Bedside estimation of nonaerated lung tissue using blood gas analysis
Andreas W. Reske, Eduardo Leite Vieira Costa, Alexander P. Reske, Anna Rau,
João B. Borges, Marcelo A. Beraldo, Udo Gottschaldt, Matthias Seiwerts, Dierk
Schreiter, David Petroff, Udo X. Kaisers, Hermann Wrigge, Marcelo B. P. Amato.
SUPPLEMENTAL DIGITAL CONTENT
1
Methods
Modeling the relationship between physiological shunt and PaO2
To study the relationship between physiological shunt and its surrogate PaO2, we
built a model based on Berggren’s equation and on Fick’s principle (Figs. S1-S3,
Supplemental Digital Content 2, http://links.lww.com/CCM/A554; Supplemental
Digital Content 3, http://links.lww.com/CCM/A555; and Supplemental Digital Content
4, http://links.lww.com/CCM/A556, respectively). Using this model, PaO2 can be
determined from physiological shunt if the following parameters are entered (values
used in parentheses): oxygen extraction rate (0.3), pH (7.4), arterial partial pressure
of carbon dioxide (PaCO2, 40mmHg), FiO2 (1.0), hemoglobin, oxygen consumption,
and cardiac output. We used random samples of normal distributions of oxygen
consumption (mean=400ml/min and SD=20ml/min) and of hemoglobin values
(mean=10g/dl and SD=0.5g/dl). Cardiac output values were sampled from normal
distributions generated with the mean values increasing from 6.0 to 10.0 L/min in
steps of 0.5 L/min, and with a coefficient of variation of 5%. For each cardiac output
distribution, we ran the model 160 times with physiological shunt values varying from
0.025 to 0.8 in steps of 0.005.
In all the following notations, “x” represents either venous, lung capillary or arterial
blood. Hemoglobin oxygen saturation was calculated according to equation 1 (S4).
(1)
Blood oxygen content was calculated according to standard formula (equation 2)
(S5).
2
(2)
Alveolar partial pressure of oxygen was used to approximate capillary partial
pressure of oxygen assuming null diffusion gradient (equation 3) (S6).
(3)
The lung was considered as a two-compartment model consisting of shunt or perfect
oxygenation. Arterial oxygen content was calculated according to Fick's principle
(equation 4) (S2, S3).
(4)
The mathematical model
The input variables to the model were cardiac output (QT), shunt fraction
(Fshunt), pH, PaCO2, Hb, FiO2 =1, maximal oxygen extraction rate (ERmax), PvO2init,
and oxygen consumption (VO2max). In the first run, mixed venous oxygen content was
calculated according to equation 2, where x = mixed venous blood, PvO2 = PvO2init,
and SvO2 was calculated using equation 1. Arterial oxygen content was then
calculated as a perfusion weighted average of CcO2 and CvO2 according to equation
4. DO2 for each compartment was subsequently calculated by multiplying QT by the
arterial oxygen content. VO2 was calculated according to equation 5:
3
VO2 = DO2 . ERmax if DO2 . ERmax < VO2max
(5)
VO2 = VO2max
if DO2 . ERmax ≥ VO2max
A new value for the mixed venous oxygen content was then obtained using equation
6.
(6)
PvO2 and SvO2 were determined from CvO2 by solving equations 1 and 2 to an
acceptable error of 1:1000 using the Newton-Raphson method. The new calculated
PvO2 substituted PvO2init in the second run of the model yielding a new, updated
value of PvO2. This process continued until PvO2 would change by less 0.001 mmHg
each run. At this point, the algorithm stopped and gave the following output variables:
PvO2, SvO2, CvO2, PcO2, ScO2, CcO2, PaO2, SaO2, CaO2, VO21, VO21, CvO21, CvO22,
DO2, and VO2.
Some of the parameters in the model were calibrated using data obtained in the
animal experiments described below.
A more sophisticated model was used to simulate the influence of different inspired
oxygen fractions on the calculus of venous admixture. In this model, we added 49
compartments in parallel to the shunt compartment. We assumed that the remaining
non-shunting cardiac output was evenly distributed across those 49 compartments,
each one having different ventilation and, consequently, a different V/Q ratio. In each
4
compartment, end-capillary partial pressure of oxygen was allowed to equilibrate with
the alveolar partial pressure of oxygen, which was obtained by solving the mass
balance equation for oxygen (equation 7) with the Newton-Raphson method. The
model was adjusted to present an average V/Q ratio of 0.89 and a distribution with
log(SD) = 0.26. Clinically, this model would represent a patient with moderate to
severe V/Q inhomogeneity, typically found in patients submitted to low tidal-volume
ventilation (S12).
