Real-time measurement of CO 2 isotopologue ratios in exhaled breath by a hollow waveguide based mid-infrared gas sensor

: A hollow waveguide (HWG) based mid-infrared gas sensor using a 2.73 µm distributed feedback (DFB) laser was developed for simultaneously measuring the concentration changes of the three isotopologues 13 CO 2 , 12 CO 2 , and 18 OC 16 O in exhaled breath by direct absorption spectroscopy, and then determining the 13 CO 2 / 12 CO 2 isotope ratio ( δ 13 C) and 18 OC 16 O/ 12 CO 2 isotope ratio ( δ 18 O). The HWG sensor showed a fast response time of 3 s. Continuous measurement of δ 13 C and δ 18 O in the standard CO 2 sample with known isotopic ratios for ∼ 2 h was performed. Precisions of 2.20%(cid:24) and 1.98%(cid:24) for δ 13 C and δ 18 O respectively at optimal integration time of 734 s were estimated from Allan variance analysis. Accuracy of − 0.49%(cid:24) and − 1.20%(cid:24) for δ 13 C and δ 18 O, respectively, were obtained with comparison to the values of the reference standard. The Kalman ﬁltering method was employed to improve the precision and accuracy of the HWG sensor while maintaining high time resolution. Precision of 5.45%(cid:24) and 4.88%(cid:24) and the accuracy of 0.21%(cid:24) and − 1.13%(cid:24) for δ 13 C and δ 18 O, respectively, were obtained at the integration time of 0.54 s with the application of Kalman ﬁltering. The concentrations of 12 CO 2 , 13 CO 2 and 18 OC 16 O in breath cycles were measured and processed by Kalman ﬁltering in real time. The measured values of δ 18 O and δ 13 C in exhaled breath were estimated to be − 21.35%(cid:24) and − 33.64%(cid:24), respectively, with the integration time of 1 s. This study demonstrates the ability of the HWG sensor to obtain δ 13 C and δ 18 O values in breath samples and its potential for immediate respiratory monitoring and disease diagnosis


