Determination of respiratory system compliance during pressure support ventilation by small variations of pressure support

Abstract

In mechanically ventilated patients, measurement of respiratory system compliance (C_rs) is of high clinical interest. Spontaneous breathing activity during pressure support ventilation (PSV) can impede the correct assessment of C_rs and also alter the true C_rs by inducing lung recruitment. We describe a method for determination of C_rs during PSV and assess its accuracy in a study on 20 mechanically ventilated patients. To assess C_rs during pressure support ventilation (C_rs,PSV), we performed repeated changes in pressure support level by ± 2 cmH₂O. C_rs,PSV was calculated from the volume change induced by these changes in pressure support level, taking into account the inspiration time and the expiratory time constant. As reference methods, we used C_rs, measured during volume controlled ventilation (C_rs,VCV). In a post-hoc analysis, we assessed C_rs during the last 20% of the volume-controlled inflation (C_rs,VCV20). Values were compared by linear regression and Bland–Altman methods comparison. Comparing C_rs,PSV to the reference value C_rs,VCV, we found a coefficient of determination (r²) of 0.90, but a relatively high bias of − 7 ml/cm H₂O (95% limits of agreement − 16.7 to + 2.7 ml/cmH₂O). Comparison with C_rs,VCV20 resulted in a negligible bias (− 1.3 ml/cmH₂O, 95% limits of agreement − 13.9 to + 11.3) and r² of 0.81. We conclude that the novel method provides an estimate of end-inspiratory C_rs during PSV. Despite its limited accuracy, it might be useful for non-invasive monitoring of C_rs in patients undergoing pressure support ventilation.

1 Introduction

A valid measurement of respiratory system compliance (C_rs) is essential in the assessment of the diseased lung status during mechanical ventilation [1,2,3] During volume-controlled ventilation (VCV), C_rs can be determined as tidal volume (V_T) divided by the difference between plateau airway pressure (P_plat) and positive end-expiratory pressure (PEEP):

$${C_{{\text{rs}}}}=\frac{{{V_T}}}{{{P_{{\text{plat}}}} - {\text{PEEP}}}}$$

(1)

Alternatively, C_rs and resistance (R_rs) can be calculated during different modes of mechanical ventilation with a least squares fit (LSF) using the equation of motion of the respiratory system,

$${\text{P}_{{\text{aw}}}}{\text{(t)=}}\frac{{{V_T}{\text{(t)}}}}{{{C_{{\text{rs}}}}}}+{{\text{V}}^{\text{'}}}({\text{t}}){\text{*~}}{{\text{R}}_{{\text{rs}}}}+{{\text{P}}_{\text{o}}}$$

(2)

where P_aw denotes the measured airway pressure, V’ denotes air flow and P₀ the mathematically estimated alveolar pressure at the beginning of inspiration. The LSF technique can also be used for assessment of intratidal changes in C_rs during a volume-controlled inspiration [4]. A decrease in C_rs during the course of inspiration can be interpreted as alveolar overdistension, whereas an increase in C_rs during inspiration can be interpreted as an indicator of tidal recruitment [4, 5]. Adjustment of mechanical ventilation according to the intratidal course of C_rs has shown promising results in preliminary clinical studies [6, 7].

In clinical practice, a large number of patients are switched from controlled to assisted modes of mechanical ventilation like pressure support ventilation (PSV) early in the course of their disease [8]. In the presence of spontaneous breathing efforts, the results of the abovementioned equations become inaccurate due to the additional respiratory muscle pressure (P_mus) generated by the patient [9]. Different methods to overcome this problem have been proposed which employ some form of end-inspiratory airway occlusion for assessment of C_rs when spontaneous breathing is present [10, 11]. These methods require the patient to relax the respiratory muscles during the airway occlusion, a precondition that is not always met by patients undergoing assisted mechanical ventilation. Moreover, an end-inspiratory occlusion interferes with the normal spontaneous breathing pattern during assisted modes of mechanical ventilation like PSV. Another method was recently proposed by Al-Rawas and coworkers, which elegantly transforms the equation of motion by applying the expiratory time constant to estimate C_rs, R_rs and P_plat during various ventilatory modes [12]. This method may only be applied under the prerequisite that a time point during the course of inspiration is found, where the patient’s P_mus is negligible [13, 14]. This may not always be possible in patients with strong inspiratory efforts. Therefore, an alternative method for continuous monitoring of C_rs during PSV is desirable.

