Mechanical Power in Pressure-Controlled Ventilation: A Simple and Reliable Bedside Method

Abstract

BACKGROUND:

Mechanical power (MP) represents the amount of energy applied by the ventilator to the respiratory system over time. There are two main methods to calculate MP in mechanical ventilation. The first is the geometric method, which directly measures the dynamic inspiratory area of the pressure-volume loop during the respiratory cycle. The second involves using various algebraic equations to estimate MP. However, almost all calculations are either complex or not reliable compared with the geometric method, considered the gold standard. This study aimed to develop an easy to use, reliable equation for bedside calculation of MP and to compare its accuracy with other existing equations for calculating MP.

METHODS:

In a preliminary study, we measured MP in 56 cases who were mechanically ventilated and without spontaneous breathing efforts. The measurements were done at the ICU of a single university medical center in the Netherlands.

RESULTS:

We found that the MP can be accurately calculated using an equation that incorporates the plateau pressure in 56 cases in 42 patients. The MP estimated with our new proposed equation (MP calculated using plateau pressure) correlated well with the reference value of MP with a bias of 0.2 J/min. The 95% limits of agreement (LoAs) were –3.1 to + 3.4 J/min. Other equations give the following bias and LoAs; bias of –0.8, LoA –3.8 to 1.9 J/min (van der Meijden equation), bias of –1.9, LoA –3.7 to –0.0 J/min (comprehensive Becher equation), bias of –2.4, LoA –4.5 to –0.3 J/min (simplified Becher equation), and a bias of –1.9, LoA –3.7 to 0.1 J/min (linear model equation).

CONCLUSIONS:

The equation we propose to calculate MP in pressure-controlled ventilation is a reliable, simple, and accurate alternative for the previously published equations. Consequently, this method is highly suitable for routine use in clinical practice.

KEY POINTS

Question: A new simple and accurate equation to calculate mechanical power in pressure-controlled ventilation for use at the bedside.

Findings: The equation we propose is a reliable and notably simple alternative for the previously published equations. Although the limits of agreement are slightly higher, mean bias remains around zero.

Meaning: This method is highly suitable for routine use in clinical practice, especially in places where a comprehensive calculation of mechanical power cannot be integrated into a patient data management system.

Mechanical power (MP) in mechanical ventilation is the amount of energy applied to the respiratory system by the ventilator over time. It combines several variables, such as tidal volume (Vt), driving pressure, flow, respiratory rate, and end-expiratory pressure, into one single parameter, which is expressed in Joules/min. All of these acting mechanical forces could contribute to ventilator-induced lung injury (1, 2). Several studies have shown that a higher MP is independently associated with higher in-hospital mortality and several other important patient-centered outcomes in ICU patients receiving mechanical ventilation (3, 4).

Cressoni et al (5) proposed the concept of MP and derived and validated an algebraic formula for the calculation of MP in patients who are passively ventilated in volume-controlled ventilation (VCV) mode. Van der Meijden et al (6) and Becher et al (7) independently derived and validated equations for pressure-controlled ventilation (PCV) (Equations 2–4 in Measurements). Since then, several authors have described formulas for both VCV and PCV (8, 9).

The reference method for measurement of the MP is to multiply the work of a single breath by the respiratory rate. The work of a single breath is defined as the area between the inspiratory limb of the dynamic pressure-volume (PV) loop and the zero-pressure axis. This area is calculated with numerical integration of PV loop data, which is a complex method and not easy to perform at the bedside.

The challenge in calculating the energy of a breath in PCV is to describe the nonlinear behavior of the flow (in other words, the decelerating flow pattern). This will lead to a nonlinear volume increase with a nonlinear shape of the PV loop (Fig. 1) and depends on the inspiratory pressure, compliance, and resistance (10). On top of that, pressure rise time can be applied in PCV. Depending on the type or brand of ventilator, the default settings of inspiratory rise time vary from 50 to 200 ms. Applying and adjusting for rise time affects the nonlinear path of the inspiratory limb on the PV loop and, thus, the area of the PV loop.

Figure 1.

