the PFT equipment software, thereby extending the applicability of this novel measurement.

## Methods

The analysis was performed on a subcohort of a dataset of 21 253 consecutive prebronchodilator spirometry tests done in the Cleveland Clinic Pulmonary Function Laboratory5 on 9328 distinct adult patients who underwent same-day lung volume determinations by either body plethysmography6–8 or helium dilution.9 10 Eligible subjects were adults >18 years. The AEX values were available in 15 308 tests, on which all the AEX approximations were calculated and used for analysis.

Spirometry was performed and interpreted according to the current American Thoracic Society (ATS)/European Respiratory Society (ERS) standards and recommendations.1 11 12 Body plethysmography and helium dilution techniques were used to assess lung volumes per ATS/ERS standards and criteria.1 4 13 Spirometry, body plethysmography and helium dilution tests were performed using a Jaeger Master Lab Pro system (Wurzberg, Germany). The most recent, comprehensive and applicable reference values, as published by the Global Lung Initiative (GLI), were used for spirometry interpretation.2 14 For lung volumes, reference values from Crapo *et al*
15 were used. Per ATS/ERS recommendations,13 an obstructive ventilatory defect was defined by FEV_{1}/FVC below the lower limit of normal (FEV_{1}/FVC_{LLN}) in the presence of FVC ≥FVC_{LLN}. Restriction was diagnosed when three criteria were satisfied: FEV_{1}/FVC ≥ FEV_{1}/FVC_{LLN}, FVC <FVC_{LLN}, and TLC <TLC_{LLN}. If FEV_{1}/FVC < FEV_{1}/FVC_{LLN}, FVC <FVC_{LLN} and TLC < TLC_{LLN,} then a diagnosis of mixed ventilatory defect was established. In this analysis, small airways disease was not assessed, as the number of subjects with all necessary flows and volumes for the computing AEX approximations was too small to be useful in the models.

We defined four spirometric variables, AEX_{1} to AEX_{4}, that were derived from the areas of triangles and trapezoids delineated by expired volumes during the specific portions of the forced exhalation and the respective instantaneous flows. As such, AEX_{1} was derived from FVC and one instantaneous flow, peak expiratory flow (PEF; figure 2A); AEX_{2} was calculated from FVC and two flows, PEF and forced expiratory flow at 50% FVC (FEF_{50}; figure 2B), AEX_{3} was computed from FVC and three flows: PEF, forced expiratory flow at 25% (FEF_{25}) and at 75% FVC (FEF_{75}, figure 2C); and AEX_{4} was constructed from FVC and all four flows: PEF, FEF_{25}, FEF_{50} and FEF_{75} (figure 2D). Their formulas are shown here:

Descriptive statistical analysis of available variables was performed. Categorical variables were presented as frequencies or group percentages. Continuous variables were characterized as mean±SD (for normally distributed variables) or as median and 25th–75th IQR (for non-normal distributions). Student’s t-test and analysis of variance were used to compare mean values, while categorical variables were compared using χ^{2} test. The Tukey-Kramer HSD method was used to compare means among pairs when the variances were similar, while the Wilcoxon or Kruskal-Wallis rank sum tests were performed as non-parametric methods when variances were unequal, as appropriate.

Exploratory recursive decision trees were used, followed by bootstrap forest partitioning using contributory variables from the first phase. Bootstrap forest models typically fit a response value (in this case: ventilatory impairment as a categorical variable) by averaging many decision trees fitting bootstrap samples of the training data. The prediction based on the final bootstrap forest model is an average of the predicted values of the observation over all decision trees. In the end, the bootstrap forest models assessed the performance in diagnosing various spirometric patterns of several parameters: FEV_{1} and FVC per cent predicted (using GLI equations), FEF_{50}*100/0.5*FVC and AEX_{4}. The main characteristics of these models were: 66%/33% training/validation rates, up to 10 000 trees per forest, with a minimum of 10 and maximum of 2000 splits per tree, early stopping and 21 minimum size for splits.

Statistical significance was satisfied when p values <0.05. Statistical analyses were performed using JMP Pro 14 software.

## Results

A total of 15 308 test sets were used to validate AEX_{1}, AEX_{2}, AEX_{3} and AEX_{4} (table 1). Fifty-one per cent (7822) of the subjects were men and 49% (7486) were women. Eighty-seven per cent of the tested individual were self-identified Caucasians and 13% were African-Americans. The mean age±SD was 56±14 years. The helium dilution technique was used to measure lung volumes in 40%, and body plethysmography was used in 60% of the subjects. Table 2 illustrates the main functional parameters of the test set. Using GLI predictive equations, 28%, 51%, 16% and 5% of the tests used for this analysis had normal spirometry, obstruction, restriction, or a mixed pattern.