It has been shown that the patient’s adaptation to respiratory muscle loading and unloading does not occur immediately but with a latency of a few breaths [15]. If repeated small changes in pressure support during ongoing PSV have no immediate effect on P_mus, it should be possible to calculate C_rs from the change in V_T induced by the change in PS, using the expiratory time constant to correct for different inspiration times and for the absence of an end-inspiratory pause. We hypothesized that this method could be used to obtain an accurate estimate of C_rs during ongoing PSV.

2 Materials and methods

2.1 Study setting

The present study was a prospective, single-center pilot study involving 20 mechanically ventilated patients in two surgical intensive care units (ICUs). We included ICU patients who were on assisted mechanical ventilation with PSV or suitable for PSV as per clinical decision. Exclusion criteria were age < 18 years, pregnancy, hemodynamic instability, and severe chronic obstructive pulmonary disease. The study was approved by the local ethics committee (A125/12, 23-05-2012) and written informed consent was obtained from the patients or their legal representatives before study inclusion.

2.2 Preparation for the study

All patients were ventilated with an Evita XL ventilator (Dräger Medical, Lübeck, Germany). PEEP setting was maintained at the level set by the physician in charge. P_aw and V’ were recorded at the Y-piece of the breathing circuit using a Bicore 2 device (CareFusion, Yorba Linda, CA, USA) at a sampling rate of 100 Hz. The study period consisted of two measurement periods that were applied to each patient in random order. Measurements were performed during VCV (measuring period VCV) and during PSV (measuring period PSV).

2.3 Measuring period PSV

Sedation was titrated to achieve a level on the Richmond Agitation and Sedation Scale (RASS) [16] of − 2 to − 3. Pressure rise time (T_ramp) was set to 0.2 s and the pressure support termination criterion to 25% of peak inspiratory flow. The pressure support level was adapted to achieve a target V_T of 6–8 ml/kg predicted body weight. The 100 ms occlusion pressure (P0.1) was measured as an indicator of respiratory drive.

For our experimental method, the pressure support level was manually increased or decreased for one single breath by 2 cmH₂O after every 5th to 7th breath. It was immediately switched back to the previous value for the next breath (Fig. 1). This was repeated 10 to 15 times. Subsequently, pressure support level was manually decreased by 2 cmH₂O after every 5th–7th breath and immediately returned to baseline for the next breath. This was also repeated 10–15 times.

Fig. 1

An example of a patient examination with an increase in pressure support level by 2 cmH₂O during the second breath (a). The corresponding volume curve is displayed in b. The increase in pressure support level lead to an increase in tidal volume of 69 ml. P _aw airway pressure, t time, V _T tidal volume

2.4 Measuring period VCV

During measuring period VCV, the patients were sedated to obtain a value on the Richmond Agitation and Sedation Scale of − 4 to − 5. The absence of spontaneous breathing activity was confirmed clinically and by visual analysis of the P_aw and V’ curves. If spontaneous breathing activity was detected despite deep sedation, a non-depolarizing neuromuscular blocking agent was administered (Rocuronium, MSD Sharp & Dohme GmbH, Haar, Germany) at a dose of 0.6 mg per kg of predicted body weight. V_T was adjusted to 6–8 ml/kg predicted body weight and respiratory rate was set to achieve clinically acceptable minute ventilation while avoiding air-trapping caused by incomplete expiration. C_rs during VCV (C_rs,VCV) was then determined during VCV with constant inspiratory flow and an end-inspiratory pause of at least 0.25 s. These ventilator settings were also maintained for at least five consecutive breaths.

