J Appl Physiol 95: 2064–2071, 2003.
First published July 18, 2003; 10.1152/japplphysiol.00385.2003.
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 Guérin1,6
1
Service de Réanimation Médicale et d’Assistance Respiratoire, Hôpital de la Croix-Rousse, 69004 Lyon; 2Service
de Réanimation Médicale, Centre Hospitalier Lyon-Sud, 69310 Pierre Bénite, France; 3Service de Réanimation,
Centre Hospitalier Saint Luc-Saint Joseph, 69007 Lyon; 4Service de Réanimation Polyvalente, Hopital d’instruction
Des Armées, 69003 Lyon; 5Service de Réanimation Chirurgicale, Centre Hospitalier Lyon Sud, 69310 Pierre Bénite;
and 6Equipe d’accueil 1896, Laboratoire de Physiologie, Claude Bernard University, 69008 Lyon, France
Submitted 17 April 2003; accepted in final form 13 July 2003
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, 69004
Lyon, France (E-mail: [email protected]).
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.
acute respiratory distress syndrome; mechanical ventilation;
volume-pressure curves; acute lung injury
2064
8750-7587/03 $5.00 Copyright © 2003 the American Physiological Society
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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:
2064–2071, 2003. First published July 18, 2003; 10.1152/
japplphysiol.00385.2003.—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 cmH2O (median 1 cmH2O)
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.
LUNG AND CHEST WALL V-P CURVES IN ALI
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 2002. 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 PO2
(PaO2) to inspired O2 fraction (FIO2) ⬍ 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 PaO2/FIO2 ⬍ 300 and no echocardiographic argument for an elevated left atrial pressure. Cardiogenic pulmonary edema (CPE) was defined as bilateral
radiographic lung infiltrates associated with PaO2/FIO2 ⬍ 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 (V̇) 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 cmH2O; Biopac Systems, Santa Barbara, CA). Changes in lung volume were
obtained by numeric integration of the V̇ signal. Pressure at
J Appl Physiol • VOL
the airway opening (Pao) was measured proximal to the
endotracheal tube with a piezoresistive pressure transducer
(Gabarith 682002, 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 682002; 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 V̇, 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 3.7.1 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
(0.2–0.4 mg/kg) and fentanyl (1–3 ␮g/kg) and paralyzed with
atracurium (0.3–0.5 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
V̇ 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 FIO2. After a
stabilization period of 5 min, blood was drawn from the
arterial line to determine blood gases. Then FIO2 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 V̇ 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 cmH2O 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.
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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.
2065
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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,
V̇, 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 ⫹ 关b/共1 ⫹ e⫺共P⫺c兲/d兲兴
(1)
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.
J Appl Physiol • VOL
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.
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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
cmH2O, and d ⫽ 10 cmH2O. 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 ⫹ 1.317 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 ⬍ 0.05. SPSS for Windows
version 11.0.1 (SPSS, 2001) was used for the statistical analysis.
2067
LUNG AND CHEST WALL V-P CURVES IN ALI
RESULTS
Table 1. Data of the 36 patients at time
of measurements
Age, yr
Ideal body weight, kg
BMI, kg/m2
SAPS II (range 0–194)
Lung injury score (range 0–4)
Days to investigation
Tidal volume, ml/kg ideal body wt
PEEP, cmH2O
Respiratory frequency, min⫺1
Inspiratory time, s
Expiratory time, s
FIO2
PaO2, Torr
PaO2/FIO2
PaCO2, Torr
pH
Median
IQR
68
66
26
60
1.8
2
6.8
8
16
1.2
2.2
52
90
174
42
7.37
59–75
59–75
22–27
47–75
1.4–2.5
1–3
6.1–8.0
6–10
14–20
1.0–1.4
1.9–2.8
40–70
77–105
138–200
36–49
7.33–7.43
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
Respiratory System
Lung
Chest Wall
Patient
Group
Pmci,
cmH2O
Pmcd,
