Data are presented as n or mean±sd. CMV: conventional mechanical ventilation; HFV: high-frequency ventilator; F_I,O2: inspiratory oxygen fraction; P̄_aw: mean airway pressure; ΔP: oscillatory pressure amplitude; P_a,O2: arterial oxygen tension; MOF: multiple organ failure; P̄_tr: mean tracheal pressure. ^#: total number of patients treated with HFO-TGI; 19 and 19 patients received intermittent HFO-TGI for ≤3 and ≥5 days, respectively. ^¶: total number of patients treated with HFO-TGI and then returned to CMV, after fulfilling the criteria for weaning from HFO-TGI (see Methods section and fig. 1). ⁺: total number of patients treated with CMV alone because they did not fulfil the criterion for return to HFO-TGI (see Methods section and fig. 1). ^§: on days 2, 4, 5 and 9, five patients (one still on HFO-TGI and four on post-HFO-TGI CMV) died of MOF after achieving P_a,O2/F_I,O2 >150 mmHg during their last HFO-TGI session; within days 5–9, six patients died (four of MOF, one of hypoxaemia and one of a iatrogenic pneumothorax not related to any study protocol intervention) while still on HFO-TGI and without achieving P_a,O2/F_I,O2 >150 mmHg during that particular HFO-TGI session (see eResults section in the online supplementary material). ^ƒ: 124 (55.6%), 65 (29.1%) and 34 (15.2%) out of 223 of HFO-TGI sessions lasted <8, 8–18 and >18 h, respectively; in 16 patients, the maximum uninterrupted use of HFO-TGI ranged from 30.1–102.2 h; 177 (79.4%) out of the 223 sessions were administered to all 61 (100%) patients on days 1–4; after the morning of day 5, the remaining 46 (20.6%) sessions were administered to 19 (31.1%) patients. ^##: HFV-set F_I,O2 averaged over the duration of the daily HFO-TGI sessions; actually delivered F_I,O2 was further increased by the use of 100% oxygen flow TGI; HFV F_I,O2 was set at 100% during 1) the recruitment period, 2) the application of the additional recruitment algorithm (fig. 1) and 3) the 15-min periods preceding and 5-min periods corresponding to the physiological measurements of the stabilisation period. ^¶¶: parameter value averaged over the duration of daily HFO-TGI. ⁺⁺: average pressure drop determined by measuring the P̄_tr just prior to TGI initiation and after TGI discontinuation (see Methods section, fig. 1 and the eResults section in the online supplementary material); pressure drop ranged from 2.0–10.4 cmH₂O depending on tracheal tube size, HFO frequency and ΔP, and presence of secretions; recent data [8] showed that under similar HFV settings and tracheal tube cuff leak conditions, the addition of a TGI flow similar to that used in the present study results in an average increase of 1.5 cmH₂O in P̄_tr (see online supplementary material). ^§§: eight patients were already tracheotomised before study entry, whereas a further five patients were tracheotomised during the study intervention period; during 176 (78.9%) out of the 223 HFO-TGI sessions, 53 (86.9%) out of the 61 patients were ventilated through orotracheal tubes (inner diameter 8.19±0.30 mm, range 7.50–9.00 mm); during 47 (21.1%) out of the 223 HFO-TGI sessions, 13 (21.3%) out of the 61 patients were ventilated through tracheostomy tubes (inner diameter 8.58±0.11 mm, range 8.00–9.00 mm). ^ƒƒ: 50.6±2.2% (range 45.0–55.2%) of the minute ventilation of the pre-session CMV; TGI flow ranged 4.5–8.5 L·min⁻¹.