2.5 Calculation of time constant during PSV

For the calculation of the expiratory time constant (τ) during PSV, all expirations were divided into ten slices of equal volume (please see Fig. 2 for a schematic graphical illustration). The time constant τ was calculated separately for all volume slices as the slope of the flow-volume curve of each slice. Equally, the coefficient of determination (r²) of the flow-volume curve was determined for each slice by using a linear regression fit. To determine τ_PSV for an individual patient, the mean τ was calculated from all expiratory slices with an r² of > 0.95 from ten consecutive breaths. To avoid disturbances from residual muscle activity or other interferences, the first and the last slice of every expiration and all slices with r² < 0.95 were excluded from the analysis.

Fig. 2

Schematic representation of the division of the expiratory flow-volume loop into ten slices of equal volume. The expiratory time constant was determined as the mean slope of the regression lines from all slices with an almost linear flow-volume relationship, defined by a coefficient of determination (r²) of more than 0.95. The first and the last slice of every breath were ignored

2.6 Calculation of compliance during PSV

The compliance C_rs during PSV (C_rs,PSV) was calculated from the change in tidal volume ΔV_T divided by the change in mean inspiratory P_aw caused by the variation of pressure support (ΔP_insp), considering T_ramp, inspiration time (T_insp) and τ. The solution of the linear equation of motion (Eq. 2) following an initial pressure ramp can be computed in closed form for 0 ≤ t ≤ T_Ramp:

$${\text{V(t)~=~}}{{\text{y}}_{{\text{ramp}}}}{\text{(t)~=~}}{\text{P}_{{\text{insp}}}} \cdot {{\text{C}}_{{\text{rs}}}} \cdot ({\text{t}} - {{{\uptau}}}+{{~{\uptau}}} \cdot {{\text{e}}^{ - \frac{{\text{t}}}{{{{\uptau}}}}}})$$

(3)

The solution after changing to constant pressure at t₁ = T_ramp can be computed by superposition. A ramp with positive slope starting at t₀ = 0 and continuing until t₂ = T_insp (for which the equation of motion can be solved according to Eq. 3) is superimposed by a ramp with negative slope starting at t₁ = T_ramp (Fig. 3). The solution during this phase of inspiration (T_Ramp ≤ t ≤ T_insp) can thus be derived as as follows:

Fig. 3

Illustration of the linear superposition for determining the temporal behavior of the inspiratory volume. The superposition of the initial ramp by a negative ramp starting at T_ramp yields the desired constant pressure until T_insp

$${\text{V}}({\text{t}}) = {\text{y}}_{\text{ramp}} ({\text{t}}) - {\text{y}}_{\text{ramp}} ({\text{t}} - {\text{T}}_{\text{Ramp}}) = {\text{P}}_{\text{insp}} \cdot {\text{C}}_{\text{rs}} \cdot {\text{e}}^{{-\frac{\text{t}}\uptau}} \left( {\uptau - \uptau \cdot {\text{e}}^{{ - \frac{{\text{T}}_{\text{ramp}}}{\uptau }}} } \right)$$

(4)

For our method, a change in V_T was induced by performing a manual variation in pressure support level. When subtracting the breath after the change in P_insp from the preceding breath, we obtain:

$${C_{{\text{rs,PSV}}}}=\frac{{{{{\Delta}}}{{\text{V}}_T}}}{{\Delta {P_{{\text{insp}}}}}} \cdot \frac{{{T_{ramp}}}}{{\tau \cdot {e^{\frac{{ - {T_{insp}}}}{\tau }}} \cdot (1 - {e^{\frac{{{T_{ramp}}}}{\tau }}})}}$$

(5)

To compensate for natural variations in P_mus, the median C_rs,PSV was calculated from all variations of pressure support level.

