Pigs were anesthetized with propofol and fentanyl, tracheotomized and mechanically ventilated in volume-controlled mode, with constant inspiratory flow, V _T 10 mL · kg^-1, inspired fraction of oxygen (FiO₂) 0.21, zero end-expiratory pressure, and RR adjusted to achieve normocapnia using Engström Carestation^® ventilator (General Electric Healthcare, Madison, WI, USA). Muscle relaxation was obtained with pancuronium bromide. Right jugular vein was cannulated with a 3-lumen 8.5-Fr catheter for drug administration. Carotid artery was cannulated with an 8.5 Fr catheter. FiO₂ was increased to 1 at the end of animal preparation.

Air flow was measured using a small volume pneumotachograph (PN 281637, Hamilton medical AG, Bonaduz, Switzerland). Pressure at the airway opening was measured using a connecting tube with lateral aperture connected between the endotracheal tube and the pneumotachograph. Signals of arterial blood pressure, pressure at the airway opening, and air flow were read by transducers (Becton Dickinson, Sandy, UT, USA), connected to an A/D card (MP 100; Biopac Systems, Santa Barbara, CA, USA), acquired at 200 Hz and analyzed with Acknowledge^® software (Biopac Systems, Santa Barbara, CA, USA). Tracheal pressure was measured through an air filled catheter introduced down the endotracheal tube, positioned 2 cm distal to the tube tip, and connected to the ventilator, to obtain alveolar pressure 4 .

EELV_WI-WO was assessed by the ventilator, by using the nitrogen washout/washin technique 1 , from continuous measurement of end-tidal O₂ and CO₂ during a 0.1 change of FiO₂ using pediatric sensors (Pedi-lite+, Dahtex-Ohmeda Inc, Madison, WI, USA). The average value of the washout and washin measurements during 1 to 0.9 and 0.9 to 1 FiO₂ changes was given by the ventilator.

EELV_CT was calculated using lung CT, as previously described 2 . CT calibration using the manufacturer phantom was performed before each CT study. The CT scanner (Biograph mCT/S, Siemens, Munich, Germany) was set as follows: interval 1 mm, voltage 120 kV, pitch 1.2 mm, and field of view 300 mm. Whole lung CT images were taken during 15 s end-expiratory. CT raw data were reconstructed as 1-mm-thick contiguous slices using a medium smooth filter (B31f). Image segmentation was manually performed over the whole lung using Turtleseg^® software 5 6 (http://www.turtleseg.org). Gas volume in each lung voxel was computed from the CT number using the following formulas 2 :

Gas volume = CTnumber - 1 , 000 × voxel volume for lung voxels with CT number ≤ 0 .

Gas volume = 0 for lung voxels with CT number > 0.

EELV_CT was computed as the sum of gas volume in all the voxels defined by lung segmentation.

Expected EELV on zero end-expiratory pressure was deemed as 33 mL · kg^-1 body weight as previously published in normal anesthetized pigs 7 .

ARDS was performed by saline lavage at ventilatory settings mentioned above. Intra-tracheal instillations of 1,000 mL aliquots of 0.9% sodium chloride warmed at 37°C were repeated until PaO₂/FiO₂ ratio was <100 mmHg. RR may be increased up to 35 breaths per min to maintain pH above 7.20, then kept constant except at the end of experiment, where at the highest V _T, it was decreased to maintain peak airway pressure below 100 cm H₂O.

Then, PEEP was set to 20 cm H₂O, V _T to 6 mL · kg^-1, and a recruitment maneuver was performed by applying a continuous airway pressure of 40 cm of H₂O over 40 s. A decremental PEEP trial was then performed from 20 to 2 cm H₂O by 2 cm H₂O steps of 10 min each. At the end of the decremental PEEP trial, animals were randomized into three PEEP groups, for which PEEP level was set according to either highest compliance (n = 4), or highest EELV_WI-WO (n = 5), or PEEP-FiO₂ table (n = 4) 8 . This randomization was used to deliver a wide PEEP range during the final part of the study, in order to obtain multiple combinations of PEEP and V _T, so as to perform a multivariate analysis adjusted for PEEP and V _T. One pig died just after the PEEP trial before randomization, and was kept in the final analysis. The selected PEEP was applied for 1 h, and V _T was adjusted to maintain plateau pressure of the respiratory system ≤30 cm of H₂O.

