# Calculation of mechanical power for pressure-controlled ventilation

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The mechanical power (MP) is a single variable encompassing important ventilator-related causes of lung injury that can be calculated using a set of parameters routinely measured during volume-controlled ventilation (VCV) . A recent analysis of two large databases revealed that high MP is independently associated with mortality in critically ill patients on mechanical ventilation . As the equation for calculation of MP used for these analyses is based on the assumption of VCV with a linear rise of airway pressure (Paw) during inspiration, it is not suitable for calculating MP during pressure-controlled ventilation (PCV) . Here, we describe two equations for estimating MP during PCV and assess their validity in patients ventilated with this mode.

We retrospectively analyzed PCV data of patients enrolled in two previously published studies [4, 5]. We excluded datasets obtained during assisted spontaneous breathing and during VCV.

Under the assumption of an ideal “square wave” Paw during inspiration, MP during PCV was calculated according to the simplified equation

$${\text{MP}}_{\text{PCV}} = \, 0.098 \cdot {\text{RR}} \cdot V_{\text{T}} \cdot \left( {\Delta P_{\text{insp}} + {\text{ PEEP}}} \right),$$

where ΔPinsp is the change in Paw during inspiration, PEEP is the positive end-expiratory pressure (both cmH2O), VT is the tidal volume (l) and RR is the respiratory rate (1/min), with 0.098 as a correction factor to obtain the result in J/min.

Taking into account inspiratory pressure rise time (Tslope), MP was additionally calculated according to the comprehensive equation

$$MP_{{{\text{PCV}}({\text{slope}})}} = 0.098 \cdot {\text{RR}} \cdot \left[ {(\Delta P_{\text{insp}} + {\text{PEEP}}) \cdot V_{{{\text{T}} }} {-} \Delta P_{\text{insp}}^{2} \cdot C \cdot \left( {0.5 {-} \frac{R \cdot C}{{T_{\text{slope}} }} + \left( {\frac{R \cdot C}{{T_{\text{slope}} }}} \right)^{2} \cdot \left( {1 {-} {\text{e}}^{{\frac{{ - T_{\text{slope}} }}{R \cdot C}}} } \right)} \right)} \right],$$

where C is the compliance (l/cmH2O) and R is the resistance (cmH2O/l/s). The derivation of both equations and the determination of respiratory mechanics during PCV are outlined in the ESM.

To obtain reference values (MPref), data of Paw and flow recorded by the ventilator (Evita XL; Dräger, Lübeck, Germany) at a sampling rate of 100 Hz were integrated to calculate the area of the pressure–volume loop and subsequently multiplied by 0.098$$\cdot$$RR to obtain the result in J/min. For each patient, one average value of MPref, MPPCV and MPPCV(slope) was calculated from all breaths recorded during a period of PCV with unchanged ventilator settings. Intra-individual variability was assessed by calculating the coefficient of variation between all breaths analyzed during this period.

MPPCV and MPPCV(slope) were compared to MPref by linear regression and the Bland–Altman method comparison. Numerical results are expressed as mean ± standard deviation.

We analyzed PCV datasets obtained from 42 patients (age 55 ± 18 years; 29 male; height 174 ± 9 cm; PaO2/FiO2 195 ± 78 mmHg; 29 patients with ARDS) ventilated with external PEEP of 8 ± 5 cmH2O, RR 14 ± 4/min, ΔPinsp 14 ± 4 cmH2O, VT 545 ± 161 ml and Tslope 0.2 ± 0.03 s. Calculated auto-PEEP was 0.81 ± 0.77 cmH2O.

On average, MPref was 15.6 ± 6.9 J/min. With the simplified equation, we calculated values for MPPCV of 16.3 ± 7.1 J/min, which were highly correlated to MPref (r2 = 0.981; bias + 0.73 J/min; 95% limits of agreement (LoA) − 1.48 to + 2.93 J/min; Fig. 1a, b). With the comprehensive equation, the determined values of MPPCV(slope) averaged 15.6 ± 6.9 J/min, almost identical to MPref (r2 = 0.985; bias + 0.03 J/min; 95% LoA − 1.91 to + 1.98 J/min; Fig. 1c, d). The between-breath coefficients of variation for MPref, MPPCV and MPPCV(slope) were 0.02 ± 0.02, 0.04 ± 0.05 and 0.03 ± 0.03, respectively.

The simplified equation allows estimation of MP for PCV with a small bias caused by disregarding Tslope. The comprehensive equation corrects this bias but requires knowledge of Tslope, R and C. If only VT, RR, PEEP and ΔPinsp are known, the simplified equation may still yield acceptable results for most clinical situations.

## References

1. 1.

Gattinoni L, Tonetti T, Cressoni M et al (2016) Ventilator-related causes of lung injury: the mechanical power. Intensive Care Med 42:1567–1575

2. 2.

Neto AS, Deliberato RO, Johnson AW et al (2018) Mechanical power of ventilation is associated with mortality in critically ill patients: an analysis of patients in two observational cohorts. Intensive Care Med 44:1914–1922

3. 3.

Zhao Z, Frerichs I, He H et al (2019) The calculation of mechanical power is not suitable for intra-patient monitoring under pressure-controlled ventilation. Intensive Care Med. https://doi.org/10.1007/s00134-019-05536-x

4. 4.

Pulletz S, Adler A, Kott M et al (2012) Regional lung opening and closing pressures in patients with acute lung injury. J Crit Care 27(27):323.e11–323.e18

5. 5.

Becher T, Bui S, Zick G et al (2014) Assessment of respiratory system compliance with electrical impedance tomography using a positive end-expiratory pressure wave maneuver during pressure support ventilation: a pilot clinical study. Crit Care 18:679

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Correspondence to Tobias Becher.

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Tobias Becher and Dirk Schädler received lecture fees from Drägerwerk AG & Co. KGaA (Lübeck, Germany). Matthias van der Staay is an employee of imt and works for imtmedical, Buchs, Switzerland. The other authors report no conflicts of interest.

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