## 2 Materials and Methods
### Application to a Functional Brain Mapping Study  
In functional brain mapping studies, the measured hemodynamic concentration changes' time courses are compared to the patient theoretical hemodynamic responses. These theoretical responses are obtained by convolving the hemodynamic impulse response function to the window function representing the patient physiological stimulus. The functional areas may be identified by testing the Pearson correlation coefficients (computed between the concentration changes' time courses and the theoretical hemodynamic responses) and the concentration changes averaged over the patient activity period with several \(T\)-tests [5; 25]. Another technique derived by BOLD fMRI (blood oxygenation level dependent, functional magnetic resonance imaging) is the NIRS SPM (near-infrared spectroscopy statistical parametric mapping) analyses [13; 14] that use a general linear model and random field theory to identify the functional areas in a pixel-wise manner. We built a simulation of the grey matter hemodynamic and metabolic responses following a patient physiological stimulus based on the Monte Carlo framework described in Section 2.4. The intrinsic signal was acquired during 60 s at 0.5 frames per second with the integration time set to 33 ms. The following paradigm was simulated: 18 s of rest, 20 s of neuronal stimulation, followed by 22 s of rest. We incorporated the temporal hemodynamic response, as well as the temporal oxCCO response following neuronal activation. The hemodynamic responses were obtained by convolving the hemodynamic impulse response function to the window function representing the patient physiological stimulus. The oxCCO response function was introduced by [PERSON] et al. [45] to describe the metabolic response in the primary and adjacent visual cortex for a stimulus of 6 to 24 s. The theoretical time courses can be roughly represented by the function \(h(t)=a.t^{2}.e^{-t}\) convolved with the window function representing the patient physiological stimulus. In this function, \(t\) represents the time (in s) and \(a\) is the characteristic amplitude of \(\Delta C_{oxCCO}\). The theoretical temporal variation of the \(\Delta C_{HbO_{2}}\), \(\Delta C_{Hb}\), and \(\Delta C_{oxCCO}\) values are represented in Figure 5. Note that these values varied homogeneously in the modeled tissue. During these absorption perturbations, the other optical coefficients were kept constant. With these simulations, we can evaluate the potential benefit from using hyperspectral imaging for the computation of hemodynamic brain maps instead of using a standard RGB camera (see our previous studies [5; 11; 12]). This approach aims to simulate the quantitative values that are computed in clinical functional brain mapping applications. This makes it possible to test the influence of the optimal spectral band configuration on the quantities measured in clinical applications. For this purpose, the Pearson correlation coefficient is computed. The correlation coefficient was calculated between the  
Figure 5: Theoretical \(\Delta C_{HbO_{2}}\) (in red), \(\Delta C_{Hb}\) (in blue), and \(\Delta C_{oxCCO}\) (in green) responses following the patient physiological activity. \(\Delta C_{HbO_{2}}\) and \(\Delta C_{Hb}\) are expressed by the left vertical axis. \(\Delta C_{oxCCO}\) is expressed by the right vertical axis. The blue rectangle represent the “patient” physiological stimulus. theoretical hemodynamic time courses (see Figure 5) and the hemodynamic time courses simulated with the optimal spectral configuration of the hyperspectral camera (see Section 2.6). The correlation coefficient was also computed with the data simulated with RGB imaging. We can also investigate the ability of hyperspectral imaging to monitor the brain metabolism. For this purpose, the Pearson correlation coefficient values were computed between the theoretical oxCCO time course (see Figure 5) and the \(\Delta C_{oxCCO}\) time courses simulated with the optimal spectral configuration of the hyperspectral camera (see Section 2.6).