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Anesthesiology:
doi: 10.1097/ALN.0b013e318283c81f
Critical Care Medicine

Pulmonary Shunt Is Independent of Decrease in Cardiac Output during Unsupported Spontaneous Breathing in the Pig

Vimlati, Laszlo M.D., Ph.D., D.E.S.A.*; Larsson, Anders M.D., Ph.D.; Hedenstierna, Goran M.D., Ph.D.; Lichtwarck-Aschoff, Michael M.D., Ph.D.§

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Abstract

Background: During mechanical ventilation (MV), pulmonary shunt is cardiac output (CO) dependent; however, whether this relationship is valid during unsupported spontaneous breathing (SB) is unknown. The CO dependency of the calculated venous admixture was investigated, with both minor and major shunt, during unsupported SB, MV, and SB with continuous positive airway pressure (CPAP).
Methods: In seven anesthetized supine piglets breathing 100% oxygen, unsupported SB, MV (with tidal volume and respiratory rate corresponding to SB), and 8 cm H2O CPAP (airway pressure corresponding to MV) were applied at random. Venous return and CO were reduced by partial balloon occlusion of the inferior vena cava. Measurements were repeated with the left main bronchus blocked, creating a nonrecruitable pulmonary shunt.
Results: CO decreased from 4.2 l/min (95% CI, 3.9–4.5) to 2.5 l/min (95% CI, 2.2–2.7) with partially occluded venous return. Irrespective of whether shunt was minor or major, during unsupported SB, venous admixture was independent of CO (slope: minor shunt, 0.5; major shunt, 1.1%·min−1·l−1) and mixed venous oxygen tension. During both MV and CPAP, venous admixture was dependent on CO (slope MV: minor shunt, 1.9; major shunt, 3.5; CPAP: minor shunt, 1.3; major shunt, 2.9%·min−1·l−1) and mixed-venous oxygen tension (coefficient of determination 0.61–0.86 for all regressions).
Conclusions: In contrast to MV and CPAP, venous admixture was independent of CO during unsupported SB, and was unaffected by mixed-venous oxygen tension, casting doubt on the role of hypoxic pulmonary vasoconstriction in pulmonary blood flow redistribution during unsupported SB.
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What We Already Know about This Topic

* During mechanical ventilation, increasing cardiac output concomitantly augments pulmonary shunt, which is explained in part by a progressive inhibition of hypoxic pulmonary vasoconstriction
* However, the effect of cardiac output on shunt has not been examined during spontaneous breathing
* This study determined whether pulmonary shunt is independent of cardiac output during spontaneous breathing, when cardiac output is intentionally modulated
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What This Article Tells Us That Is New

* During unsupported spontaneous breathing, pulmonary shunt was not dependent on either cardiac output or mixed-venous oxygen tension
OXYGENATION improves when spontaneous breaths are allowed to alternate with or to take place on top of mechanical breaths during mechanical ventilation (MV).1–3 Whether this improvement is exclusively attributable to spontaneous breathing (SB)–induced reopening of collapsed lung regions has been questioned. Recent studies suggest an SB-induced improvement of ventilation/perfusion matching independent of reopening collapsed areas.4,5
During MV, increasing cardiac output (CO) concomitantly augments pulmonary shunt, which is explained by a progressive inhibition of hypoxic pulmonary vasoconstriction (HPV). Raising CO increases mixed-venous oxygen tension (PvO2), and this results in higher oxygen tension at the HPV sensor site, attenuating the hypoxic vasoconstrictor response.6–8 Moreover, a rising CO increases pulmonary artery pressures, which then distend/recruit pulmonary vessels perfusing nonaerated regions.9 However, the effect of CO on shunt has not been examined during SB. In a previous study, we did not find any major impact of CO on venous admixture (QVA/QT) during unsupported SB in a porcine lung collapse model.10 Therefore, we speculated that, in addition to the above-mentioned mechanisms for CO-dependent shunt during MV, the increased airway pressure (Paw) during MV could counteract HPV by augmenting impedance to blood flow toward ventilated lung regions. However, in that previous study, we did not control for changes in CO.10 Therefore, the primary aim of the present study was to examine whether pulmonary shunt is independent of CO during SB when CO is intentionally modulated. A secondary aim was to investigate the effect of airway pressures, when increased by continuous airway pressure (CPAP) or MV, on the CO dependency of the pulmonary shunt.
We hypothesized that CO had no major effect on QVA/QT during SB, and that the higher airway pressures during MV and CPAP (spontaneous breathing at airway pressure corresponding to MV) were associated with CO dependence of the pulmonary shunt.
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Materials and Methods

