## 3 Results
### Hemodynamic and Metabolic Monitoring
The \(\Delta C_{oxCCO}\) values averaged over the \(10^{3}\) noisy measurements have a good match with the theoretical metabolic response with and without spectral correction. When the spectral bands are corrected, there is on average a 0.5% underestimation of the \(\Delta C_{HbO_{2}}\) values, a 4.4% overestimation of the \(\Delta C_{Hb}\) values, and a 15% overestimation of the \(\Delta C_{oxCCO}\) values compared to the theoretical measurements. When the spectral bands are not corrected, there is on average a 25% underestimation of the \(\Delta C_{HbO_{2}}\) values, a 42% underestimation of the \(\Delta C_{Hb}\) values, and a 19% underestimation of the \(\Delta C_{oxCCO}\) values compared to the theoretical measurements. The correlation coefficients computed between the theoretical HbO\({}_{2}\) response and the \(\Delta C_{HbO_{2}}\) time courses are higher when the spectral bands are corrected (\(r=0.843\pm 0.043\)) than when they are not (\(r=0.749\pm 0.068\)). The correlation coefficients computed between the theoretical Hb response and the \(\Delta C_{Hb}\) time courses are higher when the spectral bands are corrected (\(r=0.780\pm 0.063\)) than when they are not (\(r=0.577\pm 0.112\)). The correlation coefficients computed between the theoretical oxCCO response and the \(\Delta C_{oxCCO}\) time  
Figure 12: Hemodynamic and metabolic monitoring following neuronal activation computed with the optimal spectral configuration obtained with the simulation-based method (see Figure 7). The dashed lines represent the theoretical hemodynamic and metabolic 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. courses are higher when the spectral bands are corrected (\(r=0.256\pm 0.177\)) than when they are not (\(r=0.177\pm 0.175\)). The correlation coefficient values are summarized in Table 5.  
In Figure 13, the hemodynamic and metabolic monitoring following a simulated neuronal stimulation was computed using RGB imaging. The standard deviation averaged over all time measurements is equal to 1.24 \(\upmu\)mol\(\cdot\)L\({}^{-1}\), 1.04 \(\upmu\)mol\(\cdot\)L\({}^{-1}\), and 1.54 \(\upmu\)mol\(\cdot\)L\({}^{-1}\) for \(\Delta C_{HD\Omega_{2}}\), \(\Delta C_{Hb}\), and \(\Delta C_{oxCCO}\), respectively. The computed \(\Delta C_{HD\Omega_{2}}\), \(\Delta C_{Hb}\), and \(\Delta C_{oxCCO}\) values do not have a good match with the theoretical hemodynamic and metabolic responses. During the stimulation period, there is on average a 169% underestimation of the \(\Delta C_{HD\Omega_{2}}\) values, a 147% underestimation of the \(\Delta C_{Hb}\) values, and a 1036% overestimation of the \(\Delta C_{oxCCO}\) values compared to the theoretical measurements. We can notice that there is an important crosstalk between the chromophores. The \(\Delta C_{Hb\Omega_{2}}\) values were mainly interpreted as Hb variations, the \(\Delta C_{Hb}\) values as oxCCO variations, and the \(\Delta C_{oxCCO}\) as HbO\({}_{2}\) variations. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Hyperspectral Imaging**} \\ \cline{2-4}  & \multicolumn{1}{c}{**Spectral Correction**} & \multicolumn{1}{c}{**No Spectral Correction**} \\ \hline \(\mu(r_{HD\Omega_{2}})\) & \(-0.727\) & 0.843 & 0.749 \\ \(\sigma(r_{HD\Omega_{2}})\) & 0.072 & 0.043 & 0.068 \\ \hline \(\mu(r_{Hb})\) & \(-0.499\) & 0.780 & 0.577 \\ \(\sigma(r_{Hb})\) & 0.126 & 0.063 & 0.112 \\ \hline \(\mu(r_{oxCCO})\) & 0.880 & 0.256 & 0.177 \\ \(\sigma(r_{oxCCO})\) & 0.030 & 0.177 & 0.175 \\ \hline \hline \end{tabular}
\end{table}