## 2 Materials and Methods
### Data Acquisition and Preprocessing for DOT Measurements  
To acquire the DOT data, a DYNOT 232 instrument manufactured by NIRx Medizintechnik GmbH in Berlin, Germany, was utilized. The instrument employs continuous-wave measurements and operates with two laser sources at frequencies of 760 nm and 830 nm. The measurements were performed in a time-multiplexed scanning fashion with a sampling rate of 1.8 Hz. For light transmission and detection, optical fibers (optodes) were used, allowing near-infrared (NIR) light to travel to and from the DOT device. In this study, a total of thirty-two optical fibers were employed to measure hemodynamic changes in the contralateral cerebral hemisphere, specifically the left side. These optical fibers were configured as source-detector pairs, enabling the establishment of 1024 optical channels to capture and analyze the changes in the measured light intensity. The optodes were arranged in a rectangular grid at a distance of 1 between each of them, covering the C3 position referring to the EEG 10-20 system [9] (Figure 1a).  
Optical channels were preprocessed following the approach in prior studies that includes the following: (1) optical channels were filtered using Bayesian filtering to remove physiological noise [10]; (2) optical fiber grid positions on individual heads were marked for a posterior translocation from individual space to precalculated forward model space from the Brain-Modeler tool from NIRx NAVI imaging. The Brain-Modeler tool utilizes finite element models (FEMs) [11] to describe uniform optical properties (\(\mu\)a = 0.06 cm\({}^{-1}\), \(\mu\)s 0 = 10 cm\({}^{-1}\)). This tool defines the source-detector pair placement on the head's surface and the internal optical properties, creating a forward model that characterizes changes in boundary data due to absorption variations in the tissue for each channel-node combination. A submesh was selected for the cerebral hemisphere, depending on the positions of the fiber grid. The left hemisphere's submesh comprised 4518 nodes and 19,573 tetrahedrons with dimensions of 7.65 cm (width) \(\times\) 7.05 cm (height) \(\times\) 7.20 cm (thickness), as depicted in Figure 1b. (3) DOT volume reconstruction employed the normalized differ  
Figure 1: Finite model element (FEM) selection. (**a**) Atlas with an FEM (blue) covering the sensory-motor cerebral area C3. (**b**) Localizations of optical fibers (circles) on the boundary. Red dots correspond to source–detector pairs. Yellow dots correspond to EEG 10–20 system.  
ence method [12], which establishes a connection between surface head measurements and changes in the internal optical properties relative to a reference medium, utilizing the perturbation approach [13]. Alterations in absorption at two distinct wavelengths were leveraged to generate reconstructed images representing relative concentrations of oxyhemoglobin (HbO) and deoxyhemoglobin (HbR) with the aid of extinction coefficients for both wavelengths [14]. Reconstructing DOT images presents a challenge, as it involves the inversion of the weight matrix J, which becomes an ill-posed problem due to the significant attenuation of NIR light with increasing depth. To address this, the weight matrix is inverted using a truncated singular value decomposition algorithm with the selection of the truncated number of singular values determined by the minimum description length as a selection criterion. A total of 1397 DOT volume series with a size for each volume of 64 \(\times\) 64 \(\times\) 64 voxels were reconstructed for each hemoglobin state, HbO and HbR.