## 2 Materials and Methods
### Simulation of the Patient Cortical Activation  
Following the patient physiological activity, a hemodynamic change occurs in the activated cortical areas with an increase of the oxygenated hemoglobin concentration (\(C_{HbO_{2}}\)) and a decrease of the deoxygenated hemoglobin concentration changes (\(C_{Hb}\)). These hemodynamic changes are not the only ones that occur during a patient physiological activity. The concentration of the oxidative state of cytochrome-c-oxidase (\(C_{oxCCO}\)) also varies [22]. Cytochrome-c-oxidase (CCO) is an enzyme in the mitochondria that is involved in the aerobic metabolism of glucose. The total concentration of CCO does not change over a short time period (in the order of hours). However, it is possible to assess the differences between the oxidized and reduced states of CCO to obtain an indicator of the change in the CCO redox state.  
The patient cortical activation was simulated by Monte Carlo simulations [34]. A volume of 60 mm \(\times\) 60 mm \(\times\) 60 mm of grey matter was modeled under a homogeneous white light illumination. Each voxel of the modeled tissue included the information of optical parameters (absorption \(\mu_{s}\), scattering \(\mu_{s}\), anisotropy \(g\) coefficients, and refractive index \(n\)). A white light illumination was simulated by scanning the optical parameters along the entire illumination spectrum (from 400 nm to 1000 nm in steps of 1 nm). The size of the modeled tissues was chosen in accordance with the photon sensitivity profile [5,35] computed for the detector situated at the center of the top face of the volumes. To avoid any photon loss and inexact results due to the boundary conditions (the simulation of the travel of a packet of photon stops when this packet of photon leaves the volume), the size of the models was set to \(60\times 60\times 60\) voxels with a resolution of 1 mm\({}^{3}\). The \(10^{8}\) packets of photons were homogeneously illuminating the modeled surface. The optical mean path length and the diffuse reflection spectra were measured at the detector position with an integration time set to 33 ms, and the diffuse reflection spectra was normalized to a unitary source.  
The optical parameters were taken from the literature and correspond to a nominal physiological condition [36, 37, 38, 39, 40, 41]. The anisotropy, reduced scattering coefficients, and the refractive index used in the Monte Carlo simulations are summarized in Table 1. The scattering coefficient \(\mu_{s}\) was calculated from the reduced scattering coefficient (\(\mu_{s}\)) and the anisotropy coefficient (\(g\)): \(\mu_{s}=\mu_{s}/(1-g)\). In Table 1, \(\lambda\) denotes the wavelength dependence of the reduced scattering coefficient (in nm).  
\begin{table}
\begin{tabular}{c c c} \hline
**Anisotropy Coefficient \(g\)** & **Reduced Scattering Coefficient \(\mu_{s}\) (cm\({}^{-1}\))** & **Refractive Index \(n\)** \\ \hline
0.85 [42] & 40.8.5\(\frac{\lambda}{500}\)[39] & 1.36 [38] \\ \hline \end{tabular}
\end{table}
Table 1: Anisotropy, reduced scattering coefficients, and refractive index used in the Monte Carlo simulations.  
Figure 4: SNR values of each spectral channel of the RGB and hyperspectral cameras.  
The absorption coefficients were calculated using the chemical composition of the chromophores of the simulated tissues, which are summarized in Table 2.  
The chemical differences between the activated and non-activated grey matter are represented by a 5 \(\upmu\)mol\(\cdot\)L\({}^{-1}\) increase of \(C_{Hb\text{O}_{2}}\), a 3.75 \(\upmu\)mol\(\cdot\)L\({}^{-1}\) decrease of \(C_{Hb}\), and a 0.5 \(\upmu\)mol\(\cdot\)L\({}^{-1}\) increase of \(C_{oxCCO}\). These concentration changes are consistent with those defined in the literature. The reflection spectra and the optical mean path length were measured at the center of the top face of the volume.