The Uppsala Animal Ethics Committee (Uppsala, Sweden) approved the protocol; the guidelines regarding animal care from the Institute for Laboratory Animal Research†† were followed. Seven piglets weighing 24.3–27.3 kg were studied.
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Preparation and Measurements
The piglets were premedicated with 2.2 mg/kg tiletamine plus 6 mg/kg zolazepam (Zoletil; Virbac, Carros, France). After IV induction with 8 mg/kg ketamine and 1 mg/kg morphine, anesthesia was maintained with IV infusion of 20 mg·kg−1·h−1 ketamine and 1 mg·kg−1·h−1 morphine. After a 10-ml/kg IV bolus of dextran 60 (Macrodex; Meda, Solna, Sweden), 10 ml·kg−1·h−1 of Ringer’s acetate was administered IV. In supine position, kept over the whole experiment, an endotracheal tube (Mallinckrodt, Athlone, Ireland) with 9.0-mm internal diameter, cut at 21-cm length, was inserted via a tracheotomy, and connected to the ventilator (Servo-i; Maquet, Solna, Sweden). A central venous line and a pulmonary artery catheter (CritiCath SP5107H; Becton Dickinson, Singapore) were inserted via the right internal jugular vein. For partial occlusion of the venous return, an additional pulmonary artery catheter was placed via a femoral vein cut-down, and floated with an inflated balloon cephalad (usually just beyond 50 cm, approximately at the level of the diaphragm) until blood pressure dropped, indicating decreased venous return. An arterial line was placed via a branch of the subclavian artery, and cystostomy was performed for urine drainage.
Hemodynamic signals were sampled at 2000 Hz and recorded on a computer for offline analysis (BioPac Systems, Santa Barbara, CA). CO was measured with the thermodilution technique (Solar 8000; Marquette, Milwaukee, WI) using three injections of 10 ml of ice-cold saline (injected at random over 4–5 s according to the manufacturer’s instructions); the reported mean value is a result of three individual measurements (usually within ±0.2 l/min). Blood samples were taken for analyses of pH, PvO2, arterial oxygen tension, and arterial carbon dioxide tension (PaCO2) (ABL3; Radiometer, Copenhagen, Denmark); mixed-venous and arterial oxygen saturation was measured in a cooximeter calibrated for porcine hemoglobin (OSM3; Radiometer). Venous admixture, calculated with the Berggren equation,11 was used as a proxy for pulmonary shunt; derived hemodynamic variables were calculated according to standard formulae.
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Experimental Protocol
All animals were initially breathing spontaneously with zero end-expiratory pressure and no pressure support (i.e., unsupported SB) with a triggering sensitivity of −1 cm H2O and a fraction of inspired oxygen of 1.0 for 30 min. Tidal volume (VT) was obtained by integrating the respiratory flow from a Fleisch pneumotachograph (Series 3700; Hans Rudolph, Inc., Shawnee, KS) placed between the endotracheal tube and the Y-piece of the ventilator tubing. At the end of this period, respiratory rate and VT were averaged over 2 min (i.e., control period) and were then used for setting VT and respiratory rate during the volume-controlled mechanical ventilation of the animal.
Three ventilatory modes were used to study whether Paw impacts on the CO–QVA/QT relationship: (1) unsupported SB with low Paw, (2) MV with increased Paw but respiratory rate and tidal volume corresponding to those during SB, and (3) spontaneous breathing during CPAP at mean Paw corresponding to mean Paw during MV. Eight cmH2O of positive end-expiratory pressure, but no pressure support, was applied during CPAP settings.
CO was actively modulated by partial balloon occlusion of the venous return in the inferior vena cava.12 After 10 min on a particular ventilatory mode (i.e., MV, SB, or CPAP), baseline measurements were obtained and then the venous return was partially occluded by slowly inflating the balloon of the catheter placed in the inferior vena cava until mean arterial blood pressure fell by at least 40%; 5 min later, measurements were repeated. If CO was found to be less than 1 l/min, the occluding balloon was slightly deflated and the procedure was repeated after 5 min. After releasing the balloon, the next setting was delayed until hemodynamics were restored.
The effect of CO on QVA/QT was investigated at two shunt levels. Pure oxygen breathing during the preparation with healthy lungs resulted in minor shunt5 (smin); major shunt (smaj) was induced by blocking the ventilation of the entire left lung with a 7-French spherical Arndt bronchial blocker13 (Cook Medical, Inc., Bloomington, IN), placed and inflated in the left main bronchus under fiberoptic control. Disconnecting the entire left lung from ventilation created a pulmonary shunt that was not recruitable by increased airway pressures. For setting MV with smaj, VT and respiratory rate were obtained during SB with smaj, after the stabilization of arterial oxygen tension, after the occlusion of the left main bronchus. The smin condition always preceded smaj, whereas within smin and smaj all particular settings (SB, MV, and CPAP) were performed in random order, determined beforehand by Internet randomizer.#
To suppress spontaneous breathing during MV, titrated doses of IV suxamethonium (0.5–1 mg/kg) were given; no SB/CPAP setting was started until the effect of muscle relaxant had worn off. No purposeful/spontaneous movements, other than respiratory, were observed during SB, justifying the use of muscle relaxation during MV. At the conclusion of the experiment, animals were killed by an overdose of IV potassium under deep anesthesia.
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Statistical Analysis
The CO–QVA/QT relationship was the primary interest of the study; the sample size needed to detect a coefficient of determination (R2) ≥ 0.5, based on earlier observations,10 at α = 0.05 and β = 0.2 (80% power), was estimated to be six animals. As variables obtained by repeated measures are not independent observations, mixed-model ANOVA was used for group comparisons, whereas the association between variables of interest was analyzed by linear mixed-model regression14 on the raw data. Estimation of models and R2 was likelihood-based;** for hypothesis testing maximum likelihood, whereas for parameter estimates restricted maximum likelihood estimation was used.15 In mixed-model ANOVA, ventilatory mode (MV, CPAP, and SB), shunt level (smin, smaj), and partial occlusion of venous return were regarded as fixed effects, and random intercepts for individual animals were allowed. In mixed-model regressions, the null hypothesis was that the explanatory variable had no fixed effect on the dependent variable, which was tested individually for each combination of ventilator mode and shunt level (six comparisons); beside the fixed effect, random intercepts and slopes for the individual animals were allowed. Backward stepwise multiple regressions and P values for fixed effects were calculated with the maximum likelihood test16 (increase of −2 × log-likelihood on exclusion of the examined parameter). Details are provided in the Appendix. When multiple comparisons were made, P values were adjusted by the Holm procedure. Statistical significance was assumed for values of (adjusted) P ≤ 0.05. All statistical analyses were performed with R Environment for Statistical Computing (version 2.14; R Foundation for Statistical Computing, Vienna, Austria; with lme4 package version 0.999375–42). Values are presented as mean (95% CI).
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Results