Introduction
Breathing gas analysis is an effective method for disease diagnosis or metabolic status monitoring.Breathing gas diagnostics have the advantage of being non-invasive and highly safe compared with other diagnostic methods.It can even easily collect samples of elderly people or newborns with severe illness and provide real-time results for doctors and patients, which is important for the diagnosis of early diseases.The main components of human exhaled gases include nitrogen (78%), oxygen (15-18%), water vapor (5%), carbon dioxide (4-6%) and argon (1%), hundreds of volatile organic compounds, as well as respiratory gases in the order of one millionth or less [1][2], some of which have been proven to be useful markers for disease diagnosis and metabolic disorders [3].The changes in the contents of 13 CO 2 , 12 CO 2 , and 18 OC 16 O in respiratory gases are inseparable from the health of the human body, among which 13 C is especially often used to diagnose whether a suspected patient is infected with Helicobacter pylori.While a 13 C-urea breath test (UBT), patients showing a delta over baseline (DOB) value higher than 4% being considered positive for H. pylori infection [4].Apart from 13 C, the 18 O isotope in breathing gas can be used as a potential biomarker for diagnosis of diabetes [5][6], and provides a non-invasive diagnostic method for accurately assessment of type 2 diabetes (T2D) and distinguishing type 1 diabetes (T1D) from T2D.Therefore, the real-time online measuring of the δ 13 C and δ 18 O in breath CO 2 is of great significance.
At present, the methods of isotope abundance detection mainly include mass spectrometry (IRMS) [7] and laser absorption spectroscopy [8][9].Although mass spectrometry can meet the requirements of measurement accuracy and precision well, it also has some defects, such as sample pretreatment, high price, and difficulty to achieve on-line measurement.In addition, mass spectrometry requires reliable operation and maintenance by professional technicians, which greatly limits the application of this technology.In recent years, laser absorption spectroscopy has been developed to measure stable isotope.This technology has the advantages of high selectivity, high detection sensitivity, fast response, small size and simple operation, and has attracted extensive attention from researchers.Laser absorption spectroscopy for the measurement of 13 CO 2 / 12 CO 2 ratio in respiratory gases has focused on the three main absorption bands of CO 2 at 1.6, 2.0, 2,7 and 4.3 µm.In the near-infrared 1.6 µm band, the absorption line strength of CO 2 molecules is relatively weak, and the multi-pass cell cannot achieve good measurement precision [10], so the high-finesse optical cavity is usually used to increase the absorption path length, thereby improving measurement precision [11][12].In the near-infrared 2.0 µm band, the absorption line strength of CO 2 molecules is two orders of magnitude higher than that of the 1.6 µm band.It does not require a long effective optical path or a precise cavity operation to achieve a certain absorption depth, so it's widely employed in the literatures [13][14][15]; and on this basis, various filtering algorithms (Kalman filtering [16], Savitzky-Golay adaptive filtering [17], empirical mode decomposition (EMD) adaptive algorithm [18], Wiener filtering [19] and wavelet denoising [20], etc.) are used to reduce system noise, thereby improving the detection sensitivity and measurement precision of 13 CO 2 in breathing gas.Among them, Kalman filtering method is most effective in improving detection precision.In the mid-infrared 4.3 µm band, the CO 2 molecular line intensity is three orders of magnitude stronger than that of the 2.0µm band.In recent years, this band has received more and more attention from researchers [21].In the above research, various traditional gas cells such as multi-pass cells and optical cavities were used as sample cells, but the volume of these conventional gas cells was more than 100 ml, and the gas replacement time was long, resulting in a slow response time of the system.Many respiratory gas measurements even require pre-acquisition of samples and off-line testing.The hollow waveguide has very small sample volume (∼1 ml), which enables rapid update of the breathing gas in the cell, fast response time (∼3 s) and online measurement [22][23][24][25].As shown in Table 1, hollow waveguide (HWG) serving simultaneously as both light guides and gas transmission cell has been considered as a most ideal gas absorption cell for 13 CO 2 / 12 CO 2 isotope ratio measurements [26][27][28][29][30][31].The spectral region near 2.7 µm currently covered by commercially available compact DFB lasers with modest cost meets the requirement of CO 2 isotopologue ratios measurement to a high degree, though the absorption line intensities of CO 2 are hundreds of times weaker than those at 4.3 µm.Meanwhile, no literature has reported measurement of δ 18 O in respiratory CO 2 using HWG based spectroscopic methods, to our best knowledge.
In our experiment, a mid-infrared HWG gas sensor for measurement of CO 2 isotopologue ratios (δ 13 C and δ 18 O) in the breathing gas was developed.The performance of the HWG sensor was evaluated.Kalman filtering was employed to reduce the system noise and improved the detection precision with a high time resolution.The concentrations of 12 CO 2 , 13 CO 2 and 18 OC 16 O in breath cycles were measured and processed by Kalman filtering, at the same time values of δ 18 O and δ 13 C in exhaled breath were determined.

Experimental principle
According to Beer-Lambert law, absorption A(v) is related to output light intensity I(v) and incident light intensity I 0 (v).
where c is the number of molecules absorbed per cubic centimeter (in mol/cm 3 ), σ(v) is the frequency-dependent absorption cross section (in cm 2 /mol), and L is the optical absorption path length (in cm).The integral absorption A I (cm −1 ) can be expressed as: where S(T) is the line strength of the absorbing molecule at a temperature of T in cm•mol −1 , and n is the isotope abundance (ascertained by the HITRAN 2016 database).The gas stable isotope ratio and the isotope delta value [32] can be expressed as: wherein x and a are represented as rare isotopic species ( 13 CO 2 , 18 OC 16 O) and abundant isotopic component ( 12 CO 2 ), respectively.R is the measured ratio of rare/abundant isotopes, R sam and R cal are the measured ratio of rare/abundant isotopes for the gas sample with and for the calibration gas, respectively.δ 13 C cal and δ 18 O cal are known δ-value of the calibration gas.R VPDB is the isotope ratio of the Vienna Peedee Belemnite (VPDB) standard.R VPDB−CO2 is Vienna Peedee Belemnite derived CO 2 (VPDB-CO 2 ).

