We used two data sets of invasively mechanically ventilated children with and without lung injury [16]. The need for consent for the first study was waived by the Institutional Review Board (IRB) of the University Medical Center Groningen [16]. In this study recordings were made of the ventilator flow-time, pressure-time and oesophageal pressure-time scalar. The second study was approved by the IRB (NL46097.042.13), and written informed consent was obtained from the parents or legal caretakers. For this study recordings were made of the ventilator flow-time, pressure-time and the electrical activity of the diaphragm. Anonymous data from both studies were aggregated for the analyses presented here.

Both data sets included prospectively collected 30-minutes recording (Jan – Nov 2018 and Feb – July 2015) from patients < 18 years [16]. Because during respiratory entrainment patient’s breathing frequency matches an external stimulus only patients able to trigger the ventilator were included. Patients with congenital or acquired neuromuscular disorders, severe traumatic brain injury (i.e., Glasgow Coma Score < 8), uncorrected congenital heart disorder, chronic lung disease and severe pulmonary hypertension were excluded. In addition for this secondary analysis data from subjects who were on a ventilation mode without a set mandatory ventilator breath rate (i.e., a continuous spontaneous ventilation [CSV] mode) were excluded.

The aggregate data included anonymized patient characteristics (age, gender, weight, admission diagnosis), ventilator settings (mode, pressure above PEEP (PAP), PEEP, mean airway pressure (Pmean), pressure support (PS), expiratory tidal volume (Vte ml/kg, actual bodyweight), set mandatory breath rate, inspiratory time and fraction of inspired oxygen (FiO2), and oesophageal pressure), and clinical characteristics; prior use of neuromuscular blockade (NMB) for moderate/severe acute respiratory distress syndrome (ARDS), amount of analgesia-sedation in the 4 h preceding the recording, Comfort B score as marker of patient comfort, endotracheal tube (ETT) size and percentage of ETT leakage [17, 18]. If ETT leakage exceeded 18% patients were excluded. All patients were ventilated with one type of ventilator (Avea, Vyaire Medical, Yorba Linda, USA). In patients < 15 kg a proximal flow sensor was used. Ventilator data were acquired through the Ventilator Open XML Protocol (VOXP) interface at a sampling rate of 100 Hz. The electrical activity of the diaphragm (EAdi) was measured through transcutaneous recording of the electromyographic diaphragm signal (dEMG) (and other respiratory muscles i.e., the intercostal and abdominal muscles) at a sampling rate of 500 Hz using the Porti (TMSi, Oldenzaal, The Netherlands) using one pair of Ag/AGCl electrodes (EasyTrode TM Pre gelled Electrodes, Multi Bio Sensors Inc, El Paso, USA) bilaterally placed at the costo-abdominal margin at the nipple line for the dEMG. Data acquisition and analysis was peformed using Polybench (Applied Biosignals GmbH, Weener, Germany) and Matlab R2018a (Mathworks, Natick, MA, USA).

Definition of entrainment, neural breathing frequency, entrained and non-entrained reverse triggering

We applied previously published definitions of entrainment and RT [1, 6,7,8, 19]. Briefly, RT was defined as a patient effort after the start of a time triggered mandatory breath, either displaying a regular pattern (i.e., entrained RT) or as a single event (i.e. non-entrained RT) (Fig. 1D and F). Pattern of entrained RT could occur in a 1:1, 1:2 or in 1:3 ratio, thus one time triggered mandatory breath followed by a patient effort, one out every two time triggered mandatory breaths followed by one patient effort or one out every three time triggered breaths followed by one patient effort. We considered entrained RT if there were four or more consecutive RT breaths [19]. During respiratory entrainment the patient breathing frequency matches an external stimulus creating a fixed patient respiratory rhythm. Due the nature of this fixed rhythm, breathing variability, of both patient triggered and reverse triggered breaths, during respiratory entrainment will be lower compared to the breathing variability during normal spontaneous breathing [6,7,8,9]. To express the degree of entrainment (i.e. loss in breathing variability) the coefficient of variation calculation (CoV) is used. This statistical measure us used to assess the relative variability and is expressed as a percentage (standard deviation/mean*100). The time interval (sec) of the breathing cycle and CoV were calculated for time triggered mandatory breaths (TTOTMECH), patient triggered (TTOTNEU) and RT breaths [1]. CoV < 15% was considered as respiratory entrainment [9]. For each entrained RT breath, non-entrained RT breath, and patient triggered breath, we calculated phase angle and its CoV. Examples of phase angle, breathing, CoV for each type of breath and used definitions are described in Fig. 1; Table 1. To determine the characteristics of patient triggered and entrained RT breaths, we calculated for each single breath tidal volume (Vte), oesophageal pressure-time-product (PTP), delta oesophageal pressure (ΔPes), integrated EAdi signal (dEMGINT) and amplitude from the EAdi (ΔdEMG) signal. PTP was calculated by integrating the area under the oesophageal pressure versus timetracing form the beginning until the end of inspiration [20].

Definition of reverse triggering with breath stacking

To detect RT with breath stacking, all double triggering events were manually annotated. Double triggering was defined as two consecutive ventilator cycles separated by a short expiratory time, i.e., half of the inspiratory time or less [21]. Each double triggering event was labeled as patient-triggered or as a ventilator initiated (Table 1).

Data selection and analysis

First, we screened the full 30-minute recordings for stable RT events (Fig. 2). If detected up to five stable reverse triggering patterns per recording were randomly selected. To identify differences in breaths characteristics for each individual patient, if available, an equal number of patient triggered, entrained RT triggered and time triggered mandatory breaths were used for analytical purposes.

To study the occurrence of single non-entrained RT and neural mechanical coupling, we only analyzed data from patients with dEMG-recordings. Patients with entrained RT events were excluded. These patients were screened for non-entrained RT events. Patients with merely oesophageal pressure measurements were excluded because these measurements reflects patient effort and does not provide information about neural expiratory timings. Among these patients, we used a randomly selected five minute tracing to estimate the occurrence of non-entrained RT. The time between each neural effort (i.e., effective, and ineffective efforts) was determined to calculate neural breathing frequency. By using our previous validated algorithm each breath was classified as time triggered mandatory, patient triggered, ineffective, double triggering or non-entrained RT [22]. In addition, breaths were manually annotated as breath after a mandatory time triggered breath and before and after non-entrained RT breath. For each patient the percentage of RT breaths was calculated.

Statistical analysis

The Shapiro-Wilk test was used to test for normal distribution. Normally distributed continuous data are presented as mean and SD. When the assumption of normality was not met, data are presented as median and 25–75 interquartile range (IQR). Categorical data are presented as percentage (%) of total. When comparisons between groups were made, continuous data were analyzed using the Mann-Whitney U test. Spearman’s rank correlation coefficient was used to calculate the correlation between two variables. Statistical analysis was performed with statistics software (IBM SPSS Statistics 27, IBM, Armonk, USA). P values below 0.05 were considered statistically significant.