Vol. 90, Issue 4, 1282-1290, April 2001
A method of reconstruction of clinical gas-analyzer signals
corrupted by positive-pressure ventilation
A. D.
Farmery and
C. E. W.
Hahn
Nuffield Department of Anaesthetics, University of Oxford,
Radcliffe Infirmary, Oxford OX2 6HE, United Kingdom
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ABSTRACT |
The use of sidestream infrared
and paramagnetic clinical gas analyzers is widespread in anesthesiology
and respiratory medicine. For most clinical applications, these
instruments are entirely satisfactory. However, their ability to
measure breath-by-breath volumetric gas fluxes, as required for
measurement of airway dead space, oxygen uptake, and so on, is usually
inferior to that of the mass spectrometer, and this is thought to be
due, in part, to their slower response times. We describe how
volumetric gas analysis with the Datex Ultima analyzer, although
reasonably accurate for spontaneous ventilation, gives very inaccurate
results in conditions of positive-pressure ventilation. We show that
this problem is a property of the gas sampling system rather than the technique of gas analysis itself. We examine the source of this error
and describe how cyclic changes in airway pressure result in variations
in the flow rate of the gas within the sampling catheter. This results
in the phenomenon of "time distortion," and the resultant gas
concentration signal becomes a nonlinear time series. This corrupted
signal cannot be aligned or integrated with the measured flow signal.
We describe a method to correct for this effect. With the use of this
method, measurements required for breath-by-breath gas-exchange models
can be made easily and reliably in the clinical setting.
breath-by-breath analysis; capnography; sidestream
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INTRODUCTION |
BREATH-BY-BREATH
ANALYSIS of respiratory gas flux requires integration of
contemporaneous airway flow and gas concentration signals. In addition,
both signals need to have sufficiently fast response characteristics
(11) so that errors in the process of integration are
minimized throughout the time course of any signal
"transient." Methods to improve the signal response in gas
analyzers have been described previously (1, 3, 6, 17).
Despite this, however, accurate breath-by-breath analysis of gas flux
with most sidestream infrared and paramagnetic clinical gas analyzers,
although possible in spontaneous ventilation, is not easily practicable
in ventilated patients, although it is frequently described in the
literature (2, 4, 9, 10, 17). This problem has not
been addressed previously. The reasons for it and a means to overcome
it are described below.
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BACKGROUND |
Problems with the performance of sidestream clinical gas
analyzers in ventilated patients came to our attention during work in
this laboratory using the single-breath test for CO2
(7) and in the development of the sine wave inspiratory
forcing technique (15, 16) for use in the clinical
environment with nonspecialized gas monitors. These techniques require
breath-by-breath volumetric analysis of CO2,
O2, and N2O. Our initial experiments gave
disappointingly inaccurate results for alveolar volume and dead space
because of errors in the computation of mixed-inspired and -expired gas concentrations. However, we could ascribe the observed error neither to
deficiencies in signal response time nor to misalignment of the flow
and concentration signals, both of which were rigorously assessed and
optimized (5, 6). A clue to the problem was revealed when
it was noticed that, in spontaneously breathing individuals, the
mixed-expired concentration computations gave accurate results in all
cases. Clearly, some property of positive-pressure ventilation was
affecting the performance of the gas analyzer. It was demonstrated
experimentally that pressure fluctuations (of the magnitude seen
clinically) at the sampling site did not cause significant alterations
in the magnitude of the measured concentration value, and so it was
still not immediately clear how variations in breathing system pressure
could corrupt the gas concentration signal. The remaining possibility
was that the gas concentration signal was being corrupted, not in the
ordinate but in the abscissa; i.e., the signal was being distorted in
the time domain.
The Concept of Time Compression
Ozanne et al. (13) noted that, when mass spectrometry
was used in "multiplex mode," the practice of sampling and
analyzing at different sample flow rates produced a phenomenon that
they called "time compression." The time compression ratio is given by the ratio of the rates at which the sample was aspirated at the
proximal end and discharged from the distal end of the catheter. It can be shown theoretically that, if the sample flow rate of our
clinical gas analyzer were to be sensitive to cyclic fluctuation in
breathing system pressure, then time compression or dilation would
corrupt the signal in the time domain within a breath.
