Quantitative variable are expressed as mean±sd. In order to overule pseudoreplication due to repeated measurement to the same animal, mixed effect regression models were use built with nlme package. In these cases, the animal was included as a random intercept. Model marginal (related to fixed factors) and conditional coefficients of determination for mixed-effect models were calculated using MuMIn package. A similar approach was used when fitting analysis of variance models.
Statistical analysis was performed with R version 3.3.3 (2017-03-06).
Baseline respiratory parameters were as follows: Vt=295±83.95 ml, PaFiO2=125.68±70.16 mmHg, pH=7.2±0.06, PaCO2=62.09±13.63 mmHg, inspiratory static PAW=31.43±4.15 cmH2O and compliance=14.51±5.48 ml/cmH2O.
| 0 | 5 | 10 | 15 | 20 | 25 | 30 | P | |
|---|---|---|---|---|---|---|---|---|
| Airway mechanics | ||||||||
| freqm | 23.09±6.09 | 22.91±5.75 | 23.09±6.09 | 22.73±5.46 | 23.09±6.09 | 22.73±5.46 | 23±5.68 | 0.43 |
| Tvem | 303.02±82.56 | 293.18±85.71 | 299.66±83.02 | 300.55±82.66 | 298.64±83.97 | 301.32±83.4 | 297.1±91.46 | 0.12 |
| autoPEEP | 2.25±2.07 | 1.07±1.01 | 0.74±1.19 | 0.86±0.85 | 0.8±0.65 | 0.78±0.73 | 0.64±0.91 | 0.00034 |
| Pplat | 33.32±5.94 | 34.02±5.58 | 33.62±4.32 | 35.49±5.07 | 40.46±4.68 | 48.1±7.19 | 57.59±8.31 | <2e-16 |
| DeltaPAirway | 31.07±6.63 | 27.95±5.78 | 22.88±4.59 | 19.62±4.84 | 19.66±4.77 | 22.32±7.41 | 26.96±8.66 | 7.4e-10 |
| CStatic | 9.97±2.9 | 10.74±3.55 | 13.42±4.03 | 15.82±5.01 | 15.75±5.25 | 14.67±6.25 | 12.16±6.75 | 2.7e-09 |
| Raw | 38.18±7.93 | 35.54±5.92 | 25.38±6.4 | 23.81±4.85 | 22.14±5.38 | 22.06±4.62 | 19.97±7.26 | 4.6e-15 |
| Transpulmonary mechanics | ||||||||
| Ptp-esp | -8.11±7.03 | -3.82±6.5 | -1.06±5.91 | 3.18±4.95 | 6.23±5.27 | 9.29±5.24 | 12.54±5.79 | <2e-16 |
| Ptp-insp | 19.33±4.31 | 19.87±4.38 | 17.9±3.88 | 19.2±3.13 | 21.76±4.48 | 25.66±5.54 | 33.31±4.5 | 1.1e-10 |
| DeltaPTp | 27.44±6.69 | 23.69±5.68 | 18.96±4.78 | 16.02±4.54 | 15.54±4.75 | 16.37±4.47 | 20.77±5.5 | 8.8e-08 |
| Etorax | 1.51±0.48 | 1.67±0.51 | 1.34±0.5 | 1.31±0.5 | 1.37±0.94 | 1.62±0.96 | 1.78±1.05 | 0.23 |
| Ep/Etot | 0.85±0.05 | 0.82±0.04 | 0.82±0.06 | 0.8±0.05 | 0.79±0.11 | 0.77±0.1 | 0.8±0.09 | 0.33 |
| Ptp-inspElas | 29.63±5.73 | 28.93±5.57 | 28.2±4.75 | 29.03±4.74 | 32.28±5.74 | 36.53±5.36 | 45.76±5.77 | 1e-08 |
| Gas exchange | ||||||||
| PH | 7.16±0.06 | 7.16±0.08 | 7.2±0.06 | 7.21±0.07 | 7.2±0.08 | 7.23±0.09 | 7.2±0.06 | 0.00011 |
| PaCO2 | 72.59±15.88 | 70.55±12.32 | 64.7±13.91 | 60.74±10.74 | 60.62±12.77 | 57.55±15.7 | 59.37±14.34 | 4.1e-07 |