Hemodynamics and Pulmonary Shunting
Table 1
Table 1
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Independent of venous return (VR), heart rate was slightly lower during MV than during CPAP and unsupported SB in smin, but similar in all smaj settings. At baseline, CO, mean arterial blood pressure, and mean pulmonary artery pressure were similar in all settings; with partial VR occlusion, CO, mean arterial blood pressure, and mean pulmonary artery pressure decreased (table 1).
Table 2
Table 2
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Anesthesia, supine position, and pure oxygen breathing resulted in a minor pulmonary shunt. At both shunt levels, QVA/QT was lower during unsupported SB and CPAP compared with MV. QVA/QT decreased with partial occlusion of VR during MV and CPAP at both shunt levels, but not during unsupported SB (table 2).
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CO dependency of Qva/Qt
Minor Shunt Setting.
Fig. 1
Fig. 1
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Fig. 2
Fig. 2
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Qva/Qt depended on CO during MV (R2 = 0.75) and CPAP (R2 = 0.73); by contrast, when animals were breathing spontaneously at zero end-expiratory pressure, no CO dependence of Qva/Qt could be seen (fig. 1). The Qva/Qt–PvO2 relationship was similar: Qva/Qt increased during MV (R2 = 0.61) and CPAP (R2 = 0.69) with PvO2, but not during unsupported SB (fig. 2).
Stepwise backward selection showed a significant effect of CO on QVA/QT during MVsmin but not during CPAPsmin, when the effect of PvO2 had already been taken into account, whereas when the effect of CO was already included, PvO2 no longer had a significant effect on QVA/QT.
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Major Shunt Setting.
The pattern with smaj was the same as with smin: during MV and CPAP, Qva/Qt depended on CO (MV, R2 = 0.76; CPAP, R2 = 0.79) (fig. 1) and PvO2 (MV, R2 = 0.77; CPAP, R2 = 0.86) (fig. 2); whereas during unsupported SB, Qva/Qt was not dependent on either CO or PvO2.
Stepwise backward selection showed a significant effect of CO on QVA/QT during CPAPsmaj but not during MVsmaj, when the effect of PvO2 had already been taken into account. However, when the effect of CO was included, PvO2 no longer had a significant effect on QVA/QT.
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Respiratory Parameters
VT, approximately 6 ml/kg, was similar in all settings. Respiratory rate, and subsequently minute ventilation, was lower during CPAP with smin (P < 0.001) but not with smaj. Mean airway pressures were comparable in MV and CPAP, both with smin and smaj, but lower during unsupported SB (P < 0.001 for both smin and smaj). Partial VR occlusion did not impact on mean airway pressures.
PaCO2 was similar in all settings and unchanged during partial VR occlusion in all groups except with CPAP, where PaCO2 decreased slightly (1 kPa [0.3–1.8]; P = 0.038) during partial VR occlusion. Arterial pH was at a similar level in all settings, as animals compensated for any PaCO2 increase (table 2).
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PvO2 and Oxygen Consumption
Table 3
Table 3
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PvO2 was similar in all settings at baseline and lower during partial VR occlusion (table 2). PvO2 paralleled CO in all groups (table 3). Oxygen consumption was independent of the ventilatory mode and not altered by partial VR occlusion; however, it was significantly, by approximately 35%, higher during smaj (table 2).
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Discussion

