Journal of Applied Physiology
Vol. 83, No. 3,
pp. 884-896,
September 1997
GAS EXCHANGE, MECHANICS, AND AIRWAYS
Cardiac output and mixed venous oxygen content measurements by
a tracer bolus method: theory
Justin S.
Clark,
Yuxiang J.
Lin,
Michael J.
Criddle,
Antonio G.
Cutillo,
Adelbert H.
Bigler,
Fred L.
Farr, and
Attilio D.
Renzetti Jr.
Department of Biomedical Engineering and Medical Physics, LDS
Hospital, Salt Lake City 84103; and Department of Medical Informatics,
Division of Respiratory, Critical Care and Occupational (Pulmonary)
Medicine, Department of Internal Medicine, University of Utah School of
Medicine, Salt Lake City, Utah 84132
ABSTRACT
- INTRODUCTION
- MODEL DESCRIPTION
- METHODS
- RESULTS
- DISCUSSION
- APPENDIX
- ACKNOWLEDGEMENTS
- FOOTNOTES
- REFERENCES
ABSTRACT 
Clark, Justin S., Yuxiang J. Lin, Michael J. Criddle,
Antonio G. Cutillo, Adelbert H. Bigler, Fred L. Farr, and Attilio D. Renzetti, Jr. Cardiac output and mixed venous oxygen content measurements by a tracer bolus method: theory. J. Appl.
Physiol. 83(3): 884-896, 1997.
We present a bolus method of
inert-gas delivery to the lungs that facilitates application of
multiple inert gases and the multiple inert-gas-exchange technique
(MIGET) model to noninvasive measurements of cardiac output (CO) and
central mixed venous oxygen content
Reduction in recirculation error is made possible by 1)
replacement of sinusoidal input functions with impulse inputs and
2) replacement of steady-state analyses with transient
analyses. Recirculation error reduction increases the inert-gas
selection to include common gases without unusually high (and difficult
to find) tissue-to-blood partition coefficients for maximizing the
systemic filtering efficiency. This paper also presents a practical
method for determining the recirculation contributions to inert expired
profiles in animals and determining their specific contributions to
errors in the calculations of CO and
from simulations
applied to published ventilation-perfusion ratio
(
/
) profiles.
Recirculation errors from common gases were found to be reducible to
the order of 5% or less for both CO and
whereas
simulation studies indicate that measurement bias contributions from
recirculation, / mismatch, and
the / extraction
process can be limited to 15% for subjects with severe
/ mismatch and high inspired
oxygen fraction levels. These studies demonstrate a decreasing
influence of / mismatch on
parameter extraction bias as the number of inert gases are increased.
However, the influence of measurement uncertainty on parameter
extraction error limits improvement to six gases.
multiple inert-gas-exchange technique; ventilation-perfusion ratio
INTRODUCTION
A PRACTICAL, NONINVASIVE METHOD for measuring cardiac
output (CO) and mixed venous oxygen content
could
provide an alternative to central venous catheterization, thereby
eliminating a serious risk factor associated with monitoring CO
and/or 
Viewed as the sum of effective pulmonary blood flow
(eff ) and effective shunt (s),
CO can be measured noninvasively by using 1) current or
improved inert-gas techniques for measuring eff, and
2) a noninvasive technique for measuring s,
which depends on noninvasive acquisition of
However, current
inert-gas techniques for measuring eff have found
little clinical acceptance. The rebreathing (RB) methods require
subject cooperation, which limits their use. Hyperventilation
associated with RB modifies the cardiopulmonary status of the patient,
including alteration of CO (7). Errors due to recirculation also
present a dilemma to this method, since avoidance of recirculation
error reduces the amount of data available for analysis.
Stout et al. (15) introduced an open-circuit, multiple-breath (MB)
method for determining eff that does not require
patient cooperation or introduce hyperventilation. However, the same
recirculation dilemma cited for the RB method also exists for the MB
method.
As a solution to the recirculation dilemma, Zwart et al. (21)
introduced a steady-state (SS), open-circuit method for determining the
overall ventilation-perfusion ratio
(/). The method utilizes a
time-modulated inert-gas concentration profile introduced at the
airway. The / is determined from
comparisons of peak-to-peak amplitudes of the steady-state expired and
inspired inert-gas concentration profiles. Ventilation is measured
independently. Reduction of recirculation error is controlled by
systemic filtering efficiency, which is maximized by selection of the
inert gas. A high filtering efficiency is obtained through the use of
the inert gas halothane, which has a high tissue-to-blood solubility ratio. Thus, the SS method removes the recirculation error vs. data
availability dilemmas of both the RB and MB methods while eliminating
the need for subject cooperation.
