Department of Intensive Care, Princess Alexandra Hospital, Brisbane,
Australia 4102
Recent computed tomography studies show that
inspired gas composition affects the development of anesthesia-related
atelectasis. This suggests that gas absorption plays an important role
in the genesis of the atelectasis. A mathematical model was developed that combined models of gas exchange from an ideal lung compartment, peripheral gas exchange, and gas uptake from a closed collapsible cavity. It was assumed that, initially, the lung functioned as an ideal
lung compartment but that, with induction of anesthesia, the airways to
dependent areas of lung closed and these areas of lung behaved as a
closed collapsible cavity. The main parameter of interest was the time
the unventilated area of lung took to collapse; the effects of
preoxygenation and of different inspired gas mixtures during anesthesia
were examined. Preoxygenation increased the rate of gas uptake from the
unventilated area of lung and was the most important determinant of the
time to collapse. Increasing the inspired
O2 fraction during anesthesia
reduced the time to collapse. Which inert gas
(N2 or
N2O) was breathed during
anesthesia had minimal effect on the time to collapse.
nitrogen splinting; nitrous oxide; pulmonary collapse; perioperative atelectasis
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INTRODUCTION |
ATELECTASIS DEVELOPS with the induction of anesthesia.
It is visible on computed tomography (CT) scans in 90% of healthy
subjects as dependent lung densities (1, 6-10, 24-27).
Clinical studies indicate that absorption atelectasis plays a key role
in the genesis of anesthesia-related atelectasis (22).
Theoretical studies examining the effect of inspired gases on
absorption atelectasis have suggested atelectasis is promoted by using
N2O, instead of
N2, in the inspired gas mixture;
critical ventilation-perfusion
(
A/
)
is higher (3, 31), and, if complete airway occlusion occurs, then the
time to collapse is shorter (11, 30). In contrast, the limited data
available from clinical studies suggest that whether
N2 or
N2O is breathed during anesthesia
has little effect on the amount of atelectasis (5). The theoretical
studies assume that mixed venous inert gas concentrations are constant.
This is valid at "steady state" but not during the induction of
anesthesia, when inert gas concentrations in mixed venous blood change
rapidly, particularly if N2O is administered.
This paper presents a theoretical mathematical model of the kinetics of
absorption atelectasis during anesthesia that incorporates a model of
peripheral inert gas exchange. This enables the kinetics to be studied
during the early stages of anesthesia.
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METHODS |
General description of the model.
The model consists of two major compartments, lung and tissue. Before
the induction of anesthesia, the lungs were modeled as an ideal lung,
with normal ventilation. At the induction of anesthesia, the lung
compartment is divided into two subcompartments, one of which continues
to ventilate whereas the other is unventilated (see Fig.
1). The ventilated lung compartment is modeled as an ideal lung, whereas the unventilated lung is modeled as a closed collapsible cavity (11). The tissue compartment models peripheral inert
gas exchange, tissue O2
extraction, and CO2 production. It
consists of four peripheral tissue subcompartments as described by
Wagner (29).
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Fig. 1.
Overview of model. Before induction
(left), lung is modeled as an ideal
lung, perfused by entire cardiac output
(tot). After
induction (right), lung is divided
into a ventilated lung compartment and an unventilated lung
compartment. Four tissue compartments extract
O2, produce
CO2, and exchange inert gases, to
produce mixed venous blood.
L and
p: lung and pocket , respectively;
CO2,
CO2 production; VRG, vessel-rich
group; MG, muscle group; FG, fat group; VPG, vessel-poor group.
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Initial conditions are set according to the scenario to be modeled. Gas
exchange from each compartment is described by a series of differential
equations. Integration with respect to time allows the gas contents of
the various compartments to be plotted against time; of particular
interest are the changes in volume within the unventilated lung compartment.
Preinduction phase.
The preinduction phase allows the effects of preoxygenation to be
examined. Anesthesia has not been induced, so airway closure has not
occurred. The lungs were modeled as an ideal lung, consisting of two
subcompartments, the alveolar compartment and the lung tissue
compartment (see Fig. 2). The volume of the alveolar
compartment (VA; 3,000 ml
BTPS) and that of the lung tissue
compartment (VL,ti, 600 ml) were
maintained constant. Instantaneous equilibration of the gases between
these two compartments is assumed. Gases dissolve in the lung tissue
compartment according to their individual Ostwald solubility
coefficients (
L,ti). Inspired
gas reaches the lung compartment at a rate
AI,
and alveolar gas leaves at a rate
AE, where
is ventilation. Mixed venous blood perfuses the
lung compartment, and perfusion limitation of gas uptake is assumed.