2.7 Determination of reference values during VCV

The reference value C_rs,VCV was calculated from the mean of five volume-controlled inspirations as follows:

$${C_{{\text{rs,VCV}}}}{\text{=~}}\frac{{{V_T}}}{{{P_{{\text{plat}}}} - {\text{PEEP}}}}$$

(6)

2.8 Post-hoc analyses

In a post-hoc analysis, intratidal C_rs of the last slice of inspired volume (C_rs,VCVfin) was calculated using the SLICE method [4]. For this purpose, the inspiration during VCV was divided into six slices of equal volume, omitting the first and the last 5% of inspired volume. Assuming a constant R_rs during the constant-flow phase of inspiration, C_rs,VCVfin was calculated from the last slice before the end of inspiration using a linear least-squares approximation.

Furthermore, we separately assessed the agreement between C_rs,PSV and C_rs,VCV as well as C_rs,VCVfin, respectively, for the subgroups of patients who did or did not require neuromuscular blockade during VCV. We also separately assessed the agreement between the values of C_rs,PSV that had been obtained from increases and decreases in PS (C_rs,PSV+2, C_rs,PSV−2, respectively) and the reference value C_rs,VCV.

Finally, we determined C_rs with the method published by Al-Rawas and Co-Workers (C_{rs, τe}) in [12] according to the equation

$${{\text{C}}_{{\text{rs}},{{{\uptau}e}}}}=\frac{{{{\text{V}}_{\text{t}}}+{{\mathbf{\tau }}_{\text{e}}}{\text{*inhaled~flow~rate}}}}{{{{\text{P}}_{{\text{aw}}}} - {\text{PEEP}}}}$$

where τ _e was determined from the slope of the expiratory flow-volume curve between 0.1 and 0.5 s after the start of exhalation. Inhaled flow rate, V_t and P_aw were determined according to [13, 14] at a time point close to the end of inhalation, 50 ms before the beginning of exhalation.

2.9 Blood gas analysis

Arterial partial pressure of oxygen (PaO₂) with the corresponding inspired fraction of oxygen (FiO₂) were obtained from the last blood gas sample taken before the beginning of the study procedure.

2.10 Statistical analyses

The basic calculations were performed with Excel Version 2011 for Mac (Microsoft, Redmond, USA). For the statistical analyses, Prism Version 6 (GraphPad, La Jolla, USA) was used. The measured data were tested for normal distribution using the D’Agostino Pearson omnibus normality test. Data were compared to the reference measurement by a two-sided paired t test (if normally distributed) or by a Wilcoxon matched-pairs signed rank test (if not normally distributed). Correlation between values was assessed by linear regression. Bias and 95% limits of agreement (LoA) were calculated by Bland–Altman analysis. All values are presented as means ± standard deviations unless otherwise specified. Numerical values are presented as mean ± standard deviation for normally distributed data or as median, 25th–75th percentile for non-normally distributed data.

3 Results

The study protocol was successfully applied to all patients included in the study. Baseline characteristics of the studied patients are given in Table 1. All values were normally distributed with the exception of P0.1. During VCV, the patients were ventilated with an average V_T of 7.5 ± 1.6 ml/kg predicted body weight and a respiratory rate of 17.2 ± 6.5 breaths/min, resulting in a total minute ventilation of 7.9 ± 1.5 L/min. During PSV, patients were ventilated with a V_T of 8.9 ± 2.1 ml/kg predicted body weight at a respiratory rate of 17.7 ± 5.8 breaths/min, resulting in a total minute ventilation of 9.7 ± 2.4 L/min. The applied PEEP level was 10.3 ± 3.2 cmH₂O. The set PEEP level remained unchanged throughout the study period. The average PaO₂/FiO₂ ratio was 224 ± 91 mmHg. The median P0.1 during PSV was 3.1, 1.9–4.1 cmH₂O/100 ms. Neuromuscular blockade was required in 9 out of 20 patients.

Table 1 Baseline characteristics of the studied patients

3.1 Determination of time constant during PSV

Overall, 32% of all analyzed slices of the expiratory flow-volume curves during PSV had an r² of higher than 0.95. After excluding all remaining sections with r² smaller than 0.95, we found an average value of 0.69 ± 0.20 s for τ_PSV. A detailed summary of the percentage of excluded slices for all sections analyzed can be found in Table 2.

