Bohr and B-E V_D/V_T in a ARDS model

Materials and methods

Statistical analysis

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 (evaluates both fixed and random factors) 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).

Results

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 P_AW=31.43±4.15 cmH₂O and compliance=14.51±5.48 ml/cmH₂O.

Measurements by PEEP

Table 1: Measurements by PEEP level

	Baseline	0	5	10	15	20	25	30	P
Airway mechanics
Tvem	295±83.95	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
Pplat	31.43±4.15	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	<0.001
PEEPtot	10.21±0.98	2.25±2.07	6.07±1.01	10.74±1.19	15.86±0.85	20.8±0.65	25.78±0.73	30.64±0.91	<0.001
DeltaPAirway	21.22±4.32	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	<0.001
CStatic	14.51±5.48	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	<0.001
Raw	27.1±11.17	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	<0.001
Transpulmonary mechanics
Ptp-insp	16.94±5.22	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	<0.001
Ptp-esp	-0.7±6.06	-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	<0.001
DeltaPTp	17.64±3.89	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	<0.001
Etorax	1.22±0.7	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	0.228
Ep	5.93±1.7	8.96±2.79	7.99±2.51	6.21±1.74	5.19±1.59	5.13±1.68	5.36±1.73	6.95±2.35	<0.001
Etot	7.15±2.24	10.47±2.92	9.66±2.85	7.55±2	6.5±1.98	6.5±1.89	6.98±2.14	8.73±2.88	<0.001
Gas exchange
PH	7.2±0.06	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	<0.001
Pa/FiO2	125.68±70.16	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	<0.001
PaCO2	62.09±13.63	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	<0.001
Pa-ACO2	29.98±7.86	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	<0.001
PA-aO2	509.7±65.58	571.31±30.27	570.07±28.35	526.41±60.52	421.33±125.55	304.74±166.03	96.92±129.11	67.6±50.19	<0.001
Dead space
Bohr	0.52±0.05	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	<0.001
Vdphys	150.5±41.47	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	<0.001
Vdaw/VT	0.33±0.09	0.32±0.08	0.35±0.1	0.33±0.1	0.39±0.07	0.44±0.1	0.48±0.11	0.53±0.13	<0.001
VDaw	103.77±31.93	93.73±33.11	99.08±33.66	108.09±32.82	118.01±40.12	129.28±42.72	140.44±47.85	150.2±50.4	<0.001
VdalV/VTalV	0.25±0.03	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	<0.001
VTalV	187.81±60.65	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	<0.001
VdB-E/Vt	0.76±0.05	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	<0.001
VdalvB-E/Vtalv	0.64±0.13	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	<0.001
Hemodynamics
FC	122.18±31.5	114.27±25.71	121.18±31.86	119.73±30.28	116.36±33.75	122.64±35.54	127.91±35.4	122.2±36.07	0.825
TAM	93.27±14.33	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	3.12±1.08	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	0.112
VVS	8.25±2.38	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	<0.001
Pulse pressure	40.73±14.06	51.45±7.58	48.18±10.76	48.36±6.98	49.36±12.64	38.45±11.66	34.27±9.95	34±7.63	<0.001
Lung ultrasound
Dorsal	8 (8-8)	8 (8-8)	8 (8-8)	8 (8-8)	7 (7-8)	6 (5-6.75)	3 (2-3.75)	2 (2-2)	<0.001
Ventral	4.5 (4-5.75)	4 (4-6.5)	4.5 (4-5.75)	4 (4-4.75)	4 (3-5)	3.5 (3-4)	2 (2-3)	2 (2-3)	<0.001
Total	12.5 (12-13.75)	12 (12-14.5)	12.5 (12-13.75)	12 (11.25-12.75)	11 (10.25-12)	9 (8-11)	5 (4.25-6)	4 (4-5)	<0.001
Atelectasis (quadrants)	2 (2-2)	2 (2-3)	2 (2-2)	2 (2-2)	1 (1-2)	0 (0-1)	0 (0-0)	0 (0-0)	<0.001

Figure 1: Main physiological variables according to PEEP level.

Figure 2: Comparison V_D/V_T and expiratory P_L relationship according to the equation.

Total V_D/V_T and expiratory P_L disclose a curve relationship with differents slopes. Airway V_D/V_T increases as expiratory P_L increases. The relationship between alveolar V_D/V_T and expiratory P_L 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 V_D/V_T equations.

