# Raman Spectroscopy as Noninvasive Method of Diagnosis of Pediatric Onset Inflammatory Bowel Disease
## 2 Materials and Methods
### Raman Measurements  
Raman measurements were performed by means of a DXR-SmartRaman Spectrometer (Thermo Fisher Scientific, Waltham, MA, USA) using a diode laser with the excitation wavelength of 785 nm. All the Raman spectra were acquired over the wavenumber range of 400-3300 cm\({}^{-1}\), with a resolution of 1.9 cm\({}^{-1}\) and irradiated with a laser power of 24 mW, coming out from a 50 um spot. Vials containing fecal extract were accommodated into their sample holder and the 180-degree sampling accessory for the DXR-SmartRaman Spectrometer was used for measurements. This sampling accessory, that has the typical 180-degree backscattering geometry for collecting Raman scattered radiation, is designed as a simple device to accommodate vials, tubes, powders and other samples in a variety of formats. It can allow the use of specialty cells, including cryogenic, high-temperature, electrochemical and controlled-humidity chambers, and results particularly useful in environments that value diverse sample formats over highly automated data collection. In order to obtain high signal-to-noise ratio (S/R) spectra, each Raman spectrum was obtained after collecting 32 sample frames, and the duration of each exposure for each frame was set equal to 60.0 s. Total acquisition time was 32 min for each spectrum. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **IBD Group** & **non-IBD Group** \\ \hline
**Median age and SD \({}^{*}\)** & 15.6 (3.15) & 12.6 (5.17) \\
**M:F ratio** & 1.4 & 1.5 \\
**UC vs. CD in IBD group** & CD 62.5\% & - \\  & UC 38.5\% & - \\
**Mean (min-max) calprotectin levels (mg/kg)** & 820 (2360-161) & 37 (2.5–89) \\
**Final diagnosis in non-IBD group** & - & IBS \({}^{**}\) (70\%), RAP \(\lx@sectionsign\) (30\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Demographic, clinical and baseline features of inflammatory bowel (IBD) and non-IBD group. Experimental data in the 1300-1800 cm\({}^{-1}\) range were fitted by a multiple curve-fitting routine provided in the PeakFit 4.0 software package (Systat Software, Inc., San Jose, CA, USA). The fitting procedure we adopted was a nonlinear regression procedure (a nonlinear least squares fitting) that adjusts the parameters in small steps in order to improve the goodness of the fit, by minimizing the sum of the squares of the vertical deviations \(r^{2}=\sum[y_{i}-f(x_{i},a_{1},a_{2},\ldots,a_{n})]^{2}\) of a set of \(n\) data points from a function \(f\). The analysis of the second derivative of the spectra was preliminary applied in order to gain, by evaluating the minima in the obtained profiles, a first indication of the minimum number of band components and their peak positions, according to a procedure already successfully applied in the analysis of Raman spectra of supramolecular systems [36]. In associated systems, the width of a vibrational band shape suffers homogeneous and non-homogeneous enlargement, therefore the Voigt profile, which is a convolution of Lorentzian with Gaussian, is suitable for band shape analysis. In the light of this, the experimental data were deconvoluted into the minimum number of Voigt \(V(\omega)\) fitting functions, defined as the following convolution of a Lorentzian with a Gaussian curve:  
\[V(\omega)=\frac{\left\{\int_{-\infty}^{+\infty}\frac{\omega_{Vg}\exp\left(-x^ {2}\right)dx}{\Gamma_{VL}^{2}+\left[\left(\frac{\omega-\omega_{Vg}}{\Gamma_{ VG}}\right)-x\right]^{2}}\right\}}{\int_{-\infty}^{+\infty}\frac{\exp \left(-x^{2}\right)dx}{\Gamma_{VL}^{2}+x^{2}}}, \tag{1}\]  
in which \(\omega_{Vg}\) and \(\omega_{Vg}\) are the amplitude and the center frequency, \(\Gamma_{VG}\) is related to the Gaussian half width at half maximum (\(\Gamma_{G}=\Gamma_{VG}\sqrt{2\ln 2}\)) and \(\Gamma_{VL}\) depends on the ratio of the Lorentzian half width at half maximum to \(\Gamma_{VG}\) (\(\Gamma_{L}=\Gamma_{VG}\cdot\Gamma_{VL}\)). All parameters (\(a_{Vg}\), \(\omega_{Vg}\), \(\Gamma_{VG}\), \(\Gamma_{VL}\)) were left free to vary upon iteration.