Respiratory mechanics modifies the impact of ventilator settings on clinical outcome in patients with acute brain injury

Abstract

Purpose

To investigate whether respiratory system elastance (E_RS) modifies the associations of tidal volume (V_T) and respiratory rate with clinical outcomes in mechanically ventilated patients with acute brain injury.

Methods

In this post hoc analysis of the VENTIBRAIN study, E_RS was computed as the ratio of driving pressure (ΔP) to V_T/PBW. Effect modification by E_RS on outcome associations was assessed.

Results

In 1158 patients, V_T was similar across E_RS tertiles (median 7.9, 7.6 and 7.1 mL/kg), resulting in a marked ΔP gradient across tertiles (median 5, 9, and 12 cmH₂O). Higher V_T was associated with lower ICU mortality in patients with low E_RS (OR 0.52, 95%CI 0.36–0.74) but not in those with high E_RS (OR 1.16, 95% CI 0.89–1.51; P_int < 0.001). Higher respiratory rate was associated with worse outcomes, particularly at low E_RS, with the association attenuating at higher E_RS. The Bayesian optimal V_T/PBW decreased continuously with E_RS, from 11.4 mL/kg at E_RS 0.5 cmH₂O/(mL/kg) (≈ ΔP 6 cmH₂O) to 4.4 mL/kg at E_RS 2.5 cmH₂O/(mL/kg) (≈ ΔP 11 cmH₂O), while the optimal respiratory rate increased from 15 to 19 breaths/min. At constant alveolar ventilation, 1-cmH₂O ΔP increase had comparable prognostic impact to ≈ 3 breaths/min respiratory rate increases. These results were consistent irrespective of ARDS diagnosis.

Conclusions

The impact of ventilator settings is modulated by E_RS. A physiological framework for V_T adjustment could consider ΔP along with the respiratory rate required to maintain isocapnia, with outcome effects governed by a trade-off of ≈ 3 breaths/min per 1-cmH₂O change in ΔP.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1007/s00134-026-08562-8.

Take-home message

In mechanically ventilated patients with acute brain injury, respiratory system elastance modifies the impact of ventilator settings: higher tidal volume is associated with lower mortality when elastance is low, but not when elastance is high. Tidal volume associated with the best outcome falls continuously as respiratory system elastance rises, from ~11 to ~4 mL/kg PBW, irrespective of ARDS diagnosis. Ventilator settings could be individualized on respiratory mechanics rather than set at a fixed target, balancing driving pressure reduction against the respiratory rate required to maintain isocapnia — a trade-off of approximately 3 breaths/min per 1 cmH2O of driving pressure.

Background

Low tidal volume (V_T) ventilation, originally proposed to prevent ventilator-induced lung injury in the acute respiratory distress syndrome (ARDS) [1–3], has shown mixed effects in broader populations [4–8]. Patients with acute brain injury have been excluded from major trials due to the need for precise PaCO₂ control to manage cerebral perfusion and intracranial pressure [9–11].

A recent randomized trial in patients with acute brain injury without ARDS showed that reducing V_T to 6 mL/kg may be neutral, or even detrimental, in terms of clinical outcome [12]. This may indicate that the effects of V_T depend on the broader ventilatory context, including the need for compensatory increases in respiratory rate to maintain PaCO₂ within a safe range [13]. These results raise the question of whether patient-level respiratory mechanics, rather than a fixed-V_T target, should guide ventilatory management.

In a recent large observational study (VENTIBRAIN) [14, 15], patients ventilated with higher V_T had better outcomes. However, higher driving pressure (ΔP) was associated with increased mortality. These findings may appear paradoxical at first glance, since ΔP is mathematically linked to V_T [16, 17]. However, ΔP also depends on respiratory system elastance (ΔP = V_T × E_RS), meaning that the same V_T may generate substantially different ΔP according to heterogeneous E_RS. These findings may reflect heterogeneity in E_RS across the VENTIBRAIN study population, which would be consistent with data indicating that E_RS modulates the impact of V_T on clinical outcome in ARDS [18]. These interactions may also help explain the U-shaped association observed between respiratory rate and outcomes, as the trade-off between V_T and respiratory rate at constant alveolar ventilation may shift depending on E_RS.

In this secondary analysis of the VENTIBRAIN study, we assessed whether E_RS modifies the associations of V_T and respiratory rate with clinical outcomes in patients with acute brain injury, and whether the V_T associated with the lowest mortality differs across levels of E_RS.

Methods

Study design and population

This is a secondary analysis of the VENTIBRAIN study, a prospective multicenter observational cohort that enrolled 2095 mechanically ventilated adults with acute brain injury across 74 intensive care units (ICU) in 26 countries between November 2020 and October 2023. The study design, inclusion and exclusion criteria, data collection procedures, and ethical approvals have been described elsewhere [14]. Briefly, eligible patients were adults (> 18 years) with a primary non-anoxic acute brain injury (traumatic brain injury, intracerebral hemorrhage, subarachnoid hemorrhage, or acute ischemic stroke) requiring intubation and mechanical ventilation in the ICU.

From the parent cohort, patients were eligible for analysis if they had at least one valid plateau pressure or driving pressure recording during the ICU stay (allowing computation of E_RS) and a documented height for predicted body weight (PBW) calculation. After excluding patients with neither criterion met, 1158 patients were included in the analysis (Supplementary Fig. 1).