| HCO3 | 25.26±3.89 | 25.55±3.85 | 25.05±3.74 | 24.37±3.64 | 23.27±3.43 | 23.7±4.61 | 23.47±5.01 | 0.0035 |
| Pa/FiO2 | 50.95±22.01 | 54.74±19.54 | 105.72±58.81 | 215.75±124.33 | 332.49±169.2 | 548.55±140.55 | 571.19±56.03 | <2e-16 |
| Dead space | ||||||||
| PeCO2 | 10.87±3.41 | 13.02±5.48 | 12.99±4.24 | 13.72±4.33 | 12.24±3.31 | 11.17±3.23 | 10.65±3.1 | 0.0018 |
| PECO2 | 10.13±2.3 | 11.7±5.18 | 12.25±3.82 | 13.47±4.51 | 11.71±2.99 | 10.65±2.88 | 9.54±3.22 | 0.00075 |
| PACO2 | 21.17±6.62 | 24.35±10.03 | 27.39±9.59 | 30.97±12.41 | 31.32±10.87 | 32.27±12.24 | 34.02±13.53 | 3.2e-07 |
| PetCO2 | 27.99±16.06 | 33.18±16.47 | 35.88±12.6 | 39.93±13.93 | 39.66±14.11 | 38.08±12.78 | 40.29±15.09 | 0.00018 |
| Pa-ETCO2 | 44.6±23.92 | 37.37±21.11 | 28.82±18.65 | 20.8±15.43 | 20.95±15.33 | 19.47±13.16 | 19.08±14.1 | 1.2e-10 |
| Pa-ACO2 | 51.43±12.88 | 46.21±10.9 | 37.31±10.95 | 29.77±10.21 | 29.3±8.06 | 25.29±4.95 | 25.35±4.26 | 5.6e-12 |
| VCO2br | 4.32±2.13 | 5.07±3.11 | 5.37±2.89 | 5.71±2.95 | 5.02±2.74 | 4.59±2.5 | 4.18±2.7 | 5.3e-05 |
| Bohr | 0.51±0.08 | 0.52±0.09 | 0.53±0.06 | 0.55±0.05 | 0.61±0.07 | 0.65±0.08 | 0.69±0.1 | <2e-16 |
| Vdphys | 149.33±48.88 | 147.74±45.8 | 155.5±42.02 | 166.8±47.34 | 178.48±49.81 | 190.97±56.04 | 198.6±59.73 | <2e-16 |
| alV | 55.6±20.07 | 48.66±16.25 | 47.41±14.36 | 48.8±14.12 | 49.2±15.86 | 50.53±16.54 | 48.4±19.13 | 0.061 |
| VTalV | 202.79±64.6 | 192.65±67.85 | 190.31±61.41 | 183.44±53.01 | 167.5±58.1 | 158.08±56.54 | 142.77±63.18 | 2.7e-14 |
| VdalV/VTalV | 0.27±0.05 | 0.26±0.05 | 0.25±0.02 | 0.27±0.03 | 0.3±0.03 | 0.33±0.03 | 0.35±0.06 | 6.7e-10 |
| VdB-E/Vt | 0.86±0.02 | 0.83±0.06 | 0.8±0.06 | 0.77±0.05 | 0.8±0.03 | 0.81±0.04 | 0.84±0.04 | 0.00034 |
| VdalvB-E | 157.95±51.56 | 139.7±47.12 | 130.95±41.69 | 112.07±40.26 | 105.89±41.04 | 98.41±38.83 | 87.81±39.63 | 4e-15 |
| VdalvB-E/Vtalv | 0.79±0.04 | 0.75±0.11 | 0.71±0.12 | 0.61±0.11 | 0.63±0.07 | 0.64±0.07 | 0.65±0.12 | 1.3e-05 |
| Hemodynamics | ||||||||
| TAS | 123.55±31.71 | 126.27±28.92 | 124.73±18.43 | 125±16.73 | 114.55±14.31 | 104.18±20.4 | 100.3±16.71 | 0.0035 |
| TAM | 94±30.1 | 96.45±29.04 | 94.82±17.57 | 94.27±18.3 | 90.73±14.17 | 81.09±17.41 | 78.9±14.25 | 0.058 |
| IC | 4.84±1.1 | 3.68±1.13 | 4.22±0.32 | 3.58±0.9 | 3.42±1.28 | 3.76±1.5 | 2.98±1.1 | 0.11 |
| VVS | 6.5±2.56 | 6.5±1.77 | 7.25±1.49 | 9.62±3.89 | 15.38±6.16 | 19±9.77 | 29.57±14.36 | 5.3e-09 |
As expected, PL shows a linear relationship with PAW (marginal and conditional mixed model R2 are 0.83 and 0.98 respectively, P= \(2.693\times 10^{-47}\)).