Blood flow to the lung compartment and to the peripheral tissues was
maintained constant at 6 l/min, giving a blood flow-to-alveolar volume
ratio of 2:1. The tissue compartment consists of four peripheral tissue
subcompartments (see Fig. 1): vessel-rich group (VRG), muscle group
(MG), fat group (FG), and vessel-poor group (VPG) as described by
Wagner (29). Each has its individual blood flow, volume, and solubility
for each inert gas. Perfusion-limited gas transfer of inert gases
between blood and the tissue compartments is assumed. The partial
pressures of the inert gases in mixed venous blood are determined by
the mixing of blood leaving the four tissue subcompartments. The tissue
compartment extracts 250 ml O2
STPD/min and produces 200 ml
CO2
STPD/min.
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Fig. 2.
Ventilated lung compartment. This compartment consists of alveolar gas
and lung tissue subcompartments. Alveolar gas subcompartment receives
inspired gas at a constant inspired alveolar ventilation
(AI) and is
perfused by mixed venous blood. Gas exchange occurs between alveolar
gas subcompartment and lung tissue subcompartment, which has a constant
volume and known solubilities for each gas. Instantaneous equilibration
of gases between these 2 subcompartments is assumed.
AE, expired
alveolar ventilation; PI,
PA, and
 : inspired, alveolar, and mixed
venous partial pressure, respectively;
VA, volume of alveolar
compartment; VL,ti and
L,ti, volume and Ostwald
solubility coefficient of lung tissue compartment, respectively.
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Initial conditions are set assuming that air has been breathed until
equilibration has been reached (see APPENDIX
A). The alveolar partial pressure of
CO2
(PACO2)
is set at 40 Torr, and other alveolar partial pressures are calculated
by the ideal alveolar gas equation. The inspired
ventilation to the lung compartment (i.e.,
AI) that
satisfies these initial conditions is calculated and then maintained
constant (4.376 l/min BTPS in the
standard version of the model). Inert gas partial pressures in arterial
and venous blood, and in the tissue compartments, are then set equal to
alveolar values. At the start of the preinduction phase, the inspired
gas composition is set either at air (no preoxygenation scenario) or to
an inspired O2 fraction
(FIO2) of 1.0 (preoxygenation scenario). Once initial conditions are set, the model
is an "initial-value problem," whereby gas exchange at the different compartments is determined by a series of 12 differential equations (see APPENDIX B). The
changes in the system with time were solved with Gill's modification
of the Runge-Kutta method (23). The duration of the preinduction phase
is set according to the scenario to be modeled; in the standard version
of the model, this period was 3 min.
Postinduction phase.
At the induction of anesthesia, two changes are made to the model.
First, the lung compartment is further divided into two subcompartments, one of which continues to ventilate whereas the other
is unventilated (see Fig. 1). Second, the inspired gas mixture is
changed according to the scenario to be modeled.
The unventilated lung compartment (or pocket) represents dependent
areas of lung, the airway to which closes at induction of anesthesia.
The unventilated lung compartment is modeled as a closed collapsible
cavity, where gas composition and volume vary with gas uptake but total
pressure is maintained constant at barometric pressure (11). A lung
tissue subcompartment was not included, because of previous work
showing that including such a compartment makes minimal difference to
the time the unventilated lung takes to collapse (11). Mixed venous
blood perfuses the pocket, and perfusion limitation of gas exchange is
assumed. The ventilated lung compartment and the peripheral tissue
compartments are modeled in a similar manner as before induction of anesthesia.
Initial conditions for the postinduction phase depend on the scenario
to be modeled (see APPENDIX C). The
initial partial pressures of gases in the pocket and the ventilated
lung compartment are set equal to the alveolar partial pressures at the
end of the preinduction phase. Alveolar volume in the ventilated lung
compartment (i.e., VA) is
reduced by the initial volume of the pocket (300 ml, which is 10% of
preinduction alveolar volume in the standard version of the model),
then maintained constant. Lung tissue volume in the ventilated lung
compartment (i.e., VL,ti) is
reduced so that the ratio of lung tissue volume to alveolar volume in
this compartment is unchanged. The initial partial pressures of gases
in the four tissue compartments are set equal to the pressures in the
corresponding compartments at the end of the preinduction phase. Total
lung blood flow is maintained constant at 6 l/min, but the blood flow
per unit volume to the nonventilated lung is initially set at 1.5 times
that of the lung as a whole. This gives a blood flow-to-alveolar volume
ratio for the nonventilated lung compartment of 3:1 and that for the
lung compartment (ventilated + nonventilated) of 2:1. This
blood flow is then maintained constant, except where hypoxic pulmonary
vasoconstriction (HPV) is incorporated into the model (see
APPENDIX E).
