and hence PL,eio = PL,eeo + (Pao,eio − PEEPtot ) × (1 − Ecw / ERS ) (Eq. 2),

Unit, Tianjin Chest Hospital, Teaching Hospital of Tianjin Medical University, Tianjin, China

REFERENCES

where ∆PL is the difference of the transpulmonary pressure at end-inspiration (PL,eio) and end-expiration occlusions (PL,eeo) and PEEPtot is the total positive end-expiratory pressure. Unfortunately, Gulati et al (1) used a simplified equation (Eq. 1) including only the Ecw/ERS ratio and Pao,eio, which neglects the values of PEEPtot and PL,eeo. Thus, the overestimation of PL,eio should not come as a surprise when considering the low mean Ecw/ERS ratio (0.25) and a marked discrepancy between PEEPtot and PL,eeo (i.e., a high mean PEEPtot of 17.4 cm H2O and a negative mean PL,eeo value of –2.9 cm H2O) in this population. In a similar acute respiratory distress syndrome (ARDS) population (3) with a mean Ecw/ERS of 0.22, it has been shown that PL,eeo averaged –2.8 cm H2O and ranged widely from –15 to 5 cm H2O. Such substantially negative values of PL,eeo in such populations will make the overestimation of PL,eio by the Ecw-based method even unavoidable, given that PL,eeo should always be taken into account when calculating PL,eio (Eq. 2). Our reasoning agrees perfectly well with findings from a previous study in a similar population (i.e., mean Ecw/ERS of 0.22). In this study, Loring et al (3) demonstrated that the value of PL,eeo, which was completely ignored by Gulati et al (1), was the most important determinant of PL,eio, such that 62% of the variance in PL,eio was explained by PL,eeo. In addition, the combination of lung elastance and tidal volume, which is equal to (Pao,eio – PEEPtot) × (1 – Ecw/ERS), correlated weakly with PL,eio (R2 = 0.23) (3), further supporting our conclusion that PL,eio calculated as Pao,eio × (1 – Ecw/ERS) is not an adequate surrogate for the real transpulmonary pressure at end-inspiration occlusion, at least in the study population of Gulati et al (1). Actually, the Ecw-based method used in this study, which is a simplified version of the standard method (2), is correct and can provide reliable estimation of PL,eio only if both Ppl and airway pressure are equal to zero at functional residual capacity (4). Unfortunately, this minimum prerequisite is highly unlikely to be fulfilled in patients with ARDS (5). Thus, we believe that such Ecw-based method used by Gulati et al (1) for estimating PL,eio does not account for the key determinant of PL,eio (i.e., PL,eeo and PEEPtot) and the resulting erroneous estimation is unavoidable, especially in their study population with a low Ecw/ERS ratio. We are not saying that such Ecw-based method is useless in all clinical circumstances and are convinced that further work is needed to identify illustrative subgroups of patients with ARDS, in whom the use of Ecw-based method proposed by Gulati et al (1) can still be justified. The authors have disclosed that they do not have any potential conflicts of interest. Yang Liu, MD, Medical Intensive Care Unit, Pingjin Hospital, Logistics College of the Chinese People’s Armed Police Forces, Tianjin, China; Yu Mu, MD, PhD, Coronary Care e54

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1. Gulati G, Novero A, Loring SH, et al: Pleural Pressure and Optimal Positive End-Expiratory Pressure Based on Esophageal Pressure Versus Chest Wall Elastance: Incompatible Results. Crit Care Med 2013; 41:1951–1957 2. Chiumello D, Carlesso E, Cadringher P, et al: Lung stress and strain during mechanical ventilation for acute respiratory distress syndrome. Am J Respir Crit Care Med 2008; 178:346–355 3. Loring SH, O’Donnell CR, Behazin N, et al: Esophageal pressures in acute lung injury: Do they represent artifact or useful information about transpulmonary pressure, chest wall mechanics, and lung stress? J Appl Physiol (1985) 2010; 108:515–522 4. Staffieri F, Stripoli T, De Monte V, et al: Physiological effects of an open lung ventilatory strategy titrated on elastance-derived end-inspiratory transpulmonary pressure: Study in a pig model. Crit Care Med 2012; 40:2124–2131 5. Pelosi P, Goldner M, McKibben A, et al: Recruitment and derecruitment during acute respiratory failure: An experimental study. Am J Respir Crit Care Med 2001; 164:122–130 DOI: 10.1097/CCM.0000000000000741

