Sigmoidal equation for lung and chest wall volume-pressure curves in acute respiratory failure

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1 J Appl Physiol 95: , First published July 18, 2003; /japplphysiol Sigmoidal equation for lung and chest wall volume-pressure curves in acute respiratory failure Cécile Pereira, 1 Julien Bohé, 2 Sylvaine Rosselli, 3 Emmanuel Combourieu, 4 Christian Pommier, 3 Jean-Pierre Perdrix, 5 Jean-Christophe Richard, 1,6 Michel Badet, 1 Sandrine Gaillard, 1,6 François Philit, 1 and Claude Guérin 1,6 1 Service de Réanimation Médicale et d Assistance Respiratoire, Hôpital de la Croix-Rousse, Lyon; 2 Service de Réanimation Médicale, Centre Hospitalier Lyon-Sud, Pierre Bénite, France; 3 Service de Réanimation, Centre Hospitalier Saint Luc-Saint Joseph, Lyon; 4 Service de Réanimation Polyvalente, Hopital d instruction Des Armées, Lyon; 5 Service de Réanimation Chirurgicale, Centre Hospitalier Lyon Sud, Pierre Bénite; and 6 Equipe d accueil 1896, Laboratoire de Physiologie, Claude Bernard University, Lyon, France Submitted 17 April 2003; accepted in final form 13 July 2003 Pereira, Cécile, Julien Bohé, Sylvaine Rosselli, Emmanuel Combourieu, Christian Pommier, Jean-Pierre Perdrix, Jean-Christophe Richard, Michel Badet, Sandrine Gaillard, François Philit, and Claude Guérin. Sigmoidal equation for lung and chest wall volume-pressure curves in acute respiratory failure. J Appl Physiol 95: , First published July 18, 2003; / japplphysiol To assess incidence and magnitude of the lower inflection point of the chest wall, the sigmoidal equation was used in 36 consecutive patients intubated and mechanically ventilated with acute lung injury (ALI). They were 21 primary and 5 secondary ALI, 6 unilateral pneumonia, and 4 cardiogenic pulmonary edema. The lower inflection point was estimated as the point of maximal compliance increase. The low constant flow inflation method and esophageal pressure were used to partition the volumepressure curves into their chest wall and lung components on zero end-expiratory pressure. The sigmoidal equation had an excellent fit with coefficients of determination 0.90 in all instances. The point of maximal compliance increase of the chest wall ranged from 0 to 8.3 cmh 2O (median 1 cmh 2O) with no difference between ALI groups. The chest wall significantly contributed to the lower inflection point of the respiratory system in eight patients only. The occurrence of a significant contribution of the chest wall to the lower inflection point of the respiratory system is lower than anticipated. The sigmoidal equation is able to determine precisely the point of the maximal compliance increase of lung and chest wall. acute respiratory distress syndrome; mechanical ventilation; volume-pressure curves; acute lung injury THE CHOICE OF THE RIGHT LEVEL of positive end-expiratory pressure (PEEP) and the way to select it in patients with acute respiratory distress syndrome (ARDS) are still a matter of debate (20). Although assessment of the volume-pressure (V-P) curve of the respiratory system is not one of the recommended criteria for management of ARDS, by setting PEEP above the lower inflection point of the respiratory system determined from static inflation V-P curve, two groups of investigators observed an improvement of outcome in ARDS patients. In a randomized controlled study, Amato et al. (2) found a marked reduction of mortality in the group in which PEEP was set above the lower inflection point, the so-called lung-protective strategy, compared with the control group in which PEEP was set regardless of the V-P curve, so-called conventional ventilation. Ranieri et al. (19) randomized ARDS patients into a lung-protective ventilation group and a conventional ventilation group. They observed a reduction of both lung and systemic levels of proinflammatory cytokines together with less organ dysfunction in the lung-protective ventilation group. For routine assessment of V-P curves to determine the appropriate level of PEEP, some methodological and semantic problems should be resolved. First, the assessment of the inflation limb of the V-P curve in ARDS patients is confusing because various terms such as Pflex, lower inflection point, and knee are used to define the sudden increase in compliance that occurs at low lung