AI is
maintained constant at the preinduction value. Once initial conditions
are set, the model is an initial-value problem, with 16 differential equations (see APPENDIX
D), which is solved with Gill's modification of the
Runge-Kutta method (23).
Scenarios modeled.
The changes in volume and composition within the pocket were examined
for a variety of inspired gas mixtures during anesthesia. Each gas
mixture consisted of O2 and a
single inert gas, either N2 or
N2O. A range of
FIO2 from 0.21 to 1.0 was
modeled, both with and without preoxygenation for 3 min.
The effects of including or not including HPV in the model, varying the
initial volume of the pocket from 1 to 30% of preinduction alveolar
volume, and varying the duration of preoxygenation from 0 to 60 min
were also examined. The program was written by using Think Pascal
(Symantec) and run on a Macintosh LC with a Motorola 68882 math coprocessor.
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RESULTS |
Unless stated otherwise, the results presented in Figs.
3-5
and Table 1, and described in the following
paragraphs are for the standard version of the model, with the initial
volume of the pocket set at 10% of the preinduction alveolar volume,
HPV incorporated, and with a preinduction time of 3 min. The pattern of
results described here was consistent over all versions of the model.
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Fig. 3.
Time to collapse of unventilated lung compartment.
PreO2, 3 min of preoxygenation.
N2 or
N2O is inert gas breathed after
induction. Collapse occurred faster with preoxygenation than without.
The higher the inspired O2
fraction (FIO2) after
induction, the faster the collapse. Time to collapse is largely
independent of whether inspired gas mixture after induction contains
N2 or
N2O.
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Fig. 4.
Changes in composition and volume (vol; dot-dashed lines) of
unventilated lung compartment. A: no
preoxygenation, with O2 and
N2O breathed after induction.
B: no preoxygenation, with
O2 and
N2 breathed after induction.
C: preoxygenation for 3 min, with
O2 and
N2O breathed after induction.
D: preoxygenation for 3 min, with
O2 and
N2 breathed after induction.
Results for postinduction
FIO2 of 0.4 is shown.
PpN2,
PpN2O, and
PpO2:
pocket partial pressure of N2,
N2O, and
O2, respectively (solid lines);
N2,
N2O,
and  : mixed venous partial
pressure of N2,
N2O, and
O2, respectively (dotted lines).
Pocket and mixed venous CO2
partial pressures are not shown. Time to collapse is much faster with
preoxygenation than without; which inert gas is breathed after
induction has only a small effect.
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Fig. 5.
Effect of varying duration of preoxygenation. Time to collapse for a
range of preoxygenation times
(middle; min) when a mixture
of N2O and
O2
(FIO2 = 0.21-1.0)
was breathed postinduction
(left) and when a mixture
of N2 and
O2 was breathed postinduction
(right) is shown. Longer
preoxygenation decreased time to collapse, with most of this effect
occurring as preoxygenation time was increased from 0 to 3 min.
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Table 1.
Prediction by the model of the time after induction of anesthesia that
the unventilated area of lung takes to collapse
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The main result centered on the time that the pocket took to collapse.
Preoxygenation for 3 min increased the rate of collapse substantially.
For any given inspired gas composition after induction, collapse was at
least four times faster with preoxygenation for 3 min than without.
With preoxygenation for 3 min, collapse was complete in ~0.5 h even
when air was breathed postinduction; when FIO2 was 1.0 postinduction,
collapse was complete in <10 min. In contrast, without
preoxygenation, collapse took >4 h when air was breathed; collapse
took >0.5 h when FIO2 was
1.0 postinduction. Both with and without preoxygenation, the higher
the FIO2 after
induction, the faster the rate of collapse. Without preoxygenation, the
time to collapse was largely independent of whether
N2 or
N2O was breathed after induction. With preoxygenation for 3 min, breathing
N2O rather than
N2 after induction reduced the
time to collapse by no more than 31%. Including HPV in the model
prolonged the time to collapse, and this effect was greater without
preoxygenation. These findings suggest that the presence or absence of
preoxygenation is the most important determinant of the kinetics of
absorption atelectasis during anesthesia, that the
FIO2 after induction plays
an important though lesser role, and that whether
N2 or
N2O is breathed after induction is unimportant.
The second result of interest was the changes in composition and volume
of the pocket (see Fig. 4, A-D). In
all scenarios, the partial pressure of
CO2 in the pocket
(PpCO2)
equilibrated rapidly with the mixed venous partial pressure of
CO2
(
). The partial pressure of
O2 in the pocket
(PpO2) always
equilibrated with the mixed venous partial pressure of
O2
() before the pocket had
collapsed, but if preoxygenation had been performed and then high
FIO2 breathed,
equilibration was not reached until late in the time course of
pocket collapse.