Graphic representation of the dynamic pressure-volume loop during pressure-controlled ventilation. A, A dynamic pressure-volume (PV) loop showing the three components of mechanical power (MP) in pressure-controlled ventilation. In this case, peak airway pressure (P_peak) is 12 cm H₂O and plateau pressure (P_plat) is 11 cm H₂O. The red dotted line is indicative, not exact. B, The blue and yellow zones represent the real PV loop, which is the MP of a single breath. The blue and orange zones are the MP as calculated with our new equation, using P_plat instead of P_peak (an equal pressure line is at P_plat). The yellow zone is subtracted from the real PV loop, while adding the orange zone. Simplified equation MP = 0.098 · RR · Vt · P_plat. Paw = airway pressure, PEEP = positive end-expiratory pressure, RR = respiratory rate, Vt = tidal volume.

Becher et al (7) ignore the pressure rise time and nonlinear behavior of the inspiratory limb of the PV loop in their simplified equation, resulting in a square-shaped PV loop. This equation is simple and ideally suited for bedside use. However, as they mentioned, this will lead to an overestimation of MP. This overestimation will increase further under conditions where the pressure rise time is not zero.

The comprehensive equation by Becher et al (7) accounts for both pressure rise time and the nonlinear behavior of the inspiratory limb on the PV loop. However, their method is very complicated. Trinkle et al (9) also include the pressure rise time and the path of the inspiratory limb in their comprehensive equation. Van der Meijden et al (6) developed an equation that describes the nonlinear inspiratory limb on the PV loop, not accounting for the pressure rise time.

They all try to mathematically correct the loss of area of the PV loop in PCV (Fig. 1). This should result in accurate and, according to some authors, simple equations to use at the bedside. However, trying to make the most accurate and reliable equation comes at a cost: the equations become more complicated and lose their attraction as a bedside tool.

We addressed this by developing an alternative calculation of the MP in PCV that can be easily used at the bedside. We validated this method comparing it with the measured MP.

METHODS

Study Population

Patients on mechanical ventilation who were admitted to the ICU of the Leiden University Medical Center from January 2021 to May 2021 were eligible for inclusion. Patients could be included if they were 18 years old or older, were mechanically ventilated in a controlled mode, had no spontaneous breathing activity, and if consent was given to use their data by the patient or legal representative. Patients were excluded if they had any spontaneous breathing activity or showed patient-ventilator interactions like reverse triggering.

Measurements

Geometric Method

The MP was calculated from the recorded dynamic PV loop data from the mechanical ventilator (Hamilton C6S; Hamilton Medical AG, Bonaduz, Switzerland). Flow, volume, and airway pressure were recorded on a dedicated data acquisition system (Hamilton Medical AG). Data recording lasted at least 7 minutes to obtain a reliable measurement. Before recording, an inspiratory and expiratory hold maneuver was done to obtain the plateau pressure (P_plat) and total positive end-expiratory pressure (PEEP) for compliance/elastance calculations. MP was calculated from the measured data using MATLAB (Version 2020 b; Natick, MA). The work of a breath is defined as the area between the inspiratory limb of the dynamic PV loop and the zero-pressure axis. This area is calculated with numerical integration from the obtained PV data. The work is multiplied with the frequency per minute to obtain the MP in J/min.

New MP Calculation

The goal was to develop a MP calculation that is both simple to use and minimizes overestimation, that is, as close as possible to the measured values. We hypothesized that the overestimation of MP calculated with the simple method according to Becher et al (7) could be reduced by using the P_plat instead of the peak pressure (Fig. 1). The equation we propose is:

$${\displaystyle \begin{array}{l}{\displaystyle \mathrm{M}{\mathrm{P}}_{\mathrm{P}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}}=0.098\cdot \mathrm{R}\mathrm{R}\cdot \mathrm{V}\mathrm{T}\cdot {\mathrm{P}}_{\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}}}\end{array}}$$ (Eq. 1)

Other Mechanical Power Equations

We compared our equation (MP calculated using P_plat [MP_Pplat], Eq. 1) with the following equations for calculation of the MP: van der Meijden (MP_vdM, Eq. 2), the comprehensive Becher (MP_cB, Eq. 3), the simplified Becher (MP_sB, Eq. 4), and the linear model (MP_LM, Eq. 5).