We found, in accordance with a previous study from our group, that during unsupported SB, pulmonary shunt was not dependent on either CO or PvO2. In addition, we could confirm the well-known observation that pulmonary shunt does depend on cardiac output and PvO2 during MV.7,8,17 Interestingly, CPAP was also accompanied by CO- and PvO2-dependent pulmonary shunt.
The CO dependency of pulmonary shunting during MV is a consistent phenomenon seen in different species,17,18 including humans,19 as well healthy12 as focally20 or diffusely17 diseased lungs, and irrespective of whether CO is modulated pharmacologically,17,21 mechanically,17 or by bleeding/volume repletion.12 However, the responsible mechanisms have not been fully elucidated. Increased blood flow, increased PvO2,22,23 increased mean pulmonary pressure, and decreased pulmonary vascular resistance17 are all associated with increased shunt. Sandoval et al. propose that PvO2 mediates the CO-dependent shunting,22 and this raises the possibility that HPV would act as the link between CO and shunt, as HPV is attenuated not only by increased PvO2 but also by increased pulmonary artery pressure.9 In our data, PvO2 seemed not to be able to explain all the effects of CO on QVA/QT; however, this study was not designed to answer such a question. In contrast, during SB, the pulmonary shunt was lower, and the pulmonary vascular bed accommodated an increased CO without a concurrent increase of the pulmonary shunt.
In all settings, and irrespective of the magnitude of the shunt, lower CO resulted in lower PvO2 (as oxygen consumption was maintained), and, as expected,22,23 lower PvO2 was associated with lower QVA/QT during MV and CPAP. However, despite an equally decreased PvO2, lower PvO2 was not associated with altered QVA/QT in unsupported SB settings, where QVA/QT was already lower than during MV. This finding challenges the concept that during unsupported SB the main mechanism of pulmonary blood flow redistribution is HPV; as in that case, the HPV should have been less effective at higher PvO2.6 The PvO2-dependent HPV was either less important for the redistribution of pulmonary blood flow during SB (irrespective of the magnitude of the shunt) or a complementary, yet unidentified mechanism redistributing pulmonary blood flow independent of HPV was active during SB. The negative intrapleural pressure generated during SB might have a role in pulmonary blood flow redistribution, as negative-pressure ventilation has been recently shown to increase oxygenation and decrease pulmonary shunt compared with MV in surfactant-depleted rabbits24 and in humans with acute respiratory distress syndrome.25
The beneficial effect of SB on pulmonary blood flow redistribution was lost during CPAP, where QVA/QT was found to be CO and PvO2 dependent. Increased mean Paw was the common denominator of MV and CPAP compared with SB. Increased Paw is transferred along the airways toward alveoli, augmenting the impedance of perialveolar vessels.26 With the impedance of those perialveolar vessels of ventilated areas increased, HPV might not be able to effectively divert pulmonary blood flow away from atelectatic lung areas.
SB can promote alveolar recruitment,2 and affect ventilation distribution.27 We cannot categorically exclude that regional ventilation, rather than regional perfusion, was modulated by the ventilatory mode. This is, however, rather unlikely, as (1) in our earlier studies with almost 40% of the lung tissue atelectatic we found no substantial recruitment of lung collapse within 30 min, during neither SB nor MV5; and (2) in supine pigs, during mechanical ventilation at a fraction of inspired oxygen of 1.0 and with CO comparable to that seen with unrestricted venous return in the present study, the multiple inert gas elimination technique shows complete absence of areas with a low ventilation/perfusion ratio (0.001–0.1) during one-lung ventilation,28 whose improvement in regional ventilation could decrease pulmonary shunt. Furthermore, as each ventilatory mode served as its own control during CO modulation, lung recruitment could not explain our observations.