With no preoxygenation, equilibration of
PpO2 with
took ~2 min.
If N2O was breathed after
induction (see Fig. 4A) the mixed
venous partial pressure of N2
(N2)
fell and the mixed venous partial pressure of
N2O
(N2O)
rose, favoring movement of
N2 out of the pocket and
N2O into it. Because of its higher
solubility, N2O moved in faster
than N2 moved out, so the pocket
expanded. The partial pressure of
N2O in the pocket
(PpN2O)
followed
N2O closely, except that the
PpN2O-N2O
gradient sometimes widened during rapid fluxes
of O2 and
CO2. The partial pressure of
N2 in the pocket
(PpN2) never
approached equilibration with
N2. After the early rapid gas fluxes, gas left the pocket at a relatively rapid rate. Volume fell slightly as
O2 and
CO2 equilibrated with mixed venous
blood, rose as N2O entered the
pocket, then fell as a gradient for both
N2 and
N2O to leave the pocket was established.
If N2 was breathed after induction
(see Fig. 4B), volume fell rapidly
as O2 and
CO2 equilibrated with mixed venous
blood. A state of constant composition was soon reached, where
PpN2
substantially exceeded
N2,
and gas left the pocket at a relatively slow rate, determined mainly by
the
PpN2-N2
gradient and the relatively low solubility of
N2.
For the same FIO2, which
inert gas was breathed after induction did not greatly affect the
PpN2-N2
gradient after the rapid early gas fluxes.
With preoxygenation for 3 min, the pocket initially contained mainly
O2, so despite rapid initial
uptake from the pocket, equilibration of
PpO2 with
took 5-7 min.
If N2O was breathed after
induction (see Fig. 4C),
rose, causing influx of N2O into
the pocket, and
PpN2O roughly
followed N2O.
N2
fell slowly with N2
washout from the tissue compartment. PpN2 rose
initally as N2 was concentrated by
uptake of other gases, then fell slowly. Volume fell rapidly until
PpO2
equilibrated with , then fell
more slowly.
If N2 was breathed after induction
(see Fig. 4D),
N2
was maintained or rose, depending on the
FIO2. In both
cases, N2
was at first higher than
PpN2,
so N2 moved into the pocket; PpN2 rose
because of flux into the pocket and the concentration of
N2 in the pocket by
O2 uptake; when
PpN2 rose above
N2,
N2 flux out of the pocket began.
Volume fell rapidly until
PpO2
equilibrated with , then fell
more slowly at a constant rate determined mainly by the
PpN2-N2
gradient and the relatively low solubility of
N2.
For the same
FIO2, which
inert gas was breathed after induction made little difference to the
PpN2-N2
gradient after the rapid early gas fluxes.
The initial volume of the pocket varied from 1 to 30% of preinduction
alveolar volume (f = 0.01-0.3) and compared with the standard model
(f = 0.1). The overall pattern of results
was similar: preoxygenation for 3 min substantially increased the rate
of collapse; breathing high
FIO2 postinduction increased
the rate of collapse, but this effect was smaller than that of
preoxygenation; and which inert gas was breathed after induction made
little difference. However, the size of the initial volume of the
pocket did affect the absolute time to collapse. For most scenarios, as
the size of the pocket increased, so did the time to collapse, but
there were some exceptions. If the difference between the time to
collapse at f = 0.1 and the time to collapse at
the f of interest are expressed as a percentage
of the time to collapse at f = 0.1, then the
maximum difference was 
12% at f = 0.01, 7% at f = 0.05, 19% at
f = 0.20, and 49% at f = 0.3.
The duration of preoxygenation varied from 0-60 min (see Fig. 5).
Longer preoxygenation decreased the time to collapse. This effect was
greater at low postinduction
FIO2. Most of the effect
occurred as the preoxygenation time was increased from 0 to 3 min;
longer preoxygenation produced relatively small reductions in the time
to collapse.
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DISCUSSION |
With the induction of anesthesia, functional residual capacity
(FRC) falls by 20%, and atelectasis is visible on CT scans as
dependent lung densities. The amount by which FRC is reduced, and the
size of the area of atelectasis, is independent of whether intravenous
or inhalational anesthesia or muscle relaxation is used, intermittent
positive pressure ventilation is used, or spontaneous ventilation is maintained (7). The average amount of atelectasis seen
on CT scans after induction corresponds to 8-10% of the whole lung (21), so not all the decrease in volume is due to atelectasis.
