A prospective cohort was included from the mixed ICU of Medisch Spectrum Twente, a tertiary referral hospital in Enschede, the Netherlands. The protocol was approved by the medical ethical committee of Arnhem-Nijmegen, the Netherlands (CCMO-number NL75951.091.21), and registered in the Dutch Trial Register (NL9654). Written informed consent was obtained from the patients’ legal representatives. Patients were eligible if aged ≥ 18 years, invasively ventilated for at least 48 h, and ventilated in pressure support mode (SPN-CPAP/PS, Drägerwerk AG & Co. KGaA, Lübeck, Germany) with a FiO2 ≤ 60%, a SpO2 ≥ 90%, and a Richmond Agitation and Sedation Scale (RASS) score ≤ 0. Exclusion criteria were a BMI > 30 kg/m2 at ICU admission, a persistent pneumothorax, a history of neuromuscular disease, or pregnancy. The BMI criterion was set, as obesity adds to the complexity of acquiring adequate signal-to-noise ratios in diaphragmatic sEMG data [9].

sEMG was measured with pre-gelled Ag/AgCl electrodes (3M™ Red Dot™ 2560 electrodes, 3M Deutschland GmbH, Neuss, Germany) connected to actively shielded electrode cables (TMSi, Oldenzaal, the Netherlands). Diaphragmatic sEMG (sEMGdi) measured at the eighth intercostal space in the right anterior axillary line. An ECG lead was recorded from the sternal angle to the lower costal margin in the mid-axillary line for QRS complex detection. The skin was cleansed with alcohol before electrode application. EMG and ECG signals were acquired with a Mobi-6 device (TMSi, Oldenzaal, the Netherlands) with bipolar channels (12.2 nV/bit, amplification factor: 19.5) at a sample rate of 2048 Hz using the TMSi MATLAB interface. Airway pressure (Paw), flow (F) and volume (V) tracings from the Dräger Infinity V500 ventilator (Drägerwerk AG & Co. KgaA, Lübeck, Germany) were acquired at 100 Hz through the ventilator’s RS232 interface.

Measurements were performed every other weekday, as long as the patient still met the inclusion criteria. Measurements could be called off for medical reasons at the discretion of the attending physician. An incremental PEEP trial was performed based on the clinically set PEEP, with levels according to the protocol in Table 1. Other ventilator settings were maintained as dictated by routine clinical care.

Each PEEP step started with an adaptation phase of at least 5 min [9], extended up to 10 min in case of coughing or movement artefacts. Three spontaneous inspiratory efforts against an occluded airway (Pocc) were recorded, alternated with non-occluded breaths to resume a regular breathing pattern. Awake patients were instructed to continue quiet breathing during the end-expiratory occlusions. Additional Pocc measurements were performed in case of observable movement artefacts in the raw sEMG tracings, e.g., due to coughing or non-respiratory movements.

sEMG signals were pre-processed using the ReSurfEMG [10] library as described in more detail in Additional Files 1 and 2. The sEMG signals were bandpass filtered using a 20–500 Hz third order Butterworth filter. QRS-complexes were detected in the ECG lead and eliminated by gating with a window of 100 ms. The sEMGdi envelope, representing the electrical activity of the diaphragm (sEAdi), was calculated using a moving 200 ms RMS filter. The gating procedure was applied twice to the datasets of patients 7 and 16, because of the occurrence of two prominent ECG peaks resulting from a bundle branch block and a paced rhythm, respectively.

Occluded breaths were automatically detected in the Paw channel as negative deflections relative to the set PEEP. The corresponding diaphragmatic activity peaks were identified from sEAdi. Respiratory muscle pressure output and neural activation during Pocc were calculated as the area under the curve relative to a moving baseline, resulting in a pressure–time-product over Pocc (PTPocc) and electrical-time-product over sEAdi (ETPdi). Moving baselines for both sEAdi and Paw were calculated by applying a moving 33rd percentile filter over a centralised window of 5 s with a step size of 200 ms as adapted from [6].

sEAdi recordings showing no respiratory activity were manually excluded. If multiple inspiratory efforts occurred within one end-expiratory occlusion, only the first occluded breath was included in the analysis. All PEEP trials having at least one adequate PTPocc and ETPdi value at each PEEP level were included in the statistical analysis. To allow for between-trial comparison in the absence of a maximal voluntary manoeuvre [8], PTPocc and ETPdi values were normalised relative to their median values at a PEEP of 9 cmH2O, as a PEEP of 9 cmH2O occurred in all PEEP trials (Table 1). Normalised NMCdi was calculated from the normalised PTPocc and ETPdi values:

$$}_} =\frac}_,\text}}}_,\text}}$$

(1)

Upon visual inspection, a subset of Pocc and sEAdi peaks showed physiologically improbable characteristics (Fig. 1C), introducing large uncertainty in the calculated PTPs and ETPs. Moreover, high baseline variability resulted in ill-behaved on- and offset detection in some traces (Fig. 1B). Therefore, the moving baseline and parameter calculation algorithms were improved relative to Graßhoff et al. [6] (Fig. 1B, Additional Files 1 and 2), and advanced waveform analysis was performed to assess NMCdi quality, assigning tolerant and strict criteria (Fig. 1C and Table 2). The sEAdi baseline was calculated over a 7.5 s window and amplified relative to its variance in the same window, and the PTPs and ETPs were supplemented with the area under the baseline (Fig. 1C.ii). Pocc peaks were excluded if they showed abrupt or irregular cessation of the inspiratory effort (Fig. 1C.i). sEAdi peaks were excluded if the interpeak interval of the peaks (Tdi) closely resembled the inter-beat interval of the heart (THR), or if the sEAdi peaks had a substantial area under the baseline (AUB) or a low signal-to-noise ratio (SNR, Fig. 1C.ii). sEAdi peaks that differed from a bell-shape were also excluded (Fig. 1C.iii). A detailed description of these post-processing steps is provided in Additional Files 1 and 2.

Quality criteria – A. Example of an included manoeuvre, B. Baseline crossing detection, C. Quality assessment of the i. occlusion manoeuvre (Pocc) morphology, ii. sEAdi signal-to-noise ratio (SNR) and area under the baseline (AUB), and iii. sEAdi peak morphology

Data were analysed as median (interquartile range, IQR) unless stated otherwise. The effect of PEEP on NMCdi (Eq. 1) was examined using Generalised Estimating Equations (GEE) in SPSS (v. 28.0, IBM, Chicago, IL, United States) using those PEEP trials that had at least one adequate data point at each PEEP level (PTPocc and ETPdi). GEEs correct for the clustered nature of the data by estimating more robust standard errors of the regression coefficients. The effect of PEEP on NMCdi, after updating the moving baseline and applying the tolerant and strict cut-off criteria (Fig. 1C, Table 2), was assessed accordingly. P < 0.017 was considered significant, resulting from an original α of 0.05 with a Bonferroni correction for repeated testing. The effect of the exclusion criteria on repeatability and data quality was assessed according to the coefficient of variation (CoV) of NMCdi. CoV was calculated as:

$$\text= \frac}_}}}}\text },$$

(2)

with MSEw the mean sample variance of NMCdi expressed as the within group mean squared error, and \(\overline}\text\) the grand mean of NMCdi, both calculated over all included PEEP levels.