The authors reply:

W

e thank Drs. Liu and Mu (1) for their thoughtful analysis of the mathematics and physiology underlying the elastance-based method for determining transpulmonary pressure. They describe the flawed mathematics and logical inconsistency of the simplified formula that we presented (Eq. 1 in [1]), relating transpulmonary pressure (PL) to airway pressure (Paw) and the ratio of lung elastance to total respiratory elastance (EL/Ers or EL/Etot). They go on to derive the correct expression (Eq. 2 in [1]) relating transpulmonary pressure to elastances of chest wall and respiratory system, including measured values of airway and esophageal pressure (thereby including the constant of integration). Drs. Liu and Mu (1) support the validity of this equation by citing our previous article (2), concluding, “… the value of [transpulmonary pressure during end-expiratory occlusion], which was completely ignored [in Eq. 1 presented] by Gulati et al (3), was the most important determinant of the value of [transpulmonary pressure at endinspiratory plateau]…” We agree with this analysis by Drs. Liu and Mu (1). However, we would emphasize that the elastance-based method now in use is, in fact, the simplified and mathematically incomplete Equation 1 presented in our report! This method, originally described in articles by Gattinoni et al (4, 5) and used by others (6, 7), is summarized by the equations “Ppl = Paw × Ecw/Etot” (6) and “PL = Paw × EL/Ers” (5), in which pleural (Ppl) and transpulmonary pressures are calculated from elastances and airway pressure. Although the correct Equation 2 is based on an equation presented by Chiumello et al (8), that article only reports changes in transpulmonary pressure and presents no equation that directly relates transpulmonary pressure to elastances. Recent articles using the elastance-based method show that February 2015 • Volume 43 • Number 2

Online Letters to the Editor

measured values of pleural (esophageal) and transpulmonary pressure are not used in the calculation. For example, Grasso et al (6) calculated transpulmonary pressure at the end-inspiratory plateau from Ecw/Ers and plateau pressure values only. The elastance-based method is also evident in the calculated values of transpulmonary or pleural pressure at various lung volumes, which are nearly proportional to airway pressure (6, 7, 9). The correct Equation 2 is consistent with the conventional “direct” method of calculating transpulmonary pressure (3, 10), which requires measuring and using the actual values of transpulmonary (or esophageal) pressure, not just tidal changes in those pressures. Finally, we agree that the clinical utility of either method can only be determined through clinical trials. Dr. Loring received support for article research from the National Institutes of Health (NIH). Dr. Talmor received grant support from the National Heart, Lung, and Blood Institute and received support for article research from the NIH. Stephen H. Loring, MD, Daniel Talmor, MD, MPH, Department of Anesthesia, Critical Care and Pain Medicine, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA

REFERENCES

1. Liu Y, Mu Y: Chest Wall Elastance in the Estimation of the Transpulmonary Pressure: How Should We Use It? Crit Care Med 2015; 43:e53–e54 2. Loring SH, O’Donnell CR, Behazin N, et al: Esophageal pressures in acute lung injury: Do they represent artifact or useful information about transpulmonary pressure, chest wall mechanics, and lung stress? J Appl Physiol (1985) 2010; 108:515–522 3. Gulati G, Novero A, Loring SH, et al: Pleural pressure and optimal positive end-expiratory pressure based on esophageal pressure versus chest wall elastance: Incompatible results. Crit Care Med 2013; 41:1951–1957 4. Gattinoni L, Carlesso E, Cadringher P, et al: Physical and biological triggers of ventilator-induced lung injury and its prevention. Eur Respir J Suppl 2003; 47:15s–25s 5. Gattinoni L, Chiumello D, Carlesso E, et al: Bench-to-bedside review: Chest wall elastance in acute lung injury/acute respiratory distress syndrome patients. Crit Care 2004; 8:350–355 6. Grasso S, Terragni P, Birocco A, et al: ECMO criteria for influenza A (H1N1)-associated ARDS: Role of transpulmonary pressure. Intensive Care Med 2012; 38:395–403 7. Staffieri F, Stripoli T, De Monte V, et al: Physiological effects of an open lung ventilatory strategy titrated on elastance-derived end-inspiratory transpulmonary pressure: Study in a pig model. Crit Care Med 2012; 40:2124–2131 8. Chiumello D, Carlesso E, Cadringher P, et al: Lung stress and strain during mechanical ventilation for acute respiratory distress syndrome. Am J Respir Crit Care Med 2008; 178:346–355 9. Chiumello D, Cressoni M, Carlesso E, et al: Bedside selection of positive end-expiratory pressure in mild, moderate, and severe acute respiratory distress syndrome. Crit Care Med 2014; 42:252–264 10. Talmor D, Sarge T, Malhotra A, et al: Mechanical ventilation guided by esophageal pressure in acute lung injury. N Engl J Med 2008; 359:2095–2104 DOI: 10.1097/CCM.0000000000000804

Critical Care Medicine

Prone Positioning in Acute Respiratory Distress Syndrome To the Editor:

R

egarding the effects of prone positioning on overall mortality, we believe that Lee et al (1) have misinterpreted the results of their own meta-analysis in a recent issue of Critical Care Medicine. In specific, we would like to report the following: 1. The authors report that no publication bias was seen on visual inspection of funnel plots. However, the funnel plot for main analysis, provided in supplement, clearly shows bias on visual inspection. In the absence of bias, the plot should approximately resemble a symmetrical (inverted) funnel. If there is bias, for example, because smaller studies without statistically significant effects remain unpublished, this will lead to an asymmetrical appearance of the funnel plot with a gap in a bottom corner of the plot. Supplement Figure 2 in (1) shows a wide gap in the right-bottom corner. 2. Risk ratio describes the multiplication of the risk that occurs with use of an experimental intervention (in this case, prone positioning). For example, a risk ratio of 2 for patients in the supine position group would imply that events in this group are twice than in those with prone positioning. We used the same data that the authors provided in Figure 2 in (1). Specifically, we used the “events” and total sample size (n) for patients in prone positioning and separately for those in supine position. Calculating the pooled risks ratio, we get a relative risk of 0.86 (95% CI, 0.75–1.0; p = 0.054). Clearly, the results get statistically insignificant when analyzed using this approach. 3. Constructing the funnel plot for the pooled relative risk estimate (above), we get a funnel plot that shows publication bias on visual inspection as well on statistical confirmation. From this funnel plot, we get an Eggers test of the intercept that has a p value of 0.03 (one-tailed), suggesting statistically significant publication bias. 4. The authors also report that no study unduly influenced the pooled estimate of the prone position. However, the analytic approach for this observation is not explained in their Methods section. We conducted a meta-analysis of the data (events/n) provided in Figure 2 in (1). Although, we arrived at the same pooled estimate of odds ratio, upon conducting a sensitivity analysis, we found that systematic exclusion of the studies by Gattinoni et al (2), Guerin et al (3), Chan et al (4), and Demory et al (5) leads to statistically significant results, whereas that for the remaining seven studies leads to statistically insignificant results. Clearly, some studies did exert influence on the overall pooled estimate. 5. In the meta-regression, authors stated that a negative trend for overall mortality was observed when the actual duration of prone positioning was longer and that the effect of the duration of prone positioning on mortality did not achieve statistical significance. However, a meta-regression using the unrestricted maximum likelihood method for the association of duration of prone positioning (per session) with www.ccmjournal.org

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