After 1 h of applied selected PEEP, eight levels of V _T (4, 5, 6, 7, 8, 10, 15, 20 mL · kg^-1) ranging from 100 to 625 mL, were applied for 2 min leaving PEEP level unchanged. EELV_WI-WO and EELV_CT were measured immediately after ARDS onset, at the end of each PEEP step during the PEEP trial, and at the end of each V _T change. A 15-s end-inspiratory pause was performed to check the absence of air leak in each experimental condition. Some experimental conditions were not available since pneumothorax occurred in several pigs at high V _T or since EELV_WI-WO values were lacking for technical reasons, ending up in 218 data points in final analysis (see Additional file 1: Table S1 for description of lacking data points).

Statistical analyses were performed using R software 9 , with packages nlme 10 , MethComp 11 , pROC 12 , OptimalCutpoints 13 , and multcomp 14 . Values were expressed as mean ± standard deviation (SD). The level of statistical significance was set below 0.05.

EELV_WI-WO and EELV_CT were compared using a linear mixed-effects model, and Bland and Altman representation 15 . Limits of agreement were computed using alternating regression 16 since bias was non-constant and the experimental design involved repeated measurements.

To control for an effect of confounding variables on the bias, a linear mixed-effects model was built using PEEP, V _T, EELV_CT at ARDS onset and their interactions as factors with fixed effect, pigs as factor with random effect 17 , and bias as dependent variable. Model simplification was performed using a backward stepwise algorithm.

Percentage error was computed as × SD_Bias/mean_EELV 18 . As percentage error was not reported in the two previously published studies that compared EELV_WI-WO and EELV_CT 2 19 , Cartesian data of these studies were reanalyzed, being uplifted using a scientific program allowing extraction of individual data points from a digitalized graph (DataThief III^® 20 ) as follows: a digital copy of each regression plot was analyzed with DataThief from the portable document format file of the journal articles, and the extracted data were exported as two columns of X-Y coordinates, with each row representing an extracted data point, allowing computation of percentage error of each study.

Changes in EELV between consecutive measurements were computed for EELV_WI-WO (ΔEELV_WI-WO) and EELV_CT (ΔEELV_CT). Ability of the WI-WO technique to track changes in EELV was assessed using four-quadrant and polar plots. The four-quadrant plot relates ΔEELV_WI-WO and ΔEELV_CT, with upper right and lower left quadrants being quadrants of agreement (in which both EELV_WI-WO and EELV_CT have the same directional changes) and lower right and upper left quadrants being quadrants of disagreement (in which EELV_WI-WO and EELV_CT have opposite directional changes). Concordance rate was defined as the percentage of data points falling into one of the two quadrants of agreement, expressed as a percentage of the total number of data points 21 . The main drawback of the four-quadrant plot is the lack of quantification of the distance between each data point and the line of identity, leading to the development of polar plot analysis 21 . Polar plot is obtained by a 45° clockwise rotation of the four-quadrant plot, changing the dimensions of the radius to mean ΔEELV 22 , lining up the line of identity along the horizontal axis. Data points with positive and negative directional changes are located on the right and the left side of the polar plot, respectively, and the polar angle represents the angle of each data point with line of identity. A 0° polar angle depicts a perfect agreement between ΔEELV_WI-WO and ΔEELV_CT, while polar angles in the range 45° to 135° and 225° to 315° depict disagreement between directional changes of EELV_WI-WO and EELV_CT. The following variables are computed from polar plots: (1) angular bias as the mean angle between all data points and polar axis 21 , reflects the difference in calibration between the reference and test methods; (2) radial limits of agreement as the radial sector containing 95% of the data points, after conversion of negative deflections to positive ones, is a polar version of the 95% confidence limits and is similar to the limits of agreement in Bland and Altman analysis 21 .