A second limitation of both the MB and SS models, as reported, is their
failure to account for /
distribution inhomogeneities. Whereas the method of Zwart et al. (21)
has been reported to be capable of extension to a multigas,
multicompartment model system for dealing with inhomogeneity, no such
extension has yet been reported. This may be due, in part, to
difficulties in finding gases that have sufficient filtering
efficiencies.
This paper presents a combined method for measuring CO and
that depends
heavily on its ability to deal with both recirculation and
inhomogeneity. By combining transient features of the MB method and
steady-state features of the SS method, systemic filtering efficiency
is increased sufficiently to extend the choice of inert tracers to
common gases. This increase in gas selection makes the multiple
inert-gas-exchange technique (MIGET) model (18) a practical means for
dealing with / inhomogeneity. Both
transient and steady-state data are provided by bolus delivery of inert gases (tracers) to the airway by using a bolus-generation device [previously reported for measuring alveolar ventilation
(A), oxygen uptake, and carbon dioxide
production (1)]. Application of the bolus method further simplifies
the measurement of CO by removing the requirement of an airtight seal
and the need for a sinusoidal inert-gas concentration generator. This
paper also provides 1) an experimental verification of the
recirculation error-reduction claims of the bolus method, and
2) a computer simulation analysis of the bolus method's
ability to cope effectively with inhomogeneity in
/.
MODEL DESCRIPTION
The tracer bolus is injected into the airway (synchronized with
inspiration) for a series of sequential breaths and then ceased for an
equal number of breaths, approximating a square-wave input of period T,
as shown in Fig. 1.
Fig. 1.
Tracer bolus injection method. See text for symbol definition and
description.
[View Larger Version of this Image (14K GIF file)]
Calculation of average end-capillary perfusion
and
A.
With use of the parallel gas-exchange model of MIGET (18), the mass
balance equation for an inert tracer corresponding to lung
compartment i, approximated by continuous ventilation (see APPENDIX A for comparison with discontinuous ventilation model), is given by
|
(1)
|
where Pi(t ) is partial
pressure of tracer gas in the alveoli of compartment i;
Pci(t ) is partial pressure of tracer
gas in the end-capillary blood of compartment i;
is partial
pressure of tracer gas in the mixed venous blood;
PI(t ) is partial pressure of tracer gas in
inspired air; i is pulmonary
perfusion of compartment i;
Ii,
i is inspired and expired
ventilation of compartment i, respectively; 
b,
ti is the blood-to-gas and tissue-to-gas Ostwald
partition coefficients, respectively; Vi is the
effective gas volume of compartment i, equal to
Vgi + ti jVtii; and
Vgi, Vtii is alveolar gas and
alveolar tissue volumes of compartment i, respectively.
For inert gases, attainment of equilibrium between capillary blood and
alveolar gas is normally assumed (19), providing the equality
Pci = Pi. Equating
Pci(t ) and Pc(t ),
ignoring the time dependence of mixed venous pressure 
(the source of recirculation
addressed below), and arranging Eq. 1 into standard form
provides
|
(2)
|
To the extent that time invariance for
i,
i, and Vi can
be assumed over a measurement cycle, Eq. 2 approximates a
first-order, linear differential equation where steady-state response
to a square-wave input of a tracer gas j (a cycle consisting of
consecutive bolus breaths followed by an equal number of nonbolus
breaths as indicated in Fig. 1), having a peak-to-peak amplitude of
inspiratory pressure of gas j
(PIj), is given by
![P<SUB><IT>ij</IT></SUB>(<IT>t</IT>) = <FR><NU>P<SC>i</SC><SUB><IT>j</IT></SUB>⋅R<SUB><IT>i</IT></SUB></NU><DE>1 + &lgr;<SUB>b<IT>j</IT></SUB><A><AC>Q</AC><AC>˙</AC></A><SUB><IT>i</IT></SUB>/<A><AC>V</AC><AC>˙</AC></A><SUB><IT>i</IT></SUB></DE></FR> [1 − r<SUB><IT>ij </IT></SUB><IT>e</IT><SUP>−<IT>t</IT>/&tgr;<SUB><IT>ij</IT></SUB></SUP>] + c<SUB><IT>ij</IT></SUB>(<IT>t</IT>)](/content/vol83/issue3/fulltext/884/img011.gif)
|
(3)
|
where time constant (
) is
|
(4)
|
and where rij is defined as
|
(5)
|
where T is the square-wave period (not to be
confused with the duration of a bolus impulse),
cij(t ) is the recirculation contribution from
and Ri is defined as the ratio
Ii/i.
