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Departments of 1 Anaesthesia and 3 Respiratory Medicine, Austin and Repatriation Medical Centre, Heidelberg 3084; and 2 Department of Anaesthesia and Pain Medicine, The Alfred, Prahan 3181, Melbourne, Victoria, Australia
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Ventilation-perfusion (
A/
)
inhomogeneity was modeled to measure its effect on arterial oxygenation
during maintenance-phase anesthesia involving an inspired mixture of
30% O2 and either N2O or
N2. A multialveolar compartment computer model was
constructed based on a log normal distribution of
A/ inhomogeneity. Increasing the log SD of
the distribution of blood flow from 0 to 1.75 produced a progressive
fall in arterial PO2 (PaO2).
The fall was less steep in the presence of N2O than when
N2 was present instead. This was due mainly to the
concentrating effect of N2O uptake on alveolar PO2 in moderately low
A/ compartments. The improvement in PaO2 when N2O was present instead of
N2 was greatest when the degree of
A/ inhomogeneity was in the range typically
seen in anesthetized patients. Models based on distributions of expired and inspired alveolar ventilation give quantitatively different results
for PaO2. In the presence of
A/ inhomogeneity, second-gas and
concentrating effects may have clinically significant effects on
arterial oxygenation even at "steady-state" levels of
N2O uptake.
alveolar-arterial difference; oxygen uptake
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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THE
CONCENTRATING AND second-gas effects of rapid nitrous oxide
(N2O) uptake
(N2O) early in an
inhalational anesthetic and its effect on alveolar O2
concentration were described by Stoelting and Eger (4,
21). It is generally assumed that, after the immediate
postinduction phase of anesthesia, maintenance-phase levels of
N2O by the lungs do not
produce a significant "concentrating effect" on other alveolar
gases and, therefore, do not increase O2 uptake
(O2) or improve arterial oxygenation.
However, in a series of studies by Nunn and co-workers (15, 16, 24), it was demonstrated that arterial oxygenation was unimpaired or improved in patients who were undergoing inhalational anesthesia, breathing O2 with N2O for >0.5 h, compared with a group breathing O2 with nitrogen (N2). This result was surprising in view of the expected tendency of a soluble gas such as N2O to hasten absorption atelectasis and worsen shunt (24).
Farhi and Olzowska (5) calculated the effects of differing
inspired concentrations of N2O on the relationship between
the PO2 and PCO2 values
and ventilation-to-perfusion ratio (A/). They
demonstrated that the shape of the curve on the
O2-CO2 diagram was changed, with a
significantly elevated PO2 predicted in the presence of a moderately low A/ and high
inspired N2O. The implications for overall gas exchange in
the lung were not explored further by these authors at the time.
More recently, Korman and Mapleson (11) have offered an
expanded description of the mechanism of the concentrating and
second-gas effects. Their treatment distinguishes "constant
outflow" and "constant inflow" models based on predetermined
values for expired (AE) and inspired alveolar
ventilation (A; AI),
respectively, within a single lung compartment. These different models
may be expected to give different results when applied to the
calculation of overall gas exchange in the lung.
The application of a multicompartment analysis of log normal
distributions of AE and blood flow () in the
lung has been used by previous workers investigating the causes of
reduced efficiency of gas exchange under worsening inhomogeneity of
A/ throughout the lung. This was demonstrated
by West (25, 26) and Kelman (10) to result in
a widening of the predicted alveolar-arterial difference for all gases.
However, these early models did not take into account the
interdependent nature of exchange of multiple soluble alveolar gases.
More sophisticated models have since been applied to scenarios
representing multiple gas exchange during inhalational anesthesia.
These include a variant based on a log normal distribution of
AI, which serves to demonstrate that lung units with
very low A/ may suffer collapse when gas
uptake exceeds AI and that this process is
accelerated by the presence of N2O (2).