 V 
 V 
   PiO 2    PAO 2  CcO 2  CvO 2


Q
Q
(7)
The acronym PiO2 refers to the inspiratory partial pressure of oxygen.
Animal experiments
To obtain data for a wide range of lung aeration, we used data from an experiment
during which ten pigs (mean weight 27 kg, standard deviation 2.3 kg) were subjected
to saline lung lavage (surfactant washout) and subsequent injurious mechanical
ventilation leading to experimental acute lung injury (ALI) as described below. Arterial
and mixed-venous blood gases were obtained at different airway pressures resulting
in varying amounts of nonaerated lung.
The pigs were premedicated (intramuscular acepromazin, ketamin and midazolam),
anesthestized (continuous intravenous infusion of ketamine, thiopental and
midazolam), tracheotomized (7.0 mm ID endotracheal tube) and mechanically
ventilated (New Port e500, Newport Medical, CA, USA). Ventilator settings during
baseline pressure controlled ventilation were: driving pressure of 10 cmH2O, positive
5
end-expiratory pressure (PEEP) of 5 cmH2O, respiratory rate of 20*min-1, inspiratoryto-expiratory ratio (I:E) of 1:2 and the fraction of inspired oxygen (FiO2) was 1.0. A
pulmonary artery catheter (PAC 7.5F, CCOmbo CCO/SvO2, Edwards Lifesciences,
Germany) was introduced via the right external jugular vein for sampling of mixed
venous blood. The correct position of the PAC was confirmed by analysis of pressure
tracings. The left femoral artery was cannulated for sampling of arterial blood and
continuous blood pressure monitoring. Arterial and mixed venous blood-gases were
analyzed using a co–oximeter (ABL 800 flex, Radiometer©, Copenhagen, Denmark).
Experimental lung injury was induced by repeated lung lavage with normal saline (30
ml/kg body weight, body temperature) until the PaO2 remained stable below 100
mmHg for at least 10 minutes during ventilation with pure oxygen (S7). A mean
number of 10 (standard deviation 3.2) lung lavages was required to reach this
criterion. Immediately after the lung lavage procedure, injurious mechanical
ventilation with low PEEP (1 to 5 cmH2O) and high peak airway pressures (42 to 48
cmH2O) was started and maintained for three hours. After completion of this period of
injurious mechanical ventilation, pigs were submitted to a lung recruitment maneuver.
The lung recruitment maneuver was performed by stepwise increases of PEEP and
peak airway pressures using the following ventilator settings: respiratory rate of
20*min-1, I:E of 1:2 and FiO2 of 1.0. Maintaining a constant driving pressure of 15
cmH2O, PEEP was increased in steps of 5 cmH2O from 25 cmH2O to 45 cmH2O.
Each incremental PEEP step lasted two minutes. The sequence of incremental PEEP
steps was continued until the peak airway pressure reached 60 cmH2O or until our
blood gas-based recruitment target - PaO2 plus arterial partial pressure of carbon
dioxide (PaCO2) equal ore greater than 400 mmHg - was reached. Immediately after
the lung recruitment maneuver, a decremental PEEP titration was started during
which PEEP was decreased in steps of 2 cmH2O from 25 to 5 cmH2O. During the
6
decremental PEEP titration, each PEEP level was maintained for four minutes with a
fixed driving pressure of 6 cmH2O during pressure controlled ventilation. Arterial and
mixed-venous blood samples were drawn at the end of each PEEP step and
immediately afterwards analyzed at body temperature. At the end of the experiment,
animals were killed by an intravenous overdose of thiopental and potassium chloride.
Patients
We analyzed data of patients in whom CT scanning had been requested by the
treating physician as clinical diagnostic procedure for emergency trauma workup or in
patients from Intensive Care Unit (ICU). All patients had indwelling arterial catheters
which were placed for routine hemodynamic management through which arterial
blood was sampled for blood gas analysis immediately before or after CT.
