Capnodynamic monitoring of lung volume and pulmonary blood flow during alveolar recruitment: a prospective observational study in postoperative cardiac patients

Alveolar recruitment manoeuvres may mitigate ventilation and perfusion mismatch after cardiac surgery. Monitoring the efficacy of recruitment manoeuvres should provide concurrent information on pulmonary and cardiac changes. This study in postoperative cardiac patients applied capnodynamic monitoring of changes in end-expiratory lung volume and effective pulmonary blood flow. Alveolar recruitment was performed by incremental increases in positive end-expiratory pressure (PEEP) to a maximum of 15 cmH2O from a baseline of 5 cmH2O over 30 min. The change in systemic oxygen delivery index after the recruitment manoeuvre was used to identify responders (> 10% increase) with all other changes (≤ 10%) denoting non-responders. Mixed factor ANOVA using Bonferroni correction for multiple comparisons was used to denote significant changes (p < 0.05) reported as mean differences and 95% CI. Changes in end-expiratory lung volume and effective pulmonary blood flow were correlated using Pearson’s regression. Twenty-seven (42%) of 64 patients were responders increasing oxygen delivery index by 172 (95% CI 61–2984) mL min−1 m−2 (p < 0.001). End-expiratory lung volume increased by 549 (95% CI 220–1116) mL (p = 0.042) in responders associated with an increase in effective pulmonary blood flow of 1140 (95% CI 435–2146) mL min−1 (p = 0.012) compared to non-responders. A positive correlation (r = 0.79, 95% CI 0.5–0.90, p < 0.001) between increased end-expiratory lung volume and effective pulmonary blood flow was only observed in responders. Changes in oxygen delivery index after lung recruitment were correlated to changes in end-expiratory lung volume (r = 0.39, 95% CI 0.16–0.59, p = 0.002) and effective pulmonary blood flow (r = 0.60, 95% CI 0.41–0.74, p < 0.001). Capnodynamic monitoring of end-expiratory lung volume and effective pulmonary blood flow early in postoperative cardiac patients identified a characteristic parallel increase in both lung volume and perfusion after the recruitment manoeuvre in patients with a significant increase in oxygen delivery. Trial registration This study was registered on ClinicalTrials.gov (NCT05082168, 18th of October 2021).


Introduction
Impaired pulmonary gas exchange and decreased systemic oxygen delivery following cardiac surgery using cardiopulmonary bypass are associated with an increased risk of postoperative complications [1,2].The function of the heart and lungs are inextricably linked by the matching of ventilation and perfusion.Alveolar recruitment manoeuvres are often employed upon admission to the intensive care unit (ICU) following cardiac surgery to reduce atelectasis and to mitigate ventilation/perfusion mismatch [3,4].Such manoeuvres may have adverse effects, including dead space ventilation by alveolar overdistention, increased pulmonary resistance and right ventricular afterload, and decreased venous return and cardiac output [5,6].While alveolar recruitment manoeuvres are often guided by changes in lung compliance, pulse oximetry, mean arterial pressure or arterial blood gas results, the overall effect on systemic oxygen delivery cannot be easily derived from these variables.The ideal monitor to determine the safety and efficacy of recruitment manoeuvres should provide concurrent information on pulmonary and cardiac performance.Capnodynamic monitoring of lung volume and perfusion may be integrated with standard ventilators at the bedside and provides continuous measurements without special respiratory manoeuvres or interruptions [7,8].We hypothesised that increased end-expiratory lung volume and increased or at least maintained effective pulmonary blood flow following a recruitment manoeuvre by positive end-expiratory pressure (PEEP) would specifically identify patients with improved systemic oxygen delivery.This study in postoperative cardiac patients aimed to assess the feasibility of capnodynamic monitoring of an alveolar recruitment manoeuvre by stepwise increases in PEEP.The cardiorespiratory physiological characteristics obtained by capnodynamic monitoring were evaluated against changes in systemic oxygen delivery.