$${\displaystyle \begin{array}{l}{\displaystyle \mathrm{M}{\mathrm{P}}_{\mathrm{v}\mathrm{d}\mathrm{M}}=0.098\cdot \mathrm{R}\mathrm{R}\cdot \mathrm{V}\mathrm{T}\cdot \{{\mathrm{P}}_{\mathrm{P}\mathrm{E}\mathrm{E}\mathrm{P}}+{\mathrm{P}}_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{p}}\cdot (1-{\mathrm{e}}^{\frac{{\mathrm{t}}_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{p}}}{\mathrm{R}\cdot \mathrm{C}}})\}}\end{array}}$$ (Eq. 2)

$${\displaystyle \begin{array}{l}{\displaystyle \begin{array}{lll}& {\displaystyle \mathrm{M}{\mathrm{P}}_{\mathrm{c}\mathrm{B}}=0.098\cdot \mathrm{R}\mathrm{R}\cdot \{\mathrm{V}\mathrm{T}\cdot ({\mathrm{P}}_{\mathrm{P}\mathrm{E}\mathrm{E}\mathrm{P}}+{\mathrm{P}}_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{p}})-\mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{p}}^2\cdot \mathrm{C}\cdot }& {\displaystyle [0.5-\frac{\mathrm{R}\cdot \mathrm{C}}{{\mathrm{t}}_{\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}}}+{\left(\frac{\mathrm{R}\cdot \mathrm{C}}{{\mathrm{t}}_{\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}}}\right)}^2\cdot (1-{\mathrm{e}}^{-\frac{{\mathrm{t}}_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{p}}}{\mathrm{R}\cdot \mathrm{C}}})]\}}\end{array}}\end{array}}$$ (Eq. 3)

$${\displaystyle \begin{array}{l}{\displaystyle \mathrm{M}{\mathrm{P}}_{\mathrm{s}\mathrm{B}}=0.098\cdot \mathrm{R}\mathrm{R}\cdot \{\mathrm{V}\mathrm{T}\cdot ({\mathrm{P}}_{\mathrm{P}\mathrm{E}\mathrm{E}\mathrm{P}}+{\mathrm{P}}_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{p}})\}}\end{array}}$$ (Eq. 4)

$${\displaystyle \begin{array}{l}{\displaystyle \begin{array}{lll}& {\displaystyle \mathrm{M}{\mathrm{P}}_{\mathrm{L}\mathrm{M}}=0.098\cdot \mathrm{R}\mathrm{R}\cdot \{\mathrm{V}\mathrm{T}\cdot ({\mathrm{P}}_{\mathrm{P}\mathrm{E}\mathrm{E}\mathrm{P}}+{\mathrm{P}}_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{p}})}& {\displaystyle -0.15\cdot \mathrm{\Delta }{\mathrm{P}}_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{p}}^2\cdot \frac{{\mathrm{t}}_{\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}}}{\mathrm{R}}\}}\end{array}}\end{array}}$$ (Eq. 5)

Where C is compliance (L/cm H₂O), R is resistance (cm H₂O/L/s), RR is the set respiratory rate in breaths per minute, Vt is tidal volume in liters, P_plat is plateau pressure expressed in cm H₂O, t_insp is total inspiration time, and t_slope the inspiratory rise time. P_plat was obtained by performing an inspiratory hold maneuver. C was calculated by dividing Vt by the measured driving pressure (P_plat–PEEP). R was measured by the ventilator using the least-square fitting method described by Iotti et al (11).

The reference value of MP (MP_ref) was obtained by using the geometric method, that is, the numerical integration of the area between in inspiratory limb of the PV loop and the zero-pressure axis from the recorded dynamic PV loop data from the mechanical ventilator

$${\displaystyle \begin{array}{l}{\displaystyle \mathrm{M}{\mathrm{P}}_{\mathrm{r}\mathrm{e}\mathrm{f}}=0.098\cdot \mathrm{R}\mathrm{R}\cdot {\displaystyle \underset{{\mathrm{V}}_0}{\overset{{\mathrm{V}}_{\mathrm{T}}}{\int }}}{\mathrm{P}}_{\mathrm{a}\mathrm{w}}\mathrm{d}\mathrm{V}}\end{array}}$$ [5]

Statistics

Data were checked for normality with a Q-Q plot and the Shapiro-Wilk normality test. Continuous data are presented as mean (sd), and categorical data as n (%). Bland-Altman analysis was used to compare the different calculated values with the measured values for all equations, with the limits of agreement set at 95%. Measurements were taken twice in a patient if the ventilator settings were substantially different after a few days. Differences between the calculated MP of our proposed method and the other methods were tested for statistical significance using Student t test with equal variance under the null hypothesis that there was no difference. For the analysis, we used R (Version 4.0.1; R Core Team, Vienna, Austria) and RStudio (Version 1.3.1073; RStudio, Boston, MA).