Patients with multiple trauma were treated by the trauma team following standardized
institutional guidelines with a whole-body helical CT with contrast medium as the
central diagnostic component (S8-S10). Pressure controlled mechanical ventilation
(Oxylog 3000, Dräger, Lübeck, Germany) during primary resuscitation and
transportation to the CT suite was standardized and included the following ventilator
settings: target tidal volume of 6-8 ml/kg estimated body weight (estimated weight in
kilograms equals height in centimeters minus 100), a respiratory rate of 20*min-1 and
PEEP of 10 cm H2O unless higher PEEP had already been applied upon admission.
The FiO2 during initial resuscitation and CT was 1.0. Subsequent FiO2 adjustment
was at the discretion of the physician in charge.
7
For intensive care unit patients, all previous ventilator settings were maintained on
the
transport
ventilator
(Oxylog
3000,
Dräger,
Lübeck,
Germany)
during
transportation to the CT suite, only the FiO2 was changed to 1.0 before
transportation.
Derecruitment due to disconnection from the mechanical ventilator was prevented by
clamping the endotracheal tube.
Physiological
and
demographic
data,
ventilator
variables
and
blood
gas
measurements data had been prospectively and automatically entered into the
patient data management system of our institution.
CT scanning
All patients underwent multislice helical CT using either a Somatom Volume Zoom
(Siemens, Erlangen, Germany) or a MX-8000 IDT 16 (Philips Medical Systems,
Hamburg, Germany) scanner during uninterrupted mechanical ventilation. The
following scan protocols were used: Somatom Volume Zoom - 120 kV tube voltage,
165 mAs tube current, 4 x 2.5 mm collimation, pitch 1.1; and MX-8000 IDT 16 - 120
kV tube voltage, 180 mAs tube current, 16 x 1.5 mm collimation, and pitch 0.622.
Depending on the CT scanner, the reconstruction filters “B” (MX-8000 IDT 16) or
“B60f” (Somatom Volume Zoom) were used for reconstruction of CT image series
covering the entire thorax. Contrast material was administered when clinically
indicated (120 ml Iopamidol, Schering AG, Berlin, Germany).
8
Prediction of CT-shunt from PaO2/FiO2 values
In a final regression analysis relating PaO2/FiO2 and CT-shunt (%Mass [-200 to +100]
HU, this choice of interval is justified in the discussion section of the main text), we
choose PaO2/FiO2 as the dependent variable, since that will be used to estimate CTshunt. We performed a logit transformation of CT-shunt /100 to ensure that it remains
within the interval [0, 100] and to have much higher homoscedasticity. Supplemental
Figure 4 (Supplemental Digital Content 5, http://links.lww.com/CCM/A557) and the
value for the coefficient of determination R2=0.85 demonstrate that these quantities
are also modelled well by a linear relationship. The result of the regression analysis is
 CT-shunt

ln 
  0.79  0.00735  PaO2 / FiO2
 100  CT-shunt 
with 95% CIs of [0.52, 1.05] and [-0.0081, -0.0066] for the intercept and slope
respectively. This equation was used to calculate the results presented in Table 3 of
the main text relating PaO2/FiO2 and the predicted amounts of CT-shunt in the form
of a lookup table. In addition to this table, Supplemental Figure 4 (Supplemental
Digital Content 5, http://links.lww.com/CCM/A557) and Supplemental Figure 5
(Supplemental Digital Content 6, http://links.lww.com/CCM/A558) also illustrate the
95% confidence interval of the regression line as well as the 75% and 95% prediction
intervals within which the respective percentage of CT-shunt values predicted from
PaO2/FiO2 measurements will fall.
Preliminary validation tests
Thorough and statistically powerful validation of our findings requires sufficiently large
validation samples the collection of which is an ongoing project of our research
group. Therefore, we performed analyses on a preliminary validation sample (12
9
patients) in order to check our initial results. All patients had acute respiratory
distress syndrome (ARDS, mild to severe) according to the Berlin definition of ARDS
(S11).
Visual inspection of a plot showing the new data points of the test patients together
with the initial data revealed no obvious differences between the initial and the test
data. The same applies to comparison of the regression residuals of the test data
(calculated using the regression equation obtained with the initial data) to the
regression residuals of the initial analysis. As prediction of the amount of nonaerated
lung parenchyma from measurement of PaO2/FiO2 is to be validated here, we chose
the ln transformation of PaO2/FiO2 as the independent variable for these figures.