Figure 1 illustrates the concept of AEX, while figure 2A–D shows the triangular and trapezoidal areas used for geometric reconstruction of the parameters called AEX_{1} to AEX_{4}. Figure 3 illustrates two distinct normal flow–volume curves: one in which AEX_{1} is slightly smaller than the actual AEX (figure 3A), and a curve obtained in a subject with rapidly declining ‘distal’ expiratory flows, yet still normal, in which case the AEX_{1} is larger than AEX (figure 3B). Figure 3C–E illustrate examples of possible relationships between AEX_{1} and AEX in obstruction, restriction and in a subject with a mixed (obstructive–restrictive) ventilatory defect. Similar concepts are shown for AEX_{2}, AEX_{3} and AEX_{4} in figures 4A–E, 5A–E and 6A–E, respectively.

The means±SD for AEX, AEX_{1}, AEX_{2}, AEX_{3} and AEX_{4} were as follows: 6.6±6.1, 8.3±6.5, 6.7±5.8, 6.3±5.7 and 6.1±5.6, respectively. Figure 7 is a box-and-whisker plot showing the five variables, together with their minimal, maximal and main quartile values. Figure 8A–D includes a set of four Bland-Altman graphs that show that the smallest dispersion is achieved for the differences between AEX and AEX_{4}, with a mean of 0.52 (95% CI 0.51 to 0.54) and a SD of 0.75 (95% CI 0.74–0.76) L^{2}/s. This indicates that AEX_{4} could be used with reasonable confidence (smallest dispersion) in approximating AEX. Similarly, AEX_{1-3} are potentially useful but with less accuracy than AEX_{4} (higher dispersion). Figure 8A–D also shows that AEX_{1} to AEX_{4} tend to overestimate AEX in obstructive ventilatory defects (red markers), while in normal tests (green markers), these approximations tend to overestimate the AEX. As such, the latter finding suggests that the situations shown in figures 3B, 4B, 5B and 6B that is, ‘scooping’ of flow-volume curves in normal subjects, are more prevalent than the ones seen in figures 3A, 4A and 5A.

In an optimized bootstrap forest model using FEV_{1} and FVC per cent predicted per GLI equations, FEF_{50}*100/0.5*FVC (a previously used ratio for diagnosing mixed ventilatory patterns3 16) and AEX_{4}, the generalized R^{2}, entropy R^{2} and misclassification rates in the training/validation sets were 0.92/0.90, 0.78/0.73, and 11%/13%, respectively. In the validation set, the areas under receiver operating characteristic curve for normal, obstructive, restrictive, and mixed defects were 0.99, 0.96, 0.98 and 0.96, respectively. The term contributions in the model were as follows: 0.49 (FEF_{50}*100/0.5*FVC), 0.40 (FVC per cent predicted), 0.05 (FEV_{1} per cent predicted), and 0.04 (AEX_{4}).

## Discussion

The main finding of this analysis is that AEX_{1}, AEX_{2}, AEX_{3} and AEX_{4} are useful constructs as approximations of AEX. AEX_{4} most closely approximates AEX, presenting the lowest dispersion of the residual values. Like the original parameter, AEX, AEX_{1–4} are also shown to differentiate between normal lung function, obstruction, restriction, and mixed ventilatory defects. The approximated areas under the expiratory flow–volume loop (eg, AEX_{4}) represent alternative parameters to assess quantitatively subtle or ‘distal’ changes of the flow-volume curve area, especially for mixed ventilatory defects and/or small airway disease.5 17–19 As noted before, the terminal segment of the flow–volume curve is relatively independent of effort, being the end result of the complex interplay between airway resistance to flow (especially in the small airways) and respiratory system’s elastic recoil,20 which in practice is difficult to assess quantitatively.

In this analysis, using bootstrap forest models based on FEV_{1} and FVC per cent predicted by GLI equations, FEF_{50}*100/0.5*FVC (a validated ratio for diagnosing mixed ventilatory patterns) and AEX_{4}, the misclassification rates for mixed and restrictive ventilatory patterns were relatively low, and the contribution of AEX_{4} to these models was almost as important as FEV_{1} per cent predicted. In bootstrap forest models based only on FEV_{1} and FVC per cent predicted and AEX_{4}, the AEX_{4} contribution to the model went up to 11%, at the expense of the misclassification rate, which was up to 17% in the validation set.