For N gas-exchange compartments, the measurable expired
alveolar partial pressure
[PAj(t )] is the
flow-weighted average of the Pij(t )
profiles, given by
|
(6)
|
which, when combined with Eq. 3 and divided by
PIj, becomes
|
(7)
|
where A is given by
i , and
Cj is the total recirculation contribution to
PAj(t ) divided by
PIj. If the
Cij(t ) terms are essentially equal to
Cij(0), Cj(t )
is essentially equal to Cj(0), and the
Cj term can be eliminated by subtracting
PAj(0)/PIj
from both sides of Eq. 7, giving
|
(8)
|
The magnitude of the recirculation problem is determined by
the extent to which Cj(T) is approximated by
Cj(0), which for a given tracer is dependent on
the magnitude of T. Note that if recirculation placed no
restriction on the size of T, allowing T to become large relative to
, for t = T/2 Eq. 8 approaches
|
(9)
|
which, for n soluble tracers, constitutes a set of
n independent equations [analogous to the excretion equation
set of MIGET (18) except for the addition of the factor
Ri] from which a distribution of ventilation
/A with respect to the / is theoretically obtainable
without consideration of the transient data. (However, it is the use of
transient data that allows T to be small enough to reduce the
uncertainty from recirculation error to within acceptable limits.)
Because the values of Ri are definable in terms of
(/)i values (as
well as mixed venous and inspired values of O2 and
CO2), the presence of Ri in Eqs.
8 and 9 has essentially no influence on the
/ distribution parameter extraction
sensitivity by model parameter-fitting processes applied to both
transient and equilibrium data and Eq. sets 8 and
9, as described in METHODS. Volume
parameters become by-products of the method.
Once the / distribution has been
obtained, 
is
obtainable from the sum of the i elements given by
|
(10)
|
where A is obtained by
applying mass balance to the reference (insoluble) tracer, as
previously reported (1), giving
|
(11)
|
where
is the
average rate of bolus delivery and
is the
average alveolar partial pressure of the reference tracer, and
sg is the Ostwald gas phase solubility coefficient.
Because is under system control (and therefore is known) and
is
measurable, A is obtainable from Eq. 11. Note that no accounting of series dead space is required when
the bolus is synchronized with inspiration to assure complete passage
of the tracer bolus into the gas-exchange regions of the lung and that
the term
of Eq. 11 substitutes for the usual airtight airway seal
requirement to achieve A and
measurements. However, it should be further noted that the authors of Ref. 1 point
out that use of Eq. 11 is subject to considerable error in the
presence of pulmonary disease, presumably because of the lack of
ventilation concurrence among ventilation units (see
DISCUSSION).
Determination of
About four decades ago, Rahn and Fenn (10) established
empirical relationships for both alveolar
PO2 and PCO2
(PAO2 and PACO2, respectively) as functions of
/ for given input variables associated with mixed venous blood. These relationships formed what
became known as the O2-CO2 diagram. Subroutines
published by Olszowka and Farhi (8) provided the means to
mathematically model the O2-CO2 diagram and,
thereby, calculate the expected values of PO2
and PCO2 of compartment i
(PO2 i and
PCO2 i, respectively), for a given
(/)i value
[given values of
and mixed venous CO2 content
and
blood chemical variables hemoglobin (Hb), base excess, and
PO2 at 50% Hb saturation (P50)]. From mass balance, Ri can
be calculated in terms of gas fractions of O2 and
CO2 by
|
(12)
|
where FO2 i and
FCO2 i are fractions of
O2 and CO2 in compartment i,
respectively; and FIO2 is inspired fraction of O2.
Our approach to measuring
is an iterative
one, involving adjustment of the input values
and
until
calculated predictions PO2 i and
PCO2 i and the corresponding predictions of ventilation-weighted
PAO2 and
PACO2(given by Eqs. 13 and 14 below) are consistent with measured expired O2
and CO2 profiles. Predictions of
PAO2 and
PACO2 are given by
|
(13)
|
and
|
(14)
|
It should again be noted that representation of
PAO2 and
PACO2 in the respective expired
time profiles of O2 and CO2 is complicated by
the lack of ventilation concurrence associated with pulmonary disease
(see DISCUSSION and Ref. 1).
