## 5 Towards Applications: Human Exhalation  
Raman spectroscopy is well suited for the simultaneous detection of various gases in the analysis of human respiration [38]. Natural carbon isotopes (\({}^{12}\)C and \({}^{13}\)C) present in human breath can be used to identify various diseases. Carbon isotopes in exhaled CO\({}_{2}\) can be a valuable real-time biomarker of cachexia [39] (depletion of the body), associated with the acute phase of the reaction caused by endotoxemia (accumulation of toxic substances in the body). The acute phase reaction causes shifts in stable carbon isotopes in exhaled CO\({}_{2}\), which can be used to monitor nutrient metabolism. Isotope mass spectrometry (IRMS) exists to determine CO\({}_{2}\) carbon isotopes in human respiration [40]. This method has high accuracy, sensitivity and stability, but it is rather complex, expensive and requires large expenditures on equipment and staff training. There is a less expensive way to detect CO\({}_{2}\) isotopes using an isotope-selective non-dispersive infrared spectrometer (NDIRS) [41], but it is only suitable for simple breath tests where a small number of samples is required, for example, to detect diseases of the gastrointestinal tract and detect Helicobacter bacteria pylori [42]. This is due to a decrease in the correlation of repeated measurements with longer series of measurements.  
A Raman spectrum overview of a human exhalation measured at ambient pressure (1 atm.) is shown in Figure 7a. Its shows several intense Raman peaks at 1285 and 1388 cm\({}^{-1}\) (both-\({}^{12}\)CO\({}_{2}\)), 1556 cm\({}^{-1}\) (O\({}_{2}\)), 2328 cm\({}^{-1}\) (N\({}_{2}\)) and 2919 cm\({}^{-1}\) (\({}^{12}\)CH\({}_{4}\)). By focusing on the spectral range around \(\sim\)1300 cm\({}^{-1}\) and applying longer exposure (600 s), we were able to clearly resolve the Raman lines assigned to the isotopologues of carbon dioxide (\({}^{12}\)CO\({}_{2}\) and \({}^{13}\)CO\({}_{2}\)). The spectral position of the  
Figure 6: (**a**) Raman spectrum of high-purity (\(>\)99%) isotopically-enriched (\(>\)99.9% \({}^{13}\)C) \({}^{13}\)CH\({}_{4}\) gas. The excitation wavelength \(\lambda_{\mathrm{exc}}\) = 532.123 nm, the resolution is \(\sim\)1 cm\({}^{-1}\). Gas pressure: 1 atm. Exposure time \(\Delta t\): 1–30 s; (**b**) double-logarithmic plot of LOD vs. the exposure time, _symbols_: experimental data, _line_: linear fit according to Equation (2). Gas pressure: 1 atm.  
lines and the isotopoc wavenumber shifts agree well with the data for isotopically enriched gases, cf. Figure 4.  
The Raman spectra of isotopologues of carbon dioxide were analyzed from the point of view of the LOD in order to confirm the values obtained with the isotopically enriched gases, see Figure 4. Note that the LOD can be calculated for any gas in a gas mixture if its volume fraction \(X_{\mathrm{v0\%}}\) is known, see Equation (1). The volume fractions of \({}^{12}\)CO\({}_{2}\) and \({}^{13}\)CO\({}_{2}\) gases in human exhalation depends on different factors, e.g., the time between breathing in and out [43; 44]. We used the mean values of 4 vol% \({}^{12}\)CO\({}_{2}\) and 0.04 vol% \({}^{13}\)CO\({}_{2}\). Based on these volume fractions and the measured Raman spectra, as shown in Figure 7b, we have determined the LOD to be 225 ppm (\({}^{12}\)CO\({}_{2}\)) and 75 ppm (\({}^{13}\)CO\({}_{2}\)) at a gas pressure of 1 atm. and an exposure time of 600 s. These values agree well with the analysis performed in Table 2, considering the difference in the exposure time.