Data collection procedures, respiratory measurements, and outcome definitions have been reported in detail in the original VENTIBRAIN publication [14]. The VENTIBRAIN steering committee approved the project, and a data transfer agreement was signed in accordance with the original protocol. Ethical approval was obtained from the ethics committee of ASST-Monza (Approval 3425, 10/09/2020) and each participating center. No further ethical approval was necessary for this secondary analysis. The study was conducted according to the Declaration of Helsinki. Informed consent was managed according to local regulations.

Definition of E_RS

PBW was calculated using the ARDSNet formula (male: 50 + 0.91 × [height in cm − 152.4]; female: 45.5 + 0.91 × [height in cm − 152.4]) [1]. The primary exposure was E_RS adjusted for predicted body weight, defined as ΔP divided by V_T/PBW (algebraically equivalent to E_RS × PBW) and expressed in cmH₂O/(mL/kg). This normalization accounts for the physiological dependence of E_RS on body size, thereby providing a measure of the elastic load of the respiratory system that is comparable across patients of different statures.

Patients were classified into tertiles based on the empirical distribution of mean E_RS values during the first 7 days in the intensive care unit (ICU) stay (T1: < 0.99; T2: [0.99–1.42]; T3: > 1.42 cmH₂O/[mL/kg]).

Outcomes and subgroups

Four outcomes were examined: ICU mortality (available in 1077 of 1158 patients), hospital mortality (n = 1055), 6-month mortality (n = 1120), and unfavorable Glasgow Outcome Scale Extended (GOSE < 5; n = 1001). As a pre-specified subanalysis, results were compared between patients with and without ARDS (n = 600 and n = 558, respectively); ARDS was defined by clinician-reported recognition of the Berlin definition criteria at any time during the ICU stay [19]. This subanalysis was performed for the E_RS threshold analysis, the temporal stability of E_RS, and the E_RS-dependent optimal V_T models.

The primary pre-specified endpoint was ICU mortality; secondary endpoints, subgroup, and alternative timeframe analyses were exploratory.

Statistical analysis

Continuous variables were summarized as median (interquartile range) and compared across E_RS tertiles using the Kruskal–Wallis test. Categorical variables were summarized as n (%) and compared using the Chi-square test. All proportions were computed from available-case denominators; no imputation was performed for outcome variables. Two exposure timeframes were defined for E_RS and ventilatory variables. The primary timeframe was the individual patient mean computed across the initial 7 days (e.g., the observation period of the study) with valid measurements. For the isocapnic curve analysis, the baseline timeframe (day 0–1 average) was used as primary for consistency with the methodology of Costa et al. [20]. All primary analyses were replicated using the alternative timeframe as a pre-specified sensitivity analysis.

Assessment of selection bias. To assess potential selection bias from missing data, we compared 22 baseline characteristics and four clinical outcomes between included and excluded patients using standardized mean differences (SMD), with a threshold of |SMD| > 0.1 to identify meaningful imbalances.

Temporal stability of E_RS. To characterize the temporal behavior of E_RS during the first seven days of ICU stay, individual daily values were plotted by baseline tertile and summarized as geometric means with 95% Confidence Intervals (CI) computed on the log scale and back-transformed. A linear mixed-effects model was fitted on log-transformed E_RS, with random intercepts at both the center and the patient level. Fixed effects comprised time (centered at Day 1), tertile, their interaction, age, sex, APACHE II score, brain injury type (subarachnoid hemorrhage, intraparenchymal hemorrhage and acute ischemic stroke as indicators, traumatic brain injury as reference), ARDS status, and time-varying ventilatory parameters (V_T/PBW, PEEP, respiratory rate, ΔP; all z-scored).

Tertile-stratified logistic regression. To characterize effect modification of the V_T–outcome association by E_RS, we fitted separate logistic regression models within each E_RS tertile for each of the four outcomes. This approach avoids the linearity assumption of a single multiplicative interaction term and allows direct visual comparison of exposure–outcome curves across strata of lung mechanics. For each combination of E_RS tertile and outcome, the model was adjusted for age, sex, and APACHE II score, where all continuous predictors were z-scored within each tertile. Three exposures were examined: V_T/PBW, respiratory rate, and ΔP, all computed as the mean across the first 7 days of ICU stay. Results were reported as odds ratio (OR) with corresponding 95% CI and predicted probabilities were computed over clinically plausible ranges with 95% confidence intervals derived by the delta method. Effect modification was assessed by three complementary statistics: a likelihood ratio test for the continuous E_RS × exposure interaction (p_int), a pairwise z test comparing T3 and T1 slopes (p_T3vsT1), and a weighted meta-regression for linear trend across tertiles.

