## Abstract

Nondispersive infrared spectroscopy (NDIR) allows the continuous analysis of respiratory gases. Due to its high selectivity, simple and robust setup, and small footprint, it is also used to support ^{13}CO_{2} breath tests to assess bacterial growth in the stomach, gut, or liver function. CO_{2} NDIR signals, however, are biased by oxygen in the gas matrix. This complicates NDIR-based breath tests, if the inspired oxygen concentration has to be adjusted to the subject's requirements, or hyperoxia-induced effects were studied. To avoid the oxygen-induced bias, a “dilution” approach was developed: expired gas is mixed with N_{2} to lower the oxygen content down to the usual range of 15–20%. Accuracy and precision were tested using synthetic gas mixtures with increasing ^{13}CO_{2}-to-^{12}CO_{2} ratios (^{13}CO_{2}/^{12}CO_{2}), either based on synthetic air with ∼20% volume O_{2} or on pure O_{2}. For samples with δ^{13}C values smaller than 300 (or ^{13}CO_{2}/^{12}CO_{2} smaller than 0.003), the dilution does not significantly increase the bias in the ^{13}CO_{2}/^{12}CO_{2} determination, and the within-run imprecision is smaller than 1 δ^{13}C. The practical use of this approach was validated in a pig study using a sepsis model reflecting a clinical situation that requires an increased oxygen concentration for respiration. The N_{2} dilution eliminated the high bias in NDIR measurement, thus allowing the determination of the impact of oxygenation on glucose oxidation in patients ventilated with increased oxygen.

- breath test
- stable isotopes

substrates labeled with the stable, nontoxic, nonradioactive carbon isotope ^{13}C are used to assess organ function. Metabolic activity converts the ^{13}C-labeled substrate to ^{13}CO_{2}, which subsequently increases the ^{13}CO_{2}-to-^{12}CO_{2} ratio (^{13}CO_{2}/^{12}CO_{2}) in expired air and, in turn, allows quantification of the activity of the metabolic or physiological pathways involved (4, 9, 17, 18). The most prominent application uses [^{13}C]urea to detect an infection of the stomach by *Helicobacter pylori* (7). Other test variants use organ-specific substrates that pertain, e.g., to gut gastrointestinal passage (21), liver amino acid metabolism (19), or intestinal substrate absorption (3). The amount of ^{13}CO_{2} arising from the labeled test substance represents only a small fraction of the naturally occurring ^{13}CO_{2}. Isotope ratio mass spectrometers can reliably measure those small quantities, but they have a large footprint and large costs of ownership and maintenance and require a high qualification level for operation. As a low-cost alternative, a clinical breath test typically uses the nondispersive infrared spectroscopy (NDIR) (12, 16, 18). An infrared active gas absorbs at specific vibrational/rotational lines. This gas absorption is used as a “filter,” and, therefore, additional optical or dispersive matters, like gratings, prisms, or mechanical filters, are not needed. There is no need either to readjust a measurement channel, leading to equipment that is small, cheap, and easy to use, which, in turn, could provide the basis for online monitoring.

By molecular collisions, O_{2} broadens the NDIR rotational lines (6) and leads to a significant bias in ^{13}CO_{2} and ^{12}CO_{2} (15) measurements. Therefore, the standard NDIR technology was confined to studies with an exhaled O_{2} concentration in the range of 15–20% volume (Vol). Critically ill patients, however, are usually ventilated with higher inspiratory O_{2} concentrations. Tests that would be desirable specifically for this patient cohort, like those pertaining to gut or liver function (4, 18), are, therefore, problematic. To overcome these limitations, a pretreatment of gas samples was developed, and its applicability explored based its impact on precision and accuracy of the NDIR determinations. The overall applicability further depends on the ability to detect changes under “real life” conditions. Consequently, we applied the approach in an experimental intensive care setup to assess [^{13}C]glucose oxidation during mechanical ventilation with high-inspiratory O_{2} concentrations.

## MATERIALS AND METHODS

#### Animal studies.

The experiments were performed in the frame of a hyperoxia study (1), in adherence to the National Institutes of Health Guidelines on the Use of Laboratory Animals. The study protocol was approved by the University Animal Care Committee and the Federal Authorities for Animal Research (Regierungspräsidium Tübingen, Germany). After induction of fecal peritonitis, 20 anesthetized and instrumented domestic pigs of either sex were ventilated, with either 100% oxygen, or oxygen as needed to maintain arterial hemoglobin saturation >90%. Throughout the experimental phase of 24 h, the pigs received glucose to keep glycemia in the range of 4–6 mmol/l and a constant infusion of [1,2,3,4,5,6-^{13}C_{6}]glucose at a rate of ∼3 mg·kg^{−1}·h^{−1}. Breath gas and blood samples were taken for ∼25 different time points.