volume in most patients. Rightly speaking, the true inflection point in any curve is the point at which the curvature changes direction or sign (8). The term lower inflection point is misused in the critical care literature and has no scientific foundation. Second, an unbiased means to detect lower inflection point on the basis of an adequate algorithm with physiological meaning is mandatory. Indeed, the visual assessment of lower inflection point has been shown to have a large inter- and intraobserver variability and, hence, is not reliable (9). Third, one study has stressed that the chest wall may significantly contribute to lower inflection point of the respiratory system, indicating that determination of lower inflection point based on V-P curves of the respiratory system may not be reliable to adequately set the level of PEEP (14). It should be noted that in the latter study, on the basis of the analysis proposed by Gattinoni et al. (7), the choice of volume steps may influence Address for reprint requests and other correspondence: C. Guérin, Service de Réanimation Médicale et d Assistance Respiratoire, Hôpital de la Croix-Rousse, 103 Grande Rue de la Croix-Rousse, Lyon, France ( claude.guerin@chu-lyon.fr). The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact /03 $5.00 Copyright 2003 the American Physiological Society

2 LUNG AND CHEST WALL V-P CURVES IN ALI 2065 the results, in that the greater the magnitude of initial volume steps, the greater the lower inflection point. Venegas et al. (22) introduced the sigmoidal equation to fit inflation and deflation V-P curves of the respiratory system. With this method, they objectively defined the pressure at the point of maximal compliance increase during inflation or deflation. They found that the reproducibility of this method was excellent when they retrospectively tested data pertaining to 1) the lungs of 2 closed-chest dogs, 2) the lungs of 11 openchest dogs, and 3) the respiratory system of 10 ARDS patients. To our knowledge, this method has not been previously used to assess the V-P curve of the chest wall and lungs in patients with acute respiratory failure (ARF). Therefore, we undertook the present prospective study to assess 1) the contribution of the chest wall to the point of maximal compliance increase (Pmci) of the respiratory system of patients with ARF and 2) the fit of the sigmoidal equation to both lung and chest wall V-P curves in these patients. MATERIALS AND METHODS Patients. A prospective multicenter physiological investigation was carried out in consecutive intubated and mechanically ventilated patients with ARF in six intensive care units (ICUs) of Lyon, France, between November 2001 and September Patients were included if they met all of the following criteria: 1) age over 18 yr, 2) tracheal intubation and mechanical ventilation, 3) unilateral or bilateral infiltrates on frontal chest X-radiograph, 4) ratio of arterial PO 2 (Pa O2 ) to inspired O 2 fraction (FI O2 ) 300, 5) investigation performed in the first 5 days after ICU admission, 6) onset of ARF within the last 3 days, 7) continuous intravenous sedation and/or analgesia, and 8) written, informed consent provided from the next of kin. Patients were excluded if any of the following criteria was present: 1) chronic interstitial lung disease, 2) thoracic drainage, 3) hemodynamic instability, 4) pregnancy, 5) impossibility to stop administration of inhaled nitric oxide, and 6) informed consent denied. Clinical data collection. At the time of investigation, the following clinical variables were recorded: age, gender, ideal body weight (23), simplified acute physiology score II (12), and lung injury score (16). Acute lung injury (ALI) and ARDS were defined according to the European-American consensus conference criteria (3). Primary and secondary ALI/ARDS were defined according to standard criteria (5). Unilateral pneumonia (UP) was defined as unilateral radiographic infiltrates associated with Pa O2 /FI O2 300 and no echocardiographic argument for an elevated left atrial pressure. Cardiogenic pulmonary edema (CPE) was defined as bilateral radiographic lung infiltrates associated with Pa O2 /FI O2 300 and increased left atrial pressure assessed from echocardiography. The ARF patients were therefore classified into four