The procedure for calculating
being a by-product of the procedure) now consists of first assuming (or
measuring from a peripheral blood sample) the blood chemical values and performing the following iterative procedure.
1) Assume starting values for
and
2) Calculate the PO2 i,
PCO2 i, for each compartment,
starting with a / distribution
calculated based on uniform Ri values. (For uniform
R, the influence of R on the right-hand side of Eqs. 8 and 9 is canceled by the influence of R on
PIj, as shown in Eqs. 19 and 20 of METHODS).
3) Compare measured PAO2
and PACO2 values against predicted
values according to Eqs. 13 and 14.
4) Adjust
and 
parameters
until matches in step 3 are obtained.
5) Recalculate the /
distribution based on Ri values calculated from
Eq. 12 by using PO2 i and
PCO2 i values obtained in step
2.
6) Repeat steps 2-4 by using the
/ and R distributions obtained in
step 5. (Although this highly convergent process can be
repeated to achieve higher accuracy, in practice, repetition is not
required).
Calculation of CO.
Calculation of CO involves determination of the physiological shunt
s and adding it to
as obtained from
Eq. 10 above. By mass balance applied to O2 (Fick principle), s is given by
|
(15)
|
where CaO2 is arterial
O2 content, and by mass balance, the average end-capillary
content 
is given by
|
(16)
|
where O2 content in compartment i
(CO2 i) values are calculated from
|
(17)
|
and where O2 saturation in compartment i
(SO2 i) values are obtained from
1) PO2 i (determined above)
and 2) knowledge of the O2 disassociation
function's relationship to PCO2 i
and blood chemical parameters base excess, P50, and Hb
(13).
With an unbiased value of arterial O2 saturation, obtained
noninvasively by pulse oximetry (or by arterial sample), an unbiased calculation of CaO2 becomes available
through Eq. 17 (with "a" substituted for i where
arterial PO2 is iteratively calculated from
CaO2 by its functional relationship to the
O2 dissociation curve). Thus, with all contents of Eq. 15 determined, CO is calculated by adding
to both sides of
Eq. 15 and solving explicitly for CO to obtain
|
(18)
|
METHODS
/ distribution extraction
procedures.
Extraction of the / distribution
from Eq. 8 first requires determination of the input
PIj values that are not directly
measurable by the bolus method. The process for obtaining the input
values begins with application of Eq. 7 to the insoluble tracer
(where j = 1, b1 = 0, and
C1 = 0). Solving Eq. 7 for
PA1(T/2)/PI1 and
PA1(0)/PI1 and
combining gives
|
(19)
|
Solving for PI1 then gives
![P<SC>i</SC><SUB>1</SUB> = [P<SC>a</SC><SUB>1</SUB>(T/2) + P<SC>a</SC><SUB>1</SUB>(0)]/<LIM><OP>∑</OP><LL><IT>i</IT>−1</LL><UL><IT>N</IT></UL></LIM> R<SUB><IT>i</IT></SUB><A><AC>V</AC><AC>˙</AC></A><SUB><IT>i</IT></SUB>/<A><AC>V</AC><AC>˙</AC></A><SC>a</SC>](/content/vol83/issue3/fulltext/884/img043.gif)
|
(20)
|
where PA1(0) and
PA1(T/2) are the measurable minimum and
maximum points on the PA1(t )
profile. The PIj values for the soluble
tracers are then calculated by
|
(21)
|
where Gj represents the measurable
tracer supply gas fraction ratios of the soluble tracers to the
insoluble tracer, measurable by the multiple-gas analyzer (with
sufficient sample dilution to satisfy the dynamic range limitation of
the analyzer).
Note that when Eqs. 20 and 21 are combined with the
/ distribution defining Eqs.
8 and 9, the Ri factors cancel as the
Ri distribution approaches uniformity. This fact, plus the fact that the influence of a nonuniform Ri
distribution on (/) extraction is
small, is the basis for the iterative procedure for including
Ri in the
/ distribution extraction
method described below.