V_T and respiratory rate at constant alveolar ventilation (isocapnic curves). To evaluate the joint contribution of V_T and respiratory rate to the four outcomes at constant alveolar ventilation, we applied the isocapnic curve framework described by Costa et al. [20]. A logistic regression model was fitted as follows: logit(outcome) = β₀ + β_DP × ΔP + β_RR × respiratory rate + tertile indicators + covariates (i.e., for age, APACHE II score, PaCO₂, arterial pH, and PaO₂/FiO₂ ratio). Dead space was assumed as 1.5 mL/kg PBW (airway) plus 20% of V_T (alveolar), following Costa et al. and data available from patients with acute brain injury [13, 20]. Isocapnic curves were constructed for each subgroup by tracing combinations of V_T and respiratory rate maintaining constant alveolar ventilation at the sample median, using tertile-specific median E_RS and PBW values. The optimal ventilation point was defined as the V_T/PBW and respiratory rate combination yielding the minimum predicted OR (i.e., better outcome) along each isocapnic curve. The baseline timeframe for E_RS assessment (day 0–1 average) was used as primary for consistency with the Costa et al. methodology [20]; the mean timeframe served as sensitivity analysis (Electronic Supplementary Material).

Mechanical power was derived along each isocapnic curve using the simplified equation: 0.098 × respiratory rate × V_T × (Ppeak − 0.5 × ΔP), with V_T in liters [21, 22]. Peak airway pressure was reconstructed as P0 + ΔP, where the tertile-specific P0 (the median PEEP-plus-resistive floor, computed as measured peak pressure minus measured ΔP) was held constant, so that ΔP, plateau, and peak pressure all rose with V_T and, at each tertile’s median observed V_T, reproduced the observed peak pressure.

Elastance threshold for V_T effect reversal. To quantify the E_RS threshold at which the direction of the V_T/PBW–outcome association reverses, we fitted Bayesian logistic regression models on the four outcomes with a continuous V_T/PBW × E_RS interaction term, adjusted for age, sex, and APACHE II score (all z-scored). Bayesian estimation used the No-U-Turn sampler (PyMC; 4 chains, 2000 draws per chain, 1000 warmup, target acceptance 0.95) with non-informative priors. Convergence was confirmed by Gelman–Rubin statistic (R̂) < 1.01 (this metric indicates adequate mixing and convergence of the chains to the stationary posterior) and effective sample sizes exceeding 400. The posterior probability that V_T 6 mL/kg yields lower mortality than V_T 10 mL/kg was computed at each point along the E_RS continuum, generating an S-curve. The comparison was made between V_T 6 mL/kg and V_T 10 mL/kg, as these represent the conventional protective and liberal targets commonly used as reference in clinical practice and in previous trials [12, 23–26]. The threshold, defined as the E_RS value where this probability equals 50%, was estimated with 95% highest density intervals. A region of practical equivalence (ROPE) was assumed to be |log(OR)| < 0.163 (OR 0.85–1.18).

Elastance-dependent optimal V_T and respiratory rate. To determine the E_RS-specific ventilatory settings that minimize the predicted probability of adverse outcomes for ICU mortality, we fitted quadratic logistic regression models with an exposure-by-E_RS interaction term, adjusted for age, sex, and APACHE II score (all z-scored). The optimal V_T/PBW and respiratory rate at a given E_RS were derived analytically as the vertex of the within-model parabola, back-transformed to the original scale, and clipped to clinically plausible ranges. Bayesian (80% credible intervals) estimates were obtained. The implied optimal ΔP at each E_RS was obtained deterministically as the product of the optimal V_T and E_RS. Separate analyses were performed for ARDS and non-ARDS subgroups.

All analyses were performed in Python 3.12 (Python Software Foundation, Wilmington, DE, USA) using statsmodels 0.14 for logistic regression, PyMC 5.26 (PyMC Labs, Basel, Switzerland) with ArviZ 0.22 for Bayesian estimation, SciPy 1.16 for statistical tests, and Matplotlib 3.10 with seaborn 0.13 for figure generation. Two-sided p values below 0.05 were considered statistically significant in frequentist analyses. Full details of the statistical analysis are provided in the electronic supplementary material (ESM).

Results

From the VENTIBRAIN cohort, 733 patients were excluded for missing E_RS (i.e., absence of both plateau pressure and driving pressure recordings) and 204 for PBW calculation, yielding an analytic cohort of 1158 patients (Supplementary Fig. 1).

Among 22 baseline characteristics and four outcomes compared between 1158 included and 937 excluded patients, 12 variables exceeded the |SMD| > 0.1 threshold (Supplementary Fig. 2). Patients included in this analysis presented a slightly better prognosis compared to those excluded (e.g., ICU mortality 27% vs 35%).

Patients’ demographics and clinical characteristics according to E_RS tertiles are shown in Table 1.

Table 1.

Baseline characteristics, respiratory parameters, and outcomes stratified by tertiles of E_RS