groups, namely primary ALI/ARDS, secondary ALI/ARDS, UP, and CPE. Equipment. Airflow (V ) was measured with a heated pneumotachograph (Fleisch no. 2, Fleisch, Lausanne, Switzerland) inserted between the endotracheal tube and the Y-piece of the ventilator. The pressure drop across the two ports of the pneumotachograph was measured with a differential piezoresistive transducer (TSD160A 2 cmh 2O; Biopac Systems, Santa Barbara, CA). Changes in lung volume were obtained by numeric integration of the V signal. Pressure at the airway opening (Pao) was measured proximal to the endotracheal tube with a piezoresistive pressure transducer (Gabarith , Becton Dickinson, Sandy, UT). Changes in pleural pressure were estimated from changes in esophageal pressure (Pes) using a thin-walled latex balloon (80-mm length, 1.9-cm external diameter, 0.1-mm thickness), attached to a 80-cm-long catheter of 1.9-mm external diameter and 1.4-mm internal diameter (Marquat, Boissy-Saint-Léger, France), positioned in the midesophagus and inflated with 1 ml of air. The validity of the Pes measurement was assessed in two ways. In patients with occasional spontaneous breaths, the airways were occluded at the end of expiration and patients were asked to make inspiratory efforts. The correct position of the esophageal balloon was ascertained from the correlation between Pao and Pes during this maximal effort (15). In patients without spontaneous breathing, the esophageal balloon was inserted into the stomach, as reflected by significant positive change in pressure during a gentle manual compression done on the abdominal left upper quadrant. The esophageal balloon was then withdrawn up to the point of no change in Pes tracing during the above maneuver. The esophageal balloon was connected to a differential pressure transducer (Gabarith ; Becton Dickinson). Calibration was performed just before each experiment. The same ventilator (Horus; Taema, Antony, France) was provided by the Taema company to each participating ICU for the purpose of this study. During the measurement, the humidifier was bypassed, and a single-use low-compliance ventilator tubing of 60-cm length and 2-cm internal diameter was used. The signals of V, Pao, and Pes were recorded on a portable personal computer with data-acquisition software (MP 100; Biopac Systems). The records were stored and subsequently analyzed by use of Acknowledge software (version for Microsoft Windows 98; Biopac Systems). Protocol. The study was approved by the local ethics committee (Comité Consultatif pour la Protection des Personnes se prêtant à la Recherche Biomédicale, CCPPRB Lyon-B). Measurements were taken with the patients in the semirecumbent position. The patients were sedated with midazolam ( mg/kg) and fentanyl (1 3 g/kg) and paralyzed with atracurium ( mg/kg) for the purpose of the study. The patient was connected to the study ventilator at the ventilatory settings (volume-controlled mode under constant V inflation) established by the physician-in-charge (see Table 2), which were kept constant in each patient throughout the experiment, with the exception of PEEP and FI O2. After a stabilization period of 5 min, blood was drawn from the arterial line to determine blood gases. Then FI O2 was increased to 100% for 10 min. Next, the V-P curve determination was made as follows (Fig. 1). First, zero end-expiratory pressure was applied for five consecutive breaths. Second, the volume history was standardized by using a respiratory frequency of 18 min 1, tidal volume of 10 ml/kg, and inspiratory time/total duration of respiratory cycle of 0.33 for five consecutive breaths (13). Third, the low constant flow inflation (LCFI) method, which was automatically delivered by the ventilator, was achieved by pressing the appropriate button. The LCFI software works as follows (Fig. 1). The expiratory time is prolonged until the first zero V was reached. Then a 3-s end-expiratory occlusion is performed and followed by lung inflation at a predetermined constant flow of 8 l/min. Inflation is interrupted either when inspiratory pressure reached 50 cmh 2O or volume reached 2 liters, or on the clinician s decision. After this, the baseline ventilation was resumed immediately. After stabilization, usually obtained in 5 min, a second LCFI was performed in the same way.