The present authors have sought to investigate further the relationship
between concentrating and second-gas effects and distributions of
A/ and their effect on overall O2
exchange. We have constructed a multialveolar compartment computer
model of alveolar-capillary exchange of multiple gases (O2
and CO2 and any combination of inert gases such as
N2O or N2). This was used to predict the
effects of differing degrees of A/
inhomogeneity on O2 and arterial PO2 (PaO2) in scenarios
related to inhalational anesthesia. Results were sought from two models
based on log normal distributions of AE and
AI. These were considered to represent constant outflow and constant inflow principles of ventilation, respectively, applied to multiple compartments.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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A computer model was designed to represent the exchange of
multiple gases across the alveolar-capillary membrane. Log normal distributions of and ventilation were generated with
loge SDs varying between 0 (homogeneous lung)
and 1.75. West (25, 26) showed that, for any given mode
and log SD, identical results are obtained with a primary distribution
of either or ventilation. The structure and data flow of this
model are outlined in more detail in the APPENDIX.
Either AE or AI can be nominated
for the distribution to be generated. Where AI was
nominated, the effect of absorption atelectasis in compartments where
AE/ was less than zero was modeled. This is
based on similar assumptions as those made by Dantzker et al.
(2), who assumed that compartments with negative calculated AE would suffer collapse. Given that
steady-state gas exchange was being modeled, it was assumed that
perfusion of such compartments was shunt, with an end-capillary gas
content identical to that of mixed venous blood. Both AE
and AI for these compartments was made zero,
and the inspired ventilation from them was redistributed to the
remaining compartments by multiplying each by a scaling factor to
restore total AI to its nominated value.
Modifications incorporated by Dantzker et al. (2) to
simulate the effect of hypoxic pulmonary vasoconstriction (HPV) on the
distribution of were included. Once again, perfusion of all
compartments was scaled so that total remained at the nominated value. An iterative approach is required for these processes, where the
scaling of ventilation and perfusion progressively reduces, so that
final distributions obtained for each are consistent with nominated
target values for exchange of each gas.
West (25) demonstrated that 10 compartments are adequate
to obtain maximal precision of results for output variables from such a
model. It was found, however, that when collapse of compartments with
critically low AI/ was incorporated, 50 compartments were required to avoid noticeable quantization error
because of inclusion or exclusion of compartments with
AI/ values near the critical value.
Analysis performed.
A scenario typical of the maintenance phase of an inhalational
anesthetic was modeled involving administration of an inspired mixture
of 30% O2 and 70% N2O. This was contrasted
with a parallel situation involving 70% N2 instead.
Regardless of what type of distribution of A was
nominated (expired vs. inspired, with or without collapse of low
AI/ units), overall AE was
kept at 4.1 l/min. Overall was maintained at 4.8 l/min,
regardless of whether the effect of HPV was incorporated. Analyses were
performed with constant gas uptakes (O2:
250 ml/min; CO2 uptake: 200 ml/min; N2O: 100 ml/min). Output
variables in the primary analysis were uptakes of individual gas
species and alveolar and arterial partial pressures, on a global basis
or by compartment. For the sake of simplicity in analysis of the data,
there was no other soluble anesthetic agent in the inspired mixture.
AE). This was done on the assumption that, in the
spontaneously breathing patient, maintenance of constant arterial
PCO2 rather than AE is more
physiologically realistic, given that AE will vary
with net gas elimination. The inspired concentration of N2O
was set at zero. Two different rates of N2O elimination
(400 and 100 ml/min) were examined, with the
N2O fixed at these values.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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In the presence of N2O
of 100 ml/min, PaO2 decreased progressively as the log
SD of the distribution of increased, reflecting worsening
A/ inhomogeneity. However, where a log normal
distribution of AE or constant outflow model was
employed, the fall was significantly less steep in the presence of
N2O than when N2 was present instead.
The difference in predicted PaO2 in the presence of
N2O compared with N2 was smallest at lower SDs
of (more homogeneous lungs) and greatest (an increase of
~50%) at more severe levels of A/
inhomogeneity (Fig. 1).