Theoretical Analysis of the Consequences of the Pressure Dependency
of Sample Aspiration Rate of the Datex Ultima
See Table 1 for glossary of terms.
The acceleration of a sample within the sampling catheter, as breathing
system pressure increases, causes the sample to exit the catheter at a
greater rate than that at which it was aspirated. This acceleration or deceleration does not affect the magnitude of the concentration signal
but has the effect of compressing and dilating time. We can think of
gas concentration data as "quantal" entities in that for this
purpose we are not interested in the magnitude of the signal but in the
distortion of the time intervals between these quanta. Consider the
sampling catheter shown in Fig. 1. If a
gas concentration signal is digitized at 100 Hz, we can consider
that a quantum of gas leaves the distal end of the catheter every
10 ms. This quantum will have occupied, throughout its passage in the
catheter, a volume that we will call 
V, which equals
s(t) · t, where
s is the sample flow rate, t is time, and
t is the reciprocal of the digitization frequency.
However, when this quantum was originally aspirated into the proximal
end of the catheter, the time taken would have been
t', which is the time interval over which each
10-ms digital quantum was aspirated from the airway, which equals
V/s (t 
TT), where TT is the
transit time of the sample within the catheter. Hence
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(1)
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This means that data that appear to have been sampled over time
t were in fact aspirated over a period t'.
This represents either a dilation or contraction of time, depending on
the relative magnitudes of the real-time sample flow rate and the
sample flow rate at the time of aspiration. In other words, the
capnograms, oxygrams, etc., as displayed by the analyzer, appear as if
they are plotted as nonlinear time series. It follows from this that the "widths" of the real and measured capnogram, oxygram, etc. will
differ. To reconstruct the linear time series, each digitization sample
is no longer plotted against the time variable
n · t (where n is the
digitization sample number) but against
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Fig. 1.
Schematic diagram of a "quantum" of gas being
aspirated into and ejected from a sampling catheter.
s(t), flow rate at time of emission;
s(t TT), flow rate at time of
aspiration, where TT is transit time. V, volume occupied by
quantum.
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Effect of Time Distortion on the Process of Integration
This discrepancy is important when one considers the integration
of airway flow and concentration that occurs at each 100-Hz digitization to yield the volume of tracer gas.
where VT is tidal volume and c(V) is the actual
concentration of tracer gas as a function of volume (V). When data are
sampled digitally and when flow and concentration data points are
separated by a common time interval (i.e., 10 ms for a 100-Hz
digitization), then this integration is affected as follows
where is airway gas flow rate. Digital integration is only
possible in this way if the t values are constant and
common to both flow and concentration signals. With time distortion, the time separator is the inconstant t' for concentration
and constant t for flow.
Effect of Time Distortion on the Identification of End Expiration
and on Concentration-Flow Signal Alignment
Not only does time compression (or dilation) create errors in
integrating the concentration and flow signals, it also distorts the
timing of the point on the concentration signal that is nominated as
being "end expiratory." For CO2, the exact
identification of end-expiratory time is, of course, important for the
correct alignment of concentration and flow signals (5,
9). If there were no time distortion, then the correct
time delay would equal the apparent time difference
(
Tapparent) between the end-expiratory point
of the concentration signal and the onset of inspiratory flow. However,
if the concentration signal is a nonlinear time series, the real-time
delay equals
where N = Tapparent/t. The purpose of
this series of experiments was to examine the relationship between
breathing system pressure and sample flow rate and to devise a means of
reconstructing or linearizing the concentration time series. Because
this latter aim depends on the results of the former, we shall describe
the two parts separately.