Total VD/VT and expiratory PL disclose a curve relationship with differents slopes. Airway VD/VT increases as expiratory PL increases. The relationship between alveolar VD/VT and expiratory PL appears to fit a curved shape function when Bohr method is used, whereas it is a straight line when using BE equation. Lines in figure 2 represent individual and pooled fixed effect (dotted blue line) predicted values from quadratic functions. Table 2 and 3 show summary results from mixed models for both VD/VT equations.
| \(\beta\) | Marginal R2 | Conditional R2 | |
|---|---|---|---|
| Total | 0.53 | 0.93 | |
| Intercept | 0.54 (0.50-0.59) | ||
| PL | 0.0072 (0.0062-0.0083) | ||
| PL2 | 0.00024 (0.00016-0.00032) | ||
| Airway | 0.54 | 0.94 | |
| Intercept | 0.38 (0.32-0.43) | ||
| PL | 0.0086 (0.0075-0.0097) | ||
| PL2 | 0.00020 (0.00012-0.00028) | ||
| Alveolar | 0.26 | 0.73 | |
| Intercept | 0.27 (0.24-0.30) | ||
| PL | 0.0022 (0.0011-0.0033) | ||
| PL2 | 0.000168 (0.000084-0.000252) |
| \(\beta\) | Marginal R2 | Conditional R2 | |
|---|---|---|---|
| Total | 0.12 | 0.36 | |
| Intercept | 0.81 (0.79-0.83) | ||
| PL | -0.00203 (-0.00370–0.00035) | ||
| PL2 | 0.00013471 (-0.00000043- 0.00026985) | ||
| Airway | 0.49 | 0.85 | |
| Intercept | 0.117 (0.079-0.155) | ||
| PL | 0.0062 (0.0047-0.0076) | ||
| PL2 | 0.000094 (-0.000016- 0.000203) | ||
| Alveolar | 0.36 | 0.68 | |
| Intercept | 0.69 (0.64-0.75) | ||
| PL | -0.0081 (-0.0110–0.0053) | ||
| PL2 | 0.000037 (-0.000187- 0.000261) |
Optimized parameter where defined as follows:
Table 4 shows physiological values recorded with each optimized parameter in the rows.
| VdalV/VTalV | VCO2br | Ptp-esp | CStatic | Pplat | Ptp-inspElas | P | |
|---|---|---|---|---|---|---|---|
| PEEPtot | 8.17±5.07 | 11.48±6.84 | 11.06±6.22 | 19.1±6.33 | 8.06±5.88 | 10.64±8.16 | 0.002024 |
| Pplat | 33.22±4.53 | 35.32±7.19 | 36.47±7.6 | 37.24±5.35 | 32.91±3.98 | 34.99±7.1 | 0.073583 |
| DeltaPAirway | 25.04±7.6 | 23.84±7.35 | 25.4±4.33 | 18.13±3.62 | 24.85±6.48 | 24.35±3.49 | 0.010644 |
| CStatic | 12.73±5.76 | 13.59±6.02 | 13.05±4.63 | 17.1±5.87 | 12.3±3.36 | 13.05±3.15 | 0.0027749 |
| Bohr | 0.5±0.06 | 0.52±0.05 | 0.53±0.05 | 0.59±0.08 | 0.52±0.07 | 0.54±0.03 | 3.5862e-05 |
| VdalV/VTalV | 0.23±0.03 | 0.25±0.04 | 0.26±0.04 | 0.29±0.03 | 0.26±0.03 | 0.28±0.02 | 4.8528e-05 |
| VCO2br | 5.44±3.02 | 6.07±2.88 | 5.86±3.25 | 5.33±2.36 | 4.97±2.14 | 4.85±2.4 | 0.0065323 |
| Pa-ETCO2 | 30.65±19.41 | 27.19±18.58 | 33.54±25.37 | 18.59±14.12 | 32.97±22.38 | 35.86±29.6 | 0.021485 |
| VdB-E/Vt | 0.8±0.06 | 0.77±0.06 | 0.81±0.06 | 0.78±0.04 | 0.81±0.06 | 0.84±0.05 | 0.058531 |
| Ptp-esp | -1.81±6.11 | 0.6±6.99 | -0.26±1.58 | 5.69±8.17 | -2.54±6.91 | -1.95±5.82 | 0.032026 |
| Ptp-inspElas | 28.2±4.76 | 29.74±6.14 | 30.16±7.41 | 29.33±5.94 | 27.69±4.37 | 27.12±2.4 | 0.5356 |
| DeltaPTp | 20.87±6.67 | 19.85±6.51 | 21.01±4.29 | 13.79±3.5 | 20.33±5.88 | 19.41±4.52 | 0.06245 |
| Pa/FiO2 | 92.31±60.16 | 176.89±169.55 | 93.31±67.81 | 336.64±162.16 | 119.44±103.05 | 122.42±126.27 | 0.00027092 |
| PaCO2 | 65.35±12.73 | 63.5±14.44 | 70.72±15.38 | 59.24±12.17 | 66.45±13.25 | 68.04±20.85 | 0.11035 |
| HCO3 | 25.16±3.35 | 24.63±3.48 | 25.3±4.14 | 24.31±3.65 | 25.45±3.25 | 24.62±4.41 | 0.26509 |
Only those with significant ANOVA P above are displayed
## $PEEPtot
##
## $DeltaPAirway
##
## $CStatic
##
## $VCO2br
##
## $`Pa-ETCO2`
##
## $`Ptp-esp`
##
## $`Pa/FiO2`