Variable	Low ERS < 0.99 cmH2O/(mL/kg)	Medium ERS [0.99–1.42 cmH2O/(mL/kg)]	High ERS > 1.42 cmH2O/(mL/kg)	p value
No. of patients	386	386	386
Clinical characteristics
Age, years	61 (51–71)	57 (42–69)	57 (43–67)	< 0.001
Male sex	214 (55%)	238 (62%)	296 (77%)	< 0.001
Predicted body weight, kg	62 (52–70)	65 (57–71)	68 (62–73)	< 0.001
High-income country	172 (44%)	255 (66%)	275 (71%)	< 0.001
APACHE II score	18 (13–22)	17 (13–22)	19 (14–24)	0.001
Pupil reactivity				0.149
Both reactive	273 (73%)	297 (79%)	272 (73%)
One reactive	27 (7%)	28 (7%)	28 (8%)
Both unreactive	75 (20%)	50 (13%)	70 (19%)
LIPS score	2 (0–4)	2 (0–5)	2 (0–5)	0.016
GCS motor score				0.526
1–4 (poor)	251 (66%)	237 (62%)	244 (65%)
5–6 (good)	129 (34%)	143 (38%)	129 (35%)
Brain injury type				< 0.001
Traumatic brain injury	118 (31%)	156 (40%)	168 (44%)
Subarachnoid hemorrhage	106 (27%)	79 (20%)	50 (13%)
Intracerebral hemorrhage	114 (29%)	105 (27%)	108 (28%)
Ischemic stroke	48 (12%)	46 (12%)	60 (16%)
Highly pathological CT scan	182 (47%)	192 (50%)	171 (44%)	0.317
Neuroworsening	122 (32%)	117 (30%)	107 (28%)	0.181
Gas exchanges and respiratory parameters (Day 0)
Tidal volume, mL	480 (430–534)	470 (430–510)	477 (440–500)	0.420
Tidal volume/PBW, mL/kg	7.9 (7.1–8.8)	7.6 (6.8–8.3)	7.1 (6.5–7.9)	< 0.001
Respiratory rate, breaths/min	15 (14–18)	15 (14–18)	16 (14–20)	< 0.001
PEEP, cmH2O	6 (5–8)	5 (5–7)	5 (5–6)	< 0.001
FiO2, %	40 (30–45)	40 (35–50)	40 (40–50)	< 0.001
PaO2, mmHg	105 (88–139)	112 (92–149)	116 (90–157)	0.064
PaO2/FiO2, mmHg	300 (228–383)	290 (213–394)	278 (200–390)	0.362
PaCO2, mmHg	37 (33–41)	37 (34–41)	38 (35–42)	0.032
Driving pressure, cmH2O	5 (3–7)	9 (8–11)	12 (10–15)	< 0.001
Compliance, mL/cmH2O	82 (64–121)	50 (42–62)	38 (33–45)	< 0.001
Mechanical power, J/min	10.7 (8.5–14.2)	12.4 (9.2–17.7)	15.1 (11.2–21.2)	< 0.001
Respiratory system elastance (ERS), cmH2O/(mL/kg)	0.65 (0.39–0.88)	1.24 (1.11–1.38)	1.69 (1.49–1.94)	< 0.001
Intracranial pressure and pulmonary complications
Lowest ICP, mmHg	4 (2–6)	5 (1–10)	5 (2–10)	0.333
Highest ICP, mmHg	16 (11–19)	14 (8–19)	15 (12–20)	0.373
ICP > 20 mmHg (ever)	54 (14%)	77 (20%)	100 (26%)	< 0.001
Pneumonia	54 (14%)	66 (17%)	83 (21%)	0.022
Pneumothorax	13 (4%)	21 (6%)	30 (9%)	0.034
Pleural effusion	103 (31%)	112 (33%)	122 (36%)	0.409
Atelectasis	124 (37%)	144 (43%)	148 (43%)	0.177
Pulmonary edema	10 (3%)	14 (4%)	22 (6%)	0.094
Diagnosis of ARDS (any severity)	210 (54%)	194 (50%)	196 (51%)	0.454
Outcomes*
ICU mortality	72 (20%)	92 (26%)	125 (34%)	< 0.001
Hospital mortality	68 (20%)	103 (29%)	131 (37%)	< 0.001
6-month mortality	121 (33%)	134 (36%)	159 (42%)	0.021
Unfavorable GOSE (< 5)	200 (61%)	221 (65%)	243 (73%)	0.002

Data are median (IQR) or n (%). Continuous variables were compared across tertiles using the Kruskal–Wallis test; categorical variables were compared using the Pearson chi-square test. p values reported in the table refer to these tests

APACHE II Acute Physiology and Chronic Health Evaluation II, ARDS acute respiratory distress syndrome, CT computed tomography, ERS respiratory system elastance, FiO₂ fraction of inspired oxygen, GCS Glasgow Coma Scale, GOSE Glasgow Outcome Scale Extended, ICP intracranial pressure, ICU intensive care unit, LIPS Lung Injury Prediction Score, PaCO₂ arterial partial pressure of carbon dioxide, PaO₂ arterial partial pressure of oxygen, PBW predicted body weight, PEEP positive end-expiratory pressure

^*Data availability varied across outcomes: ICU mortality, n = 1077; hospital mortality, n = 1055; 6-month mortality, n = 1120; unfavorable GOSE (< 5), n = 1001; total study population, n = 1158

Geometric mean E_RS remained essentially constant within each tertile across the first seven ICU days, with no significant time × tertile interaction (Supplementary Fig. 3). ARDS and non-ARDS patients followed parallel trajectories within each tertile.

V_T/PBW tended to be lower and respiratory rate higher with increasing E_RS (p < 0.001 for both), but these adjustments were insufficient to offset the differences in respiratory E_RS, resulting in a marked ΔP gradient across tertiles (Fig. 1).

Fig. 1.

