## Participants

Patients were included prospectively as part of our day hospital evaluation for moderate to severe OSAS. The evaluations performed during the hospitalization were: clinical examination with collection of height, weight, neck circumference, oral examination, lung function tests, ear, nose and throat (ENT) examination by an otolaryngologist (IB) together with a measurement of nasal obstruction (acoustic rhinometry) and study of ventilatory control using a recording of tidal ventilation.

The inclusion criteria were symptoms suggestive of OSAS (snoring, apnea, restless sleep, oral breathing) and an AHI ≥ 5/h in otherwise healthy children 3 to 18 years of age (asthma included) with or without obesity. Non-inclusion criteria were midface deficiency, marked mandibular hypoplasia, prematurity (based on a report of birth at least four weeks early), genetic disorders and ongoing treatment for OSAS. This study conformed to the standards set by the latest revision of the *Declaration of Helsinki* and was approved by the Ethics Committee of Robert Debré University Hospital (study registration identity PHENOSAS: N° 2018 − 416), and the database of collected data was declared to the French regulatory agency (CNIL). The subjects and their parents were informed of the collection of their prospective data for research purposes, and they could request to be exempted from this study in accordance with French law (non-interventional observational research).

All recordings were performed on the day of ENT examination during an in-hospital stay, during the morning before the ENT examination. Recordings of tidal breathing were performed as previously described 30, lasting 20 min, with the first 5 min being discarded. During the recordings, subjects were awake and sitting in a calm and non-stimulating atmosphere. Flow rate, end-tidal PO2 (PETO2) and end-tidal PCO2 (PETCO2) were continuously monitored, and signals were digitized using the MP-100 system (Biopac System Inc., Santa Barbara, CA) at a rate of 50 Hz; these were stored for further analysis.

**End-expiratory CO**2 slope

The quality of the end-tidal CO2 slope is important to take into account when considering its ability to reflect alveolar CO2 31. We proposed a method for the calculation of a corrected expiratory slope (see Supplementary Information). This procedure permitted to search for outliers corresponding to subjects that could have performed poorly the tidal breathing recording.

**Loop gain model**

We used a constrained bivariate (minute ventilation (\({\dot{\text{V}}}_{\text{e}}\)) and PETCO2) analytical model that allowed to calculate the components of CG and PG (steady-state gains, time constants of the gains and circulatory delays) 30.

Briefly, the plant that describes the relationship between ventilation and alveolar PCO2 (PACO2) is modelled as a first order time delay system with a gain (called steady-state plant gain PG0) and a time constant (τp, which represents the time it takes for a PACO2 to reach 63% of its final value after a step change in ventilation).

(1) , where s denotes the frequency.

The “controller” describes the relationship between PaCO2 and ventilatory drive that equals ventilation in awake subjects. In this model, the controller is modelled using a static gain (CG0, or steady-state controller gain) and a time constant (τc). Changes in PACO2 are delayed by approximately 6 seconds before reaching the peripheral chemoreceptors. Delays in the time domain are modelled as exponentials in the frequency domain, hence:

(2) , where PaCO2 is the arterial PCO2 in the vicinity of the chemoreceptors and D is the delay.

Thus, this model contained five parameters only (PG0, CG0, τp, τc, and D).

By definition, PG0 should be negative and CG0 positive valued, hence a condition of model fit failure was the observation of non-physiological gain values.

The model was fitted on the changes from baseline (mean) levels of the ventilatory parameters (\({\dot{\text{V}}}_{\text{e}}\)and PETCO2) that were obtained from tidal breathing measurements while awake and thus the analyses were specifically related to chemosensitivity. Since the medium frequency band (corresponding to oscillations of 5–15 breaths/cycle) spans the range of cycle durations of periodic breathing observed experimentally, we focused on this frequency range as previously done 30.

**In-laboratory polysomnography**

Polysomnography studies were performed overnight. An Alice 6 LDx polysomnography system (Philips, Murrysville, PA) recorded the following parameters: chest and abdominal wall motion using respiratory inductance plethysmography, heart rate by electrocardiogram, arterial oxygen saturation by pulse oximetry, airflow using a 3-pronged thermistor, nasal pressure by a pressure transducer, electroencephalographic leads (C3/A2, C4/A1, F3/A2, F4/A1, O1/A2, O2/A1), left and right electrooculograms, submental electromyogram, and tibial electromyogram. Study participants were also recorded with an infrared video camera. Experienced pediatric sleep physician scored patients using standard pediatric sleep scoring criteria 32. The definition of moderate to severe OSAS was sleep disorder breathing symptoms and an apnea hypopnea index (AHI) ≥ 5 episode/h10.