Table 2 Percentage of slices of expiratory flow-volume curves with r² < 0.95

3.2 Comparison of C_rs,PSV to C_rs,VCV

The average value of C_rs,PSV was 32 ± 15 ml/cmH₂O and differed significantly from the reference value C_rs,VCV (39 ± 16 ml/cmH₂O, p < 0.0001). Both values were highly correlated (r² = 0.90; p < 0.0001). Bland–Altman analysis showed 95% limits of agreement ranging from − 16.8 to + 2.7 ml/cmH₂O (bias − 7 ml/cmH₂O) (Fig. 4).

Fig. 4

Scatter plot and Bland–Altman plot of the calculated values for respiratory system compliance (C_rs) measured during volume-controlled ventilation (C_rs,VCV) and during pressure support ventilation (PSV) with the new proposed method (C_rs,PSV). In the scatter plot, the dotted line represents the best fit between the shown values. In the Bland–Altman plot, the dashed line represents the bias whereas the dotted lines represent the 95% limits of agreement. R ² coefficient of determination

3.3 Comparison of C_rs,PSV to C_rs,VCVfin

Analyzing the compliance of the last slice of inspiratory volume using the SLICE-method, we found an average value of C_rs,VCVfin of 34 ± 14 ml/cmH₂O. This did not differ significantly from C_rs,PSV (32 ± 15 ml/cmH₂O; p = 0.06). Linear regression revealed a good correlation between C_rs,PSV and C_rs,VCVfin (r² = 0.87) and Bland–Altman methods comparison showed a small and statistically insignificant bias of − 2.4 ml/cmH₂O and 95% limits of agreement ranging from − 12.8 to + 7.9 ml/cmH₂O (Fig. 5).

Fig. 5

Scatter plot and Bland–Altman plot of the calculated values for respiratory system compliance (C_rs) measured during the last slice of volume-controlled inspiration (C_rs,VCVfin) and during pressure support ventilation (PSV) with the new proposed method (C_rs,PSV). In the scatter plot, the dotted line represents the best fit between the shown values. In the Bland–Altman plot, the dashed line represents the bias whereas the dotted lines represent the 95% limits of agreement. R ² coefficient of determination

3.4 Effect of neuromuscular blockade

For the subgroup of 9 patients that required neuromuscular blockade to suppress spontaneous breathing activity during VCV, we found an average value of C_rs,PSV of 30 ± 21 ml/cmH₂O and an average value of C_rs,VCV of 38 ± 22 ml/cmH₂O. This difference was statistically significant (p < 0.0001). The correlation of C_rs,PSV and C_rs,VCV was excellent for this subgroup (r² = 0.98; p < 0.0001).

In the subgroup of 11 patients that did not require neuromuscular blockade to suppress spontaneous breathing activity during VCV, we found an average value of C_{rs,PSV of} 34 ± 8.2 ml/cmH₂O and an average value of C_rs,VCV of 39 ± 9.4 ml/cmH₂O. This difference was also statistically significant (p = 0.008). The correlation of C_rs,PSV and C_rs,VCV was acceptable for this subgroup (r² = 0.61, p = 0.005). Figure 6 summarizes the subgroup analyses for patients with and without the need for neuromuscular blockade during VCV.

Fig. 6

Scatter plots and Bland–Altman plots of the calculated values for respiratory system compliance (C_rs) measured during volume-controlled ventilation (C_rs,VCV) and during pressure support ventilation (PSV) with the new proposed method (C_rs,PSV), separated into the subgroups of patients who required neuromuscular blockade to suppress spontaneous breathing activity during VCV (above) and who did not require neuromuscular blockade during VCV (below). In the scatter plots, the dotted lines represent the best fit between the shown values. In the Bland–Altman plots, the dashed lines represent the bias whereas the dotted lines represent the 95% limits of agreement. R ² coefficient of determination

3.5 Separate comparison of C_rs,PSV from increases and decreases to C_rs,VCV

For C_rs,PSV+2, which was calculated only from stepwise increases in pressure support, we found an average value of 30.3 ± 20.3 ml/cmH₂O, which was positively correlated to C_rs,VCV (r² = 0.80; p < 0.0001; bias = − 8.7 ml/cmH₂O, 95% limits of agreement − 27.2 to + 9.9 ml/cmH₂O) (Fig. 7).