Ventilatory settings across respiratory system elastance tertiles and effect modification by E_RS in the overall cohort. Top: panels a–c show the distribution (median and interquartile range of the first 7 days in ICU) of V_T/PBW; panel a), respiratory rate (panel b), and ΔP (panel c) across tertiles of mean E_RS. Despite a small decrease in V_T/PBW and a modest increase respiratory rate across tertiles, ΔP increased markedly. Bottom: panels d–f show the predicted probability of ICU mortality as a function of V_T/PBW (panel d), respiratory rate (panel e), and ΔP (panel f), stratified by E_RS tertiles. Lines represent E_RS tertiles. Shaded bands indicate 95% confidence intervals derived by the delta method. Each panel displays the continuous interaction p value (p_int) and the pairwise T3 vs T1 slope comparison p value (p_T3vsT1). Models adjusted for age, sex, and APACHE II score, with all continuous predictors z-scored within each tertile. Mean timeframe N = 1158

Tertile-stratified logistic regression

The association between mean V_T/PBW and ICU mortality was modified by E_RS (p_int < 0.001; Fig. 1): higher V_T was associated with lower mortality in patients with low E_RS (T1: odds ratio [OR] 0.52, [95% CI 0.36–0.74]), but this protective effect progressively disappeared in patients with medium E_RS (T2: OR 0.82 [95% CI 0.61–1.11]) and reversed toward harm in patients with high E_RS (T3: OR 1.16 [95% CI 0.89–1.51]). Results on hospital (p_int < 0.001) and 6-month mortality (p_int = 0.002) were consistent (Supplementary Fig. 4). Higher respiratory rate was associated with worse outcomes across all tertiles; although the interaction with E_RS was not statistically significant (all p_int ≥ 0.15), the magnitude of the association was considerably greater at low E_RS and tended to diminish at higher E_RS (Fig. 1 and Supplementary Fig. 4).

V_T and respiratory rate at constant alveolar ventilation

For ICU mortality, ΔP was significantly associated with outcome (OR per standard deviation increase 1.32, 95% CI 1.00–1.75, p = 0.047), with the overall effect of ΔP governed by patients with high E_RS (Fig. 1). At constant alveolar ventilation, ΔP carried consistently greater prognostic weight than respiratory rate across all outcomes: each 1 cmH₂O increase in ΔP had a similar impact on outcome as an approximately 3 breaths/min increase in respiratory rate. The V_T and respiratory rate combination associated with the lowest odds of adverse outcome shifted across E_RS tertiles: in the low-E_RS tertile, the optimum favored higher V_T with lower respiratory rates, whereas in the high E_RS tertile, it favored lower V_T with higher respiratory rates (Fig. 2). Directionally consistent results were observed for hospital and 6-month mortality, and GOSE (Supplementary Fig. 5).

Fig. 2.

Isocapnic curves showing the predicted odds ratio for ICU mortality as a function of tidal volume and respiratory rate combinations that maintain constant alveolar ventilation, stratified by E_RS tertile in the overall cohort. The odds ratio (top), corresponding driving pressure (ΔP = V_T × E_RS; middle), and mechanical power (bottom) are shown in three vertically stacked panels sharing a common tidal volume axis. Each curve traces a constant alveolar ventilation trajectory; the upper x-axis displays the corresponding respiratory rate. Circles indicate the optimal ventilation point (minimum odds ratio) for each tertile. Models adjusted for age, APACHE II score, PaCO₂, arterial pH, and PaO2/FiO₂ ratio, following Costa et al. [20]. Alveolar dead space is assumed as 1.5 mL/kg PBW (airway) plus 20% of V_T. Baseline timeframe (day 0–1 average) N = 961

Elastance threshold for V_T effect reversal

The posterior probability that V_T 6 mL/kg yields lower ICU mortality than V_T 10 mL/kg varied from near 0% at the lowest observed E_RS values—where lower V_T were potentially harmful—to 100% at the highest, illustrating that the same V_T can be detrimental or beneficial depending on E_RS. The Bayesian analysis identified the E_RS value at which V_T 6 mL/kg and V_T 10 mL/kg become equally likely to be beneficial (or harmful), which represents an equipoise threshold (Fig. 3). For ICU mortality, this threshold was 1.48 cmH₂O/(mL/kg) (95% HDI 1.15–1.98). The equipoise threshold was slightly lower for hospital mortality and 6-month mortality, indicating that for longer-term outcomes, the benefit of reducing V_T emerged at lower levels of E_RS.

Fig. 3.

Elastance threshold for tidal volume effect reversal in the overall cohort. Bayesian posterior probability (%) that V_T 6 mL/kg yields lower mortality or better neurological outcome than V_T 10 mL/kg, plotted across the mean E_RS continuum. The crossing point is the E_RS value where the posterior probability equals 50% (top row) or the odds ratio equals 1.0 (bottom row). Shaded bands indicate 95% credible intervals (Bayesian). Models adjusted for age, sex, and APACHE II score

Elastance-dependent optimal V_T and respiratory rate

Optimal V_T/PBW (i.e., the value associated with the lowest probability of adverse outcome) decreased from 11.4 mL/kg at E_RS 0.5 cmH₂O/(mL/kg) (yielding a ΔP ≈ 6 cmH₂O) to 4.4 mL/kg at E_RS 2.5 cmH₂O/(mL/kg) (yielding a ΔP ≈ 11 cmH₂O), a gradient of approximately 1.7 mL/kg per 0.5 cmH₂O/(mL/kg) increment in E_RS (posterior probability of a non-zero curvature in the optimal V_T/PBW–E_RS relationship = 100%). Because optimal V_T fell steeply as elastance rose, the corresponding optimal ΔP did not continue to increase but plateaued within a lung-protective range (~11–12 cmH₂O) at moderate-to-high E_RS. Optimal respiratory rate increased with E_RS (from 15 to 19 breaths/min across tertiles; posterior probability of a non-zero curvature in the optimal respiratory rate–E_RS relationship = 99%) (Fig. 4).