3 2066 LUNG AND CHEST WALL V-P CURVES IN ALI Postsampling smoothing of the Pes signal was used to allow for cardiac artifacts. The digital records of Pao, Pes, PL, V, and volume against time were exported into a spreadsheet program (Matlab 6.1, The Mathworks, Natick, MA). An algorithm was developed to fit the experimental data points of Pao, Pes, and PL to lung volume to the following sigmoidal equation (22) V a b/ 1 e P c /d (1) where V is the lung volume above functional residual capacity (FRC) and P is the pressure of the respiratory system, chest wall, or lung (Fig. 2). This equation has four parameters with physiological significance (22). Parameter a is expressed in units of volume and represents the lower asymptote volume. Parameter b is also expressed in units of volume and represents the total change in volume between lower and upper asymptotes. Parameter c is the inflection point of the sigmoidal curve. Parameter d is proportional to the pressure range within which most of the volume change takes place. Initial guess coefficients were a 0 liters, b 2 liters, c 20 cmh 2O, and d 10 cmh 2O. According to Harris et al. (9), the Pmci (where the rate of change of upward slope is maximal) was defined as c 1.317d and was used as an estimator for the lower inflection point of the respiratory system (Pmci,rs), chest wall (Pmci,w), and lung (Pmci,L). The point of maximal compliance decrease (Pmcd) was defined as c d and was used as an estimate of the upper inflection point (9). To assess the contribution of the chest wall to Pmci,rs, we reasoned that the chest wall contribution to Pmci,rs is as great as the error in the determination of Pmci,L from Pmci,rs is large. Therefore, we computed the quantity [(Pmci,rs Pmci,L)/Pmci,L] 100 and decided that a value 50% defined a significant contribution of the chest wall to Pmci,rs. Statistical analysis. Values were expressed as medians (interquartile range). Nonparametric tests were used to compare quantitative and qualitative values. Linear regression was made by using least square method. For a given patient, the V-P curve with the highest coefficient of determination for Eq. 1 was retained for the analysis. Nonparametric correlation of Spearmann was used. The level of statistical significance was set at a P value SPSS for Windows version (SPSS, 2001) was used for the statistical analysis. Fig. 1. Tracings of airway pressure (Pao; A), esophageal pressure (Pes; B), and flow (C) over time during a whole experiment in a representative patient. EEO, end-expiratory occlusion; LCFI, low constant flow inflation; PEEP, positive end-expiratory pressure; ZEEP, zero end-expiratory pressure. Left vertical arrow indicates the suppression of PEEP, middle vertical arrow the time at which expiratory time is increased before starting LCFI, and right vertical arrow the time at which the baseline ventilation is resumed. Horizontal arrow indicates the period of LCFI. Arterial blood pressure, heart rate, and pulse oximetry were monitored continuously. During the study a physician and a nurse not involved in the experiment were always present to provide for patient care. Data analysis. The transpulmonary pressure (PL) was obtained by subtracting Pes from Pao. The change in endexpiratory lung volume was assessed as difference in endexpiratory lung volume between tidal deflation and that obtained after prolonging expiration just before starting the LCFI. Fig. 2. Schematic drawing of the sigmoidal equation used for curvefitting volume-pressure (V-P) data. The 4 parameters of the model and the way to compute the points of maximal compliance increase (Pmci) and decrease (Pmcd) are indicated. For further explanations, see text.