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METHODS |
Part 1. Determination of the Relationship Between Sample
Flow Rate and Breathing System Pressure
A bench lung (14) was ventilated with a Siemens
Servo 900C constant-flow generator ventilator (Siemens, Solna, Sweden)
as shown in Fig. 2. Breathing system
pressure was measured with the pressure transducers within the
ventilator and with a Datex Ultima analyzer, which also measured airway
flow and sampled airway gas via the standard 2-m sampling catheter
(internal diameter, 1.2 mm). The sample flow rate was measured by a
differential pressure transducer (Validyne Engineering) across a
miniature flow transducer (Gould Godart BV, Bilthoven, The
Netherlands), which was calibrated with a precision flowmeter (Timeter,
Allied Healthcare) at both the proximal (inlet) end and distal (outlet)
ends of the sample catheter. Analog data from the Ultima, differential
pressure transducer, and ventilator were digitized by an
analog-to-digital converter (DAQ 700 PCMCIA card, National Instruments)
at 100 Hz and logged with LabView software. This was repeated for a
series of breaths of different volumes and flow rates. The relationship
between proximal and distal sample flow rate and breathing system
pressure (and its derivative) was examined by using multivariate
regression analysis with SigmaPlot version 4 (SPSS, Chicago, IL).
Part 2. To Validate a Means of Reconstructing Gas
Concentration Signals Corrupted By Cyclic Variations in Airway
Pressure
Method based on a first-order model.
Measurements of airway pressure, flow, and gas (CO2,
N2O, and O2) concentration were made using the
Datex Ultima instrument described above from a series of 10 patients
being ventilated tidally in volume-control mode with a Siemens
Servo 900 ventilator. All patients were receiving general anesthesia
for vitreoretinal surgery, and all but one were otherwise healthy. One
patient was obese (95 kg) and had chronic, stable asthma. In addition,
airway CO2 was measured simultaneously with a fast
(10-90% response time, 70 ms) mainstream capnometer (COSMO+,
Novametrix), a device that is unaffected by problems of time
compression, because no sample is aspirated. The sidestream analyzer
and mainstream analyzer sampled at exactly the same point, with the
sample catheter of the former being inserted via a port drilled into
the airway cuvette of the latter. Analog data were converted and logged
digitally by the method described above.
The data were processed automatically by a Matlab code (Matlab version
5, The Math Works) in the following steps: 1) enhancement of
the rise time of the gas concentration signal (6);
2) differentiation of the pressure signal; 3)
determination of the value of the compressed or dilated time step,
which is t' at each digitization as described in
Part 1 of RESULTS and Eq. 4;
4) association of the concentration value at each
digitization step with a new running-time value, which equals
rather than n · t,
where n is the sample number; and 5) use of
linear interpolation to linearize to the time series described in
step 4 above so that sequential concentration data points
were separated by uniform time intervals of 10 ms once again. This step
is necessary for correct integration of the flow and concentration signals.
Model-free method.
The same data as described above were processed automatically by a
Matlab code in the following steps: 1) enhancement of the rise time of the gas concentration signal (6);
2) identification of the midpoint (or some other defining
point; see APPENDIX) of the upstrokes of the Novametrix
mainstream and enhanced Datex capnograms (see Fig. 6A in
RESULTS); 3) similar identification of the
downstrokes of the mainstream and Datex capnograms (see Fig.
6A in RESULTS); 4) shift of
point c forward in time so that it coincides with
point a; 5) shift of point d forward
in time so that it coincides with point b; 6) use
of linear rescaling to readjust the time interval of all the
intervening points on the Datex signal between points c and
d to "stretch" the Datex signal over the Novametrix
template; the readjusted time intervals are made to be constant and
equal to
t · (nNova/nDatex),
where n denotes the number of samples between points
a and b and points c and d for
the Novametrix and Datex signals, respectively; and 7) by
use of linear interpolation, the Datex signal is interpolated to yield
a signal whose data points occur at 10-ms intervals (and synchronous
with the flow data, etc.).
This process was repeated for the other gases measured by the
instrument, namely, O2 and N2O.
Evaluation of correction methods.
For three successive breaths in each patient, the sums of the squares
of the differences (SSD) between the reconstructed Datex and the fast,
undistorted mainstream capnogram were calculated. This was expressed as
a percentage of the SSD for the "rise-time enhanced" but
unreconstructed Datex signal. In addition, the effect of time
distortion on measured mixed-expired CO2 concentration and
airway dead space using Fowler's technique (8) was
assessed by using the Novametrix mainstream and reconstructed Datex signal.
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RESULTS |
Part 1. Determination of the Relationship Between Sample Flow Rate
and Breathing System Pressure
The inconstancy of sample flow rate, measured at the proximal site
during positive-pressure ventilation, is demonstrated in Fig.