Fig. 7

Scatter plots and Bland–Altman plots of the calculated values for respiratory system compliance (C_rs) measured during volume-controlled ventilation (C_rs,VCV) and with the new proposed method during pressure support ventilation just from increases in pressure support level (C_rs,PSV+2, above) and just from decreases in pressure support level (C_rs,PSV−2, below) In the scatter plots, the dotted lines represent the best fit between the shown values. In the Bland–Altman plots, the dashed lines represent the bias whereas the dotted lines represent the 95% limits of agreement. R ² coefficient of determination

For C_rs,PSV−2, which was calculated only from stepwise decreases in pressure support, we found an average value of 33.4 ± 17.0 ml/cmH₂O, also with a positive correlation to C_rs,VCV (r² = 0.72; p < 0.0001; bias = − 5.5 ml/cmH₂O, 95% limits of agreement − 23.3 to + 12.2 ml/cmH₂O) (Fig. 7).

There was no statistically significant difference between C_rs,PSV+2 and C_rs,PSV−2.

3.6 Comparison of C_rs,τe to C_rs,VCV

Applying the method proposed by Al-Rawas et al. we found an average value of C_rs,τe of 53 ± 23 ml/cmH₂O. This was significantly higher than the reference value C_rs,VCV (38 ± 22 ml/cmH₂O; p < 0.0001). Bland Altman methods comparison revealed a bias of + 14.5 ml/cmH₂O and 95% limits of agreement of − 9.6 to + 38.6 ml/cmH₂O. There was an excellent correlation between C_rs,τe and C_rs,VCV (r² = 0.74; p < 0.0001) (Fig. 8).

Fig. 8

Scatter plot and Bland–Altman plot of the calculated values for respiratory system compliance (C_rs) measured during volume-controlled ventilation (C_rs,VCV) and during pressure support ventilation with the method proposed by Al-Rawas and coworkers (C_rs,τe). In the scatter plot, the dotted line represents the best fit between the shown values. In the Bland–Altman plot, the dashed line represents the bias whereas the dotted lines represent the 95% limits of agreement. R ² coefficient of determination

4 Discussion

In this pilot study, the non-invasive assessment of C_rs during PSV showed a good correlation with the reference values measured during VCV. However, we found a significant underestimation of C_rs with the new method. Comparing C_rs,PSV to the end-inspiratory value C_rs,VCV20, we still found a good correlation but no statistically significant bias. The 95% limits of agreement for C_rs were relatively broad which could limit the new method’s clinical applicability.

Assessment of C_rs during any assisted mode of mechanical ventilation is challenging for several reasons. Not only is the patient’s average P_mus generally unknown, but it can also exhibit a considerable breath-by-breath variability [17]. In our method, this breath-by-breath variability of P_mus was taken into account by performing repeated variations in pressure support level and by calculating the median C_rs,PSV from all variations that had been performed in an individual patient. Another challenge in the determination of C_rs during PSV is the fact that there is no inspiratory plateau phase during PSV. Instead, there is generally a flow-dependent criterion for the termination of pressure support that can be adjusted according to the patient’s individual needs and that, in our study, remained set to 25% of peak inspiratory flow, the default setting on our ventilators. Together with T_ramp, which, depending on the patient’s true T_insp accounts for a variable decrease in mean inspiratory P_aw, this pressure support termination criterion could lead to an underestimation of C_rs,PSV due to the absence of an end-inspiratory pause. In our study, we attempted to correct this underestimation by compensating for the actual T_ramp and T_insp, assuming a constant inspiratory and expiratory time constant (Eq. 5).