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The constant inflow (AI based) model produced
quantitatively different results, predicting a much smaller increase in
PaO2 when N2O replaces N2 than
that predicted by the AE-based model, even
where total gas uptakes were constrained to the same values.
In the N2O washout scenarios, a lower PaO2
was predicted in the presence of N2O compared with
N2 at all degrees of A/ inhomogeneity (Fig. 2). The effect was
relatively greatest at mild degrees of AE/
spread, where PaO2 is reduced significantly in the
presence of rapid N2O elimination (400 ml/min), although much more modestly at low rates of N2O excretion (100 ml/min).
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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PaO2 steadily declined as the log SD of the
distribution of increased. This is consistent with previously
held assumptions regarding the effect of A/
inhomogeneity on gas uptake (10, 25, 26). However, the
results of this modeling suggest that substituting N2 with
N2O can produce significant increases in arterial
oxygenation, even at a low rate of
N2O by the lung, and that
this effect is a direct result of the presence of
A/ inhomogeneity. Improvement in oxygenation
of this degree is not expected in a homogeneous lung (indicated by a
loge SD of zero in Fig. 1), where a minor rise in
PaO2 of only ~4 Torr is predicted.
Importantly, improved oxygenation is not predicted by a traditional
three-compartment model of A/ scatter, where
only shunt, dead space, and a uniform compartment are considered. If the homogeneous lung just mentioned is considered, the effect of a
superimposed true shunt fraction will only be to reduce further the
minor increase in PaO2 induced by the alveolar
concentrating effects of
N2O.
The level of N2O applied to
these calculations, using the formula of Severinghaus
(19), is consistent with the situation well into the
maintenance phase of anesthesia, where essentially steady-state
kinetics of gas exchange can be considered to be present. At
this stage, the concentrating and second-gas effects of the phase of
rapid N2O early in the
course of the anesthetic are customarily considered to have passed.
A number of authors (1, 3, 6, 12, 13) studying
distributions of AE and using the multiple
inert-gas elimination technique (MIGET) in subjects under
N2O anesthesia have demonstrated an increase in the spread
of AE/ throughout the lung (as indexed by the
log SD of the distributions) after induction of anesthesia. Dueck et
al. (3) suggested that
N2O from low
AE/ lung units may increase alveolar
PO2 and PaO2 and that this
might continue for some time after induction of anesthesia, although
the mechanism for this was not explored in detail.
The explanation for this phenomenon lies in the increased concentration
of alveolar O2 produced by
N2O, operating in lung compartments with moderately low A/. The
effect of this is to increase PaO2 and
O2 within that compartment. Figure
3 shows that the increase in
O2 in the presence of N2O
compared with N2 is greatest in those compartments with
moderately low A/. These compartments obtain
a high proportion of total and not surprisingly have a
predominant effect on the composition of mixed blood leaving the lung.
It should be noted that, according to Farhi and Olzowska
(5), significant increases in alveolar
PO2 in moderately low
AE/ lung units are not expected if the
inspired N2O concentration fraction is less than ~50%.
Thus the effect of N2O on arterial oxygenation would not be
expected to be as significant at a low inspired fraction of
N2O concentration.
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Two phenomena of interest emerge from these results. These are, first,
the significant second-gas and concentrating effects occurring in
moderately low A/ compartments where
N2O is present in sufficient concentration and, second, the
quantitatively different predictions of models based on generated
distributions of inspired and expired ventilation.
The historical development of our understanding of the mechanism of the
effect of uptake of one gas on that of other inspired gases is somewhat
confused. The term "second-gas effect" was originally applied to
the observed increase in the rate of rise of the alveolar concentration
of volatile agent when N2O was administered. The mechanism
was postulated to be that further fresh gas was indrawn to replace the
volume of N2O taken up. The term concentrating effect was
coined by Stoelting and Eger (21) when they demonstrated an increase in alveolar concentration of volatile anesthetic agent above the fresh gas concentration and is a result of contraction of
alveolar volume during rapid
N2O.