Selection of spectral lines
To simultaneously measure the concentration of CO 2 and its isotopes in the breathing gas, the distance between the absorption lines must be within the scanning range of the laser.It is also necessary to consider the interference of other breathing gases on CO 2 and its isotope measurements.According to the HITRAN 2016 database [33], CO 2 and isotopes have strong absorption lines around 2.73 µm, where the absorption line strength of CO 2 molecules is on the same order of magnitude as that in the 2.0 µm band, and does not require a long effective optical path to achieve a high absorbance.Furthermore, the simultaneous measurement of CO 2 and isotopes in the breathing gas can be achieved within the laser tuning range, and the line strengths of 12 CO 2 , 18 OC 16 O and 13 CO 2 are in the same order of magnitude.Therefore, in our experiment, the absorption lines of 12 CO 2 , 18 OC 16 O and 13 CO 2 were selected as 3661.4948cm−1 , 3661.0834cm −1 and 3660.7684cm−1 respectively, the temperature and current of the laser controller were set to 33 °C and 131 mA respectively.The range of laser wavenumber variation during one scanning was 3660.1-3661.8cm −1 , ensuring that these three isotopologues could be detected simultaneously.Table 2 gives a comparison of the strength, ground state energy and temperature coefficient among the selected three absorption lines.The temperature coefficient of the δ value is to a good approximation equal to the difference of the temperature coefficients of the rare and abundant isotopologue lines.The temperature-induced shift of the isotope ratios is given as −9.6% /K and −26.7% /K for the δ 13 C and δ 18 O, respectively.The ground state energy of 12 CO 2 is more than double the ground state energy of the other two molecules.Therefore, the temperature control accuracy of the hollow waveguide must be very high, which increases the complexity of the experimental device.A temperature control device was used to control the temperature of the HWG.The temperature was preset to 25 °C, and maintained constant within ±0.2 °C by the temperature controller.

Experimental set-up
The CO 2 and its isotope detection system in the breathing gas based on hollow waveguide are shown in Fig. 2(a).In the optical path section, the laser used was a 2.73 µm tunable DFB laser from Nanoplus.It had a collimating lens inside and a maximum output of 11.2 mW.The temperature and current of the DFB laser were controlled using a laser controller (LDC-3724, ILX Lightwave, USA).The peak-to-peak value of the sawtooth wave signal generated by the signal generator was set to be 0.8 V and its frequency was set to be 20 Hz.The sawtooth wave signal was used to modulate the laser controller to control the laser output wavenumber, so that the laser scanning range could cover the absorption lines of 12 CO 2 , 13 CO 2 and 18 OC 16 O.The gas cell module was mainly composed of a hollow waveguide (HWEA 10001600) with a length of 1 m, an inner diameter of 1 mm and an outer diameter of 1.6 mm, and a volume of about 0.78 cm 3 .The light emitted by the laser passed through the collimating lens to form paraxial parallel laser beam, which was then focused to the HWG via a focusing lens.After entering the hollow waveguide, the light was reflected back and forth on the inner wall, and the emitted light was received by a photodetector (PVI-4TE-10.6,VIGO system S.A., USA).The absorption signal from the detector was digitized with a laptop using a 14-bit analogue/digital data acquisition card controlled with a Labwindows program.A 1.2 L vacuum pump (DIVAC, Germany) was used to evacuate the hollow waveguide.The mass flow controller (GV50A, MKS, USA) and the pressure controller (640, MKS, USA) were used to control the gas flow rate in the gas chamber at 4.33 mL/s and the pressure at 200 torr, and the pressure dynamic equilibrium was achieved.
The hollow waveguide connector is shown in Fig. 2(b).In order to minimize interference from CO 2 and its isotopes in the environment, the laser and photodetector was kept at a relatively close distance from the hollow waveguide.The HWG was coiled on the surface of a plastic ring made by 3D printing with a radius of 80 mm for compactness, and then covered with a heater band.The HWG temperature was monitored with calibrated platinum resistors (Pt100).A PID temperature controller was used to control the temperature of the HWG.The HWG sensor with all components was packaged in a box.No temperature gradient along the fiber axis was observed.

Spectral line fitting
In order to obtain the integral absorption A I , the acquired absorption spectrum was fitted to a Voigt profile using an L-M multi-line fitting algorithm.During the fitting process, the baseline of the laser power as a function of current was represented by a 5-level polynomial.Figure 3 shows the experimental data of the isotope absorption line of carbon dioxide near 2.73 µm, which was measured at 296.15 K at a pressure of 33.325 KPa, the average of 100 laser scans.It can be seen from Fig. 3 that the absorption line obtained by the experimental measurement matches well with the Voigt fitting data, and the fitting correlation is as high as 0.999.The noise in fitting residual is mainly caused by the optical stripe and random noise superimposed on the absorption signal.