Fig. 4.

Optimal V_T/PBW (panel a) and optimal respiratory rate (panel b) as a function of mean E_RS for ICU mortality in the overall cohort, estimated by Bayesian quadratic logistic regression (80% credible intervals). The optimal value at each E_RS level corresponds to the nadir of the U-shaped exposure–outcome curve; the dashed line shows observed median values within equally sized bins of E_RS in the VENTIBRAIN cohort. In panel a, the corresponding optimal ΔP (= V_T × ERS) increases from ~ 6 to ~ 11–12 cmH₂O across the E_RS range (right axis); because optimal V_T falls steeply with elastance, the optimal ΔP does not continue to rise but remains within a lung-protective range. Because ΔP depends on both V_T and E_RS, the right axis reports ΔP along the optimal-V_T (model) line only; the ΔP at any other combination is given by the dotted iso-ΔP contours (constant ΔP). In this analysis, the optimal V_T is derived from the V_T–outcome relationship as a continuous function of E_RS and is not constrained to maintain constant alveolar ventilation; the ΔP shown is therefore that generated by this unconstrained optimal V_T. The clinically applicable optimum, in which V_T and respiratory rate are coupled to maintain constant alveolar ventilation, is shown in Fig. 2 and yields lower optimal V_T and ΔP values. P(curvature > 0) denotes the Bayesian posterior probability that the quadratic term is positive. Models adjusted for age, sex, and APACHE II score

Influence of ARDS recognition on the V_T–E_RS interaction

The V_T–E_RS interaction was consistent across patients classified as having ARDS and those who were not (Supplementary Fig. 6). Accordingly the equipoise threshold at which V_T 6 mL/kg became favored over V_T 10 mL/kg was comparable between non-ARDS patients (E_RS 1.53 cmH₂O/[mL/kg]) and ARDS patients (1.42 cmH₂O/[mL/kg]), at near-identical baseline E_RS (1.24 vs 1.25 cmH₂O/[mL/kg]). Non-ARDS patients received higher V_T (median 7.6 vs 7.4 mL/kg) and higher ΔP (median 10 vs 9 cmH₂O). The optimal V_T/PBW vs E_RS gradient was consistent across ARDS and non-ARDS, declining steeply with elastance in both (Fig. 5).

Fig. 5.

ARDS vs non-ARDS comparison of optimal V_T/PBW as a function of mean E_RS, estimated by Bayesian quadratic logistic regression. Solid lines represent ARDS patients; dashed lines represent non-ARDS patients. Dotted lines with circle markers show observed median V_T/PBW computed from 15 quantile bins of E_RS (minimum 8 patients per bin), separately for each subgroup. Diagonal contours are lines of constant driving pressure, calculated as V_T × ERS, with the corresponding ΔP shown on the top axis. Consistently with Fig. 4, for a given E_RS, the ΔP associated with the optimal V_T/PBW is identified by the constant-ΔP contour intersecting the optimal V_T/PBW curve at that E_RS; this optimal ΔP therefore varies along the E_RS axis. P(curvature > 0) denotes the Bayesian posterior probability that the quadratic term is positive. Models adjusted for age, sex, and APACHE II score

Sensitivity analyses are reported in the Electronic Supplementary Material and confirmed these findings.

Discussion

In mechanically ventilated patients with acute brain injury, the impact of V_T setting depends on E_RS. Lower V_T only helps patients with high E_RS, where it meaningfully reduces ΔP. In the majority of patients with low E_RS, V_T restriction provides no advantage and forces an increase in respiratory rate, which in our data was independently associated with worse outcomes. The V_T associated with the highest probability of positive clinical outcome decreases continuously as E_RS rises, supporting individualized, mechanics-based settings rather than fixed thresholds. Clinically, V_T adjustment can be guided by a physiological framework that balances ΔP reduction against the respiratory rate needed for isocapnia, with outcomes governed by a trade-off of approximately 3 breaths/min per 1 cmH₂O change in ΔP.