Korman and Mapleson (11) recently provided a more complete
description of these processes that distinguishes constant outflow and
constant inflow models based on predetermined values for
AE and AI, respectively. Unlike
the earlier classic description (21), their treatment
predicts final alveolar concentrations that agree with those calculated
by equations based on principles of mass balance applied to the
relationship of A to gas uptake. The constant
outflow principle assumes a predetermined expired alveolar volume for a
lung compartment. Net uptake of alveolar gas causes further fresh gas
to be passively drawn into the alveolus, evoking the second-gas effect.
When a constant inflow principle applies, inspired alveolar volume is
predetermined for the compartment, and net gas uptake causes shrinkage
in alveolar volume, producing a concentrating effect and a lower
expired volume. When the terms second-gas effect and concentrating
effect are used in the present study, it is to refer to the effects of
these two distinct but often concurrent mechanisms relating
A to gas exchange.
The difference between these two principles for a single compartment is
illustrated diagramatically by Korman and Mapleson (11),
and Fig. 4 is adapted from their diagram.
Constant inflow before and after equilibration of alveolar gas and
blood is represented by columns A and B,
respectively. Constant outflow before and after equilibration is
represented by columns C and D. Figure 4 is based
on a simplified analysis like theirs in which no net exchange of
vehicle gas takes place. If, for the sake of simplicity, we assume a
respiratory exchange ratio of 1.0 for the compartment, we can consider
the accompanying respiratory gases (here labeled as O2) to
function as the insoluble vehicle gas. The A/
of the compartment has been adjusted so that one-half of the
N2O in the inspired gas mixture is taken up. The diagram
illustrates that, regardless of whether a constant outflow or constant
inflow principle is applied, the final gas concentrations at
equilibrium will be the same, dictated by the
A/ and inspired concentration. However, the
volumes of gas inspired, taken up, and expired are very different.
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These principles can be applied to multiple compartments and,
substituting ventilation rates over time for static volumes, have been
applied to the computer modeling performed here. When AE is nominated for each lung compartment according
to a specified distribution, the model can be considered analogous to a
constant outflow model. Changes in gas exchange due, for example, to
changes in fractional inspired or mixed venous gas content will alter the calculated AI for that compartment, but
AE is predetermined. When a distribution of
AI is nominated instead, the model performs as a
constant inflow model, and AE is the dependent variable.
In our modeling, the constant inflow (AI based)
model produced quantitatively different results for overall gas
exchange, predicting a much smaller increase in PaO2
with N2O than that predicted by the
AE-based model, even when total gas uptakes and
total AI and AE were constrained
to the same values. The reason for this lies in the different shapes of
the distributions produced for ventilation (Fig.
5). In the constant inflow model, the
relatively high proportion of inspired ventilation taken up produces
very low or even negative values for AE in low
AI/ compartments. In these compartments, when
net gas uptake occurs, AI is necessarily higher in
the constant outflow model than in the constant inflow model, with
greater O2 and
N2O for a given combination
of alveolar and mixed venous partial pressures. The different
performance of the two distributions is accentuated in a situation of
relatively low overall inert-gas uptake, in which perfusion-driven
O2 forces down alveolar
PO2 and mixed venous
PO2, whereas further concentrating retained
inert gas in the poorly ventilated alveolus. The steepness of the
HbO2 dissociation curve at lower
PO2 values depresses the overall
PaO2 when end-capillary blood from these low
AI/ lung units mixes with the smaller volume
of blood from better ventilated regions.
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Clinical implications.
It is notable that the predicted increment in PaO2
produced by the substitution of inspired N2 with
N2O (especially as calculated using a constant outflow
model) is maximal in the range of A/ inhomogeneity commonly seen in healthy, anesthetized patients. This
corresponds with SDs of the distribution of used in these lung
models of 1.0-1.5 (1, 3, 6, 12, 13). This has possible clinical implications, and, whereas the mechanism of the
effect has been outlined above, the theoretical factors modulating this
effect as well as existing clinical data were also examined.