Table 2: Summary from the quadratic linear model of Bohr V_D/V_T and its components, as a function of expiratory P_L.

	\(\beta\)	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)

Table 3: Summary from the quadratic linear model of BE V_D/V_T and its components, as a function of expiratory P_L.

	\(\beta\)	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		0.54	0.94
Intercept	0.38 (0.32-0.43)
PL	0.0086 (0.0075-0.0097)
PL2	0.00020 (0.00012-0.00028)
Alveolar		0.36	0.68
Intercept	0.69 (0.64-0.75)
PL	-0.0081 (-0.0110–0.0053)
PL2	0.000037 (-0.000187- 0.000261)

Figure 3: Comparison V_D/V_T and inspiratory P_L relationship according to the equation.

Table 4: Summary from the quadratic linear model of Bohr V_D/V_T and its components, as a function of inspiratory P_L.

	\(\beta\)	Marginal R2	Conditional R2
Total		0.29	0.74
Intercept	0.45 (0.26-0.64)
PL	0.0037 (-0.0120- 0.0193)
PL2	0.000086 (-0.000225- 0.000397)
Airway		0.24	0.77
Intercept	0.242 (0.025-0.458)
PL	0.0067 (-0.0109- 0.0243)
PL2	0.00004 (-0.00031- 0.00039)
Alveolar		0.24	0.62
Intercept	0.25 (0.13-0.36)
PL	-0.000076 (-0.009795- 0.009643)
PL2	0.000078 (-0.000115- 0.000271)

Table 5: Summary from the quadratic linear model of BE V_D/V_T and its components, as a function of inspiratory P_L.

	\(\beta\)	Marginal R2	Conditional R2
Total		0.05	0.31
Intercept	0.75 (0.59-0.91)
PL	0.0043 (-0.0091- 0.0176)
PL2	-0.000054 (-0.000318- 0.000209)
Airway		0.16	0.59
Intercept	0.062 (-0.155- 0.279)
PL	0.0027 (-0.0150- 0.0205)
PL2	0.000042 (-0.000307- 0.000392)
Alveolar		0.04	0.36
Intercept	0.65 (0.30-1.01)
PL	0.0041 (-0.0251- 0.0332)
PL2	-0.00014 (-0.00072- 0.00043)

Figure 4: Comparison V_D/V_T and inspiratory P_AW relationship according to the equation.

Table 6: Summary from the quadratic linear model of Bohr V_D/V_T and its components, as a function of inspiratory P_AW.

	\(\beta\)	Marginal R2	Conditional R2
Total		0.33	0.9
Intercept	-0.045 (-0.216- 0.125)
PAW	0.023 (0.016-0.031)
PAW2	-0.00018 (-0.00026–0.00010)
Airway		0.25	0.8
Intercept	-0.256 (-0.535- 0.023)
PAW	0.025 (0.013-0.037)
PAW2	-0.000203 (-0.000335–0.000071)
Alveolar		0.44	0.7
Intercept	-0.0029 (-0.1323- 0.1266)
PAW	0.0105 (0.0046-0.0163)
PAW2	-0.000075 (-0.000137–0.000012)

Table 7: Summary from the quadratic linear model of BE V_D/V_T and its components, as a function of inspiratory P_AW.

	\(\beta\)	Marginal R2	Conditional R2
Total		0.02	0.17
Intercept	0.81 (0.62-0.99)
PAW	-0.00015 (-0.00867- 0.00837)
PAW2	0.0000087 (-0.0000842- 0.0001017)
Airway		0.18	0.58
Intercept	-0.2359 (-0.4696–0.0022)
PAW	0.0147 (0.0041-0.0253)
PAW2	-0.000128 (-0.000243–0.000012)
Alveolar		0.06	0.3
Intercept	0.99 (0.60-1.39)
PAW	-0.0129 (-0.0309- 0.0052)
PAW2	0.000118 (-0.000079- 0.000314)

Figure 5: Comparison V_D/V_T and driving P_AW relationship according to the equation.

Table 8: Summary from the quadratic linear model of Bohr V_D/V_T and its components, as a function of driving P_AW.

	\(\beta\)	Marginal R2	Conditional R2
Total		0.12	0.38
Intercept	0.88 (0.67-1.09)
PAW	-0.021 (-0.036–0.005)
PAW2	0.000318 (0.000037-0.000598)
Airway		0.2	0.38
Intercept	0.83 (0.58-1.08)
PAW	-0.0283 (-0.0470–0.0097)
PAW2	0.000414 (0.000079-0.000750)
Alveolar		0.03	0.18
Intercept	0.36 (0.23-0.49)
PAW	-0.0061 (-0.0158- 0.0037)
PAW2	0.000121 (-0.000055- 0.000297)

Table 9: Summary from the quadratic linear model of BE V_D/V_T and its components, as a function of driving P_AW.