4 LUNG AND CHEST WALL V-P CURVES IN ALI 2067 Table 1. Data of the 36 patients at time of measurements Median IQR Age, yr Ideal body weight, kg BMI, kg/m SAPS II (range 0 194) Lung injury score (range 0 4) Days to investigation Tidal volume, ml/kg ideal body wt PEEP, cmh 2O Respiratory frequency, min Inspiratory time, s Expiratory time, s FI O Pa O2, Torr Pa O2 /FI O Pa CO2, Torr ph IQR, interquartile range; BMI, body mass index, SAPS II, Simplified Acute Physiology Score; PEEP, positive end-expiratory pressure; FI O2, inspired O 2 fraction; Pa O2, arterial PO 2;Pa CO2, arterial PCO 2. RESULTS Among the 42 patients enrolled during the study period, six with negative values of point of maximal compliance increase were excluded from the present analysis. These were five men and one woman whose baseline characteristics, ventilatory settings, and arterial blood gases were not significantly different from the 36 other patients. Two had indirect and one direct ALI/ARDS, two had UP, and one had CPE. One had negative Pmci,L only, one had both negative Pmci,rs and Pmci,L, and the remaining four had negative Pmci,w only. The present report is therefore based on 36 patients (25 men): 21 primary ALI/ARDS, 5 secondary ALI/ARDS, 6 UP, and 4 CPE. The characteristics of the 36 patients are given in Table 1. As shown in Table 2 and Fig. 3 in a representative patient, Eq. 1 provided an excellent fit, with coefficients of determination ranging from to for the respiratory system, to for the lung, and to for the chest wall. In the six patients excluded from the final Table 2. Individual values of Pmci and Pmcd for respiratory system, lung, and chest wall obtained from Eq. 1 on zero end-expiratory pressure classified according to the group of acute respiratory failure Patient Group Pmci, cmh2o Respiratory System Lung Chest Wall Pmcd, Pmci, cmh2o R 2 cmh2o Pmcd, Pmci, cmh2o R 2 cmh2o Pmcd, cmh2o R 2 1 P P P P P P P P P P P P P P P P P P P P P S S S S S UP UP UP UP UP UP CPE CPE CPE CPE Pmci, point of maximal compliance increase; Pmcd, point of maximal compliance decrease; R 2, coefficient of determination; P, primary acute lung injury; S, secondary acute lung injury; UP, unilateral pneumonia; CPE, cardiogenic pulmonary edema. The numbers of patients in the left first column refer to the order in which the investigation has been done.

5 2068 LUNG AND CHEST WALL V-P CURVES IN ALI Fig. 4. Relationship of Pmci of the respiratory system (Pmci,rs) to that of the lung (Pmci,L). Dotted line is the identity line, and continuous line is the regression line. Fig. 3. V-P curves of respiratory system (A), lung (B), and chest wall (C) in patient 26. Continuous black lines are the experimental raw data obtained from the LCFI method. Continuous green lines are the sigmoidal equation curve-fitted data. Vertical bars are the Pmci and Pmcd whose values can be found in Table 2. analysis because negative value of Pmci was found, the fitting was nevertheless excellent, with coefficients of determination In the 36 patients, for the respiratory system, lung, and chest wall, the median (interquartile range) values of Pmci were 9 (6 13), 6 (4 12), and 1 (1 2) cmh 2 O, respectively; those of Pmcd were 31 (26 36), 25 (19 32), and 5 (3 8) cmh 2 O, respectively; those of c were 21 (16 23), 17 (11 21), and3(2 5) cmh 2 O, respectively. Between the respiratory system and the lung, the values of Pmci, Pmcd, and c were statistically significantly different (P 0.001). Between the four groups of patients, the values of Pmci, Pmcd, and c did not significantly differ. There was a significant contribution of the chest wall to Pmci,rs in eight patients (22% of the whole sample) (Table 2): 5 out of 21 (23.8%) with primary ALI/ARDS (patients 3, 11, 13, 26, 27), 2 out of 6 (33%) with UP (patients 22, 35), and 1 out of 4 (25%) with CPE (patient 6). As shown on Fig. 4, there was a close correlation between Pmci,rs and Pmci,L. The increase in slope was 10%, indicating that Pmci,rs reflects Pmci,L, on average, in this sample. The difference (Pmci,rs Pmci,L) and Pmci,w (Fig. 5) correlate up to Pmci,w of 3 cmh 2 O. Above this value, the relationship is much more scattered, indicating that the curvature of the V-P curve of the chest wall plays a role in these patients and therefore the chest wall mechanics must be taken into account. DISCUSSION In this study, the sigmoidal equation was used to assess the presence and the magnitude of the lower Fig. 5. Relationship of the difference between Pmci,rs and Pmci,L to Pmci of the chest wall (Pmci,w). Continuous middle line is the regression line, and 2 outer continuous lines are the 95% confidence interval limits over all the experimental points.