3A, where the measured flow
rate is shown as a solid line. The resting gas-analyzer sample flow
rate was 195 ml/min in this example. However, as the breathing system
pressure increased to its peak of 30 cmH2O (3 kPa), the gas
sample flow increased to ~250 ml/min. The relationship between sample
flow and breathing system pressure does not appear to be a simple one.
There are noticeable "spikes" in the flow signal occurring at the
points of maximum rise and fall in the pressure signal. Because it
appeared that the sample catheter was behaving as an "impulse
line," i.e., that flow is a function of both breathing system
pressure and its first derivative (dP/dt), a first-order
regression equation was fitted (SigmaPlot version 4, SPSS) of the form
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(2)
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where s (proximal) is proximal sample
flow rate, k1 is the baseline flow rate,
k2 and k3 are the
appropriate regression coefficients (see Fig. 3A legend),
and P is pressure.
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Fig. 3.
A: plot of sample flow rate at the proximal
site and airway pressure against time. Bottom trace shows
airway pressure against time. Top traces show the measured
sample flow rate (solid line) and the fitted regression equation
(dotted line). Equation is of the following form:
s = k1 + k2 · P(t) + k3 · dP(t)/dt,
where k1 = 195, k2 = 1.8, k3 = 0.8, P is pressure, and dP/dt is pressure and its first
derivative. Correlation coefficient is R = 0.92. B: plot of sample flow rate against time at the distal site.
Solid line, measured flow rate; dotted line, fitted regression
equation. Regression equation is of the following form:
s = k1 + k4 · P(t) + k5 · dP(t)/dt,
where k1 = 195, k4 = 1.6, and
k5 = 0.23. Correlation coefficient is
R = 0.91.
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The regression function (derived from a number of breaths of different
sizes and pressures) is also plotted in Fig. 3A (dotted line) and is overlaid on the real data. Figure 3B shows
the same treatment applied to the sample flow measured at
the distal site [s (distal)]. The regression
equation in this case is
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(3)
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where k4 and k5 are
the appropriate regression coefficients (see Fig. 3B legend).
With knowledge of both of these relationships, Eq. 1 can be
written as follows
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(4)
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Hence, by plotting each concentration data point against
instead of against t0 + n · t, any signal can be reconstructed
to resemble a linear time series. One potential problem with this
approach is that one needs to know the value of TT so that the
appropriate value for proximal flow can be substituted in the
denominator of Eq. 4. Because the sample flow is not
constant, TT is not readily known. We have used two solutions to this
problem: one reductionist and one iterative. The details are given in
the APPENDIX, where it is shown that, if only a single
expiration is considered [as in the single-breath test
(7)], it is a valid simplification to set the denominator
in Eq. 4 to equal the constant k1.
Part 2. To Validate a Means of Reconstructing Gas Concentration
Signals Corrupted By Cyclic Variations in Airway Pressure
Method based on a first-order model.
Figure 4 shows capnograms measured by the
Datex Ultima sidestream and the Novametrix mainstream instruments for a
series of breaths from the obese patient with chronic, stable asthma.
This example is chosen because the phase 3 plateau is markedly sloping, and thus the fidelity of any correction of time-domain distortion is
more readily demonstrable. The breathing system pressure is also
displayed. The signal from the sidestream instrument is delayed relative to the pressure signal, as is typical. It is also narrower than the mainstream signal. Figure
5A shows an individual breath from this series. The response time of the raw Datex signal (solid line) has been enhanced according to the method of Farmery and Hahn
(6); thus it is of a similar order as the mainstream
instrument (75 ms; dotted line). All signals in Fig. 5A have
been aligned at their apparent end-expiratory points (see
APPENDIX for details of this technique), which gives the
impression that the "front edge" of the sidestream capnogram is
delayed. This latter signal is then reconstructed according to
Eq. 4.
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Fig. 4.
Series of breaths from a 90-kg patient with chronic,
stable asthma, ventilated as part of an elective ophthalmic operation.
A: airway pressure against time. B: both
mainstream (dotted line) and sidestream (solid line) capnograms.
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Fig. 5.