10
We also tested whether the amount of nonaerated lung parenchyma (nonaerated
lung mass within -200 to +100 HU) predicted from PaO2/FiO2 (measured during
100% oxygen ventilation) of the new patients would fall into the 75% prediction
intervals given in Table 3 of the main text. Because we have only few validation data
for testing the prediction intervals given in Table 3, we omit further statistical
analyses, but mention in passing that 10 out of the 12 values lie within the 75%
prediction interval. This corresponds well to what one expects. Taking these new
results from the validation sample into account, we feel reassured that our results do
apply to mechanically ventilated patients with a clinically relevant spectrum of lung
conditions, including ARDS patients and we look forward to presenting more powerful
validation results in the future.
11
References for the Supplemental Digital Content
S1.
Berggren SM: The oxygen deficit of arterial blood caused by
nonventilating parts of the lung. Acta Physiol Scand 1942; 4(suppl
XI):1– 92.
S2.
Riley RL, Cournand A: Analysis of factors affecting partial pressures of
oxygen and carbon dioxide in gas and blood of lungs; theory. J Appl
Physiol 1951; 4:77-101
S3.
Riley RL, Cournand A, Donald KW: Analysis of factors affecting partial
pressures of oxygen and carbon dioxide in gas and blood of lungs;
methods. J Appl Physiol 1951; 4:102-120
S4.
Severinghaus JW: Simple, accurate equations for human blood O2
dissociation computations. J Appl Physiol 1979; 46:599-602
S5.
Roughton FJ, Severinghaus JW: Accurate determination of O2
dissociation curve of human blood above 98.7 percent saturation with
data on O2 solubility in unmodified human blood from 0 degrees to 37
degrees C. J Appl Physiol 1973; 35:861-869
S6.
Riley RL, Cournand A: "Ideal" Alveolar air and the analysis of
ventilation-perfusion relationships in the lungs. J Appl Physiol
1949; 1:825-847
S7.
Lachmann B, Jonson B, Lindroth M, et al: Modes of artificial
ventilation in severe respiratory distress syndrome. Lung function and
morphology in rabbits after wash-out of alveolar surfactant. Crit Care
Med 1982; 10:724-732
S8.
Schreiter D, Reske A, Stichert B, et al: Alveolar recruitment in
combination with sufficient positive
end-expiratory
pressure
12
increases oxygenation and lung aeration in
patients
with
severe
chest trauma. Crit Care Med 2004; 32:968-975
S9.
Reske AW, Reske AP, Heine T, et al: Computed tomographic
assessment of lung weights in trauma patients with early posttraumatic
lung dysfunction. Crit Care 2011; 15:R71
S10.
Huber-Wagner S, Lefering R, Qvick LM, et al: Effect of whole-body CT
during trauma resuscitation on survival: a retrospective, multicentre
study. Lancet 2009; 373:1455-1461
S11.
The
ARDS
Definition
Syndrome-The
Task Force.
Berlin
Acute
Definition.
Respiratory Distress
JAMA
2012;
307:doi:10.1001/jama.2012.5669
S12.
Feihl F, Eckert P, Brimioulle S, Jacobs O, Schaller MD, Mélot C, Naeije
R. Permissive hypercapnia impairs pulmonary gas exchange in the
acute respiratory distress syndrome. Am J Respir Crit Care Med 2000;
162:209-215
13
Supplemental Figure Legends
Supplemental Figure 1:
Supplemental Figure 1 illustrates the regression of the logarithmically (ln)
transformed PaO2/FiO2 on Riley‘s approximation to shunt for theoretical data from
model simulations (left panel), data from the animal experiment in pigs with acute
lung injury (middle panel) and data from the 77 patients with single data-points (right
panel). All PaO2/FiO2 measurements or simulations were made during 100% oxygen
ventilation. For the definition of Riley‘s approximation to shunt, the reader is referred
to the Methods section of the main manuscript. The red dashed lines correspond to
the least squares regression lines. PaO2/FiO2 - arterial partial pressure of oxygen
divided by the fraction of inspired oxygen (FiO 2). ln, natural logarithm. R2 - coefficient
of determination.