Location in article (line) Corrections or deletions
Page 2, line 106 The sentences: "Therefore, the real-time online measuring of the δ 13 C andδ 18 O breath CO2 is of great significance." is corrected is "Therefore, the real-time online measuring of the δ 13 C and δ 18 O in breath CO2 is of great significance."Page 6, line 506 (170 ppm) and 4.24% (42400 ppm) respectively, and the corresponding δ 13 C and δ 18 O values are −24.05%and −30.22% determined by calculation using Eqs.( 4) and ( 5) respectively.

Response time
Standard CO 2 gases at concentrations of 0%, 3%, 7%, 11%, and 15% were prepared by dynamically mixing purity CO 2 with N 2 using two mass flow controllers at P=33.325 KPa and T=296.15K.The absorption signals were measured with different concentrations of CO 2 gas, and the corresponding concentration values were obtained by fitting.The relationship between the concentration and the change in time at different 13 CO 2 concentrations is shown in Fig. 4. It can be seen from Fig. 4 that when the CO 2 gas channel is open, concentration of 13 CO 2 rises rapidly after a rise delay time τ d (0-10% of the concentration levels in rising or falling process) of 0.54 s, and the concentration of 13 CO 2 is stabilized at 0.033% after 3 s response time τ r (10-90% of the concentration levels in rising or falling process); when the CO 2 gas channel is closed, 13 CO 2 concentration drops rapidly after 0.54 s of falling delay time τ d , and the concentration of 13 CO 2 decreases to zero after 2.7 s response time τ r .The response time of the system is mainly determined by the structure of the gas chamber, the gas flow rate through the gas chamber, and the processing time required by the data acquisition system.

Long-term performance of measurement of CO 2 isotopologue ratios
The Allan Variance [34] is a method commonly used to assess system stability and detection limits.Under the condition of P=33.325KPa and T=296.15K, the reference samples of CO 2 isotope (δ 13 C=-21.34%, δ 18 O=-30.89%) calibrated by isotope mass spectrometry (IRMS) were measured, and an absorption spectrum was collected every 0.54 s during 1.77 h.By using the least squares algorithm to fit the measured absorption line, a continuously measured concentration value could be obtained.The corresponding δ values were calculated by Eq. ( 4).Allan variance analysis has been performed to determine the optimum integration time and the precision.It can be seen from Fig. 5 that the measurement precision of δ 13 C and δ 18 O reaches 2.20% and 1.98% respectively with the best integration time of 734 s.Table 3 shows the averaged values of δ 13 C and δ 18 O are −20.85% and −32.19% respectively, and the absolute deviations of the measured values are −0.49% and −1.20% respectively.After Kalman filtering, the measured values of δ 13 C and δ 18 O in the 0.54 s are −21.13%and −32.02% respectively, the absolute deviations of the measured values are 0.21% and −1.13% respectively, and the measurement precision is 5.45% and 4.88% respectively with a 0.54s time resolution.Though the demonstrated precision cannot meet the requirement of clinical goals, like diagnosis of infection with Helicobacter pylori and assessment of diabetes demanded a precision better than 1% [35], methods for further improvement of measurement precision include: (1) increasing the length of the HWG to increase the absorption path length in the HWG; (2) using wavelength modulation spectroscopy techniques to reduce system noise; (3) controlling temperature of the HWG within ±0.1 °C. to further reduce temperature-induced δ-value drift.

Real-time online measurement of respiratory cycle
To verify the practicality and effectiveness of the 12 CO 2 , 13 CO 2 , and 18 OC 16 O measurement systems for breathing, a sequence diagram of real-time changes in CO 2 and isotope concentrations during a tidal breathing was measured.The pressure in the hollow waveguide was controlled to be 33.325KPa, and the breathing gas was introduced into the HWG cell by breath tube according  to the direction of gas passage shown in Fig. 2 (a).The volume of each exhaled gas in the human body was about 460 ml [36], so the average 10 spectra were selected as one data point.The actual acquisition time was 312 s with time interval of 1.08 s.The respiratory gas circulation process was measured in real time.Figure 6 shows that the real-time CO 2 and its isotope concentration changes during a tidal breathing and the results of Kalman filtering.The measured values of δ 13 C and δ 18 O in the exhaled gas after Kalman filtering were −21.34% and −33.64% respectively, and the measurement precision was 27.32% and 28.27% respectively.The reasons for the fluctuation of the measurement results are as follows: (1) The concentration of CO 2 and isotopes in the tidal breathing process continuously rises and changes; (2) The interference effect in the hollow waveguide, fluctuations in temperature, unstable flow during human breathing, and differences in the temperature of the breathing gas itself and the temperature in the gas cell can also affect the measurement precision; (4) In terms of data processing, the fitting algorithm also brings a certain deviation.Although the deviation is small, it is still a non-negligible factor in the calculation of isotope abundance.