#### Breath test and definition of delta values.

In a typical breath test, the expired air is collected in bags, both before and after ingestion of the labeled substrate, and, subsequently, the difference in the ^{13}CO_{2}^{/12}CO_{2} of these samples is determined. A δ^{13}C value relates the sample ^{13}CO_{2}^{/12}CO_{2} to that of an external standard, a naturally occurring CaCO_{3} mineral (5) with a ^{13}CO_{2}/^{12}CO_{2} of 0.011224. A δ^{13}C value is defined as (1) Breath test values range from 10 to 300 δ^{13}C. The steps described below are specific for the device of Fischer Analysen Instrumente (Leipzig, Germany) and build upon the “Uras” NDIR module of ABB Automation (Frankfurt, Germany). Details of the NDIR technology are provided as “Supplemental data”. (The online version of this article contains supplemental data.) Nonlinearities between signal and concentration values are corrected, to a large extent, by permanently programmed functions at the digital processing of the detector signals. Hence, raw data or read-out values for NDIR signals (denoted as δ^{13}C_{read}) are taken to be directly proportional to the ^{13}CO_{2}/^{12}CO_{2} of the sample, up to an unknown “offset value” (δ^{13}C_{offset}). Correction of the read out with the offset gives the final δ^{13}C values: (2) The offset value is influenced by the O_{2} and CO_{2} concentrations of the analyzed gas matrix. The corresponding functional relationship is determined empirically. This determination is the only necessary tuning step. The user can easily perform it. A respiratory sample is stepwise and automatically mixed with CO_{2}-free ambient air to generate O_{2}/CO_{2} compositions that may arise when breathing ambient air at variable depth and frequency. For the different mixing steps, CO_{2}, O_{2} concentration, and δ^{13}C values are recorded. Figure 1 uses these measurements to define a tuning function between δ^{13}C offset and sample CO_{2} concentration values, and a second function that defines O_{2}/CO_{2} compositions, for which this tuning function holds. This function is called the working range of the device. It has the form: (3) where *a* denotes the intercept (intersection point of the function with the O_{2} axis), *b* is the slope for the line, and the subscript w links it to the working range line.

#### Correction of the O_{2}-induced bias.

A mathematical correction of the bias at the conversion of raw data to isotope ratio values appeared to be nonsatisfying, leading to a hardware solution (8), where the gas sample is diluted with N_{2} gas seeking a dilution level, so that the resulting O_{2}/CO_{2} composition meets the working range of the NDIR device. This optimal dilution, found with a three-step approach, is demonstrated graphically in Fig. 2 for a respiratory sample with ∼40%Vol O_{2}. In *step 1*, a series of dilution steps with N_{2} gas is performed, and, for each dilution, O_{2}, CO_{2}, and δ^{13}C_{read} values are measured. Using these measurements, a first “dilution line” is generated via regression for a function between O_{2} and CO_{2} concentrations: (4) where *a*_{o} and *b*_{o} are the slope and intercept of the O_{2} curve, respectively. At optimal dilution, the working range line (*Eq. 3*) and the dilution line (*Eq. 4*) have a common CO_{2} concentration value. This CO_{2} concentration is called CO_{2} at optimal dilution. Solving *Eqs. 3* and *4* for this common value gives: (5) In *step 2*, from measured δ^{13}C_{read} and CO_{2} concentration values, a second dilution line is created: (6) where *a*_{r} and *b*_{r} are slope and intercept, respectively. It predicts the δ^{13}C_{read} value from diluted CO_{2} concentrations. Inserting the CO_{2} at optimal dilution in *Eq. 6* gives the δ^{13}C_{read} value expected for this dilution. In *step 3*, according to *Eq. 2*, the raw δ^{13}C_{read} value has to be corrected for its δ^{13}C offset value to obtain the final δ^{13}C value. Therefore, one has to find a δ^{13}C offset for the CO_{2} at optimal dilution, which is demonstrated in Fig. 2 using the δ^{13}C offset tuning graph. All of these steps are performed automatically, and one determination requires ∼3–5 min.