Supplemental Figure 2:
Supplemental Figure 2 illustrates the influence of the fraction of inspired oxygen
(FiO2) on the correlation between venous admixture (in the case of FiO 2 below 1) or
physiological shunt (pure oxygen ventilation), respectively, and lnPaO2/FiO2. The
plots represent simulated data, using a multi-compartment model with 49
compartments
representing
moderate
to
severe
ventilation-to-perfusion
inhomogeneity and one shunt compartment (see supplemental Methods). This
situation is typically found in patients submitted to low tidal-volume ventilation. The
wider scattering of data points associated with lower FiO2 obviously degrades the
correlation and is the consequence of two phenomena: a) in the presence of low V/Q
units with critically low alveolar-PO2, random changes in cardiac output, hemoglobin
14
concentration or oxygen consumption (as simulated in the model) have larger impact
on PaO2 and on the calculus of venous admixture; and b) we simulated changes in
FiO2 around the mean (50%), with a standard deviation (SD) of 10% to reproduce
slightly varying FiO2 values during the patient evolution. Despite the proper
computation of the FiO2 actually applied, the impact on venous admixture and on
PaO2/FiO2 is non-linear, causing additional scattering.
Supplemental Figure 3:
Supplemental Figure 3 illustrates the influence of the fraction of inspired oxygen
(FiO2) on the correlation between Riley‘s approximation to physiological shunt and
CT-shunt (upper panels) and between the logarithmically (ln) transformed PaO2/FiO2
and CT-shunt (lower panels). Data in this figure were obtained in a subgroup of 27
patients out of the 77 patients with single data-points for whom we had PaO2/FiO2
measurements for both, 50% and 100% oxygen (with a time interval of approximately
ten minutes between measurements and where one data point had to be removed
since it was an outlier with very large leverage). The use of 100% oxygen improved
the correlations but note that this correlation analysis is not robust enough to
demonstrate the influence of FiO2 conclusively. Most of these patients had low levels
of CT-shunt, thus representing healthier conditions than the simulations with greater
ventilation-to-perfusion inhomogeneity in Supplemental Figure 2 (Supplemental
Digital Content 3, http://links.lww.com/CCM/A555). For the definition of different shunt
entities, the reader is referred to the Methods section of the main manuscript. The
thick red dashed lines correspond to the least squares regression lines and the black
dashed lines mark the 95%CIs of the regression line. PaO2 - arterial partial pressure
of oxygen. ln - natural logarithm. %Mass-200
to +100 HU
(left panel) refers to the lung
15
mass within the given interval of Hounsfield Units (HU) expressed as percentage of
the total lung mass. R2 - coefficient of determination.
16
Supplemental Table 1. Patient data
Number of patients (female)
Number of CTs / patient
Age (years)
Body mass index
Multiple trauma patients (%)
Other patients (%)
Patients with ARDS (%)
Time to first CT (hours)
Time to repeat CT (hours)
Contrast medium
PEEP (cm H2O)
PIP (cm H2O)
PaO2/FiO2 at CT (mm Hg)
PaCO2 at CT (mm Hg)
delta PaO2/FiO2 (mm Hg)
Hemoglobin (g*dl-1)
Total lung weight (g)
Total lung volume (ml)
%V-100 to +100 HU (%)
%V-500 to -100 HU (%)
%M-100 to +100 HU (%)
%M-200 to +100 HU (%)
%M-500 to -100 HU (%)
single CT
77 (17)
45 (15-82)
25.7 (20.2-37.0)
61 (79 %)
16 (21 %)
34 (44 %)
2.0 (0.75-437)
69 (90 %)
10 (6-20)
25 (19-37)
327 (54-664)
46.7 (27.3-128.0)
10.6 (5.5-15.3)
992 (636-3019)
3738 (1568-6213)
3.5 (0.1-53.7)
7.0 (1.8-43.6)
12.0 (0.7-78.8)
15.8 (1.3-82.5)
15.6 (5.4-50.8)
repeat CT
8 (1)
2 (2-4)
30 (17-75)
24.3 (19.9-29.7)
7 (87%)
1 (13%)
5 (63 %)
1.7 (1.3-120.0)
29 (7-334)
8 (75 %)
10 (10-20)
23 (16-37)
301 (48-592)
48.8 (32.4-78.1)
113 (13-441)
10.0 (8.9-14.5)
1381 (783-3017)
3715 (2078-6351)
5.4 (0.3-45.9)
19.5 (5.6-35.6)
14.2 (0.8-63.7)
20.8 (1.6-71.5)
28.9 (10.3-44.5)
Supplemental Table 1 lists descriptive, physiological and quantitative CT data. Data
are given as median (minimum-maximum). CT - computed tomography; Body mass
index - weight in kilograms divided by the square of the height in meters; ARDS - all
patients with acute respiratory distress syndrome defined according to reference 65;
Time to first CT - median time between commencement of mechanical ventilation and
CT; Time to repeat CT - median time between two consecutive CT; PEEP - positive
end-expiratory pressure; PIP - peak inspiratory pressure during pressure controlled
mechanical ventilation; PaO2/FiO2 - arterial partial pressure of oxygen divided by the
fraction of inspired oxygen, both measured at the time of CT; PaCO2 - arterial partial
pressure of carbon dioxide measured at the time of CT. %V refers to the lung volume
within the given range of Hounsfield Units (HU) expressed as percentage of the total
lung volume. %M was calculated accordingly and expressed as percentage of the
total lung mass.