Atelectasis during anesthesia could be caused by three basic mechanisms
(20): compression atelectasis, loss of surfactant atelectasis, or
absorption atelectasis. Initially, it was thought that compression
atelectasis was the major mechanism (1), but more recent work has shown
that very little atelectasis develops during anesthesia if
preoxygenation is avoided and O2
and N2 with an
FIO2 of 0.3 is breathed
after induction (22). This argues strongly for gas absorption being the
main mechanism. Absorption atelectasis can occur by either complete
airway occlusion (16, 19) or by reduction of the inspired
A/
to below a critical level (3).
With the induction of anesthesia, diaphragmatic tone is reduced and FRC
falls (27). If FRC is reduced below closing capacity, airway closure
will occur. Beyond the site of airway closure, gas will be trapped
during at least part of the respiratory cycle, with a predisposition to
absorption atelectasis. The importance of muscle tone and changes in
FRC in the genesis of atelectasis is illustrated by ketamine
anesthesia. With ketamine anesthesia, muscle tone is maintained, FRC
does not change, and atelectasis does not develop; only if muscle
paralysis is added do FRC fall and atelectasis develop (27).
Theoretical and clinical studies.
Gunnarson et al. (5) examined the amount of atelectasis that developed
on CT scans after induction of anesthesia and muscle paralysis. Two
groups were examined: one breathed a mixture of N2O and
O2 with an
FIO2 of 0.4 after induction,
and the other received a mixture of
N2 and
O2 with an
FIO2 of 0.4. Atelectasis was
present on scans 10 min after induction and progressively increased on
subsequent scans, with no difference between the two groups. Dantzker
et al. (3) calculated the effect of inert gas solubility and
FIO2 on critical
A/ with a theoretical model. He found that, when a mixture of
O2 and an inert gas with
an FIO2 of 0.4 is breathed,
critical A/
was 20 times greater when the inert gas was
N2O than when it was
N2. This suggests that more
extensive atelectasis should develop when
N2O instead of
N2 is breathed. Joyce et al. (11) calculated the time that an area of lung takes to collapse, when the
airway to it becomes occluded. If the same gas mixture was breathed
before and after the occlusion, the calculated times for collapse were
214 min (11) for 30% O2-70%
N2 and 8 min (11) for
30% O2-70%
N2O. Webb and Nunn (30) calculated
that, if air was breathed before the occlusion and 30%
O2-70%
N2O afterward, complete absorption
took just over 100 min. This suggests that atelectasis develops more
rapidly when N2O is breathed
instead of N2 and is consistent
with the results from an experimental dog model (2, 12). However,
neither the calculations nor the experimental models were designed to
mimic the gas fluxes during the early phases of
N2O uptake during anesthesia, as
they assume that mixed venous gas partial pressures remain constant. This explains the difference between the results of these studies and
the results of Gunnarson et al. (5). Our model (HPV not incorporated)
predicts that if there is no preoxygenation, and a mixture of
O2 and an inert gas with an
FIO2 of 0.4 is breathed
after induction of anesthesia, complete collapse will take 87.6 min if
the inert gas is N2 and 84.1 min
if it is N2O. The predictions are
in agreement with the findings of Gunnarson et al. of progressive
development of atelectasis over 90 min, with no difference between the
N2O and
N2 groups.
Rothen et al. (22) examined the amount of atelectasis visible on CT
scans 20 min after induction of anesthesia and muscle paralysis. One
group (high-FIO2 group) was
ventilated with an FIO2 of
1.0 during induction, then subsequently with
N2 and
O2 with an
FIO2 of 0.4. The other group
(low-FIO2 group) was
ventilated with N2 and
O2 with an
FIO2 of 0.3 during and after
induction. In the high-FIO2
group, there was more atelectasis on the 20-min scan than on a control scan before induction, whereas atelectasis was minimal on both scans in
the low-FIO2
group. Some of the low-FIO2 group were also scanned at 70 min, and there was more atelectasis than earlier. Our model predicts that with preoxygenation and breathing
of O2 and
N2 with an
FIO2 of 0.4, complete collapse will take <20 min, whereas without preoxygenation and breathing O2 and
N2 with an
FIO2 of 0.3, complete collapse will take >2 h. If ventilation with an
FIO2 of 1.0 during induction
of anesthesia is analogous to preoxygenation in our model, then our
predictions agree with the findings of Rothen et al.
Limitations of the model.
The model assumes that atelectasis develops because of complete airway
closure at induction of anesthesia, with subsequent absorption of
trapped gas. With complete airway closure, atelectasis is inevitable;
altering inspired gas composition can only affect time to collapse.