N2O, this would be trivial.
With the use of their data, the expected improvement in
PaO2 in the presence of N2O would be
expected to be only ~5%, assuming no inhomogeneity of
AE/, (even less if the effect of a typical
shunt of ~10-15% is incorporated). However, with the assumption
of a typical degree of A/ inhomogeneity of an
essentially log normal pattern among their anesthetized subjects, improvements in arterial oxygenation in the presence of N2O
are entirely explained by our model.
Alveolar collapse and absorption atelectasis.
The clinical phenomenon and theoretical basis of absorption atelectasis
have been well described, and the kinetics of reduction of gas volume
in a homogeneous segment of lung due to
O2, where conducting airways are
obstructed, has been quantified by previous authors (2, 7,
24). Compared with the situation prevailing when pure
O2 is inhaled, it can be shown that the speed and magnitude of the effect is greater when N2O is present and markedly
reduced when N2 is present instead. Dantzker et al.
(2) applied a computer model involving a log normal
distribution of AI to demonstrate that lung units
with very low A/ may suffer collapse when gas
uptake exceeds AI. This threshold level of
AI/ was higher in the presence of soluble
gases, such as N2O, and at higher inspired O2 concentrations.
AI/ was incorporated in all cases examined in
the present study, with the associated considered to be shunt.
Dantzker et al. (2) showed that the threshold value of
AI/ for alveolar collapse when
N2O is present is considerably higher. This predictably produced a much greater number of low AI/
compartments suffering collapse and a higher proportion of total
becoming shunt in all scenarios modeled by us with
N2O. However, at no point was PaO2
predicted in our modeling to be lower in the presence of N2O, despite the larger proportion of total
perfusing nonventilated lung compartments. Therefore, the concentrating
effects of N2O on alveolar
PO2 in moderately low
AI/ compartments consistently outweighed the
effect of the increased proportion of involved in shunting.
Relationship of ventilation to gas exchange.
This type of computer modeling of gas exchange requires that a
distribution of ventilation be nominated. This distribution must be
assumed to be a reasonable generalization of the type of distribution
seen in the population being modeled. Previous workers (1, 3, 6,
12, 13, 18, 22) have demonstrated, using the MIGET, that
subjects both awake (spontaneously breathing) and undergoing general
anesthesia with controlled ventilation exhibit patterns of
A/ matching throughout the lung, essentially consistent with a log normal distribution, although variations on this
pattern are seen in a variety of physiological and pathological situations. Common variations are seen in patients with normal lungs,
such as a "shelf" of low A/
subunits, which can transform into true shunt, typically seen after
administration of 100% O2. The SD of the distribution is
seen to increase with age and also with anesthesia.
AE (constant outflow)
models and AI (constant inflow) models, particularly
in relation to calculated PaO2, pose the question for
computer modeling of gas exchange: what ventilatory distribution, when
applied to such a model, gives the most physiologically realistic
results? Is it inspired ventilation, expired ventilation, or some other
ventilatory parameter? The different predicted behavior of the lung in
oxygenation of the blood in the presence of a soluble and an insoluble
gas, such as N2O and N2, may provide some
guidance when correlated with the available clinical data.
Clinical studies carried out in the past using MIGET are based on
calculations of the proportion of expired ventilation that is not part
of anatomic dead space (19) and thus relate to a AE-based or constant outflow principle and computer
model. However, the function of many artificial ventilators used in
clinical anesthesia practice may be better described by a constant
inflow principle (11, 14), where the inspired tidal volume
delivered to the patient is set. It has also been suggested that a
constant outflow model relates more closely to the situation of
spontaneous ventilation. Here the subjects regulate the degree of
expansion of the thorax with each breath in response to their
respiratory drive. All gas inflow is the result of the negative
intrathoracic pressure generated whether actively by chest expansion or
passively by uptake of gas across the alveolar-capillary membrane.