17
Supplemental Table 2. Regression results
Univariate Analysis
Multivariate Model
Independent
Partial
Attributable
Variables
Correlation
P-value
Variance
P-value
%M-100 to +100 HU
%M-200 to -100 HU
%M-300 to -200 HU
%M-400 to -300 HU
%M-500 to -400 HU
%M-100 to -500 HU
PaCO2
Hemoglobin
PEEP
PIP
Body Mass Index
Total lung weight
Trauma vs. others
Contrast material
-0.90
-0.65
-0.50
-0.32
-0.11
-0.42
-0.51
0.17
-0.39
-0.48
-0.37
-0.58
0.39
0.24
<0.0001
<0.0001
<0.0001
0.004
0.36
<0.0001
<0.0001
0.15
<0.0001
<0.0001
0.001
<0.0001
0.001
0.04
81.5 %
5.7 %
1.2 %
0.7 %
0.8 %
-
<0.0001
<0.0001
0.64
0.43
0.39
0.44
0.01
0.32
0.09
0.18
0.03
0.50
0.02
0.25
89.3 %
<0.0001
Best multivariate model
Supplemental Table 2 lists the results of univariate and multivariate regression
analyses involving variables potentially explaining differences in the logarithmicall (ln)
transformed PaO2/FiO2 in patients with single CT. %M refers to the lung mass within
the given range of Hounsfield Units (HU) expressed as percentage of the total lung
mass. PaCO2 - arterial partial pressure of carbon dioxide measured at the time of CT;
PEEP - positive end-expiratory pressure; PIP - peak inspiratory pressure during
pressure controlled mechanical ventilation; Body mass index - weight in kilograms
divided by the square of the height in meters. Attributable variance refers to the
percentage of variance in the ln transformed PaO2/FiO2 explained by the independent
variables shown. It corresponds to the R2 change resulting from inclusion of the
indicated variable into the pre-adjusted model. Only the variables in bold italic font
were included in the multivariate model.
18
Supplemental Table 3
Look-up table for prediction of CT-shunt from PaO2/FiO2 values
PaO2/FiO2
predicted CT-shunt (%)
75% prediction interval (%)
40.00
62.1
46.5 to 75.5
50.00
60.3
44.7 to 74.1
60.00
58.5
42.9 to 72.6
70.00
56.7
41.2 to 71.1
80.00
54.9
39.4 to 69.6
90.00
53.1
37.7 to 68.0
100.00
51.3
36.0 to 66.3
120.00
47.6
32.7 to 62.9
140.00
44.0
29.6 to 59.4
160.00
40.4
26.6 to 55.8
180.00
36.9
23.9 to 52.1
200.00
33.5
21.3 to 48.4
220.00
30.3
19.0 to 44.8
240.00
27.3
16.8 to 41.2
260.00
24.5
14.9 to 37.6
280.00
21.9
13.1 to 34.3
300.00
19.5
11.5 to 31.0
320.00
17.3
10.1 to 28.0
340.00
15.3
8.9 to 25.1
360.00
13.5
7.7 to 22.4
380.00
11.9
6.7 to 20.0
400.00
10.4
5.9 to 17.7
420.00
9.1
5.1 to 15.7
440.00
8.0
4.4 to 13.9
460.00
6.9
3.9 to 12.2
480.00
6.1
3.3 to 10.7
500.00
5.3
2.9 to 9.4
520.00
4.6
2.5 to 8.2
540.00
4.0
2.2 to 7.2
560.00
3.5
1.9 to 6.3
580.00
3.0
1.6 to 5.5
600.00
2.6
1.4 to 4.8
19
This table lists values of CT-shunt and the respective 75% prediction interval (PI)
which were predicted from PaO2/FiO2 values. For a future patient, the 75% PI
specifies the range within which a single CT-shunt value which was predicted from a
PaO2/FiO2 value will lie with 75% certainty. Such a PI should not be confused with
the much narrower confidence interval for the mean of future measurements of CTshunt for a given PaO2/FiO2. The somewhat unconventional 75% PI was chosen here
to provide the clinician with an interval narrow enough to suggest a course of action,
but broad enough to include a good majority of the expected values.