Methods
This single-centre, pragmatic, prospective, observational open study was approved by the South Western Sydney Local Health District Human Research Ethics Committee (2020/ETH00778, 15th of April 2020) with waiver of written consent and was performed in accordance with the ethical standards as laid down in the 1964 Declaration of Helsinki and its later amendments.Verbal information was provided to the person responsible.The study is reported as per the STROBE guidelines for observational studies [9] (Online Resource 1, Table S1).
Adult patients admitted to ICU following cardiac surgery using cardiopulmonary bypass between February 2021 and February 2022 were screened for inclusion within the first hour of admission to ICU.Inclusion criteria were: the treating clinical team agreed to PEEP titration for potential alveolar recruitment, a pulmonary arterial catheter had been inserted intraoperatively and mechanical ventilation with full patient-ventilator synchrony was expected to remain for at least another two hours.Exclusion criteria were: postoperative bleeding with imminent return to operating theatres, ongoing or imminent need for mechanical circulatory support, haemodynamic instability (> 50% increase in vasopressor administration after fluid loading in the first hour or noradrenaline > 0.3 µg kg −1 min −1 ).
All patients were sedated (propofol, fentanyl) and mechanically ventilated (Draeger V500, Draeger, Lubeck, Germany) in a volume-controlled mode (PEEP of 5 cmH 2 O, respiratory rate RR of 12 min −1 with an inspiratory-to-expiratory ratio of 1:2, tidal volume (TV) 6-8 mL kg −1 ideal body weight, inspired fraction of oxygen (F i O 2 ) initially set at 0.5 and then titrated to a peripheral oxygen saturation > 95% as per institutional protocol).Cardiac output was measured as the average of triplicate pulmonary arterial thermodilution injections within a ± 10% range and indexed to the body surface area as cardiac index (CI).Arterial and mixed venous blood samples were simultaneously obtained and immediately analysed (GEM Premier 5000, Artarmon, New South Wales, Australia).

Study procedures
Patient and clinical characteristics were recorded in eligible subjects.The tracheal tube was temporarily clamped in endinspiration and the standard ventilator changed to a research Servo-I ventilator (Maquet Critical Care, Solna, Sweden) with the F i O 2 , TV and PEEP settings unchanged.Patients continued in a volume-controlled mode but the research ventilator used a modified breathing pattern to add short expiratory holds to 3 out of 9 consecutive breaths to induce cyclical changes in the alveolar partial pressure of CO 2 of at least 3 mmHg.The RR was adjusted to maintain an overall unchanged minute ventilation.The capnodynamic algorithm to derive end-expiratory lung volume and effective, i.e. nonshunted, pulmonary blood flow has been described in detail elsewhere [7,8,10].The effective pulmonary blood flow refers to the physiological efficacy of this portion of cardiac output for gas exchange as it flows through ventilated lung units.Volumetric capnograms were created in real-time by combining data from a mainstream infrared CO 2 sensor (Capnostat®, Philips Respironics, Philadelphia, PA, USA) and the integrated flow signal in the Servo-I ventilator.The capnogram data were exported to a laptop running dedicated software (Matlab®, Mathworks, Natick, MA, USA) that displayed real-time measurements of end-expiratory lung volume and effective pulmonary blood flow as described below in Calculations.All ventilator and capnodynamic data were stored as comma separated values in individual files for each patient for subsequent analyses.Both effective pulmonary blood flow [7,11] and end-expiratory lung volume [8,10] have been established against standard methods to monitor cardiac output and functional residual capacity, respectively.After 20 min of baseline PEEP (PEEP BL-5 ) recording, the cardiac output was measured and arterial and mixed venous blood gases analysed.The PEEP was then increased to 10 (PEEP MID-10 ) for 15 min followed by a further increase to 15 (PEEP HIGH-15 ) for 15 min with a complete set of measurements performed at the end of each PEEP level.The PEEP was then returned to the baseline level (PEEP RTRN-5 ) and a final set of measurements performed after 15 min.After the study procedures had been completed, the patient was reconnected to the standard ventilator.All study procedures and gas exchange data were open to the managing clinical team and upon study completion ventilator settings could be changed at their discretion.Ventilator and capnodynamic data were analysed off-line using custom software (www.icuma ps.org/ visua lizer) that calculated the mean values over 30 breaths that were sampled from the end of each PEEP level recording.

Outcome measure
The primary outcome was a change in systemic oxygen delivery index (DO 2 I) after the recruitment manoeuvre, comparing PEEP RTRN-5 to PEEP BL-5 , and patients were classified as responders if DO 2 I at PEEP RTRN-5 increased by more than 10% from PEEP BL-5 and as non-responders for all other changes (≤ 10%).A complementary analysis using only changes in EELV was also performed, given that changes in lung volume alone are often reported to reflect successful lung recruitment.An increase by > 10% in EELV comparing PEEP RTRN-5 to PEEP BL-5 was used to classify responders.