For this study, we decided to determine the time constant only from those slices of expiration that exhibited an almost linear flow-volume relationship. With this approach, we tried to avoid any phases of expiration with residual inspiratory muscle activity as well as phases of expiration with forced expiratory muscle activity. A linear flow-volume relationship is typical for passive emptying in a first-order model with one resistance and one compliance. However, a constant residual P_mus during slices of exhalation would also result in a linear flow-volume relationship and cannot be detected by our method. Whether the proposed “slice” method is ideal for determining τ_e during PSV and which is the ideal number of slices as well as the ideal cut-off value for r² remains to be investigated.

Despite the good correlation between C_rs,PSV and C_rs,VCV, the mean C_rs,PSV was significantly smaller than the mean C_rs,VCV. This may be caused by several reasons. First, a small difference in P_mus caused by the variations in pressure support level cannot be entirely excluded. If the patient’s P_mus becomes smaller with higher pressure support level and vice versa, this would result in an underestimation of C_rs with our method. Second, our model for correction of the pressure support termination criterion and T_ramp (Eq. 4) assumes the inspiratory pressure delivered by the ventilator to be constant after the end of the set ramp. This may not be the case during PSV, especially in patients with strong inspiratory effort (Fig. 1). Third, our approach is based on a simple one-compartment model of RSM that assumes C_rs to be constant throughout the inspiratory period. In patients with heterogenous lung disease, C_rs may show a volume-dependent intratidal variability [4, 18]. In cases of overdistension, where C_rs becomes smaller during the “upper” part of the inspiratory pressure–volume loop, our method would underestimate the true value of C_rs. Therefore, the observed bias may have been caused by a certain degree of intratidal overdistension induced by the tidal volume of 8.9 ± 2.1 ml/kg predicted body weight during PSV at the clinically set PEEP of 10.3 ± 3.2 cmH₂O. This overdistension could have decreased respiratory system compliance in the course of inspiration. To test this hypothesis, we conducted a post-hoc analysis, comparing C_rs,PSV to the end-inspiratory C_rs during VCV, measured using the Slice method for the final part of inspired V_T. Remarkably, the bias between C_rs,PSV and C_rs,VCVfin was negligible and not statistically significant. Therefore, it seems likely that C_rs,PSV reflects C_rs at the end of inspiration and is smaller than the average C_rs in patients with overdistension. An assessment of C_rs,PSV at different levels of PEEP could further elucidate this relationship and is planned for future work. In combination with other methods for determination of C_rs during PSV, our method might therefore be used as a diagnostic tool for determining overdistension.

4.1 Alternative methods for determination of respiratory system mechanics during PSV

Approximately 20 years ago, Iotti et al. demonstrated that it is possible to determine RSM during PSV [9]. In their study, the authors used high levels of pressure support aiming at decreasing P_mus to a minimum. This would then allow a proper calculation of the patients’ respiratory system mechanics using a least-square fit method. However, applying high levels of pressure support may disturb the patients’ breathing pattern and may influence the weaning course. Furthermore, this method is not able to provide continuous data of the breathing mechanics during weaning.

In 2001, Younes et al. introduced a method for the determination of C_rs [11] and another method for the determination of R_rs [19] during proportional assist ventilation (PAV). Both methods need a specially modified respirator which can automatically apply an end-inspiratory hold maneuver for determination of C_rs and a short decrease of P_aw (“pulse”) during the early inspiratory phase for determination of R_rs. The authors found a good correlation for both methods when compared to reference values measured during controlled mechanical ventilation. These estimates of C_rs and R_rs can be used for automated control of PAV with load-adjustable gain factors [20] (PAV+). However, in a prospective observational study on post-cardiac surgery patients conducted by Patel and coworkers, evaluating the accuracy of C_rs and R_rs determined by the aforementioned method, unacceptably large bias of − 17 cmH₂O and 95% LoA ranging − 55 to + 22 cmH₂O were found for C_rs when compared to the reference method [21]. Patel et al. concluded that the estimates of respiratory mechanics by PAV + are too inaccurate to be clinically useful. In view of these contradictory results of Younes et al. and Patel et al. regarding the accuracy of the measured RSM during PAV, it remains unclear whether this method provides valid values for C_rs and R_rs that can be used as a monitoring tool.