With the PIj values determined, two
methods for extracting the /
distribution become available. The simplest method mathematically
involves use of Eq. set 9 with an estimate of
PAj(
) substituted for
PAj(T/2). The
PAj() values for the soluble inert
tracers are estimated by fitting the multiexponential expiration
profile of each tracer to a single exponential and by accepting the
3 extrapolation point as 95% of each respective
PAj() value; whereas the
PAj() for the insoluble tracer is
equal to PI1 (see Eq. 7), which is calculated directly by Eq. 20. (This is quite fortunate, since the insoluble tracer is always the farthest from equilibrium.) The
/ distribution is then calculated
by use of Eq. set 9 (2) in an analogous manner to that
of MIGET. The reliability of this extrapolation equilibration method
for / distribution extraction is
dependent on the accuracy of the PA() extrapolation, which decreases as 1) T is reduced to meet recirculation-based uncertainty specifications, and 2) lungs become progressively less uniform in terms of , , and V.
With the / distribution determined,
and
determined by
|
(22)
|
A and
values are provided
by Eqs. 11 and 10, respectively.
For situations in which the extrapolations may be inadequate, the
accuracy dependencies on T and the degree of nonuniformity can largely
be overcome by adding volume parameters directly to the
parameter-fitting process applied to transient data and Eq. set
8, which we refer to as "the transient method." An
outline of this method is as follows.
1) Total gas volume ( Vgi) is
obtained from insoluble-gas data only. Advantage is taken of the fact
that the reference PA() value is available, being equal
to PI1 (as described above).
2) Input values for the Downhill Simplex Method (9) are
determined by randomly selecting 50 sets of initial values and comparing with the data, with Vgi
constrained by the value of step 1 and
i constrained by Eq. 11. The set of values corresponding to the lowest error is selected
for step 3.
3) The results of step 2 are applied to the Downhill
Simplex Method. The resulting output values are then applied as inputs to the Downhill Simplex Method.
4) Step 3 is repeated two times, using the previous
output values as inputs.
To maximize computational efficiency and minimize potential convergence
problems, the number of compartments is set to provide a
total number of i and
i unknowns equal to the number of
independent equations of Eq. sets 8 and 9. However, improved efficiency and convergence trade off against
decreased accuracy as the number of compartments decreases. Based on
the results of simulation studies described below, the largest number of compartments for which a significant improvement in accuracy of
CO and
measurement can be attained in subjects with severe / mismatch appears to be
four. Of the four compartments, one represents a shunt
( = 0), whereas the remaining three are ventilation compartments without constraints placed on their respective
/ values. The appropriate number of
inert gases for extracting the / distribution of this
four-compartment model is six. This inert-gas number is reduced to five
when a dead-space compartment is created from one of the ventilation
compartments by restricting its to zero. Four gases
are appropriate when the number of compartments is reduced to three,
whereas three gases are appropriate when one ventilation compartment
has its restricted to zero. The least
number of gases that can be applied to the bolus method is two, which
corresponds to a two-compartment model.
Experimental procedure for measuring recirculation.
A lobe isolation preparation was devised, allowing the recirculation
component of bolus injections to be viewed separately from the injected
tracer profiles. This was accomplished by isolating the left lobes of
the lungs of dogs from the right lobes by a double-lumen Kottmeier
endobronchial tube, providing separate ventilation by a double-cylinder
Harvard animal respirator (model 608), as shown in Fig.
2. The tidal volumes were adjusted to
minimize the expired CO2 difference between left and right
lobes. Separation was checked by introducing helium in the right tube
and measuring the helium concentration in the left. Zero concentration
in the left tube indicated adequate separation. Separation was
routinely checked for throughout each experiment.
Fig. 2.
Dual-piston Harvard animal ventilator and its connections to dog lungs,
set up to perform recirculation studies. Exh, exhaust.
[View Larger Version of this Image (21K GIF file)]
With this animal preparation, bolus measurements were made on each of
the lungs separately; the advantage of this preparation for studying
recirculation error was that both lungs, being perfused with blood
having common mixed venous tracer values, provided a direct measurement
of the tracer venous return signal from the noninjected lobes. For
example, if the right and left lobes were matched in terms of
/, the recirculation profile of the
injected set was provided by the expired inert-gas profile of the
noninjected set. The general procedure for determining the
recirculation contribution to the expired profile is described in
APPENDIX B.
Measurements of recirculation profiles of soluble tracers
were obtained in five dogs. The injector was adjusted to inject a bolus
volume of 5 ml/breath in 300 ms, delayed 10 ms from the initiation of inspiration. Such bolus injections were provided for 16 consecutive breaths (with the respirator set at 11 breaths/min), followed by no injections for an equal number of breaths. This provided
a total period T of ~3 min, which was approximately equal to 6
[for acetylene (C2H2)] for the five dogs of
the study. Experiments in which T was decreased to 1.5 min were
performed to establish the systemic filtering efficiency as a function
of T. The bolus consisted of 10% C2H2, 10%
methylvinylether (MVE), 20% dimethylether (DME), 10%
sulfurhexafluoride (SF6) with the balance
nitrogen. The b values for these gases were determined
by mass balance (using the inverse of the manometric Van Slyke method).