Our findings provide a unifying mechanistic framework for several apparently discordant trials. In PReVENT trial [8], conducted in a heterogeneous non-ARDS ICU population, V_T 6 vs 10 mL/kg yielded no difference in outcome. Our data offer a direct explanation: when E_RS is not accounted for, a fixed-V_T comparison averages over patients with high E_RS (V_T restriction beneficial) and patients with low E_RS (V_T restriction unnecessary and forces a disproportionate compensatory rise in respiratory rate). These opposing effects cancel, driving the comparison toward the null. Results from the recent PROLABI sharpen this interpretation [12]: by enrolling brain-injured patients without ARDS, a population characterized predominantly by low E_RS, low V_T (6 mL/kg, bundled with higher PEEP) was precisely tested in the subgroup in which our analysis predicts that V_T restriction should be detrimental, because it costs significant increases in respiratory rate with minimal benefits on ΔP. Consistently, PROLABI reported higher mortality and a worse composite outcome with the protective strategy. Two caveats apply: the protective arm coupled lower V_T with higher PEEP, so V_T and PEEP effects cannot be separated, whereas our framework isolates the E_RS-conditioned tidal exposure; and PROLABI was stopped early for administrative reasons, so its estimates require confirmation. Both features, however, are concordant with our central thesis.

Taken together, PReVENT and PROLABI illustrate the two ways a fixed-V_T prescription fails: dilution of benefit in heterogeneous-E_RS populations, and frank harm when low V_T is imposed on predominantly low-E_RS patients. This mirrors, at the population level, the ARDS evidence itself: meta-analyses pooling heterogeneous low- versus high-V_T definitions show no mortality benefit [27], and only trials with a large V_T separation (6 vs 12 mL/kg) demonstrated survival advantage [1, 28]. The common thread is that V_T per se is not the operative variable; the E_RS-conditioned tidal exposure—ultimately ΔP—is, consistent with the classical study by Amato et al. [17].

Our findings may help reconcile some observations questioning ΔP-outcome associations in non-ARDS patients [29, 30], in whom E_RS is generally low. This generates limited variance in ΔP, carrying no prognostic signal, because it does not reflect meaningful mechanical stress. The prognostic relevance of ΔP depends on E_RS being sufficiently high for V_T to generate injurious mechanical stress [16].

This observation has a clear physiological explanation. An increase in E_RS reflects a decrease in functional lung size, even in lungs without ARDS [31–33]. For a given V_T to generate injurious strain, lung size must be sufficiently reduced, so that the ratio of V_T to resting lung volume becomes harmful [34]. When compliance (low E_RS) is preserved and the lung is large, the same V_T distributes over a greater volume of aerated tissue, generating low strain per individual alveolar unit. In this setting, reducing V_T offers no protection from strain but imposes the cost of higher respiratory rate, whose potential harmful effects, related to strain rate, are not offset by any meaningful reduction in tidal stretch [35, 36]. This is particularly relevant in patients with acute brain injury, who may require higher alveolar ventilation for tight PaCO₂ control [37].

Our data indicate that there is no single optimal ΔP. Because ΔP is the product of V_T and E_RS, the ΔP compatible with the best outcome is conditional on E_RS and rises with it before reaching a plateau within a lung-protective range. The point is not that a low ΔP is undesirable, but that the benefit of lowering it depends on what it costs in respiratory rate to remain isocapnic: at low E_RS, where ΔP is already low and reflects little strain, reducing it further requires a disproportionate rise in respiratory rate and is not worthwhile, whereas at high E_RS, the same reduction in V_T lowers ΔP substantially at modest respiratory-rate cost—because the V_T-to-ΔP gain (E_RS) is itself steeper when the lung is stiff. For this reason, we have framed titration around V_T, which, together with respiratory rate, is the variable the clinician sets, rather than around ΔP, which is its consequence. ΔP nonetheless remains a useful bedside signal, provided that it is read not against a fixed target but as a quantity to be exchanged against respiratory rate along the isocapnic curve. Mechanical power integrates these variables into a single index of energy delivery and provides a useful global ceiling [21, 38]; it does not, however, uniquely determine how a given alveolar ventilation should be partitioned between V_T and respiratory rate, since multiple V_T–respiratory-rate combinations may yield the same power. The ΔP–respiratory-rate exchange we describe can be viewed as the operational rule for this partition within an acceptable energy envelope, not as an alternative to mechanical power.

These results have relevant clinical implications.

First, VENTIBRAIN data show that, in clinical practice, V_T was characterized by minimal clinically meaningful variation across E_RS tertiles. Our findings suggest that this strategy may be harmful in both directions: in patients with high E_RS, V_T commonly used in practice may still generate excessive ΔP, whereas in patients with low E_RS, unnecessarily restrictive V_T may require compensatory increases in respiratory rate to maintain alveolar ventilation, incurring the cost of a higher respiratory rate for a negligible reduction in ΔP, and hence in mechanical stress [21, 36].

Second, V_T–E_RS interaction was consistent across ARDS and non-ARDS patients. Notably, 190 patients in the highest E_RS tertile were never diagnosed with ARDS, despite having respiratory mechanics indistinguishable from the 196 ARDS patients in the same stratum. This observation, together with the fact that ARDS diagnosis in VENTIBRAIN relied on clinician-reported recognition, suggests that a substantial proportion of lung injury in this population may have been clinically unrecognized. Failure to recognize ARDS not only precludes protective V_T selection, but may also result in the omission of other evidence-based interventions [39]. The absence of a broader protective bundle may amplify the injurious impact of inappropriate V_T in patients that were not formally classified as ARDS. This is consistent with LUNG SAFE data, which showed that ARDS diagnosis is missed in 40% of patients [40, 41]. These findings argue against using the clinical diagnosis of ARDS as the only trigger for adjusting mechanical ventilation settings. Instead, E_RS, and hence ΔP, may provide a more reliable and continuous signal for individualizing V_T prescription, regardless of whether formal ARDS criteria are recognized at the bedside.