A: effect of positive-pressure ventilation on
the shape of the capnogram and its reconstruction based on a
first-order model. Dotted line, mainstream signal; solid line, Datex
signal (rise-time enhanced); dashed line, reconstruction of this latter
signal according to the first-order model. All signals are aligned at
apparent end-expiratory point. B: volumetric capnogram
derived from the same breath as in A. Dotted line,
mainstream comparator; solid line, Datex signal (rise-time enhanced);
dashed line, the latter signal reconstructed according to the
first-order model.
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The SSD between the reconstructed Datex and the "true" mainstream
signals is shown in Table 2. The effect
of time distortion and its correction on the volumetric capnogram [and
hence on the computation of mixed-expired concentration and on airway
dead space using Fowler's method (8)] is shown in Fig.
5B. A summary of these data from all patients is shown in
Table 3.
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Table 2.
Effect of time distortion on measured capnograms for positive-pressure
ventilation and performance of methods to correct it
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Table 3.
Effect of time distortion on measured mixed-expired CO2
concentration and on Fowler dead space for positive-pressure
ventilation and performance of methods to correct it
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Model-free method.
Figure 6A shows an
individual breath from the series shown in Fig. 4. The raw Datex
CO2 signal has been enhanced according to the method
of Farmery and Hahn (6) so that its response time is of a
similar order as the mainstream analyzer (75 ms). This enhanced signal
is then reconstructed according to the algorithm described in the
METHODS section. After linear rescaling and interpolation, the reconstructed sidestream signal is shown in Fig. 6B.
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Fig. 6.
A: reconstruction of a corrupted
sidestream capnogram using a mainstream template and linear rescaling.
Dotted line, mainstream capnogram; solid line, sidestream capnogram.
Points a-d: points on the upstrokes
(a and c) and downstrokes (b and
d) of the mainstream (a and b) and
sidestream (c and d) capnograms, where the rise
fraction is 0.3. The time between a and b is
3.15 s and between c and d is 2.95 s,
i.e., the sidestream capnogram has apparently been compressed by 200 ms. B: effect of positive-pressure ventilation on the shape
of the capnogram and its reconstruction based on a model-free method of
linear rescaling. Dotted line, mainstream signal; solid line,
reconstructed sidestream signal.
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The SSD between the reconstructed Datex and the true mainstream signals
is also shown in Table 2. The effect of time distortion and its
correction on the computation of mixed-expired concentration and on
airway dead space using Fowler's method in these patients is also
shown in Table 3.
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DISCUSSION |
Figure 3 demonstrates how the sample aspiration rate is not
constant under conditions of positive-pressure ventilation. This relationship between airway pressure and aspiration flow rate approximates to a first-order or impulse line system, and this has been
modeled with reasonable closeness by the regression functions (Eqs. 2 and 3), which are also shown in Fig. 3.
The reason that some mass spectrometers are not similarly affected is
that their sampling catheters have a very fine bore and, consequently,
a high resistance (and low-flow rate; 
20 ml/min). This
high-resistance catheter buffers the variation in flow rate in the face
of cyclically varying airway pressure. However, some mass
spectrometers, e.g., the Marquette RAMS 200 (12), have
high-flow (250 ml/min), low-resistance catheters. This instrument has a
pulsed crystal-driven sample inlet valve designed to stabilize the
pressure within the ionization chamber. We do not know whether the
output of this instrument is sensitive to cyclic airway pressure.
The sampling-catheter flow rate varies not only in time, but also with
distance along the catheter, and so a sample will be aspirated and
discharged from the catheter at different rates. This differential
results in the phenomenon of time compression (or dilation), which will
occur with each digitization, resulting in a nonlinear output.
Time Compression
Having modeled the first-order relationship between airway
pressure and sample flow rate at proximal and distal sites
(Eqs. 2 and 3), we used this model to
test the hypothesis that time compression (described by Eq. 1) was responsible for the observed effect on the capnogram,
oxygram, etc., by attempting to reconstruct the sidestream signal using
Eq. 4 (and using a mainstream signal as a comparator). The
first-order model of the pressure dependency of sample flow fits the
data closely, as shown in Fig. 3. That sample flow rate should be
related to airway pressure is intuitive, but its relationship to
dP/dt is less so. A detailed discussion of impulse line
theory is beyond the scope of this paper.