With ventilation at a low
A/,
altering inspired gas composition affects not only time to collapse but
also critical A/,
which may determine whether atelectasis develops.
The timing of airway closure during anesthesia has not been well
defined by experimental studies. If airway closure does not occur until
several minutes after induction, then gas in the alveoli at induction
will be largely replaced by gas breathed subsequently. The gas breathed
before induction would have little effect on gas uptake from
unventilated lung. There is evidence that airway closure occurs very
early during anesthesia. First, the gas breathed during induction is
critical in determining the amount of atelectasis that develops (22).
This argues that airway closure occurs before washout of alveoli with
the postinduction inspired gas. Second, atelectasis can be demonstrated
on CT scans at 10 min after induction. Even with complete
denitrogenation by prolonged breathing of an FIO2 of 1.0 before airway
closure, a lung unit will take ~8 min to collapse when an
FIO2 of 1.0 is breathed
after airway closure (11). This suggests that airway closure must have
occurred very early, to allow sufficient time for collapse to occur.
Perfusion limitation of inert gas uptake from the lung is assumed, but
this is widely accepted in the physiological literature (28). Although
equilibration of O2 and
CO2 between gas in the unventilated area of lung and the blood perfusing it may not be complete under some circumstances, this should not introduce
significant error into calculations of gas uptake (11). Before
induction, the lung has been modeled as an ideal lung, and after
induction the ventilated lung compartment has been modeled as an ideal
compartment. This is unlikely to result in significant error if the
lungs are normal.
The model assumes that cardiac output,
O2 consumption,
CO2 production, and inspired
alveolar ventilation remain constant. Many anesthetic agents reduce
cardiac contractility, and cardiac output often falls with the
induction of anesthesia. O2
consumption and CO2 production
usually fall by ~10%. Most anesthetic agents depress respiratory
drive, and minute ventilation falls in the spontaneously breathing
subject. In the mechanically ventilated subject, minute ventilation
will be maintained. The model does not incorporate the tidal nature of
ventilation or the pulsatile nature of cardiac output.
The distribution of blood flow between the ventilated and unventilated
lung compartments will vary with the vascular resistances of the two
compartments. Because of HPV, these resistances will vary with the
alveolar partial pressure of O2
(PAO2), PpO2, and
. The adjustment for HPV
is given in APPENDIX E and is based on
data from Marshall et al. (18).
N2O obtunds the HPV response (4).
There are insufficient data to quantify the effect of HPV in the
presence of N2O, but the effect
should lie between the extremes of normal HPV and no HPV. The results
for these extremes are presented in this study.
If a circulation time delay between peripheral tissues and the lung is
not included in models of inert gas uptake, significant errors are only
present in the first 2 min of uptake or elimination (17). The lack of
such a time delay in our model is unlikely to introduce significant
error, because the shortest time to collapse found by the model was
over 7 min. Varying the volume of any of the four peripheral tissue
subcompartments by ±20% changed the time to collapse by <4%.
In normal lung, diffusion equilibrium exists between the lung tissue
and gas in the alveoli, but this is not necessarily the case as an area
of lung collapses. An analysis of gas uptake from unventilated lung has
shown that this does not result in >10% error in predicted times to
collapse of an area of unventilated lung (11).
Explanation of the findings of the model.
First, we consider the standard version of the model when air is
breathed before induction. Because of the low solubility of
N2, the limiting factor
determining how long the pocket takes to collapse is
N2 uptake. When the airway closes,
the amount of trapped N2 is the
same regardless of what is breathed afterward. Uptake of
N2 is determined by
N2 solubility and the
PpN2-N2 gradient. For the same postinduction
FIO2, which inert gas
was breathed postinduction made little difference in the time to collapse or in the
PpN2-N2 gradient.
This may be explained by the following argument. After the early rapid
gas fluxes,
PpO2 and
PpCO2 have
equilibrated with and
, whereas barometric pressure (PB) and the saturated vapor
pressure of water
(PH2O)
are constant; the sum of the partial pressures of inert gases in the
pocket equals PB PH2O , which is constant for a
given FIO2 regardless of
which inspired gas mixture is breathed. When no
N2O is breathed,
PpN2 = PB PH2O . When
N2O is breathed,
PpN2O closely
approximates
N2O,
so PpN2 = PB PH2O N2O.
Thus when N2O instead of
N2 is breathed,
PpN2 is reduced by an amount approximately equal to
N2O.
Therefore, the
PpN2-N2 gradient is the same whether N2O
or N2 is breathed postinduction, provided that any change in
N2
is matched by an opposite change in
N2O.