Bias and angular bias were compared to zero using Mann-Whitney U test. Multiple comparisons were performed with Dunnett’s test using PEEP 0 as a reference.

The ability of the WI-WO technique to detect a change in EELV greater than 100, 150, 200, 250, and 300 mL was tested by computations of area under receiver operating characteristic (AUC) curve. The optimal cut-off points were computed using the Youden J statistic.

EELV_WI-WO and EELV_CT were significantly correlated (R ² = 0.63, p < 0.001). The regression equation between EELV_WI-WO and EELV_CT, had an intercept of 96 mL (p < 0.001) and a slope of 0.58 mL^-1 (p < 0.001; Figure 2). Bland and Altman representation exhibited a non-constant bias, decreasing toward more negative values as mean EELV increased (Figure 3). The difference between EELV_WI-WO and EELV_CT was related to their mean value by the following equation:

EELV WI - WO - EELV CT = - 1.28 – 0.33 × EELV WI - WO + EELV CT / 2 .

Limits of agreement of the bias were ±398 mL (Figure 3), and percentage error was computed to 57%. A significant interaction between PEEP, V _T, EELV baseline value on the bias between methods was identified (Table 1) and reported (Figure 4). The bias between methods was strongly influenced by PEEP level, increasing at higher PEEP regardless the V _T level. The bias further increased when high PEEP was combined to low V _T, when EELV at baseline was low.The bias at PEEP 0 amounted to -54 ± 101 mL, was not significantly different from 0, and was compared to bias values at higher PEEP. As shown in Figure 5, the bias at PEEP 10 and higher did significantly differ from PEEP 0, while non-significant differences were found for lower PEEP.

AIC, Akaike information criterion; EELV, end-expiratory lung volume; EELV _Base, EELV baseline value (ARDS onset, PEEP 0 cm H₂O); PEEP, positive end-expiratory pressure; V _T, tidal volume.

ΔEELV_WI-WO values adequately tracked ΔEELV_CT changes against time (Figure 6). Concordance rate over all measurements amounted to 79%, and slightly increased after exclusion of small changes in EELV which do not reflect trending ability (Table 2).

Exclusion threshold refers to exclusion of data points with change in end-expiratory lung volume between consecutive time points below or equal to 100, 150, 200, and 300 mL, respectively. SD, standard deviation.

Results of the polar plot analysis are reported in Figure 7, and in Table 2. The angular bias amounted to -4° ± 37° for all measurements. After exclusion of EELV changes ≤100 mL, the angular bias amounted to 3° ± 25°, and was not statistically different from 0. Radial limits of agreement were wide when all measurements were taken into account (±78°), but where narrowed to ±51° after exclusion of EELV changes ≤100 mL. Increasing the exclusion threshold of EELV changes up to 300 mL did not improve the radial limits of agreement (Table 2). Diagnostic performance of EELV_WI-WO to detect absolute EELV changes greater than 100, 150, 200, 250, and 300 mL is presented in Table 3. Diagnosis accuracy was fair for detection of absolute EELV changes above 200 mL (AUC 0.79 (CI 95% 0.70 to 0.89)), and good for detection of absolute EELV changes above 300 mL (AUC 0.89 (CI 95% 0.83 to 0.95)).

AUC, area under receiver operating characteristic curve; CI 95%, 95% confidence interval; ΔEELV _CT , absolute change in end-expiratory lung volume assessed by computed tomography between consecutive time points; ΔEELV _WI-WO , absolute change in end-expiratory lung volume assessed with the nitrogen washin-washout technique between consecutive time points; NLR, negative likehood ratio; NPV, negative predictive value; PLR, positive likehood ratio; PPV, positive predictive value; Se, sensitivity, Sp, specificity.