6 LUNG AND CHEST WALL V-P CURVES IN ALI 2069 inflection point of the chest wall in intubated, sedated, and mechanically ventilated patients with various ARF conditions. We have found that 1) a significant lower inflection point of the chest wall was present in 22% of the patients (8/36) and 2) the sigmoidal equation was of value to assess the lower inflection point of the chest wall. Our study suffered from several limitations. First, the investigation was done only at zero end-expiratory pressure and, therefore, the effects of PEEP on the parameters of the sigmoidal model were not investigated. Second, the use of the esophageal balloon to estimate pleural pressure in the supine position has been questioned. We have tried to minimize the cardiac artifacts as much as possible. Moreover, the absolute value of esophageal pressure is highly dependent on the initial pressure and volume of the esophageal balloon and the volume injected to it. On the other hand, relative changes in these pressures during inflation tend to be more reliable. In this connection, it should be noted that the esophageal balloon method is currently the only way to estimate pleural pressure in humans. Whether the chest wall should be taken into account as part of management of patients with ARF is a question of clinical relevance. The determination of chest wall mechanics indeed gives access to lung mechanics and therefore allows setting the ventilator from targets pertaining to the lungs directly. Pelosi et al. (17) have found chest wall mechanics abnormalities in patients with ALI. The same group also reported that chest wall elastance was normal in patients with primary ALI but markedly increased in patients with secondary ALI (5). The chest wall elastance correlated with intra-abdominal pressure in this study (5), a result in line with the findings of Ranieri et al. (18), who emphasized on the role of abdominal distension as observed in the postoperative setting. Mergoni et al. (14) first suggested that the chest wall mechanics could contribute to the lower inflection point of the respiratory system by studying 13 patients with ALI/ARDS (four with primary lung injury). Eleven of them exhibited a lower inflection point of the chest wall, which was in seven of them (53% of the whole sample) the major or the unique contributor to the lower inflection point of the respiratory system. In our study, a significant contribution of the chest wall to the Pmci,rs was less prevalent than in the study of Mergoni et al., regardless the ARF group studied. Some differences between the two studies should, however, be pointed out. First, we investigated more patients, earlier after onset of mechanical ventilation. Second, the method to construct the V-P curve was different in that we used LCFI at 8 l/min whereas Mergoni et al. inflated the respiratory system with an automated supersyringe that delivered a constant flow rate of 3 l/min. It is unlikely that this discrepancy influenced the results. In a previous study, our laboratory found that the rate of inflation below 15 l/min during LCFI did not change the value of the lower inflection point of the respiratory system (4). Third, the analysis of the chest wall V-P curve was performed in our study for two reasons. Contrary to Mergoni et al., we did not just use the raw data of the Pes signal but smoothed it to avoid cardiac artifacts. Moreover, we used a mathematical model to perform an unbiased determination of the lower inflection point of the chest wall (see below). Finally, assessment of the contribution of chest wall to Pmci,rs is a difficult task actually. In their study, Mergoni et al. (14) did not quantitatively determine the contribution of chest wall to lower inflection point of the respiratory system. By using a quantitative attempt, we have found a lower prevalence of a significant contribution of the chest wall to Pmci,rs. The correlation between Pmci,rs Pmci,L and Pmci,w is significant (Fig. 5) as evidenced by a coefficient of determination of 0.77, i.e., 77% of the variance of the relationship are explained by the linear model. However, there are too few points above 3 cmh 2 Otomake any meaningful statements about scatter above and below this level. Moreover, there is quite a low number of data within the 95% confidence interval limits. In our study, the sigmoidal equation was able to precisely fit the chest wall and lung V-P curve of 36 patients with ARF of various etiology. To our knowledge, this is the first study that provides such results in human lung and chest wall. As already pointed out (9), Eq. 1 is symmetric around the true inflection point and there is no physiological reason of the V-P curve to have symmetric upward concavity and downward concavity. Harris et al. (9) explained the excellent fit of their data by the fact that inflation pressures were 40 cmh 2 O, and therefore most of the data were included to the left of Pmci,rs. In the present study, we have observed that the sigmoidal model fitted the experimental data very well with inflation pressure of the