Calculation of mechanical power for pressure-controlled ventilation

Dear Editor,

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) [1]. A recent analysis of two large databases revealed that high MP is independently associated with mortality in critically ill patients on mechanical ventilation [2]. 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 (P_aw) during inspiration, it is not suitable for calculating MP during pressure-controlled ventilation (PCV) [3]. 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” P_aw 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 ΔP_insp is the change in P_aw during inspiration, PEEP is the positive end-expiratory pressure (both cmH₂O), V_T 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 (T_slope), 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 (MP_ref), data of P_aw 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 MP_ref, MP_PCV and MP_PCV(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.

MP_PCV and MP_PCV(slope) were compared to MP_ref 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, ΔP_insp 14 ± 4 cmH₂O, V_T 545 ± 161 ml and T_slope 0.2 ± 0.03 s. Calculated auto-PEEP was 0.81 ± 0.77 cmH₂O.

On average, MP_ref was 15.6 ± 6.9 J/min. With the simplified equation, we calculated values for MP_PCV of 16.3 ± 7.1 J/min, which were highly correlated to MP_ref (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 MP_PCV(slope) averaged 15.6 ± 6.9 J/min, almost identical to MP_ref (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 MP_ref, MP_PCV and MP_PCV(slope) were 0.02 ± 0.02, 0.04 ± 0.05 and 0.03 ± 0.03, respectively.

Fig. 1

a, c Correlation between mechanical power calculated with the simplified equation for pressure-controlled ventilation (MP_PCV, a) and the comprehensive equation (MP_PCV(slope), c) with the reference value MP_ref. b, d The corresponding Bland–Altman plots, plotting the difference between calculated values and reference values vs. the means of both methods

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