Calculations
The DO 2 I, shunt fraction (Q s /Q t ), fractional dead space (V d / V t ), body surface area and predicted body weight were calculated using standard equations.The compliance of the respiratory system (C rs ) was calculated from the equation of motion (Online Resource 1, Calculations).Both cardiac output and systemic oxygen delivery were indexed to the body surface area (CI; cardiac index, L min −1 m −2 , and DO 2 I; oxygen delivery index, mL min −1 m −2 ), respectively and end-expiratory lung volume was indexed to predicted body weight.
The capnodynamic method is based on the differential Fick equation for carbon dioxide (CO 2 ) [12].With the assumption that the lung volume, pulmonary blood flow and the mixed venous content of CO 2 (C v CO 2 ) remain constant during each 9-breath measurement cycle, the induced variability in expired CO 2 makes it possible to solve the nine capnodynamic equations with the least square method to obtain the three unknown parameters: end-expiratory lung volume, C v CO 2 and effective pulmonary blood flow.The capnodynamic equation describes a mole balance of CO 2 between the transport of CO 2 to and from the lungs and the rate of change in the CO 2 content of the lungs and is expressed as: The F A CO 2 represents the mean alveolar fraction of CO 2 measured at the mid-point of the slope of phase III of the volumetric capnogram [13], n is the current breath, n − 1 is the previous breath, ∆t n is the current breath cycle time, C v CO 2 is the mixed venous content of CO 2 , C c CO 2 n is the content of CO 2 in the pulmonary capillary blood calculated from F A CO 2 and TVCO 2 n is the volume of CO 2 eliminated by a breath.The capnodynamic equation system is applied in a continuous breath-by-breath fashion where every 10th breath is replacing the first one in the nine-breath cycle.

Statistical analyses
The main study protocol was finalised on the 7th April 2020 and is deposited on the Open Science Framework (https:// osf.io/ 93r7n/?view_ only= d4a8e 76bc2 8b4ae 6a1d6 42d4a 75665 9b) with this report focusing on gas exchange as per the ClinicalTrials.govregistration.A sample size of 54 patients was calculated to detect a PEEP associated difference in end-expiratory lung volume by 500 mL from a baseline of 1500 mL with a standard deviation of 550 mL [14,15], including a 10% measurement error, accepting a two-sided risk for type I error of 0.05 at a power of 0.90.A cohort of 70 patients was targeted to account for study attrition.Descriptive results are reported as mean ± standard deviation or median and interquartile range (IQR) for normally and non-normally distributed data, respectively, assessed by the D'Agostino-Pearson omnibus normality test and inspection of the Q-Q plots.A mixed factor ANOVA with PEEP set as the within-subjects effect and the DO 2 I response set as the between-subjects effect was performed with Greenhouse-Geisser correction for homogeneity of variance.Post-hoc testing was performed with Bonferroni correction for repeated measurements and the main effects reported as mean differences with their 95% confidence interval (95% CI) for significant findings.Correlations are reported with Pearson's r and regressions shown including the 95% CI from 1000 bootstraps.Statistical significance was set at a two-sided p-value of < 0.05.All analyses were performed using R statistical software (version 4.0.3,R Foundation for Statistical Computing, Vienna, Austria).