Signal Reconstruction: First-order Model
Using knowledge of the relationship between pressure and flow, and
from the theory of time compression (Eq. 1), it is possible to devise an algorithm to reconstruct signals distorted by
positive-pressure ventilation. There are a number of assumptions
involved in this approach. First, the coefficients in regression
equations in Eq. 4 are derived from experimental data, which
are imperfect and whose derivatives are sensitive to the frequency
response and averaging of the measurement system. Second, the time
delay (TT) between aspiration and emission is not precisely known; thus
the regression function in the denominator of Eq. 4 cannot
be determined a priori. We have used two approaches to this problem,
one reductionist and one iterative, which are detailed in the
APPENDIX. Despite this, however, the calculation of
t' and the reconstruction and interpolation of the signal
do produce a reasonable correction, sufficient at least to support our
hypothesis of the time-compression mechanism for the observed
phenomenon. The mean SSD is 9.2% of the unreconstructed signal, but
there is a wide spread of values, with the coefficient of variation
being 0.45. Reconstructing the signals using this model improves the
estimation of series dead space by Fowler's method. The Datex signal
gives a marked error, with a mean overestimation of 55%. The maximum
error observed in one individual case was 75%. This error is reduced
to a mean of 7.9% by signal reconstruction, although there was some
variation in this error.
Signal Reconstruction: Mainstream CO2 Signal Template
and Linear Rescaling
Although the first-order model is useful in characterizing the
nature and cause of the signal distortion, it is unlikely to be a
practical correction algorithm because of the complexity of the
processing required and the variability in the coefficients in
Eq. 4, which are likely under different experimental
conditions and with different catheters. For this reason, we sought to
use the mainstream CO2 signal as a template to reconstruct
other gas signals in the time domain. Reconstructing the Datex
CO2 signal by this method may seem pointless because, as it
requires a mainstream CO2 template, nothing is gained
because one might as well use the mainstream instrument for making
measurements in the first place. However, for a multigas analyzer such
as the Ultima, O2 and N2O signals can be
processed in the same way (steps 1-7 in METHODS, Part 2 section). This is particularly
straightforward in the case of N2O because, in the Ultima,
the signal has a rise time identical to that of CO2 and is
contemporaneous with it. Therefore, whatever process is required to
reconstruct the CO2 signal can be applied directly to the
N2O signal without having to identify the upstrokes and
downstrokes of the latter.
Practical Outcome
This model-free method of reconstruction has a number of
advantages. First, no assumptions are made about a first-principles model, and so it is likely to be more robust. Indeed, the errors in
estimation of mixed-expired concentrations and dead space in Table 3
show not only a smaller error (3.2%), but also a smaller variance, in
keeping with the more robust nature of this technique. Second, not only
does this method correct for the effects of time distortion, but it
automatically aligns flow and concentration signals because it fits the
signal to a (near) real-time template. Third, there is less uncertainty
about the output of the method in practice, because it can be compared
with the mainstream signal at a glance. Fourth, the execution of this
code (in Matlab in our case) is considerably more straightforward.
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APPENDIX |
Identification of End-expiratory CO2 and Flow Points
The capnograms in Fig. 5 are aligned at their respective
apparent end-expiratory points so that their SSDs from the comparator (mainstream) signal can be compared.
This was achieved by using a version of the method of Cochrane et al.
(5) and Jacobson and Breen (9) by identifying when the CO2 signal derivative became negative for 10 successive sample points. The first of these 10 points was nominated as
being end expiratory. If much fewer than 10 points are used, a false identification may be made if the signal is noisy or contains cardiogenic oscillations. If much more than 10 samples are used, the
conditions may never be met. Similarly, the point on the flow signal
corresponding to the onset of inspiration is taken as the first point
of a series of 20 successive points where flow is "inspiratory"
(negative in our system). For general applicability, if the flow
transducer has an offset due to drift, a finite threshold (say, if flow
is less than x, where x is a suitable
threshold) can be used.