The findings of the studies of Nunn and co-workers (15, 16,
24) are consistent with these assumptions. A significant difference in PaO2 was seen between their
N2O and N2 groups when spontaneous ventilation
took place, as was predicted by the constant outflow model based on a
log normal distribution of AE. However, there was no
difference (adjusting their findings for the slightly different
inspired fraction of O2 concentration of the groups) in the
presence of controlled ventilation, as was predicted by the constant
inflow model based on a log normal distribution of AI with collapse of critically low
AI/ segments. Dueck et al. (3),
studying subjects under controlled ventilation with O2 and
either N2 or N2O, also found no difference in
arterial oxygenation.
When compared with the predictions of the computer models outlined,
these studies provide evidence, on the basis of arterial oxygenation,
that each mode of ventilation is characterized by its own predominant
A principle (constant inflow or constant outflow).
Diffusion hypoxia and A/ inhomogeneity.
Not surprisingly, a lower PaO2 was predicted in the
presence of N2O compared with N2 at all degrees
of A/ inhomogeneity. This is the basis of
so-called "diffusion hypoxia." The effect is relatively
most severe at mild degrees of AE/
spread, where PaO2 is reduced significantly in the
presence of rapid N2O elimination (400 ml/min), although
much more modestly at low rates of N2O excretion (100 ml/min). Whereas this depression of PaO2 is greater the higher the rate of N2O elimination occurring, it can be
seen that the major contributor to hypoxemia at severe degrees of
A/ inhomogeneity is mismatch of
A/ itself rather than N2O elimination.
A/ inhomogeneity is to
reduce fractional elimination (26). The practical outcome
of this in terms of N2O kinetics will be a prolongation of
the phase of washout of inert gas from the body. The reduction in
PaO2 during N2O washout (as compared with
an O2-N2 mixture) is less in absolute terms at
higher levels of inhomogeneity. Furthermore, the N2O
elimination rate will be lower with more severe inhomogeneity;
therefore, the reduction in PaO2 expected at a given
time postanesthesia with N2O compared with N2
can be expected to be still less. However, the clinical consequences of
any reduction may be considered more severe: when the baseline is low,
the duration of the effect is more prolonged.
Conclusion.
A multicompartment model of a log normal distribution of
A/ values predicts that concurrent
administration of O2-N2O mixtures results in
clinically significant second-gas and concentrating effects in low
A/ lung units. The effect of the enrichment of alveolar O2 in these compartments is improved arterial
oxygenation compared with an O2-N2 mixture,
even in the presence of the very modest rates of
N2O seen well into a
prolonged inhalational anesthetic.
N2O is predicted to occur at
levels of A/ inhomogeneity typically seen in
anesthetized subjects. The increase is small when a log normal
distribution of AI is modeled but is substantial
when a log normal distribution of AE is nominated.
Consideration of the mechanics of A in relation to
gas uptake suggests that spontaneous ventilation is more consistent
with a model characterized by a log normal distribution of
AE (constant outflow principle). Controlled
ventilation is consistent with a distribution predominantly of
AI (constant inflow principle). Under this
hypothesis, data from this modeling are consistent with previously
published clinical measurements of PaO2 under anesthesia.
In the presence of significant A/
inhomogeneity, second-gas and concentrating effects on oxygenation may
be clinically significant even at steady-state levels of
N2O.
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APPENDIX |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Computer Program: Generation of Log Normal Distributions
Using a routine described by West (25), a frequency distribution ofAE per unit volume of lung
(AE/vol) or per unit volume (/vol)
can be generated. The distribution is Gaussian in shape when the
abscissa (AE/vol) is plotted logarithmically. As
pointed out by Kelman (10), description of a log normal
distribution in terms of a "mean" is unhelpful, and the
distribution can best be described in terms of two parameters: the mode
(or AE/vol of peak frequency) and the log SD. The
position of the first SD with a log normal distribution can be located
as that point at which the frequency is 60.65% of the mode frequency
on the left of it. This is also the point of maximal negative slope.