Results
The study flow of patients is shown in Fig. 1 with the characteristics for the 64 patients that completed the study shown in Table 1.
The PEEP BL-5 haemodynamic and systemic perfusion variables were within normal limits for postoperative cardiac surgery patients without any significant differences between groups (Table 2).Twenty-seven (42%) of 64 patients increased DO 2 I after the recruitment manoeuvre by > 10% to meet the study primary outcome of responsiveness.The incremental PEEP manoeuvre decreased MAP at PEEP HIGH-15 in responders with no significant changes to HR or CVP.No significant changes between responders and non-responders were noted for arterial lactate or S v O 2 .In responders, the CI increased after the recruitment manoeuvre (mean difference 0.83 (95% CI 0.17 to 1.48 L min −1 m −2 ), p = 0.002, PEEP RTRN-5 vs. PEEP BL-5 ), without significant differences compared to non-responders during the incremental PEEP (responders vs. non-responders at PEEP MID-10 and PEEP HIGH-15 ).Similarly, the DO 2 I increased in responders (mean difference 172 (95% CI 61 to 284 mL min −1 m −2 ), p < 0.001) while no significant differences between groups were observed during incremental PEEP.
Following the recruitment manoeuvre P plat decreased and C rs increased in responders (Table 3).Both P a O 2 and P a CO 2 increased during or after incremental PEEP with decreased Q s /Q t but without significant differences between groups.The V d /V t did not change significantly.
The mean end-expiratory lung volume at PEEP BL-5 was 22 ± 8 mL kg −1 predicted body weight and 25 ± 10 mL kg −1 predicted body weight in non-responders and responders, respectively (Online Resource 1, Figure S1).The PEEP HIGH-15 increased end-expiratory lung volume compared to PEEP BL-5 in both non-responders (mean difference 644 (95% CI 310 to 976 mL), p < 0.001) and responders (mean difference 451 (95% CI 161 to 841 mL), p = 0.009) but only in the responders was this recruited volume maintained once PEEP was decreased to PEEP RTRN-5 (mean difference 549 (95% CI 220 to 1116 mL), p = 0.042 compared to non-responders) (Fig. 2, left).The change in EELV from PEEP HIGH-15 to PEEP RTRN-5 correlated with the change in DO 2 I (r = 0.39, 95% CI 0.16 to 0.59, p = 0.002).The effective pulmonary blood flow did not change significantly during incremental PEEP but increased in responders compared to nonresponders at PEEP RTRN-5 (mean difference 1140 (95% CI Admission after cardiac surgery using cardiopulmonary bypass n=111 Not included in study: ventilator asynchrony, n=12 imminent return to OT, n=5 study team not available, n=17 PA catheter not placed, n=4 Started study protocol n=73
The complementary analysis based on EELV responses only is reported in Online Resource 1, Tables S2 and S3.In patients with a ≤ 10% change in EELV (non-responders) following the PEEP recruitment, the baseline (at PEEP BL-5 ) DO 2 I and EPBF were lower and the lactate higher compared to responders (> 10% increase in EELV), while the difference in baseline CI failed to attain statistical significance (2.28 ± 0.83 vs. 2.66 ± 0.79, p = 0.07).These differences between non-responders and responders did not persist after the recruitment (at PEEP RTRN-5 ).The C rs increased in EELV responders after the recruitment manoeuvre but no significant differences in gas exchange variables were observed.The concordance between DO 2 I and EELV criteria is shown in Online Resource 1, Table S4.