Recently, Al-Rawas and coworkers published a method for determination of plateau pressure, respiratory system compliance and total resistance during different ventilator modes using the expiratory time constant [12]. Similar to the method proposed in our manuscript, it is based on the assumption of similar inspiratory and expiratory time constants. However, since the equations proposed by Al-Rawas et al. do not incorporate a term for the P_mus generated by the patient, they require finding sections of the inspiratory cycle where P_mus is equal to or close to zero [13, 14]. When applying this method to the data from the present study, we found a significant bias of + 14.5 ml/cmH₂O, leading to an overestimation of C_rs with this method. This could be explained by residual inspiratory muscle activity, despite the fact that we chose time points very close (50 ms) to the end of inspiration for this analysis.

Our method differs from the one proposed by AL-Rawas and coworkers in that it does not assume P_mus to be zero. Instead, it applies a change in airway pressure for single breaths, assuming the induced change in P_mus to be close to zero. The advantages of the method proposed by Al-Rawas are that it does not require any specific maneuver and can be used on a breath-by-breath basis. Furthermore, it allows calculation of resistance and plateau pressure, giving a full picture of a patient’s respiratory mechanics regardless of ventilatory mode. Nevertheless, it could be inaccurate in patients with high respiratory drive, which is where our method may be advantageous for minimizing the confounding effect of the patient’s inspiratory P_mus.

4.2 Limitations

Our study has several limitations, which shall be addressed hereafter.

First, we cannot exclude a change in respiratory system mechanics caused by the switch from PSV to VCV and vice versa, which was accompanied by a deepening of sedation and, in some patients where this was not sufficient to suppress spontaneous breathing activity, neuromuscular paralysis. The loss of spontaneous breathing activity might have induced atelectases in some patients, leading to a smaller overall lung compliance. Confounding effects that could have been introduced by fluid shifts and viscous tissue effects in between the measurement periods can also not be entirely excluded.

Second and possibly related, the 95% limits of agreement between our method and the reference measurements for C_rs were still relatively broad for clinical application. Nevertheless, they provide an estimate that is closer to the actual values than the LSF method ignoring the patient’s P_mus, which is currently employed by most ventilators and leads to gross overestimations in case of strong spontaneous efforts [9].

Third, our study was not designed to answer the important question whether the proposed method is able to accurately track changes in C_rs. This needs to be done in future work before applying this method in clinical practice.

Fourth, our method is based on the assumption of relatively similar respiratory time constants during inspiration and expiration. This may not be the case in patients with chronic obstructive lung diseases (COPD) or asthma. In fact, the only patient in our study who was diagnosed with (mild) COPD had an expiratory time constant of 0.47 s, indicating there was no relevant expiratory air flow limitation in this patient. Therefore, we recommend that our method should presently not be applied in patients with expiratory air flow limitation caused by obstructive lung diseases.

Fifth, our method requires repeated changes in pressure support level and subsequent mathematical calculations that, when performed manually, are relatively time consuming. Due to the necessity of performing multiple repeated changes in PS level, obtaining a single value of C_rs currently takes about 5–15 min, depending on the patient’s respiratory rate, not taking into account any necessary computation time.

Nevertheless, the changes in pressure support level and the required calculations could easily be performed automatically by the ventilator in the future without disturbing the patient. This would allow a higher number of pressure support level changes to be performed and analyzed, which might enhance the accuracy of the calculated values for C_rs,PSV, improving the method’s clinical applicability. It may also improve the accuracy of our proposed method for determination of C_rs. An automatic application of the method is therefore highly desirable.

5 Conclusions

This pilot study shows that it is possible to determine values for C_rs during PSV with the help of small changes of pressure support level. The derived values have a strong correlation but relatively broad limits of agreement when compared to reference values obtained during VCV and appear to provide an estimate of end-inspiratory C_rs. This simple measurement maneuver might improve the monitoring of patients undergoing assisted mechanical ventilation. For this purpose, it could be implemented as an automated maneuver in a respirator.