Consider the two extremes, "induction" and "equilibration of
tissue gas exchange." At induction, only air has been breathed, so
N2
is independent of whether N2O or
N2 will be breathed later. At
equilibration of tissue gas exchange, the inert gas partial pressures
in the tissues, mixed venous blood, and the ventilated lung compartment
are equal (ignoring the small effect of blood perfusing the pocket);
PB = PH2O + PACO2 + PAO2 + N2 + N2O;
at a given
FIO2,
PH2O,
PACO2, and
PAO2
are not affected by which inert gas is breathed postinduction; thus any
difference in
N2
between breathing N2 or
N2O postinduction must be matched
by an opposite change in N2O.
Therefore, at these two extremes, the
PpN2-N2
gradient will be the same regardless of which inert gas is breathed,
providing the
FIO2 is
the same. Between these points, the
PpN2-N2 gradient will be the same only if the time course of changes in the
partial pressures of N2 and
N2O are similar in the various compartments. Wash-in of gas into the ventilated lung compartment, and
equilibration of the vessel-rich compartment with the ventilated lung
compartment, is rapid for both N2
and N2O, largely complete within 5 min. The half-life (min) for changes in
N2 in the tissue groups are VRG
(1.02), MG (22.7), FG (169), and VPG (113) and for
N2O are VRG (0.74), MG (26.1), FG
(75), and VPG (113) (29). The only major difference between the two
gases is in the FG, which receives only 5% of cardiac output. Thus for
a given FIO2, once the
initial rapid equilibration of
PpO2 and
PpCO2 with
mixed venous blood has occurred, the
PpN2-N2
gradient, and therefore the time to collapse, will be similar whether
N2O or
N2 is breathed postinduction.
Second, consider the standard version of the model when preoxygenation
is performed. Most of the gas in the pocket is
O2, which is rapidly taken up
until PpO2
equilibrates with . The effect
on time to collapse of whatever inert gas is breathed postinduction can only be relatively small. During the slow uptake phase, N2 uptake limits the total
uptake from the pocket; for a given
FIO2, the
N2 uptake is the same regardless
of whether N2O or
N2 is breathed postinduction (see
above); thus the main determinant of the duration of this phase is the
amount of N2 in the pocket at the
start of this phase. When N2 is
breathed postinduction,
N2
is maintained or rises, depending on the
FIO2; there is a greater
flux of N2 into the pocket during
the rapid phase of gas uptake than if
N2O was breathed, so the amount of N2 in the pocket at the start of
the slow uptake phase is greater and time to collapse is slightly longer.
Finally, consider the effect of variations from the standard model. The
main effect of preoxygenation is to wash
N2 out of the lung compartment,
reducing the initial amount of N2
in the pocket. This washout is virtually complete within 3 min. Further preoxygenation will wash N2 out of
other compartments, reducing N2
and hence time to collapse, but this effect is much smaller.
Once PpO2
equilibrated with , it was
lower than PO2 in the ventilated lung
compartment. If HPV was included in the model, blood flow was then
diverted away from the pocket, so collapse took longer than without
HPV. With preoxygenation, the equilibration of
PpO2 with
did not occur until most of
the gas had left the pocket, so the effect of HPV was relatively small.
Most of the N2 uptake from the
pocket occurred after equilibration of
PpO2 with
. After this equilibration,
PpN2 always
exceeded alveolar partial pressure of
N2. Blood from the pocket and the
ventilated lung compartment combines to form arterial blood. As the
pocket size increases, the fraction of cardiac output passing to it
increases; alveolar partial pressure of
N2 and, hence,
N2
rise, reducing the
PpN2-N2 gradient, so collapse takes longer. This general pattern does not apply
to all scenarios, because gas fluxes before equilibration of
PpO2 with
may override
this effect.
Conclusion.
Preoxygenation before the induction of anesthesia will promote
atelectasis. After induction, addition of
N2 or
N2O to the inspired gas mixture
will retard atelectasis. Our model predicts that whether the inert gas
is N2O or
N2 will have little effect on the
development of atelectasis. This prediction is quite the opposite of
what has been predicted previously on theoretical grounds, but it is
entirely in keeping with the limited experimental evidence to date.
Further experimental studies addressing this question are awaited with interest.
TOP
ABSTRACT
INTRODUCTION
![P<SC>a</SC><SUB>O<SUB>2</SUB></SUB> = P<SC>i</SC><SUB>O<SUB>2</SUB></SUB> − (P<SC>a</SC><SUB>CO<SUB>2</SUB></SUB>/RQ) ⋅ [1 − F<SC>i</SC><SUB>O<SUB>2</SUB></SUB>(1 − RQ)]](/content/vol86/issue4/fulltext/1116/img009.gif)
are the mixed venous O2 and CO2 content, respectively.