The equation for regression relating PaO2/FiO2 and CT-shunt found in our study was
used for calculation. This regression equation was:

CT - shunt
ln 
 100%  CT - shunt

  0.79  0.00735  PaO2 / FiO2

The 95% confidence intervals for coefficient and intercept in the regression equation
were -0.0081 to -0.0066 and 0.52 to 1.05, respectively. The calculations shown in this
table are only valid for 100 % oxygen ventilation. PaO 2/FiO2 - arterial partial pressure
of oxygen divided by the fraction of inspired oxygen (FiO2). ln - natural logarithm. CTShunt is given as percentage of the total lung mass for [-200 HU to +100] Hounsfield
Units. For further information, the reader is referred to Supplemental Figure 3
(Supplemental Digital Content 4, http://links.lww.com/CCM/A556) and Supplemental
Figure 4 (Supplemental Digital Content 5, http://links.lww.com/CCM/A557).
Supplemental Figure 4:
Supplemental Figure 4 demonstrates the linear relationship between the transformed
CT-shunt and PaO2/FiO2. CT-shunt is calculated as %Mass within the [-200 to +100]
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Hounsfield Units interval and is transformed according to ln[CT-shunt /(100- CTshunt)]. Note the uniformity of the variance over all PaO 2/FiO2 values as reflected in
the P-value of 0.97 for the Breusch-Pagan test as compared to the P-value 0.001 for
linear regression between the logarithmically (ln) transformed PaO2/FiO2 and CTshunt. This homoscedasticity is a prerequisite for the reliability of the confidence and
prediction bands. In addition to the 95% prediction interval, the somewhat
unconventional 75% prediction interval is presented here to provide the clinician with
an interval narrow enough to suggest a course of action, but broad enough to include
a good majority of the expected values.
Supplemental Figure 5:
The linear regression and confidence and prediction bands of Figure S4 are
transformed back to the “natural” units for CT-shunt in %Mass within the [-200 to
+100] Hounsfield Units interval.
Supplemental Figure 6:
Individual within-patient correlation between the logarithmically (ln) transformed
PaO2/FiO2 and CT-shunt in patients with repeat CT from the present study (left panel)
and the study by Borges et al. (right panel, see reference 12 in the main text). The
solid black lines correspond to the individual least squares regression lines, or
connect individual data points (if only two data points were available). The
corresponding correlation between changes (delta) in ln-transformed PaO2/FiO2 and
changes in CT-shunt in patients with repeat CT is illustrated in Figure 6 in the main
text. PaO2/FiO2 - arterial partial pressure of oxygen divided by the fraction of inspired
oxygen (FiO2). ln - natural logarithm. R2 - coefficient of determination. %Mass-200
to
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+100 HU
refers to the lung mass within the given interval of Hounsfield Units (HU)
expressed as percentage of the total lung mass.
Supplemental Figure 7:
Supplemental Figure 7 illustrates the relationship between "percent-volume” and
“percent-mass”
estimates
of
nonaerated
lung
(CT-shunt).
"Percent-volume"
(%Volume) was calculated as the volume of nonaerated lung within the [-100 to
+100] Hounsfield Units (HU) interval and calculated as percentage of the total lung
volume. “Percent-mass” (%Mass) denotes the mass of nonaerated lung within the [100 to +100] HU interval which is calculated as percentage of the total lung mass.
Data of the 77 patients with single data points were used for this analysis. Please
note that, independent from the function chosen to fit the relationship, expression of
CT-shunt as %Volume underestimates the true mass fraction (%Mass) of nonaerated
lung.
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