Mongrel dogs of either sex were anesthetized with pentobarbital sodium
(30 mg/kg body wt delivered in divided doses). Further doses of
thiopental sodium were given during the experiment to maintain an
absent corneal reflex. A 7-Fr Swan-Ganz catheter was introduced into
the pulmonary artery (via the femoral vein), and an arterial catheter
was inserted into the aorta via the femoral artery for obtaining
central venous blood samples for
laboratory comparisons, for arterial blood gas and pH laboratory measurements, and
for delivering the thiopental sodium.
Procedure for testing against tracer loss to tissue of the
conducting airways.
To ensure against irreversible tracer loss to tissue of the conducting
airways, flow studies were performed at the conclusion of the
recirculation studies by continuing to ventilate the dogs for a few
minutes after their hearts were stopped (by KCl injection) and by
measuring the expired tracer profiles in response to the same
square-wave bolus input profiles. Tracer loss was determined by
comparing the extrapolated equilibrium values of the tissue soluble
tracers (C2H2, MVE, and DME) to the
tissue-insoluble tracer SF6, with input values normalized
to unity.
CO and
extraction error simulation study.
The purpose of this study was to separately identify the
magnitudes of CO and
error
contributions due to 1) /
mismatch, 2) method of /
extraction, and 3) recirculation.
Error contribution specific to /
mismatch is the result of the inability of a limited amount of
noiseless inert-gas data to uniquely define real
/ distributions. However, as
pointed out by Evans and Wagner (3), the resolution of
/ distribution extractions should
not be generalized from hypothetical distributions but can only be
determined by using real data. Therefore, in this study, error
contributions specific to /
mismatch were obtained by applying Eq. set 9 (equilibrium measurements) to four published / distributions representing one
normal subject (17), and three subjects with chronic obstructive
pulmonary disease (COPD) (16) ranging from mild to severe with
FIO2 values ranging from 0.21 to
0.70.
Included in the study were two-, three-, and four-compartment models
having tracer gases ranging in number from two to six as follows:
1) the two-gas set (minimum required for the bolus method)
having b values of 0 and 0.95; 2) the three-gas
set (with dead-space compartment) having b values of 0, 0.95, and 11.1; 3) the four-gas set having b
values 0, 0.95, 2.7, and 11.1; the five-gas set (with dead-space
compartment) having b values of 0, 0.47, 0.95, 2.7, and
11.1; and 4) the six-gas set having b values of
0, 0.2, 0.47, 0.95, 2.7, and 11.1.
Comparisons of the extrapolation equilibrium and transient
/ extraction methods were simulated
by applying these methods separately to the four published
/ distributions described above.
Without literature guidance, Vgi values were
arbitrarily chosen to be proportional to an equally weighted
linear combination of i and
i, given by
|
(23)
|
The tissue (Vtii) values were arbitrarily set
equal to 0.3i.
Note, however, that no assumptions regarding the values of
Vgi and Vtii are used in the CO
and extraction processes.
For the purpose of testing our methods, these published distributions
(with added values for Vgi and
Vtii) are assumed to be true representations of a
normal subject and of three COPD "subjects" having "known"
CO and values. By generating PA(t ) profiles for O2
and CO2 as well as for inert tracers in response to bolus
delivery, simulation data become available for testing the accuracy of
the CO and
extraction techniques against known parameters of the simulation
studies.
Errors specific to / mismatch were
obtained by application of Eq. 9 (which ignores recirculation
and is not affected by volumes). The two methods of
/ extraction were compared for three values of T. Simulations were performed using the five-gas, four-compartment model and the three-gas, three-compartment model described above. Error contributions from recirculation were then quantitated by adding tracer recirculation profiles (based on the dual
lung measurements) to their respective simulated expired profiles
generated for the / extraction
method comparison studies. The recirculation profiles for each tracer
were generated from the five-dog study averages. The recirculation CO
and results,
extracted by using both the transient and extrapolated equilibrium
methods, were compared with the without-recirculation results of the
previous study.
Noise simulation procedure.