Second and third and negative SDs will be placed equidistantly along the abscissa. The magnitude of the log SD of the distribution can be
varied around a mode, and both can be specified.
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AE/vol, µ is loge mode AE/vol, and
is loge SD of AE/vol.
A range of values of AE/vol or /vol spanning
3 log SDs on either side of the mode is taken [although, where the
nominated loge of the SD was set at >1.0, a fourth SD is
added to the lower end of the range, as suggested by West
(25), in view of the presence of appreciable amounts of
in the small volume of lung represented by negligible values of
AE/vol]. From this range, the distribution is
divided into a number of compartments evenly spaced along the abscissa.
The components of the distribution can be evenly scaled so that the
total AE of the compartments combined equals any
given specified value. If /vol is given at a constant and equal
value for each compartment and scaled similarly up to a given value,
the resultant distribution of AE/ for the
compartments will also be log normal. The output of this subroutine is
a series of paired values for AE and for
each compartment, which, when summated, equal the selected total
AE and , give a desired overall
AE/, and have a predetermined variance.
Either AE or AI can be nominated
for the distribution to be generated. By substituting ventilation rates
over time for static volumes, where AE is nominated
for a lung compartment, the model can be considered analogous to a
constant outflow model as defined by Korman and Mapleson
(11), i.e., AE remains constant, despite gas exchange within the alveolus, and gas uptake and
AI are calculated from the various input parameters.
Changes in gas exchange due, for example, to changes in fractional
inspired or mixed venous gas content will not change
AE for that compartment. This assumes that net
uptake of alveolar gas causes further fresh gas to be passively drawn
into the alveolus. Where AI is nominated, a constant
inflow principle applies in which AI is constant, and net gas uptake causes shrinkage in alveolar volume and a lower AE.
In addition, the effect of absorption atelectasis in compartments where
AE/ was less than zero was modeled, on the
basis of similar assumptions as those made by Dantzker et al.
(2) that compartments with negative calculated
AE would suffer collapse. Given that steady-state
gas exchange was being modeled, it was assumed that perfusion of such
compartments was shunt, with an end-capillary gas content identical to
that of mixed venous blood. Both AE and
AI for these compartments were made zero, and the
inspired ventilation from them was redistributed to the remaining compartments by multiplying each by a scaling factor to restore total
AI to its nominated value. Modifications
incorporated by Dantzker et al. to simulate the effect of HPV on the
distribution of were included. For each compartment, is
given by
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max is the nominated of the
compartment derived form the log normal distribution. Once again,
perfusion of all compartments was scaled so that total for the
lung remained at the nominated value. An iterative approach is required
for these processes where the scaling of ventilation and perfusion progressively reduces so that final distributions obtained of each are
consistent with nominated target values for exchange of each gas.
Derivation of a Formula for a Computer Program to Calculate Alveolar Gas Concentrations in the Presence of Multiple Gas Uptake
AE-based model.
The system of equations used is based on those described by Olszowska
and Wagner (17).
AE
and , which is ventilated with an inspired mixture of
O2 and inert gases G, G', G", etc. The lung compartment
takes up these gases in a physiologically realistic manner that is
dependent on the gradient between alveolar and mixed venous content of
these gases and also eliminates CO2.
For each gas G in the alveolar gas mixture, the equation
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is a constant
that embodies the appropriate corrections for the effect of temperature
on measured gas volumes. Converting to partial pressures and
substituting the appropriate temperature conversion factor for
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(A1) |
partial pressure of
water vapor) assumed to be 713 mmHg, body temperature is 37°C, and
gas volumes are measured at STPD. For inert gases with
linear dissociation curves, content is defined by the Ostwald partition
coefficient (
), which embodies the appropriate temperature
correction (26). Converting content in blood and gas
phases to partial pressures and multiplying both sides by
PB, then for an inert gas
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(A2) |
AI/ can be defined by transposing Eq. A1 for O2
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(A3) |
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(A4) |
AE is employed, the calculation is somewhat simplified, as pointed out by Farhi and Olszowska (5) by
the fact that the value of PACO2 [and the
fractional content of CO2 in end-capillary blood
(Cc
AE, , and mixed venous CO2
content (CAI. Thus
|
(A5) |
A/.