	\(\beta\)	Marginal R2	Conditional R2
Total		0.23	0.51
Intercept	0.64 (0.52-0.75)
PAW	0.0113 (0.0031-0.0196)
PAW2	-0.0001443 (-0.0002932- 0.0000046)
Airway		0.31	0.49
Intercept	0.49 (0.34-0.64)
PAW	-0.024 (-0.036–0.013)
PAW2	0.00036 (0.00016-0.00057)
Alveolar		0.34	0.54
Intercept	0.147 (-0.074- 0.368)
PAW	0.036 (0.019-0.052)
PAW2	-0.0005 (-0.0008–0.0002)

Figure 6: Comparison V_D/V_T and alveolar minus arterial PO₂ relationship according to the equation.

Table 10: Summary from the quadratic linear model of Bohr V_D/V_T and its components, as a function of alveolar minus arterial PO₂.

	\(\beta\)	Marginal R2	Conditional R2
Total		0.41	0.79
Intercept	0.69 (0.64-0.73)
PA-aO2	-0.000352 (-0.000622–0.000082)
PA-aO22	0.00000011 (-0.00000031- 0.00000053)
Airway		0.32	0.69
Intercept	0.53 (0.47-0.59)
PA-aO2	-0.000485 (-0.000884–0.000085)
PA-aO22	0.00000028 (-0.00000034- 0.00000091)
Alveolar		0.42	0.58
Intercept	0.36 (0.33-0.38)
PA-aO2	-0.00033 (-0.00053–0.00013)
PA-aO22	0.000000283 (-0.000000033- 0.000000599)

Table 11: Summary from the quadratic linear model of BE V_D/V_T and its components, as a function of alveolar minus arterial PO₂.

	\(\beta\)	Marginal R2	Conditional R2
Total		0.2	0.35
Intercept	0.85 (0.82-0.88)
PA-aO2	-0.00049 (-0.00073–0.00025)
PA-aO22	0.00000082 (0.00000044-0.00000119)
Airway		0.35	0.64
Intercept	0.18 (0.14-0.22)
PA-aO2	0.00013 (-0.00015- 0.00041)
PA-aO22	-0.000000521 (-0.000000960–0.000000082)
Alveolar		0.29	0.49
Intercept	0.67 (0.61-0.73)
PA-aO2	-0.00063 (-0.00111–0.00015)
PA-aO22	0.0000013 (0.0000006-0.0000021)

Figure 7: Comparison V_D/V_T and arterial PCO₂ relationship according to the equation.

Table 12: Summary from the quadratic linear model of Bohr V_D/V_T and its components, as a function of arterial PCO₂.

	\(\beta\)	Marginal R2	Conditional R2
Total		0.1	0.63
Intercept	0.86 (0.50-1.23)
PaCO2	-0.0064 (-0.0173- 0.0044)
PaCO22	0.00003 (-0.00005- 0.00011)
Airway		0.08	0.62
Intercept	0.55 (0.10-1.00)
PaCO2	-0.0015 (-0.0149- 0.0118)
PaCO22	-0.000011 (-0.000109- 0.000087)
Alveolar		0.11	0.24
Intercept	0.49 (0.29-0.70)
PaCO2	-0.00544 (-0.01182- 0.00093)
PaCO22	0.000034 (-0.000015- 0.000082)

Table 13: Summary from the quadratic linear model of BE V_D/V_T and its components, as a function of arterial PCO₂.

	\(\beta\)	Marginal R2	Conditional R2
Total		0.31	0.62
Intercept	0.82 (0.60-1.03)
PaCO2	-0.0026 (-0.0088- 0.0037)
PaCO22	0.0000376 (-0.0000078- 0.0000829)
Airway		0.28	0.83
Intercept	0.294 (-0.003- 0.592)
PaCO2	-0.00033 (-0.00881- 0.00816)
PaCO22	-0.000031 (-0.000092- 0.000029)
Alveolar		0.35	0.85
Intercept	0.469 (0.052-0.887)
PaCO2	-0.001 (-0.013- 0.011)
PaCO22	0.000063 (-0.000022- 0.000148)