O2
and
![dP<SC>a</SC><SUB>O<SUB>2</SUB></SUB>/d<IT>t</IT> = [<A><AC>V</AC><AC>˙</AC></A><SC>ai</SC> ⋅ P<SC>i</SC><SUB>O<SUB>2</SUB></SUB> − <A><AC>V</AC><AC>˙</AC></A><SC>ae</SC> ⋅ P<SC>a</SC><SUB>O<SUB>2</SUB></SUB> + CF ⋅ <A><AC>Q</AC><AC>˙</AC></A> ⋅ (C<OVL>v</OVL><SUB>O<SUB>2</SUB></SUB> − C<SC>a</SC><SUB>O<SUB>2</SUB></SUB>) ⋅ (P<SC>b</SC> − P<SC>h</SC><SUB>2</SUB><SC>o</SC>)]/(V<SC>a</SC> + V<SC>l</SC>,ti ⋅ &lgr;<SC>l</SC>,ti<SUB>O<SUB>2</SUB></SUB>)](/content/vol86/issue4/fulltext/1116/img029.gif)
![dP<SC>a</SC><SUB>N<SUB>2</SUB></SUB>/d<IT>t</IT> = [<A><AC>V</AC><AC>˙</AC></A><SC>ai</SC> ⋅ P<SC>i</SC><SUB>N<SUB>2</SUB></SUB> − <A><AC>V</AC><AC>˙</AC></A><SC>ae</SC> ⋅ P<SC>a</SC><SUB>N<SUB>2</SUB></SUB> + <A><AC>Q</AC><AC>˙</AC></A> ⋅ &bgr;<SUB>N<SUB>2</SUB></SUB> ⋅ (P<OVL>v</OVL><SUB>N<SUB>2</SUB></SUB> − P<SC>a</SC><SUB>N<SUB>2</SUB></SUB>) ⋅ (P<SC>b</SC> − P<SC>h</SC><SUB>2</SUB><SC>o</SC>)]/(V<SC>a</SC> + V<SC>l</SC>,ti ⋅ &lgr;<SC>l</SC>,ti<SUB>N<SUB>2</SUB></SUB>)](/content/vol86/issue4/fulltext/1116/img030.gif)
![dP<SC>a</SC><SUB>N<SUB>2</SUB>O</SUB>/d<IT>t</IT> = [<A><AC>V</AC><AC>˙</AC></A><SC>ai</SC> ⋅ P<SC>i</SC><SUB>N<SUB>2</SUB>O</SUB> − <A><AC>V</AC><AC>˙</AC></A><SC>ae</SC> ⋅ P<SC>a</SC><SUB>N<SUB>2</SUB>O</SUB> + <A><AC>Q</AC><AC>˙</AC></A> ⋅ &bgr;<SUB>N<SUB>2</SUB>O</SUB> ⋅ (P<OVL>v</OVL><SUB>N<SUB>2</SUB>O</SUB> − P<SC>a</SC><SUB>N<SUB>2</SUB>O</SUB>) ⋅ (P<SC>b</SC> − P<SC>h</SC><SUB>2</SUB><SC>o</SC>)]/(V<SC>a</SC> + V<SC>l</SC>,ti ⋅ &lgr;<SC>l</SC>,ti<SUB>N<SUB>2</SUB>O</SUB>)](/content/vol86/issue4/fulltext/1116/img031.gif)
![dP<SC>a</SC><SUB>CO<SUB>2</SUB></SUB>/d<IT>t</IT> = [−<A><AC>V</AC><AC>˙</AC></A><SC>ae</SC> ⋅ P<SC>a</SC><SUB>CO<SUB>2</SUB></SUB> + CF ⋅ <A><AC>Q</AC><AC>˙</AC></A> ⋅ (C<OVL>v</OVL><SUB>CO<SUB>2</SUB></SUB> − C<SC>a</SC><SUB>CO<SUB>2</SUB></SUB>) ⋅ (P<SC>b</SC> − P<SC>h</SC><SUB>2</SUB><SC>o</SC>)]/(V<SC>a</SC> + V<SC>l</SC>,ti ⋅ &lgr;<SC>l</SC>,ti<SUB>CO<SUB>2</SUB></SUB>)](/content/vol86/issue4/fulltext/1116/img032.gif)
is the solubility of inert gas in blood
expressed as milliliters BTPS of gas
per deciliter of blood per millimeters Hg at 37°C, and CF is
defined as in APPENDIX A