As pointed out by Jaliwala et al. (4), measurement error becomes a
limiting factor in the construction of meaningful
/ distributions from inert-gas data
as the number of gases increases. However, the insensitivity of
/ distribution distortion (from both nonuniqueness and noise) in the prediction of arterial blood gases, as described by these authors, should also apply to
and CO. There, a
similar simulation study was designed to test the influence of
noise-induced distribution shape changes on calculated CO and
values.
Two major measurement error sources for MIGET are 1) the
measurement of inert blood gas pressures that are influenced by both the precision of gas and blood volume proportioning and measurement accuracy of gas chromatography; and 2) the uncertainty of the blood solubility values, for which there is significant intersubject variability. For the bolus method, the measurement of gas samples is
less limiting, since the step of converting dissolved gases to the gas
state does not apply. However, the influence of inert-gas blood
solubility uncertainty is the same for the bolus method as for MIGET.
Therefore, controlling uncertainty of the blood solubility values was
the mechanism chosen for adding systematic noise to quantify the effect
of noise on CO and
extraction error.
Simulation studies having two levels of noise (SDs of 2 and 4%) were
performed on the normal subject and on three COPD distributions. Total CO and
errors for three-, five-, and six-inert-gas sets, having
FIO2 of 0.21, 0.40, and 0.70, respectively, for periods T of 180 and 90 s were calculated for the
transient method. The noise contributions to extraction error were
compared with previous noise studies pertaining to the extrapolated
equilibrium method (2).
RESULTS
Recirculation error study.
Recirculation components of the PA(t ) profiles
corresponding to C2H2, MVE, and DME are
presented separately in Fig. 3, with their
corresponding PA(t ) profiles. The
PA(t ) curves have been normalized to unity, and
the relative magnitudes of the recirculation components have been
multiplied by a factor of five for better visualization. In this range
of T, the reduction in relative recirculation amplitude for each gas
was found to equal 0.45 per reduction in T by a factor of two. The
ratio of the recirculation amplitude to the PA(T/2) 
PA(0) difference (T = 180 s) for each dog, is given
in Table 1. The impact of recirculation on
the measurements of CO and
is described
below.
Fig. 3.
Comparisons of inert-gas recirculation and
PA(t ) PA(0) profiles for
acetylene (C2H2), methylvinylether (MVE), and
dimethylether (DME). Recirculation amplitudes are increased by a
factor of 5 relative to PA(t ) PA(0) profiles. PA(T/2) PA(0)
amplitudes are normalized to unity. See text for further explanation.
[View Larger Version of this Image (24K GIF file)]
|
Table 1.
Ratios of recirculation amplitude to PA(T/2) PA(0)
|
| Dog No. |
Gas
|
| N2O
|
C2H2 |
MVE |
DME |
|
| 1
|
0.016 |
0.035 |
0.056 |
0.078 |
| 2 |
0.014
|
0.030 |
0.050 |
0.071 |
| 3 |
0.025 |
0.048
|
0.070 |
0.088 |
| 4 |
0.017 |
0.042 |
0.062
|
0.080 |
| 5 |
0.018 |
0.044 |
0.064
|
0.085 |
| Average |
0.018 |
0.040 |
0.060 |
0.080 |
| SD
|
0.0042 |
0.0072 |
0.0077 |
0.0066 |
|
|
PA, alveolar pressure; T, square-wave period;
N2O, nitrous oxide; C2H2,
acetylene; MVE, methylvinylether; DME, dimethylether.
|
|
Tracer loss to tissue study.
The influence of stopped blood flow on inert tracer PA
profiles for a typical dog experiment is shown in Fig.
4A; their reference (normal
blood flow) profiles are shown in Fig. 4B. The time
constants displayed in Fig. 4A are in the order of the
bj values. Figure 4A demonstrates
that the
Pj(t )/PIj
values for all the tracers approach unity (including DME, even though equilibrium is not quite obtained in T/2 because of its large tissue
gas volume), indicating no significant irreversible gas loss to the
tissue. This conclusion is confirmed by the calculation of
which
in this instance produces a value not significantly different from
zero.
Fig. 4.
Total lung stopped-flow study. A: PA(t ) PA(0) when ventilation is maintained but total blood
flow is stopped. B: PA(t ) PA(0) profiles for normal blood flow. SF6,
sulfurhexafluoride.
[View Larger Version of this Image (15K GIF file)]
CO and
extraction error resulting from
/ mismatch.