As well as estimating the different acid-base status of mixed venous
and pulmonary arterial blood, it is necessary to take into account the
acute disturbances in acid-base balance that occur within compartments,
particularly in the face of relatively extreme degrees of
A/ mismatch that are seen in some of these. Widely varying HbO2 saturations and
PCO2 values are seen across the compartments,
and the Bohr and Haldane effects produced vary widely, affecting
O2 and CO2 carriage. For this purpose, the
Hendersen-Hasselbalch equation was used to relate
PCO2 and pH in conjunction with the following
equation relating base excess of the blood to plasma pH and bicarbonate
(HCO
![Base excess<IT>=</IT>[1<IT>−</IT>Hb<IT>·</IT>0.023]](/content/vol91/issue1/fulltext/17/img014.gif)
|
![<IT>×</IT>[(HCO<SUP>−</SUP><SUB>3</SUB><IT>−</IT>24.41)<IT>+</IT>(2.3<IT>·</IT>Hb<IT>+</IT>7.7)(pH<IT>−</IT>7.4)]](/content/vol91/issue1/fulltext/17/img015.gif)
|
|
AE, ,
mixed venous partial pressure (or mixed venous content), and inspired partial pressure of a gas, we can solve for alveolar partial pressure of the gas (and fractional end-capillary blood content for that compartment) if we know the alveolar partial pressure of the other gases in the alveolar mixture. Assuming that there is one unique set of
alveolar gas concentrations that meets the conditions set by any
combination of input values, it is possible to calculate PAG, PAG',
PAG", etc., and
PAO2 (and
Cc
AI is stipulated, it is
necessary to solve for AE to determine
PACO2 for that compartment, and thus an
iterative mechanism is required for its solution.) These alveolar
fractional concentrations will be those that reflect the effects of
uptake or output of all of the gases in the alveolar gas mixture.
The output variables for the whole lung were partial pressure of each
gas species (including CO2) in mixed alveolar gas and mixed
end-capillary blood, mixed end-capillary blood content, and uptake of
each gas. These were calculated by taking a flow-weighted average of
the outputs of all of the compartments for both alveolar gas and
end-capillary blood and total uptakes obtained by summating the uptakes
of all of the compartments. After each of these steps, the acid-base
status of the mixed end-capillary or arterial blood was further
calculated by using an iterative approach, as described above, to
arrive at final values for PACO2 and
PAO2.
A further iterative process allows nomination of the uptake of any or
all of the gases as an input variable. This was performed by varying
the mixed venous point for each gas by continuous bisection until the
set of mixed venous values is obtained that meets the conditions
specified by the inspired fractional concentration, AE/, and net exchange of each gas species for
all of the compartments.
AI-based model.
Consider a similar lung compartment with a given ratio of
AI and .
AE/
|
(A6) |
AI and then progressively coercing the
distribution of AI to be log normal using an
iterative method. The resulting solution is identical to that achieved
using Eq. A6. This method was often found to be faster, as
it obviates the need for calculation of paired values for
PACO2 and
Cc'CO2 consistent with the
AE/ obtained from Eq. A6 during
every iteration in pursuit of the solution for each compartment.
| |
FOOTNOTES |
|---|
Address for reprint requests and other correspondence: P. J. Peyton, Dept of Anaesthesia, Austin & Repatriation Medical Centre, Heidelberg 3084, Melbourne, Australia (E-mail: phil{at}austin.unimelb.edu.au).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 4 April 2000; accepted in final form 6 February 2001.
| |
REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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