Third, any intervention on V_T must be accurately weighed against its impact on respiratory rate to maintain isocapnia. We found that each 1 cmH₂O increase in ΔP had a comparable impact on outcome to an increase of approximately 3 breaths/min in respiratory rate. A practical approach is therefore to reduce V_T only when the resulting increase in respiratory rate does not exceed 3 breaths/min per 1 cmH₂O reduction in ΔP at constant alveolar ventilation, a threshold below which the benefit of lower ΔP is likely to outweigh the cost of increased respiratory rate. Conversely, if respiratory rate can be reduced by more than 3 breaths/min at the cost of increasing V_T so that ΔP increases by 1 cmH₂O, then it is beneficial to increase V_T. This trade-off critically depends on E_RS, as compliance (1/E_RS) determines how many mL of V_T increase ΔP by 1 cmH₂O. Accordingly, the values of V_T/PBW and respiratory rate yielding the highest posterior probability of benefit shifted from 11.4 mL/kg and 15 breaths/min at low E_RS to 4.4 mL/kg and 19 breaths/min at high E_RS. When V_T and respiratory rate were instead constrained to lie along isocapnic curves (Fig. 2), the optimal combination spanned a narrower range, from 8.6 mL/kg and 13 breaths/min at low E_RS to 5.8 mL/kg and 20 breaths/min at high E_RS (evaluated at tertile-median E_RS).

These exchange rates are empirical, outcome-derived equivalences rather than mechanical-injury constants. In ARDS, the injurious potential of ΔP and respiratory rate is approximately 1:4, indicating that the trade-off favors more aggressive V_T reduction [20]. In our population, this was lower (≈ 3), suggesting a narrower margin for exchanging V_T for respiratory rate. This is physiologically plausible: this difference likely reflects the higher E_RS of the ARDS population studied by Costa et al. [20], in which each unit of V_T reduction yields a proportionally larger decrease in ΔP because of lower compliance (1/E_RS). Conversely, patients with acute brain injury had on average lower E_RS, meaning that the same V_T reduction produces a smaller absolute decrease in ΔP, while the need for tight PaCO₂ control in the injured brain amplifies the clinical consequences of even modest increases in respiratory rate. In this population, the cost of each additional breath may therefore be higher than in ARDS, making indiscriminate V_T restriction less justified and mechanics-based titration particularly useful.

This study has limitations. First, as a post hoc observational analysis, findings are hypothesis-generating; confounding and unmeasured variables cannot be excluded, and prospective validation is needed. Second, 45% of the parent cohort was excluded due to missing data, though excluded patients had higher mortality across all endpoints; although residual confounding cannot be excluded, this suggests selection bias toward the null and that our estimates are conservative. The proposed trade-off between ΔP and respiratory rate is also physiologically bounded: it cannot be applied beyond the respiratory-rate range compatible with effective CO₂ clearance, since extreme V_T reduction and respiratory rate increases approach dead-space ventilation. Finally, spontaneous breathing efforts may have affected mechanics measurements; however, sensitivity analyses restricted to baseline, when patients were more likely passively ventilated, yielded concordant results.

Conclusions

In mechanically ventilated patients with acute brain injury, the effect of V_T on clinical outcomes depends on E_RS. In clinical practice, V_T is generally set too low in patients with preserved lung mechanics and too high in those with increased E_RS, with insufficient adaptation to individual compliance. These observational findings generate the hypothesis that V_T and respiratory rate could be titrated jointly along the isocapnic curve, reducing V_T only when the resulting increase in respiratory rate does not exceed 3 breaths/min per cmH₂O reduction in ΔP, a threshold at which the benefit of lower ΔP outweighs the cost of increased respiratory rate. Conversely, increasing V_T is acceptable when this allows a reduction in respiratory rate of at least 3 breaths/min per cmH₂O increase in ΔP, as the benefit of a lower respiratory rate would then outweigh the cost of higher ΔP. This physiology-grounded approach warrants confirmation in prospective trials.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

DLG, TR, AC, and MA designed the study. AS, FG, and SG performed statistical analysis. All authors contributed to manuscript drafting and critical review. All the authors reviewed the final draft of the manuscript and agreed on submitting it to Intensive Care Medicine.

Funding

Open access funding provided by Università Cattolica del Sacro Cuore within the CRUI-CARE Agreement. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability

Not applicable.

Declarations

Conflicts of interest

DLG has received payments for travel expenses by Getinge, Draeger, and Hamilton, personal fees by Draeger, GE, Fisher and Paykel and Nihon Kohden, and research grants by Fisher and Paykel and GE. ER discloses payments for Travel expenses by Burke&Burke. Lecturing fees from Draeger and Seda. Consulting fees from PALL. MA has received payments for Board participation from Maquet, Air Liquide and Chiesi, and a research grant by GE. CR is a Section Editor for Intensive Care Medicine. She has not taken part in the review or selection process of this article.

AI disclosure

Claude AI (Anthropic) was used for language editing and syntax revision. All authors retain full responsibility for the scientific content, interpretation, and conclusions of this work.