The predicted influences of /
abnormality and FIO2 on CO, and
calculations are
presented in Table 2. The calculations are
based on Eq. set 9, which eliminates the influence of
T. s/ calculations are presented to
illustrate the influence of the shunt compartment on the CO and
results.
Additionally, a true shunt (such as that represented by atelectasis) of
20% was added to the published high
/ region distribution in COPD (COPDH) (16) to further illustrate the influence of the
shunt compartment at high FIO2
levels. [Room-air high-low (HL) pattern data are not presented in
Table 2 because subjects having such distributions require elevated
FIO2 to maintain physiologically compatible
values.] Note, however, that the benefit of the shunt compartment is
reduced as the FIO2 is increased to
0.40 and virtually eliminated for an
FIO2 of 0.70 (except when true shunts are present). Because physiological shunting is reduced with
increased FIO2 (the rationale for
increasing the level of inspired O2), more tracer gases
are required to compensate for the reduced sensitivity of
O2 data for exposing low
/ units. This is well illustrated
in Table 2, which demonstrates an advantage to using up to six inert
tracers for the COPDHL as well as the COPDL
distribution patterns at an FIO2 of
0.70.
|
Table 2.
Influences of / abnormality and
FIO2 on CO and
error
|
| FIO2
|
No. of Gases
|
2 Tracers
|
3 Tracers
|
4 Tracers
|
5 Tracers
|
6 Tracers
|
True
|
| 0.21 |
0.40 |
0.70 |
0.21 |
0.40
|
0.70 |
0.21 |
0.40 |
0.70 |
0.21 |
0.40 |
0.70 |
0.21
|
0.40 |
0.70 |
0.21 |
0.40 |
0.70 |
|
| Normal |
| CO, l/min
|
4.8 |
4.8 |
4.8 |
4.8 |
4.8 |
4.8 |
5.0 |
5.0 |
5.0
|
5.0 |
5.0 |
5.0 |
5.0 |
5.0 |
5.0 |
5.0 |
5.0 |
5.0
|
| %Error |
4% |
5% |
5%
|
3% |
5% |
5% |
0%
|
1% |
1% |
0% |
0%
|
0% |
0% |
0% |
1%
|
| s/CO |
0.02 |
0.01 |
0.00 |
0.02
|
0.00 |
0.00 |
0.01 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00
|
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00
|
|
l STP/l |
0.136 |
0.146 |
0.150 |
0.137 |
0.146
|
0.151 |
0.138 |
0.149 |
0.155 |
0.139 |
0.149 |
0.155
|
0.138 |
0.149 |
0.155 |
0.138 |
0.149 |
0.155
|
| %Error |
1% |
2%
|
3% |
1% |
2% |
3%
|
0.0% |
0% |
0% |
1% |
0%
|
0% |
0% |
0% |
0%
|
| COPDH |
| CO, l/min |
4.2 |
2.8 |
2.8 |
4.8
|
3.2 |
3.1 |
5.2 |
4.1 |
4.1 |
4.5 |
4.4 |
4.4 |
4.6
|
4.6 |
4.6 |
4.6 |
4.6 |
4.6 |
| %Error |
9%
|
38% |
39% |
4% |
31%
|
32% |
13% |
10%
|
11% |
2% |
4%
|
4% |
1% |
1% |
1%
|
| s/CO |
0.42 |
0.15 |
0.14 |
0.44
|
0.16 |
0.15 |
0.34 |
0.19 |
0.19 |
0.22 |
0.20 |
0.19
|
0.20 |
0.20 |
0.20 |
0.20 |
0.20 |
0.20
|
|
l STP/l |
0.070 |
0.079 |
0.088 |
0.080 |
0.092
|
0.101 |
0.087 |
0.114 |
0.122 |
0.077 |
0.121 |
0.128
|
0.078 |
0.123 |
0.132 |
0.078 |
0.123 |
0.132
|
| %Error |
10% |
35%
|
34% |
3% |
25% |
23%
|
12% |
7% |
7% |
1%
|
1% |
3% |
0% |
0%
|
0% |
| COPDL |
| CO, l/min |
6.2 |
5.2
|
4.7 |
6.1 |
5.3 |
4.8 |
6.8 |
6.1 |
5.4 |
6.7 |
6.1
|
5.4 |
6.6 |
6.3 |
6.4 |
6.6 |
6.6 |
6.6 |
| %Error
|
7% |
22% |
29% |
8%
|
20% |
27% |
2% |
8%
|
18% |
1% |
8% |
15%
|
0% |
| |