#### Within-run and between-run imprecision.

The expired gas of a pig in stable metabolic conditions, receiving a constant infusion of uniformly labeled [^{13}C]glucose, was collected and mixed in a 20-liter bag, and sample aliquots with a volume of 1.5 liters were distributed over 12 aluminum-coated plastic bags. Different bags were measured over 16 consecutive days, four of them twice. Each run consisted of five replicated determinations. Within- and between-run imprecision was calculated according to Krower and Rabinowitz (10).

#### Bias introduced with dilution.

The bias was estimated by preparing standard samples with known, synthetic ^{13}CO_{2}/^{12}CO_{2} and comparing the measured values with those expected from preparation. To prepare the standards, aluminum-coated plastic bags were fitted with two three-way stopcocks connected in series. One and one-half liters of synthetic air (or oxygen as zero gas) were introduced by one stopcock, and 30-ml CO_{2} and graded volumes (0.01–10 ml) of diluted ^{13}CO_{2} were injected with gas-tight syringes over septa of the second stopcock. This resulted in a total CO_{2} concentration of 2.5% and a ^{13}CO_{2} labeling from 1.0 to 800 δ^{13}C. To mix the gases by induced turbulences, a 50-ml syringe was connected to the bag, and then the plunger was pulled out and pushed in as fast as possible at least 40 times for each bag.

Two other sets with O_{2} concentration values at 20, 30, 50, 75, and 97%Vol and constant δ^{13}C values of 20 and 80 were prepared in a similar way.

To assess the bias as a function of the sample labeling, a linear regression was performed on dilution measurements against isotope ratio mass spectrometry (IRMS) measurements performed by Metabolic Solutions, using a Europa 20/20 gas IRMS (Europa Scientific, Cincinnati, OH). With *a*_{b} and *b*_{b} as intercept and slope, respectively, for resulting regression line, the bias in measured δ^{13}C for a sample with a given δ^{13}C value can be estimated (11) as (7) The reference IRMS δ^{13}C measurements can only be performed with limited precision, leading to an error in the “independent” regression variable for the reference δ^{13}C value. This requires an “errors in both coordinates” regression that weights all measurements with their corresponding measurement error. Therefore, we used a corresponding algorithm (2), where the errors in measurements were estimated based on five replicates for the dilution measurements and three replicates for the reference measurements. These error estimates taken alone explained the differences between values calculated by regression and reference measurements. The sets with constant labeling and increasing O_{2} concentration values were measured with both the reference and dilution approach. The differences in measurements for both sets showed a similar tendency to increase with higher oxygen concentration values. Hence a standard linear regression of difference in measurements against sample O_{2} concentration values was performed for the combined data set. The resulting regression equation predicts the differences in measurements as a function of the O_{2} sample concentration, and its 95% confidence interval was taken as the O_{2}-dependent residual bias for measurement values, corrected with the dilution approach.

## RESULTS

Figure 3 emphasizes the importance of the dilution, especially when the O_{2} content values vary from sample to sample. It shows δ^{13}C values for samples of two groups prepared to have the same degree of labeling (δ^{13}C = 20, and δ^{13}C = 80) and increasing O_{2} content values. They were measured with and without dilution and compared with IRMS measurements, to assess the O_{2}-induced bias. Without dilution, an increase of the O_{2} concentrations from 20 to 40%Vol leads to an average increase of the bias for ∼20 δ^{13}C. The correction of the bias with the dilution approach may not be complete. Table 1 provides a crude statistical estimate for the residual bias, given as the mean over both groups. The residual bias tends to increase with the sample O_{2} concentration. The bias should be the largest for samples with O_{2} concentrations close to 100%Vol. The latter have, after dilution, low CO_{2} concentration values and hence are at the lower end of the working range. To further explore a potential bias under these conditions, a set of samples with a stepwise increasing ^{13}CO_{2}/^{12}CO_{2} to ∼800 δ^{13}C was prepared based on pure O_{2}. According to *Eq. 2*, the δ^{13}C values should be linearly related (slope = 1) to the true sample value. Linearity between measured and expected or targeted δ^{13}C value was tested by regression using isotope ratio measurements of the same samples as reference “gold standard” values.

δ^{13}C (measured) = (1.036 ± 0.0009) * δ^{13}C (expected) + 0.3 ± 0.3, *R*^{2} > 0.999, with the uncertainty given as the ±95% confidence. Table 2 shows the bias calculated with *Eq. 7*. The bias introduced by the dilution for samples with δ^{13}C values around 700 is, in the worst case (upper bound of the 95% confidence range), ∼4% of the nominal value (or 28 δ^{13}C out of 700 δ^{13}C).