Ethics

The study was approved by the local monitoring board METC-LDD, protocol nr N20.029, with an approval date of July 17, 2020. Informed consent to use patient data was obtained from the patient or their next of kin. The study was conducted in compliance with the declaration of Helsinki (Version 2013) and according to Good Clinical Practice standards.

RESULTS

MP was measured in 56 cases in 42 patients; 40 patients had COVID-19 as an admission diagnosis, one patient was diagnosed with sepsis, and one patient was admitted for postoperative care after cardiac surgery. Measurements were taken twice in a patient if the ventilator settings were substantially different after a few days. In Table 1, patient characteristics and basic measurements are shown. Data were normally distributed. The mean MP of the different methods and reference method are described in Table 2. The mean reference MP was 20.9 J/min (se, 0.8 J/min). Table 2 shows that all methods show excellent correlation with high coefficient when compared with the reference method (r² = 0.94 to 0.99).

TABLE 1.

Patient Characteristics and Basic Ventilator Measurements

Characteristic	n = 56
Female	18 (31.0%)
Age (yr)	62.89 (9.97)
Height (cm)	175.69 (9.81)
Weight (kg)	95.09 (21.41)
Body mass index (kg/m2)	30.88 (7.17)
Ideal body weight (kg)	69.90 (9.99)
Sequential Organ Failure Assessment score	8.55 (2.39)
Respiratory rate (breaths/min)	22.10 (4.42)
Total inspiration time (s)	1.03 (0.23)
Positive end-expiratory pressure (cm H2O)	12.28 (2.97)
Compliance (mL/cm H2O)	36.89 (12.59)
Inspiratory tidal volume (mL)	404.31 (88.56)
Inspiratory resistance (cm H2O/L/s)	11.25 (2.53)
Peak pressure(cm H2O)	26.43 (3.67)
Plateau pressure (cm H2O)	23.90 (3.59)
Peak inspiratory flow (L/min)	42.27 (6.81)
Driving pressure (cm H2O)	11.62 (2.54)

Data are presented as mean (sd) for continuous variables and n (%) for categorical variables.

TABLE 2.

Mechanical Power Measurements and Statistical Calculations

Measurement	Estimate	95% CI
MP reference method, mean (sd)	21.1 (6.5) J/min	19.4–22.8 J/min
MP van der Meijden, mean (sd)	21.9 (6.4) J/min	20.2–23.6 J/min
Correlation coefficient, r2	0.940
Bias	–1.0 J/min	–1.1 to –0.5 J/min
95% Limits of agreement	–3.8 to 1.9 J/min
MP comprehensive Becher, mean (sd)	22.9 (7.2) J/min	21.1–24.8 J/min
Correlation coefficient, r2	0.989
Bias	–1.9 J/min	–2.1 to –1.6 J/min
95% Limits of agreement	–3.7 to 0.0 J/min
MP simplified Becher, mean (sd)	23.5 (7.2) J/min	21.6–25.4 J/min
Correlation coefficient, r2	0.987
Bias	–2.4 J/min	–2.7 to –2.1 J/min
95% Limits of agreement	–4.5 to –0.3 J/min
MP linear model, mean (sd)	23.0 (7.1) J/min	21.1–24.8 J/min
Correlation coefficient, r2	0.989
Bias	–1.9 J/min	–2.1 to –1.6 J/min
95% Limits of agreement	–3.7 to –0.1 J/min
MP calculated using plateau pressure, mean (sd)	20.9 (6.2) J/min	19.3–22.5 J/min
Correlation coefficient, r2	0.936
Bias	0.2 J/min	–0.2 to 0.5 J/min
95% Limits of agreement	–3.1 to 3.4 J/min

MP = mechanical power.

MP measurements for the reference method and the five equations, including correlation coefficient, bias, and CIs for mean values and biases.

Bland-Altman analysis (Fig. 2) showed the largest bias for the simplified Becher method with a bias of –2.4 and limits of agreement between –4.5 and –0.3. Our proposed equation had a bias of 0.2 with limits of agreement between –3.1 and 3.4 J/min.