cmH2O
R2
Pmci,
cmH2O
Pmcd,
cmH2O
R2
Pmci,
cmH2O
Pmcd,
cmH2O
R2
1
2
3
4
7
8
9
10
11
12
13
16
17
18
19
25
26
27
29
30
34
21
23
32
33
36
20
22
24
28
31
35
5
6
14
15
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
11.6
6.4
9.4
2.8
5.7
14.2
7.1
4.3
1.3
13.3
6.8
14.2
13.5
5.2
6.3
12.6
11.4
6.7
8.7
3.6
16.0
6.0
10.0
17.9
7.5
16.4
20.4
7.7
18.0
12.0
10.3
4.7
6.0
8.7
13.1
5.5
31.0
20.0
32.5
14.1
15.0
31.0
37.4
28.5
27.9
37.9
36.1
28.4
33.9
26.1
31.0
24.4
29.3
28.4
31.0
18.0
42.0
22.0
34.6
45.0
33.0
40.6
43.2
35.7
34.8
36.6
34.0
20.2
26.0
43.6
30.1
29.3
0.998
0.992
0.997
0.999
0.995
0.997
0.998
0.997
0.999
0.999
0.995
0.997
0.991
0.998
0.999
0.991
0.999
0.999
0.999
0.999
0.997
0.996
0.999
0.998
0.999
0.994
0.992
0.999
0.994
0.998
0.996
0.996
0.994
0.998
0.994
0.996
9.2
5.5
6.2
2.4
4.3
12.0
5.8
2.9
0.5
12.8
1.9
14.3
11.5
3.6
5.6
12.4
6.5
3.6
7.5
2.8
16.0
5.6
10.4
16.2
7.4
15.6
20.8
3.3
16.3
11.2
10.8
0.9
5.2
3.5
12.9
5.2
25.0
16.5
24.6
13.2
7.3
23.7
29.7
21.2
7.1
34.6
29.6
25.2
26.8
18.1
28.0
22.7
15.8
21.9
26.0
12.5
39.0
21.0
32.5
36.0
32.4
35.5
39.0
28.0
29.9
36.0
33.0
12.0
16.0
24.3
28.4
25.6
0.997
0.990
0.996
0.997
0.975
0.995
0.995
0.995
0.989
0.999
0.993
0.997
0.992
0.997
0.998
0.989
0.998
0.998
0.998
0.994
0.997
0.996
0.998
0.995
0.999
0.994
0.986
0.999
0.991
0.997
0.998
0.989
0.992
0.993
0.991
0.994
2.3
0.4
3.2
0.9
1.1
2.0
2.5
2.0
1.7
1.1
3.8
0.6
2.1
0.4
1.4
0.5
5.7
3.7
1.4
2.4
0.6
0.8
0.5
2.0
0.3
0.9
0.0
2.7
1.6
0.5
0.0
3.7
0.7
8.3
1.1
0.2
6.4
4.0
8.2
2.6
8.2
7.3
6.2
7.5
25.1
2.6
5.1
3.6
7.6
9.3
4.0
1.4
13.0
5.9
5.6
5.5
3.0
2.7
1.5
6.1
1.3
1.8
3.2
8.6
5.1
1.1
1.1
9.9
6.0
16.4
2.3
4.9
0.997
0.992
0.989
0.991
0.999
0.996
0.983
0.998
0.999
0.983
0.952
0.981
0.980
0.999
0.931
0.991
0.999
0.975
0.995
0.985
0.997
0.932
0.983
0.973
0.993
0.989
0.986
0.984
0.999
0.967
0.969
0.999
0.994
0.992
0.995
0.995
Pmci, point of maximal compliance increase; Pmcd, point of maximal compliance decrease; R2, 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.
J Appl Physiol • VOL
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IQR, interquartile range; BMI, body mass index, SAPS II, Simplified Acute Physiology Score; PEEP, positive end-expiratory pressure;
FIO2, inspired O2 fraction; PaO2, arterial PO2; PaCO2, arterial PCO2.
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 0.991 to 0.999 for the respiratory system,
0.975 to 0.999 for the lung, and 0.931 to 0.999 for the
chest wall. In the six patients excluded from the final
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.
DISCUSSION
In this study, the sigmoidal equation was used to
assess the presence and the magnitude of the lower
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 ⬎ 0.990. 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) cmH2O, respectively; those of Pmcd
were 31 (26–36), 25 (19–32), and 5 (3–8) cmH2O,
respectively; those of c were 21 (16–23), 17 (11–21),
and 3 (2–5) cmH2O, 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)
J Appl Physiol • VOL
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.
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(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 cmH2O.
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.
LUNG AND CHEST WALL V-P CURVES IN ALI
J Appl Physiol • VOL
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 cmH2O to make
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
cmH2O, 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 cmH2O. 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
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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
2069
2070
LUNG AND CHEST WALL V-P CURVES IN ALI
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;
J Appl Physiol • VOL
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.
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tissue throughout the lung, the V-P curve exhibited a
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areas, a linear pattern of the V-P curve was observed
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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
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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
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determined.
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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.
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