**Sleep Questionnaires**

We used standard sleep questionnaires for the clinical evaluation of the study population. The modified Epworth Sleepiness Scale was used for the evaluation of excessive daytime sleepiness 33. Hyperactivity/inattention related symptoms were evaluated by the Conners' abbreviated teacher rating scale (CATRS-10) that was completed by a parent 34. Sleep-related breathing symptoms were assessed by the Brouillette questionnaire 35 and the Spruyt-Gozal questionnaire in its validated French-translation version 36.

**Pulmonary function tests**

Impedance of the respiratory system was measured using an impulse oscillatory system (IOS: Master Scope Body, Carefusion Technologies, Yorba Linda, California, USA), as previously described 37. We used the following IOS variables: resistance and reactance at 5, 10, 15, 20, 25, 30 and 35 Hz. Since OSAS may be an independent risk factor for small airway disease 9, we used an additional lung model to characterize this small airway disease.

We used the extended Resistance-Inertance-Compliance model (eRIC) capable of accounting for significant frequency dependence of the respiratory impedance, which has previously been described 37,38. In eRIC (Fig. 2A), R is partitioned in central (Rc) and peripheral (Rp) resistance of the respiratory system, while CRS is the compliance of the respiratory system (including parenchymal and conducting airways compliances). The model was fitted to the impedance data (5–35 Hz) and the minimization of a performance index allowed the calculation of model parameters, as previously done38. We used the corrected Akaike information criterion to evaluate the goodness of fit of the eRIC model on this particular data set 37.

In all subjects we measured functional residual capacity (FRC) by gas dilution according to American Thoracic Society guidelines 39. Z scores for FRC were computed with Cook and Herman reference equations for children 40. Z-scores of IOS variables were calculated according to Gochicoa-Rangel et al. 41.

**ENT examination**

All patients were assessed by an otolaryngologist with endoscopic nasal examination as standard of care for moderate to severe OSAS clinical evaluation. Fiber endoscopy was performed with a flexible endoscope after local anesthesia using lidocaine chlorhydrate 10%. Nasal obstruction was defined as obstruction from large adenoids (grade 3 or 4 according to Cassano et al.42) or turbinate hypertrophy. Oropharyngeal obstruction was defined as presence of obstructive tonsils (grade 3 or 4 according to Brodsky et al 43). The ENT specialist was blinded for the results of rhinometry.

**Acoustic rhinometry**

The measurements were conducted with the EccoVision Acoustic Rhinometer (E. Benson Hood Laboratories, Pembroke, MA) in the supine position after they were in this position for 5 min, as previously described 44. The volume of the nasopharynx was recorded and was corrected for height to obtain a normalized parameter. The calculated nasal resistance given by the apparatus (from nostril to nasopharynx) was also recorded. Nasal airway resistance was determined for each side of the nose and the total resistance calculated using Ohm’s law equation for parallel resistors: 1/RT = 1/Rr + 1/Rl, where RT is the total nasal resistance, Rr = nasal resistance on the right side, Rl = nasal resistance on the left side.

## Statistical analysis

We decided to conduct a multivariate analysis with at most five factors, one factor per dimension explored. These factors include two anthropometric factors, namely height and body mass index (BMI) z-score, one factor from ENT examination, one factor from lung function tests and one factor from polysomnography data. To perform a multivariate analysis with at most five factors, the sample size of OSAS cases would have to be ∼50 subjects (10 subjects per factor).

Results were expressed as medians [25th – 75th percentiles]. Groups were compared by means of Wilcoxon test or Kruskal–Wallis test, as appropriate. Subsequent intergroup comparisons were performed using Dunn test for multiple comparisons and p-values adjusted with the Benjamini-Hochberg method. Correlations were evaluated using Pearson's correlation coefficient. Additional statistical analyses are described in the text. A P value < 0.05 was deemed significant. No correction for multiple testing was done due to the pathophysiological design of the study 45. All statistical analyses were performed with R software version 4.1.0.