The steps shown in Fig. 2 are associated with measurement errors, which accumulate and increase the imprecision of the final determination. Table 3 shows, as a measure for imprecision, the standard deviation obtained from replicated measurements under dilution for different starting O_{2} concentrations and sample δ^{13}C values (*rows 1–3*) and compares it with the standard deviation of samples with O_{2} concentration close to ambient values that do not need the dilution (*rows 4–6*). For these samples, the standard deviation increases from 0.23 to 0.41 δ^{13}C, with δ^{13}C values increasing from 0 to 800 δ^{13}C. The corresponding standard deviations for the dilution approach applied on samples based on pure O_{2} start at 0.75 δ^{13}C and reach 0.92 δ^{13}C. Thus the dilution roughly doubles the standard deviation if the O_{2} concentration is increased to maximal values. For samples with δ^{13}C around 200, Table 3 shows that the standard deviation lies in between these extreme values for a moderately increased O_{2} concentration. These samples were taken from a separate study to analyze within- and between-run imprecision (10). Here we found a within-run component of imprecision of ∼0.5 δ^{13}C. The between-run component accounts for 1.46 δ^{13}C. It includes a minor drift of the measured δ^{13}C values over 16 days and leads to a total imprecision of 1.54 δ^{13}C.

#### “Real life” application.

Samples from a porcine peritonitis model (1) were studied. This model replicates a situation in an intensive care unit involving artificial ventilation with high O_{2} concentration. One objective of this study involving a breath test with uniformly labeled [^{13}C]glucose was to clarify whether increasing the inspired oxygen fraction would affect the glucose oxidation rate. The results of this study were analyzed to explore how the variability and bias in measurements relate to the variability in the response to an experimental treatment and finally to the biological variability of δ^{13}C values, even if no tracer was given.

Figure 4 shows the time course of the respiratory δ^{13}C values for selected animals, demonstrating a stable, initial rise, followed by a minor further increase after switching the inspiratory oxygen concentration from 21 to 100%Vol. Twenty-four hours after sepsis induction, the mean δ^{13}C value for the control group was 157 ± 12 (*n* = 9) and 178 ± 35 δ^{13}C for the high-oxygen group (*n* = 10). Combined with the enrichment values of the infused [^{13}C]glucose tracer and total CO_{2} production values, these breath values were used to estimate the rate of glucose oxidation (20). Here, significant differences were found (1): switching the inspiratory O_{2} concentration from 21 to 100%Vol significantly increased the rate of glucose oxidation from 3 ± 0.7 to 4.1 ± 0.9 mg·kg^{−1}·min^{−1}. The intersubject variability was with ±12 δ^{13}C and ±35 δ^{13}C at least 10 times higher than the dilution-induced variability in the measurements. The intergroup difference (∼21 δ^{13}C) is ∼20 times the imprecision induced by dilution.

## DISCUSSION

Our studies were performed to assess whether the dilution approach can provide reliable results and whether it affects the applicability of the NDIR approach. The applicability depends on the range of O_{2}/CO_{2} compositions that can be analyzed with the dilution and on the precision and accuracy of the resulting measurements.

What is the range of O_{2}/CO_{2} compositions that can be measured with dilution? After dilution, the final CO_{2} concentration should still be higher than the lower bound of the working range, which is ∼0.4%Vol CO_{2} (Fig. 1). For samples of 97%Vol O_{2} and 3%Vol CO_{2}, the final CO_{2} concentration was 0.6%Vol. With CO_{2} starting values of 2%Vol, the final CO_{2} concentration would reach the marginal level of 0.4%Vol. Hence, the dilution approach reaches its limits for CO_{2} < 2%Vol and O_{2} > 95%Vol. Nevertheless, this should cover most situations that can arise under artificial ventilation with increased inspiratory O_{2} concentrations.

Does the dilution impair the precision of measurements? Our estimate for the “within-run” component of the imprecision is based on ∼180 individual observations for samples with different δ^{13}C values and starting O_{2} concentrations. These data show that the imprecision increases with the dilution extend. In average, it is about twice the value obtained without dilution, but still below 1 δ^{13}C. Schadewaldt et al. (16) showed that an NDIR device with an imprecision slightly <1 δ^{13}C can reliably detect gastric emptying parameters for an ^{13}C octanoic breath test, which implies, that the dilution approach induces only a negligibly small imprecision. If a higher precision were necessary, many repetitive measurements are possible, mandatory to reduce the confidence range for the measured δ^{13}C values. For three replicated measurements, ∼100 ml of respiratory gas are required, which represents only a small fraction of the total per minute ventilation. Moreover, the gas can be stored in bags for later measurements over a few days, as we demonstrated.