Figure 2.

Bland-Altman plots showing the differences between mechanical power (MP) measured and MP calculated using the equations for estimating MP in pressure-controlled ventilation. For Bland-Altman plot of the comprehensive Becher equation, see e-supplement (http://links.lww.com/CCX/B477). MP_Pplat = mechanical power calculated using plateau pressure.

In our dataset, we observe that up to an inspiratory resistance of 16 L/cm H₂O/s and a difference between peak pressure and P_plat up to 8 cm H₂O, the percentage bias of the formula from the measured values does not exceed 11%. See e-supplement (http://links.lww.com/CCX/B477) for plots of the influence of inspiratory resistance on percentage error for all equations.

DISCUSSION

We propose a very simple and reliable method to calculate the MP in a patient ventilated in PCV mode. Our method can be easily used at the bedside and is available for everyone who can measure a P_plat.

From a thermodynamic perspective, the work of a breath is pressure times volume. This is exactly the simplified method described by Becher et al (7). It is, however, not precise. The simplified equation from Becher et al (7) ignores both the behavior of the shape of the inspiratory limb on the PV loop and the rise time, resulting in a square-shaped PV loop. This will always lead to an overestimation of MP. In thermodynamics, it is paramount to consider the path of the PV loop, which is, in PCV ventilation, characterized by nonlinear behavior.

Van der Meijden et al (6), Becher et al (7) (comprehensive), and recently Trinkle et al (9) try to mathematically describe the path of the inspiratory limb on the PV loop to improve the accuracy of their equation. Van der Meijden et al (6) does not take into account the inspiratory rise time, while the other two equations add a correction for the set rise time. From our data, it is clear that these methods fall short in comparison with the reference method. The mathematical descriptions of the thermodynamic behavior, although correct from a theoretical point of view, is still not accurate enough.

On top of that, adding correction factors to the equations will lead to an increase in complexity or an addition of several assumptions, which do not lead to more accuracy. Furthermore, using the calculated values generated by the ventilator may also lead to a reduced accuracy and precision. The complexity of these equations limits their use as bedside tool.

By using the P_plat instead of the peak pressure, the area of the calculated PV loop is corrected to a certain extent (Fig. 1). This applies to the dataset we used, where all patients were ventilated with an inspiratory rise time of 50 ms. Using a shorter inspiratory rise time will result in a greater area of the PV loop; thus, the equation will underestimate MP. On the other hand, using a longer rise time will lead to an overestimation of MP. The extent, to which the equation differs when a shorter or longer rise time is applied, is unknown.

Our proposed method had a bias around zero compared with the reference method but wider limits of agreement than the simplified Becher method. With our method, in this patient population, the maximum difference between the bias and the limits of agreement is 3.4 J/min. It is, however, important to acknowledge that the exact threshold value of MP has not yet been defined.

Association between MP and important clinical outcomes remains unclear. Furthermore, in these association studies, calculation methods were used, that is, derived methods, and not the geometric method, to estimate the MP (3).

One of the limitations of the study is the nonheterogeneous study population. We almost exclusively included COVID-19 patients with severe lung disease. It is not known if our conclusion holds in patients with different severity of lung disease.

Another point is that very high inspiratory resistance can inaccurately affect the calculation of MP with our proposed equation. This is because inspiratory resistance and inspiration time affect the Pplat. In our dataset, we observe that up to an inspiratory resistance of 16 L/cm H₂O/s and a difference between peak pressure and P_plat up to 8 cm H₂O, the percentage bias of the formula from the measured values does not exceed 11% (e-supplement, http://links.lww.com/CCX/B477).

We must emphasize that our conclusions are only valid in patients ventilated with PCV. The MP of patients ventilated with VCV with a constant flow, or other forms in which the flow is controlled, cannot be calculated with any of the methods described in this article, including the MP_Pplat.

Furthermore, the current study includes a small sample size. Future research is needed before it can be widely applied in clinical practice. First, it should investigate a meaningful correlation between the equations and the reference method in a larger cohort. Second, it should investigate exact thresholds for MP, the impact of the different components of MP, and key clinical outcome measures.

CONCLUSIONS

We propose a method for calculating MP that is simple to use and can be performed at the bedside. It compares well with the reference method for calculating MP, the geometric method.