respiratory system 40 cmh 2 O. By using the sigmoidal equation, Harris et al. compared Pmci,rs and lower inflection point as identified by eye by seven clinicians. They found a large variability among and within observers and that the lower inflection point rarely coincided with Pmci,rs (9). The procedure introduced by Gattinoni et al. (7) and used by Mergoni et al. (14) is close to the graphical determination of the lower inflection point performed by the clinicians in the study of Harris et al (9). The interpretation of the nature of lower inflection point is not entirely clear. It has long been recognized that the lower inflection point reflects reopening of previously closed small airways (8). The presence of airway closure has also been evidenced from the V-P curve in the experimental model of acute lung injury (21). There is no single reopening pressure, however, and hence the lower inflection point may reflect where the majority of the airways open. Recent investigations pointed out that alveolar recruitment during ARDS continues to occur well above the lower inflection point (10, 11). In short, this is not the closing pressure that determines the location of lower inflection point. The distribution of the alveolar damage can also contribute to the nonlinearity of the V-P curve of the respiratory system, as evidenced from lung computed tomographic scan studies (24). In case of diffuse involvement, i.e., homogenous distribution of air and

7 2070 LUNG AND CHEST WALL V-P CURVES IN ALI tissue throughout the lung, the V-P curve exhibited a nonlinear pattern with a visible lower inflection point (24). By contrast, in case of lobar involvement, i.e., nonaerated lung areas coexisting with aerated lung areas, a linear pattern of the V-P curve was observed with no detectable lower inflection point (24). In the present study, we addressed the issue of the nonlinearity of the chest wall V-P curve as a participating factor of nonnegative Pmci,rs. The contributing factors of Pmci,w in patients with ARF are not entirely understood. In normal humans, the shape of the V-P curve of the chest wall is determined by factors such as age, body size, volume and time history (1). The V-P curve of chest wall is essentially linear over a small volume range above FRC. Over a larger range of volume displacement, i.e., by studying the lung from below FRC near residual volume, the V-P curve becomes nonlinear and exhibits a concavity toward the volume axis. In this condition, the V-P curve of the chest wall has a typical knee at lung volumes below 30% of the vital capacity (1). Therefore, the reduction of FRC, which is a hallmark of ALI/ARDS, is probably a major factor explaining the occurrence of Pmci,w in ARF patients. Because we did not measure FRC, this hypothesis cannot be supported from our results. In the present investigation, six patients exhibited negative values of Pmci and were excluded from the present analysis. All the V-P curves in the present study that were excluded for negative Pmci were linear up to the upper inflection point. Therefore, the hypothesis subtending the use of the sigmoidal equation was not verified. Moreover, because we did not perform a negative pressure ventilation, the negative values of Pmci did not pertain to any actual experimental data. In the study of Harris et al. (9), three patients had also negative values of Pmci,rs. The interpretation of a negative value of Pmci with the sigmoidal model is that the maximal rate of compliance increase had occurred below the volume range investigated (9). Our study is clinically useful in that it proposes a diagnostic procedure that combines different advantages. Now, by the means of 1) esophageal balloon, 2) LCFI directly delivered from the ventilator without patient disconnection, and 3) sigmoidal equation, clinicians can have a safe, quick, reliable, and accurate method to set the ventilator from a comprehensive physiological background. Whether this approach may change the outcome of ARF patients has as yet to be determined. In conclusion, this is the first study applying the sigmoidal model to the analysis of chest wall and lung V-P curves in human ARF. The occurrence of a significant contribution of the chest wall to the lower inflection point of the respiratory system is lower than anticipated. The sigmoidal equation is able to determine precisely the point of the maximal compliance increase of chest wall and lung. We thank Olivier Tessier of Taema, Antony, France, for providing us with the ventilators dedicated to the study; Guy Annat and Jean-Paul Viale, EA 1896 Claude Bernard University Lyon, France; and all nurses and physicians of the participating ICUs for invaluable help. DISCLOSURES This study was sponsored by the Hospices Civils de Lyon and partly supported by a grant from Taema, Antony, France. Cécile Pereira was a research fellow and was supported by a grant from Taema, Antony, France and by a Grant from the Hospices Civils de Lyon. REFERENCES 1. Agostoni E and Hyatt R. 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