Discussion
This study of alveolar recruitment by incremental PEEP in postoperative cardiac patients demonstrated that the concomitant increase in end-expiratory lung volume and effective pulmonary blood flow by capnodynamic monitoring characterised patients with significantly increased systemic oxygen delivery after the recruitment manoeuvre.By measuring both end-expiratory lung volume and effective pulmonary blood flow, capnodynamic monitoring may be used to assess and guide optimal alveolar recruitment with reference to both gas exchange and perfusion.Reduction of lung volumes occurs in postoperative cardiac patients because of intraoperative deflation of the lungs with insufficient subsequent recruitment, cardiac stunning, fluid overload and pulmonary congestion leading to higher superimposed lung pressures, and prolonged neuromuscular paralysis in the supine position.Tracheal suctioning might further reduce lung volumes.The systemic inflammatory response to cardiac surgery on cardiopulmonary bypass is associated with increased shunt fraction and pulmonary ) Change in effective pulmonary blood flow (ml.min -1 ) 2500 Fig. 3 Correlation between changes in end-expiratory lung volume and effective pulmonary blood flow in patients with a ≤ 10% change (non-responders, n = 37) in systemic oxygen delivery index (DO 2 I) after recruitment manoeuvre by incremental PEEP (left graph, solid line) and in patients with a > 10% increase (responders, n = 27) in DO 2 I (right graph, dashed line).The Pearson's regression line is shown including the 95% CI in grey vascular resistance and reduced functional residual capacity.Thus, postoperative pulmonary dysfunction is multifactorial and remains a challenge in the care of cardiac surgery patients [2,3,16,17].As expected, the end-expiratory lung volume at PEEP BL-5 was low, similar to previous studies [18,19], at about half of normal, resting values [20].The reduced end-expiratory lung volume and the differences between groups were not reflected in decreased arterial oxygen tension or increased P/F ratio, in line with previous reports of weak or absent correlations to oxygenation [15,19,21], that highlights the limitations of arterial blood gas analyses to guide postoperative ventilator settings.The increased Q s /Q t together with low end-expiratory lung volume at PEEP BL-5 suggest a prominent role of postoperative atelectasis.This is a principal cause of postoperative lung dysfunction and formed the rationale for the incremental PEEP recruitment manoeuvre employed in this study.Capnodynamic monitoring demonstrated the expected increase in end-expiratory lung volume during increases in PEEP.Notably, only in responders was the increased lung volume maintained as PEEP HIGH-15 was reduced to PEEP RTRN-5.Responders therefore showed the characteristics of lung recruitment that in physiological terms is the increase in volume at the same pressure and this was associated with decreased P plat and increased C rs , consistent with opening of atelectatic lung units.In non-responders, end-expiratory lung volume returned to baseline at PEEP RTRN-5 with no significant changes in P plat and C rs , thus without features of effective lung recruitment.
The effective pulmonary blood flow was maintained during incremental PEEP which suggests that venous return and pulmonary vascular resistance were not adversely affected by alveolar overdistention during the recruitment manoeuvre.This is further supported by the unchanged V d /V t which would be expected to increase in case of alveolar overdistention.It should be noted that a decreased pulmonary shunt results in increased effective pulmonary blood flow.This plausibly explains the maintained or trend of increased effective pulmonary blood flow while cardiac index was numerically reduced during PEEP HIGH-15 .
The combined monitoring of end-expiratory lung volume and effective pulmonary blood flow made possible by capnodynamic monitoring is arguably the most important feature of this study.The increase in DO 2 I in responders following the PEEP recruitment manoeuvre (PEEP RTRN-5 vs. PEEP BL-5 ) was primarily related to increased effective pulmonary blood flow, commensurate to the observed increase in CI, that was concomitant to alveolar recruitment evidenced by increased end-expiratory lung volume.The correlation analysis of continuous changes in DO 2 I was stronger for EPBF than EELV, that further suggests that changes in blood flow, compared to lung volume, were more influential on systemic oxygen delivery after recruitment.These concurrent changes highlight the importance of cardiopulmonary interactions to explain the efficacy of the recruitment manoeuvre.Accordingly, a significant positive correlation between end-expiratory lung volume and effective pulmonary blood flow was only observed in responders.The increase (PEEP RTRN-5 vs. PEEP BL-5 ) in effective pulmonary blood flow and cardiac output in patients with increased end-expiratory lung volume, i.e., lung recruitment, suggests that they had been ventilated below the point of optimal functional residual capacity on the U-shaped correlation curve against pulmonary vascular resistance.Other possible cardiopulmonary interactions leading to increased effective pulmonary blood flow in responders include the opening of collapsed lung areas with relief of hypoxic vasoconstriction reducing pulmonary vascular resistance and right ventricular afterload; the improved compliance associated with increased lung volume, whilst tidal volumes were not changed, to reduce intrathoracic pressure swings during ventilation with less impedance to venous return; reduced intrathoracic pressures are also conducive to increased coronary perfusion pressure and improved right ventricular ejection.Taken together, these cardiopulmonary interactions could explain the increase in effective pulmonary blood flow observed in responders.Conversely, in nonresponders the increased end-expiratory lung volume was not maintained at PEEP RTRN-5 and consequently there were less of beneficial cardiopulmonary changes to effective pulmonary blood flow.In the complementary analysis, successful recruitment defined by increased EELV at PEEP RTRN-5 compared to PEEP BL-5 was associated with improved C rs but failed to encapsulate changes in pulmonary perfusion and gas exchange.The particular focus on lung volumes and compliance in most studies of recruitment maneouvres may thus overlook concomitant perfusion changes.As a corollary, the lack of superior patient outcomes in clinical trials of recruitment strategies [22] could to an extent be explained by the targeted improved lung mechanics not translating into increased oxygen delivery to support organ function.