There are few experimental or clinical data on CO dependency of the pulmonary shunt during SB; in awake near-term women, no significant correlation between CO and QVA/QT was seen.29 Arterial oxygen tension decreases during strenuous exercise; opening of preformed anatomical shunts is observed in dogs30 and humans.31 Vogiatzis et al., however, raise doubts32 concerning the role of pulmonary shunting in this particular scenario: during strenuous exercise at a fraction of inspired oxygen of 1.0, CO increases up to 28 l/min but QVA/QT is found to be only 0.5% in humans, making a CO dependency of pulmonary shunt under this particular condition rather unlikely.
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Methodologic Considerations
First, calculated venous admixture was used as a proxy of pulmonary shunt, being less accurate than shunt determined by the multiple inert gas elimination technique. However, as a fraction of inspired oxygen of 1.0 was used throughout to avoid hypoxia, especially in smaj settings, QVA/QT should reasonably agree with “true” shunt values.32,33 Second, our conclusions are valid only within the particular range of variables of the present study. Nothing can be concluded for the very high CO range,32 whereas for the very low CO range we could not exclude that even for SB there is a CO threshold, at approximately 2.5 l/min, below which QVA/QT might be CO dependent (fig. 1). Furthermore, we do not know whether a Paw threshold exists above which QVA/QT starts to depend on CO.
Third, both independent and dependent variables showed marked individual variations, inherent in living organisms, which makes the exploration of their interdependency difficult. This study was designed (powered) to evaluate the CO–QVA/QT relationship. Correlations between other variables are solely aimed at generating hypotheses for further investigation; it may well be that those other correlations that are not statistically significant still reflect dependency. However, such could be judged only on the basis of a larger study. Fourth, each regression was calculated from seven sets of two data points (however, not on seven regressions of two data points). We interpreted each correlation estimated from a regression model to indicate that lower CO results in a lower shunt level. However, we did not interpret the actual magnitude of the estimated correlations to indicate a strong or weak correlation, as this is of limited meaning to our question. Fifth, piglets have a strong HPV compared with humans and many other species.18 That QVA/QT did not change with PvO2 during unsupported SB does, however, hardly support HPV as a major mechanism of redistributing pulmonary blood flow in the unsupported SB settings of the present study. Sixth, a number of factors could have influenced HPV in this porcine model. Although morphine34 and benzodiazepines35 (zolazepam) do not affect HPV, ketamine36 (possibly even tiletamine, also an N-methyl-D-aspartate receptor antagonist) and dextran37 might have somewhat attenuated HPV. Respiratory acidosis, seen at both shunt levels, could theoretically also affect HPV; however this still seems to be an unsettled issue. In isolated lungs, hypercapnic acidosis improves HPV, but only after 3 h,38 a considerably longer time than our experiments lasted. In intact animals, hypercapnic acidosis either increases pulmonary vascular resistance without affecting the hypoxic response,39 or attenuates HPV through complex mechanisms.40 In any case, as (1) the animals served as their own controls, (2) drug dosages were similar and unchanged over time, (3) CO was similar in different ventilatory modes, and (4) there were no significant differences in PaCO2 between ventilatory modes, it is unlikely that any of the above-listed factors introduced bias into the present study. Finally, implications for the clinical contexts would be premature, when considering differences in physiology of this porcine model and humans in the above-discussed aspects. Furthermore, one-lung ventilation, in the operating room, and major pulmonary shunt induced by acute lung injury or adult respiratory distress syndrome, in the intensive care unit, comprise many more physiologic and pathologic processes than just lung collapse and ventilation/perfusion mismatch.
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Conclusion

