## 2 Subjects and Methods
### Grid Excluding the Trachea  
The DOT images suffer from a void region if no care is taken for the grid used for the finite element method [20; 21]. To create a grid excluding the void region of the trachea, we made use of MR neck images.  
The MR neck image was processed with the open-source software platform for medical image processing (3D-Slicer, version 4.10.2) [22] to generate the 3D surface geometry of the neck. First, the T2-weighted MR image was saved as the DICOM standard, which contains multiple slices and all pixels of each of the slices related to the real position and scale. Then, 3D-Slicer loaded the MRI DICOM file and contours of the neck, shoulder, trachea, and thyroid were delineated by the Segment Editor module. Finally, the Segmentations module exported the 3D surface geometry of the various objects (Figure 3a) in a standard triangulated language (STL) file format at LPS (Left, Posterior, Superior) coordinates. In Figure 3a, the grid region (see below) is indicated in yellow. All STL files contain real-scale anatomical structures of the neck using the coordinates of the MR image.  
Next, 3D-CAD imported the STL files and extracted the minimum volume that is required for the image reconstruction. Since the number of photons quickly decays when  
Figure 3: Front (top) and back views (bottom) of the segmented model and grids used for image reconstruction. (**a**) Segmented model from the MR image: the neck and body (gray), the trachea (green), the thyroid (red), and the approximate location of the grid (yellow). (**b**) Trachea–tissue boundary grid. The source positions (red) and detection positions (blue) are also shown. (**c**) Homogeneous grid. The source positions (red) and detection positions (blue) are also shown.  
near-infrared light propagates in the neck, there is no need to make the grid using the entire volume. Here, light propagation around the thyroid was numerically studied, and this rapid decay was observed [23]. The upper and lower boundaries of the volume were set as horizontal sections 10 mm above the top row and 10 mm below the bottom row of the optical fibers, respectively. The sides of the volume were sagittal sections 10 mm away from the left and right columns of the optical fibers. The posterior limit was a plane that divided the void region approximately into halves. This grid is termed the trachea-tissue boundary grid. The processed surface geometry is shown in Figure 3b. As a comparison, we made another grid by disregarding the presence of the trachea. This grid is termed the homogeneous grid (Figure 3c).  
As a last step, the processed STL files were imported into the Gmsh version 4.6.0 [24] to create 3D volume grids for use with the finite element method. The Gmsh generates a very nearly uniform volume of tetrahedral grids where nodes of the surface are not necessarily identical to the nodes from the STL file. The side length of a tetrahedron was about 1 mm. In this way, uniform grids of tetrahedrons were used for the DOT. The trachea-tissue boundary grid (Figure 3b) has 53,611 nodes and 264,526 elements, and the homogeneous grid (Figure 3c) has 57,433 nodes and 291,968 elements.