Conclusion
This paper reports the development of a mid-infrared gas sensor for measuring CO 2 and its isotope concentration in breathing gas based on hollow waveguide.The sensor has the advantages of nonintrusion, small volume, fast response time, high sensitivity and real-time online measurement.
In our experiment, a DFB laser with a center wavelength of 2.73 µm was used as the detection source.The hollow waveguide combined with direct absorption spectroscopy technology was used to achieve high precision measurement of CO 2 isotope abundance under high concentration conditions and long-term stability performance of the measurement system.The changes in CO 2 and isotope concentrations in the breathing gas from dynamic measurements are analyzed.
The system stability and measurement precision are discussed in detail.It can be seen from the experiment results that under the condition of optimal integration time of 734 s, the absolute deviations of δ 13 C and δ 18 O measurements were −0.49% and −1.20% respectively, and the measurement precision could reach 2.20% and 1.98% respectively.After Kalman filtering, the absolute deviations of δ 13 C and δ 18 O in the integration time of 0.54 s were 0.21% and −1.13% respectively, and the measurement precision was 5.45% and 4.88% respectively.The concentrations of 12 CO 2 , 13 CO 2 and 18 OC 16 O in breath cycles were measured and processed by Kalman filtering in real time.The measured values of δ 18 O and δ 13 C in exhaled breath were estimated to be −21.35% and −33.64% respectively with the integration time of 1s.This study demonstrates the ability of the HWG sensor to obtain δ 13 C and δ 18 O values in breath samples, and its potential for immediate respiratory monitoring and disease diagnosis.

Fig. 3 .
Fig. 3. Result of CO 2 isotope absorption spectra fitted to Voigt profile and fitting residuals

Fig. 4 .
Fig. 4. Comparison between measured gas concentration and standard gas concentration.

Fig. 5 .
Fig. 5.Measurement results of the reference samples of CO 2 isotopes.The upper four panels show raw measurement of δ 13 C and δ 18 O (black lines) and the corresponding Kalman-filter output (blue lines).The Allan variances plotted in the lower panel show an optimal integration time of 734 s for the present system.

Fig. 6 .
Fig. 6.Sequence diagram of the changes of 12 CO 2 , 18 OC 16 O and 13 CO 2 concentrations during tidal breathing process of a volunteer and the results of the Kalman filter.

Table 1 . Summary of various isotope ratio measurements using hollow core wave guides previously reported in the literature and the corresponding key experimental parameters). Where iHWG: substrate-integrated hollow waveguide; DAS: direct absorption spectroscopy; WMS: wavelength modulation spectroscopy; PLS: partial least-squares regression; FTIR: Fourier transform infrared spectroscopy. δ 13 C% = 1000 13 C/ 12 C sample 13 C/ 12 C reference
− 1 , TTR% = 100 (labeled tracer/unlabeled tracee) Ref. Wavelength Hollow core waveguide Length of HWG Method Stabilization time Precision Human exhaled gases mainly include N 2 , CO 2 , O 2 , H 2 O, Ar and other trace gases.According to the HITRAN 2016 database, N 2 , O 2 and Ar are not absorbed in the target spectral range, and have no effect on CO 2 and its isotopes.The concentration of CO 2 and H 2 O in human exhaled gas is about 5%, and the strongest absorption line strength of H 2 O in this range is 6.93×10 −23 cm −1 /(molecule•cm −2 ), which is stronger than that of the CO 2 isotope.Under the conditions of P=33.325KPa and T=293.15K, the absorption line in the range of 3658-3668 cm −1 with concentration of 5% CO 2 and 5% H 2 O was simulated.It can be seen from Fig.1that within this wavenumber range, H 2 O does not interfere with the measurement of CO 2 and its isotopes.