In contrast to MV and CPAP (at similar mean airway pressure as with MV), pulmonary shunting did not substantially depend on CO during unsupported SB at zero end-expiratory pressure. The CO independence of shunt during unsupported SB seemed to be related to airway pressures, as shunt was CO dependent once airway pressures were raised with CPAP to a level comparable to MV. Higher PvO2 was not associated with increased pulmonary shunt during unsupported SB, not even with major shunt, challenging the role of HPV as the main mechanism of pulmonary blood flow redistribution in this setting.
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Appendix: Hypothesis Testing of Linear Mixed-model Regressions

Table 4
Table 4
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The null hypothesis, that the explanatory variable has no fixed effect on the dependent variable, was individually tested for each combination of ventilator mode (MV, CPAP, and SB) and shunt level (smin and smaj), resulting in six comparisons. P values for fixed effects were calculated with the maximum likelihood test as described below.16 Variables are given in table 4. All statistical analyses were performed with R Environment for Statistical Computing (version 2.14; R Foundation for Statistical Computing, Vienna, Austria; with lme4 package version 0.999375–42).
1. Loaded model: dependent variable ~ fixed effect (explanatory variable) + random slope (explanatory variable) + random intercepts
2. No random slope model: dependent variable ~ fixed effect (explanatory variable) + random intercepts
Compare to loaded (1) model by maximum likelihood test.
3. If random slopes are significant: dependent variable ~ random slope (explanatory variable) + random intercepts
Compare to loaded (1) model by maximum likelihood test.
4. If random slopes are not significant: dependent variable ~ random intercepts
Compare to no random slope (2) model by maximum likelihood test.
Stepwise backward selections
1. Loaded model: QVA/QT ~ COfixed effect + PvO2,fixed effect + COrandom effect + PvO2,random effect + random intercepts
2. No COrandom effect model: QVA/QT ~ COfixed effect + PvO2,fixed effect + PvO2,random effect + random intercepts
Compare to loaded (1) model by maximum likelihood test: if P < 0.05 keep COrandom effect as significant random effect.
3. No PvO2,random effect model: QVA/QT ~ COfixed effect + PvO2,fixed effect + COrandom effect + random intercepts
Compare to loaded (1) model by maximum likelihood test: if P < 0.05 keep PvO2,random effect as significant random effect.
4. Final loaded model: QVA/QT ~ COfixed effect + PvO2,fixed effect + significant random effect(s) + random intercepts
5. No COfixed effect: QVA/QT ~ PvO2,fixed effect + significant random effect(s) + random intercepts
Compare to final loaded model (4) by maximum likelihood test: if P < 0.05, COfixed effect is significant, when the fixed effect of PvO2 is already included.
6. No PvO2,fixed effect: QVA/QT ~ COfixed effect + significant random effect(s) + random intercepts
Compare to final loaded model (4) by maximum likelihood test: if P < 0.05, PvO2,fixed effect is significant, when the fixed effect of CO is already included.
†† Committee for the Update of the Guide for the Care and Use of Laboratory Animals, National Research Council: Guide for the Care and Use of Laboratory Animals, 8th edition. Washington, DC, National Academies Press, 2011. Available at: http://www.nap.edu/openbook.php?record_id=12910. Accessed January 14, 2013. Cited Here...
‖ GE Medical Systems IT: Solar® 8000i Patient Monitor Operator’s Manual (revision A). General Electric Company, Milwaukee, WI, 2005. Available at: http://clinicalengineering.duhs.duke.edu/wysiwyg/downloads/Solar_8000i.pdf. Accessed January 14, 2013. Cited Here...
# Research randomizer. Available at: http://www.randomizer.org/form.htm. Accessed January 14, 2013. Cited Here...
** Kramer R: R2 statistics for mixed models. Proceedings of the Conference on Applied Statistics in Agriculture 2005;17:148–60. Available at: http://afrsweb.usda.gov/sp2UserFiles/ad_hoc/12000000SpatialWorkshop/19KramerSupplRsq.pdf. Accessed January 14, 2013. Cited Here...
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