An additional parameter, AEX_{7}, derived from FVC, and the flows PEF, FEF_{25}, FEF_{40,} FEF_{50,} FEF_{60,} FEF_{75} and FEF_{80} were also evaluated. While some of these instantaneous flows are generally not included in the standard reports and are not used in pulmonary function interpretation, they are easily retrievable in today’s era of digital spirometry. The mean difference between AEX_{7} and AEX_{4} was negligible (−0.063, 95% CI −0.046 to −0.082 L^{2}/s) and with a very small variance of the residuals. On balance, the more precise AEX approximation called AEX_{7} was quite similar to AEX_{4} and contributed incrementally very little to the overall diagnostic accuracy, making the AEX_{4} the best surrogate measurement as an approximation of AEX.

When the four AEX approximations (AEX_{1}to AEX_{4}) were analyzed in subjects with and without various lung diseases, they were significantly lower in patients with diagnoses of chronic obstructive pulmonary disease (COPD) or emphysema, perhaps as the result of the physiologic interplay between loss of parenchymal elastic recoil (predominant in emphysema) and higher airway resistance in the small conduits. In subjects with chronic bronchitis and in intercritical asthma (ie, in-between exacerbations), no significant differences were noted.

Our previous work showed that AEX compared favorably with traditional spirometric parameters in diagnosing physiologic respiratory derangement and in estimating the severity of impairments. Furthermore, the actual AEX was able to predict with good accuracy inspiratory capacity, inspiratory capacity/total lung capacity and residual volume/total lung capacity ratios and thus reducing the need for lung volume testing.5 17 The current investigation extends the value of the area under expiratory flow–volume loop concept by showing that it can be closely and easily approximated using universally available spirometric variables. This applies especially when existing software does not compute and report the actual AEX values. A preliminary survey of four major PFT equipment manufacturers in our market identified that, in practice, AEX is currently available in only one platform.

The current work also extends prior evaluations of AEX, which have primarily been used in pediatric testing for assessing bronchoconstriction or bronchodilation responses.18 19 21 22 In a recent article, the authors effectively constructed predicted AEX_{4} (called ‘reference flow-volume loop’) and compared it against actual AEX, thus assessing the degree of airway hyperinflation in adult patients with COPD.23 The authors confirmed our prior findings that AEX performs well in diagnosing and stratifying the severity of functional impairments,5 17 showing that AEX*100/predicted AEX_{4} has an excellent discriminating capacity for severe hyperinflation in COPD. To our knowledge, the current study is the first to compare potential approximations of AEX (AEX_{1–4}) with actual AEX and their use as alternative parameters in interpreting PFT by spirometry.

The strengths of our investigation are the large data set of PFTs (n=15 308) performed on a very diverse patient population and pathologies, methods used that included decision tree partitioning using both a training (66%) and a validation (33%) group, and high-power forest bootstrap models for assessing the performance of the investigated parameters. Potential weaknesses of our study are the availability of data from a single center, the lack of specific detail regarding underlying diagnoses, and the absence of patient follow-up or long-term outcomes. To overcome this latter weakness, we are currently examining the diagnostic performance of these parameters in other PFT data sets from other patient populations in a different center, that is, Atlanta Veterans’ Affairs PFT Laboratory. We expect that this examination of generalizability and clinical validation of these findings will be the subject of a separate, future publication.

## Conclusion

This study analyzes the performance of several approximations of the AEX based on instantaneous flows at peak expiration and at predetermined volumes (eg, FEF_{25}, FEF_{50} and FEF_{75}). The parameter AEX_{4} performs with acceptable accuracy as a surrogate marker or approximation of AEX, which makes it potentially useful in diagnosing physiologic derangement of pulmonary function and in stratifying the severity of such impairment. Further validation of these new spirometric measurements in discrete data sets is needed and is currently being assessed.

## Acknowledgments

Kevin McCarthy RCPT (data extraction).

## References

## Footnotes

Contributors Both authors contributed to the writing of this article; OCI contributed also with the statistical analysis.

Funding The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

Competing interests None declared.

Ethics approval Institutional research oversight approval was obtained to conduct the study (Cleveland Clinic IRB EX#0504).

Provenance and peer review Not commissioned; externally peer reviewed.

Patient consent for publication Not required.

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