The statistically similar end-expiratory lung volume, C rs and effective pulmonary blood flow in non-responders compared to responders at PEEP BL-5 suggest similar lung characteristics.It is however possible that pulmonary congestion, alveolar oedema with surfactant dysfunction or pleural effusions in non-responders (while still allowing end-expiratory lung volume to increase during incremental PEEP) rendered the lungs susceptible to de-recruitment once PEEP HIGH-15 was reduced to PEEP RTRN-5 , i.e., the closing pressure was above 5 cmH 2 O.It is also possible that non-responders would have required higher PEEP levels to achieve lung recruitment than PEEP HIGH-15 , i.e., the opening pressure was above 15 cmH 2 O, or that PEEP should have remained higher than the PEEP RTRN-5 after the recruitment manoeuvre.
This study has several important strengths and limitations.The study took full advantage of capnodynamic monitoring to combine end-expiratory lung volume and effective pulmonary blood flow measurements as opposed to earlier studies of either variable in isolation [7,8,11].It demonstrates the feasibility of capnodynamic monitoring at the bedside without interruption of ventilation or requirement of special procedures to identify the efficacy of an incremental PEEP recruitment manoeuvre using a physiologically relevant primary outcome of increased oxygen delivery.The results demonstrate how capnodynamic monitoring might be utilised to optimise cardiopulmonary performance during postoperative mechanical ventilation that could add to investigations of PEEP and TV combinations for which previous studies have failed to generate conclusive results [6,18,23,24].The study is limited by end-expiratory lung volume providing a global estimate akin to functional residual capacity without any information on the regional distribution of ventilation.An increase in end-expiratory lung volume might thus represent both recruitment and distention of open lung units.The parallel increase in EELV and EPBF in responders after the PEEP recruitment manoeuvre may be expected in lung units with a previous low ventilation to perfusion ratio, i.e. shunt flow.A lack of increase in EPBF after increased PEEP suggests that the lung is overdistended and/or that the venous return and thus cardiac output is reduced.Consequently, the capnodynamic method may be less sensitive to detect changes in areas with a high ventilation to perfusion ratio and other bedside methods to assess ventilation/perfusion matching could be better suited [25,26].The collected data focused on capnodynamic variables and may not have captured potential confounding reasons for the end-expiratory lung volume and effective pulmonary blood flow changes.No pre-study recruitment manoeuvre was performed to equalise the lung history in all patients.While capnodynamic monitoring could facilitate an individualised setting of PEEP based on end-expiratory lung volume and effective pulmonary blood flow responses, this approach was not used in this feasibility study and instead all patients received the same incremental PEEP intervention.The study was performed in the early postoperative phase when residual paralysis was present.Nine patients (12%) of the screened 73 could not be assessed because of spontaneous breathing.This feasibility study was not designed to assess clinically relevant endpoints such as patient outcomes or duration of mechanical ventilation.The primary outcome used a dichotomised definition of DO 2 I that risks reduced statistical power, while analyses of continuous changes in DO 2 I supported the conclusion from the binary analysis.
In conclusion, capnodynamic monitoring of end-expiratory lung volume and effective pulmonary blood flow early in postoperative cardiac patients was feasible.The cardiopulmonary effects of incremental PEEP could be assessed and identified a characteristic parallel increase in both lung volume and perfusion after the recruitment manoeuvre in patients with a significant increase in oxygen delivery.Future studies should focus on using capnodynamic monitoring to individualise ventilator settings to gain the most benefit and avoid adverse effects during postoperative mechanical ventilation.

Fig. 1
Fig. 1 Diagram outlining the flow of patients in the study.OT operating theatre, PA pulmonary artery

Table 1
Patient characteristics (n = 64) Values are mean ± standard deviation, number (%) of total or median (interquartile range) BMI body mass index, CABG coronary artery bypass grafting, APACHE acute physiology and chronic health evaluation, SOFA sequential organ failure assessment, LOS length of stay

Table 2
Haemodynamic and systemic perfusion variables Values are mean ± standard deviation MAP mean arterial pressure, HR heart rate, CVP central venous pressure, CI cardiac index, DO 2 oxygen delivery index, S v O 2 mixed venous oxygen saturation

Table 3
Respiratory variablesValues are mean ± SD RR respiratory rate, TV tidal volume; F i O 2 fraction inspired oxygen, P plat plateau pressure, C rs compliance of the respiratory system, P a O 2 arterial partial pressure of oxygen, P a CO 2 arterial partial pressure of carbon dioxide, Q s /Q t shunt fraction, V d /V t dead space fraction