## 3 Results
### Hemodynamic and Metabolic Monitoring  
The hemodynamic and metabolic monitoring (\(\Delta C_{HbO_{2}}\), \(\Delta C_{Hb}\), and \(\Delta C_{oxCCO}\) measurements) following a simulated patient neuronal stimulation (see Section 2.7) are represented in Figures 12 and 13. In Figure 12, the \(\Delta C_{HbO_{2}}\), \(\Delta C_{Hb}\), and \(\Delta C_{oxCCO}\) values were computed with the optimal spectral combination of the hyperspectral camera; see Figure 7. In Figure 13, the \(\Delta C_{HbO_{2}}\), \(\Delta C_{Hb}\), and \(\Delta C_{oxCCO}\) values were computed with the RGB camera. In these figures, the modified Beer-Lambert law was computed \(10^{3}\) times, using different Monte Carlo and intensity noise occurrences for each time iteration. When using the 121 wavelengths included between 780 nm and 900 nm [23] to quantify the concentration changes during the stimulation period (from \(t=18\) s to \(t=38\) s), there is a 1.2% underestimation of the \(\Delta C_{HbO_{2}}\) values, a 0.4% overestimation of the \(\Delta C_{Hb}\) values, and a 1.3% overestimation of the \(\Delta C_{oxCCO}\) values compared to the theoretical measurements. \begin{table}
\begin{tabular}{l c c c} \hline \hline  & \multirow{2}{*}{**RGB Imaging**} & \multicolumn{3}{c}{**Hyperspectral Imaging**} \\ \cline{3-4}  & & **Spectral Correction** & **No Spectral Correction** \\ \hline \(\mu(r_{HbO_{2}})\) & 0.949 & 0.951 & 0.904 \\ \(\sigma(r_{HbO_{2}})\) & 0.013 & 0.013 & 0.026 \\ \hline \(\mu(r_{Hb})\) & 0.989 & 0.932 & 0.783 \\ \(\sigma(r_{Hb})\) & 0.002 & 0.018 & 0.059 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pearson correlation coefficients computed between the theoretical hemodynamic responses and the simulated concentration changes’ time courses; see Figures 10 and 11. \(\mu(r_{n})\) and \(\sigma(r_{n})\) designate the mean and standard deviation, respectively, of the Pearson correlation coefficients computed with the \(10^{3}\) noisy time courses of the chromophore \(n\). Figure 11: Hemodynamic monitoring following neuronal activation computed with RGB imaging. The dashed lines represent the theoretical hemodynamic responses following the neuronal stimulation. The dispersion ranges of the measurements are represented by colored areas. The concentration changes averaged over the \(10^{3}\) noisy measurements are represented in solid lines. The concentration changes’ time courses computed with the 121 wavelengths included between 780 nm and 900 nm [23] are represented with yellow points. The ones computed with [PERSON] et al.’s wavelengths [27] are represented with black triangles. The blue rectangle represents the “patient” physiological stimulus. When using the eight wavelengths identified by [PERSON] et al. [27] to quantify the concentration changes during the stimulation period, there is a 1.7% underestimation of the \(\Delta C_{HbO_{2}}\) values, a 1.91% overestimation of the \(\Delta C_{Hb}\) values, and a 6% overestimation of the \(\Delta C_{oxCCO}\) values compared to the theoretical measurements. In Figure 12, the hemodynamic and metabolic monitoring following a simulated neuronal stimulation was computed using hyperspectral imaging. The optimal corrected and uncorrected spectral configurations of the hyperspectral camera were used to quantify the \(\Delta C_{HbO_{2}}\), \(\Delta C_{Hb}\), and \(\Delta C_{oxCCO}\) values. The quantification dispersion ranges of the corrected and uncorrected spectral configurations have approximately the same range of magnitude. The standard deviation averaged over all time measurements for \(\Delta C_{HbO_{2}}\), \(\Delta C_{Hb}\), and \(\Delta C_{oxCCO}\) are equal to 1.23 \(\upmu\)mol\(\cdot\)L\({}^{-1}\), 1.27 \(\upmu\)mol\(\cdot\)L\({}^{-1}\), and 1.07 \(\upmu\)mol\(\cdot\)L\({}^{-1}\), respectively. When the spectral bands are corrected, the \(\Delta C_{HbO_{2}}\) and \(\Delta C_{Hb}\) values averaged over the \(10^{3}\) noisy measurements have a good match with the theoretical hemodynamic responses.