The “between-run” component of the imprecision is about 1.5 δ^{13}C and larger than the “within-run” component. There is a slight increase in the mean δ^{13}C values for the daily runs, which forms a large part of the “between-run” imprecision. This drift probably does not assume importance, because, in a typical clinical setting, all samples are taken and measured at the same day. When the difference between study δ^{13}C values and a prestudy, basal, or prelabeling δ^{13}C value is calculated, the impact of the “drift” may be removed. Finally, this drift might result from a technical artifact: the “between-run” imprecision was estimated over 16 days using bags, which were all loaded at the beginning of the experiment. The CO_{2} concentration in the bags decreased over these 16 days to ∼70% of the starting values, indicating changes in the gas composition, which may affect the δ^{13}C determination.

Does the dilution impair the accuracy? Comparing via regression the mean values of dilution measurements with those of IRMS measurements of the same samples gives a slope of 1.036 and an almost perfect linearity in the range of 0 to 700 δ^{13}C. This indicates a consistent overestimation with the dilution approach of 3.5% of the actual value. This is confirmed in Table 2 for the bias in δ^{13}C determination obtained with the dilution. However, it should be noted that the NDIR machine we used relies on a hardware implemented slope of 1. Only a calibration for the basal value is performed. For the rare situations where the bias of 3.5% is not acceptable, one still can perform a minimal calibration based on one labeled sample to determine a slope correction factor, which should apply for the entire measurement range due to the established linearity of the system.

The comparison between IRMS- and NDIR-dilution measurements was based on samples with labeled CO_{2} in a synthetic O_{2}/N_{2} gas matrix. However, real breath samples contain additional components, which may interfere as contaminants with the NDIR determination. Next to humidity, predominant gas contaminants are isoprene, acetone, and α,α-dimethyl benzenemethanol (14). The IR spectra of these components do not overlap with those of ^{13}CO_{2} or ^{12}CO_{2} (http://www.webbook.nist.gov/chemistry), and humidity at measurement is controlled by the NDIR device. Hence, there is no signal interference, and our validation results should also apply to study samples.

Can the variability in measurements, as induced with the dilution approach, put the analysis and interpretation of experimental data at risk? For clarification, we take our showcase animal study to relate the dilution-induced variability to the variability in the response to treatment and to the natural variability of δ^{13}C values. The natural ^{13}C values of carbohydrates can vary up to 10 δ^{13}C, depending on the biological source. The expired δ^{13}C value of a patient can vary in the same range, if his metabolism switches from carbohydrate to fatty acid oxidation (13). Hence, during an experimental phase of a few hours, a δ^{13}C value can easily change for one unit due to alterations in the metabolism of the host. Consequently, for a save detection, the average intergroup difference should be in the range of 10 δ^{13}C. From our animal study, we can estimate that the intergroup difference is ∼15% of the actual breath test value, with an intersubject variability that is, at worse, in the same range. Hence, the tracer infusion rate should be adjusted to obtain breath δ^{13}C values in the range of 70. Under these conditions, we can expect the intersubject variability to be in the range of 5–10 δ^{13}C. This it at least five times the variability and bias we can expect for the dilution approach and measured δ^{13}C values in the range of 50–100. To generalize, if the infused tracer dose is adjusted to the minimal value necessary to overcome natural fluctuations in δ^{13}C values under conditions similar to those found in our large animal study, then we can expect that the imprecision and bias introduced by the dilution is about five times smaller than the intersubject variability.

In conclusion, we showed that the dilution to correct the O_{2}-related bias does not impair the precision of the δ^{13}C determination. The linearity was not affected either, based on the congruence between expected and measured δ^{13}C values for a set of standard samples with the maximum level of oxygenation. In all, using the dilution approach, the NDIR technology can be used for a wide range of clinical applications, and, due to the small footprint, online capability, and ease of use of the corresponding devices, it has the potential to be used for bedside monitoring.

## DISCLOSURES

H. Fischer is the general manager of a company that manufactures NDIR devices. M. Moede and W. Fabinski are or have been employees of ABB, the producer of the basic NDIR measurement cell described in this article. W. Fabinski and U. Hölscher have a patent on the dilution concept to overcome the O_{2} effect on NDIR CO_{2} isotope ratio determination.

## Acknowledgments

This work contains part of the master thesis of J. Mehring.

- Copyright © 2009 the American Physiological Society