Identification of Upstrokes and Downstrokes of Gas Signals for
the Model-free Method
For each breath i, the maximum and minimum values
from the Novametrix signal (Fmax,i,
Fmin,i) are identified. From
Fmax,i, the first of the preceding
data points to equal Fmax,i (Fmax,i Fmin,i) · (1 RF),
where RF is the rise fraction, was nominated as defining the upstroke
of the capnogram for breath i (i.e., point
a in Fig. 6A). Similarly, from
Fmax,i, the first of the subsequent data points to equal Fmax,i (Fmax,i Fmin,i) · RF was nominated as
defining the downstroke of the capnogram for breath i (i.e.,
point b in Fig. 6A). Here RF is the rise
fraction, i.e., the fraction of the inspiration-expiration
concentration step for breath i, which is taken to define
the upstrokes and downstrokes of a capnogram and hence its width. We
have used RF values between 0.2 and 0.5 and have found that no
significant difference in output can be measured for RF values between
these limits. If a small RF value is chosen, say 0.1, a false
identification of upstroke and downstroke may be made if the signal is
noisy or contains cardiogenic oscillations. If it is much larger than 0.5, the distinction between phase 2 and phase 3 of the capnogram may
be blurred (especially if the capnogram has a sloping plateau as in our
example in Fig. 6A). This process was repeated for the Datex
CO2 and O2 signals to identify
points c and d. For N2O
(whose response time and temporal alignment with the Datex
CO2 signal are identical), points c
and d are simply taken as the points contemporaneous with
points c and d for Datex
CO2. Maximum and minimum points were used rather than end
inspiratory and end expiratory, because it proved to be more robust and
not dependent on any uncertainty in identifying the former, although
the system is amenable to modification to the preference of the user.
Approaches to Determine the Value of TT in Eq. 4
Reductionist approach.
If one considers a single sidestream capnogram, say, for example, the
one whose end-tidal point occurs at about t = 8 s
in Fig. 4, it can be seen that the gas quantum in the sidestream analyzer cell at this time was aspirated from the airway at the instant
before inspiration began. At this time (t TT), airway pressure and its derivative are zero. In fact, the pressure at time
t TT remains zero for the whole expiratory capnogram, and so the denominator of Eq. 4 can be set to the constant
k1. The nonlinearity of the capnogram time
domain occurs in the latter part of the plateau, from time
tend tidal TT to
tend tidal and is effected through the changes
in airway pressure and dP/dt in the numerator of Eq. 4. If only the expiratory gas concentration profiles are of
interest, then each capnogram or oxygram or other "gasogram" can be
analyzed in this way breath by breath and aligned with flow at end
expiration. However, the condition that airway pressure is zero at time
t TT is invalid for the inspiratory gas concentration
profile. This problem can be overcome as follows.
Iterative approach.
With the reductionist approach above, the expiratory gas concentration
profiles of each breath will have the correct width, but the
inspiratory profiles will have an incorrect width. This will have the
effect of producing a breath-by-breath concentration signal with a
progressively changing phase relationship to the ventilatory flow
signal. The problem is solved by using an iterative approach to the
solution of Eq. 4. By this process, for each breath i, a value of TT in Eq. 4 is selected such that
the time difference between end-tidal points for breaths i
and i 1 [tend tidal,i tend tidal,(i 
1)]
is closest (in a least squares sense) to the time difference between
the onsets of inspiratory flow for breaths i and
i 1. With the enforcement of phase conformity in
this way, if the expiratory concentration profile is correct, then so
too must be the inspiratory profile.
| |
ACKNOWLEDGEMENTS |
A. D. Farmery is supported by joint fellowships from the
Association of Anaesthetists of Great Britain and Ireland and the British Journal of Anaesthesia and by an equipment grant from the
National Health Service (UK) Research and Development Fund.
| |
FOOTNOTES |
Address for reprint requests and other correspondence: A. D. Farmery, Nuffield Dept. of Anaesthetics, Univ. of Oxford, Radcliffe Infirmary, Woodstock Road, Oxford OX2 6HE, UK (E-mail:
andrew.farmery{at}nda.ox.ac.uk).
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 19 May 2000; accepted in final form 16 October 2000.
| |
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ABSTRACT
INTRODUCTION
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