## 4 Discussion  
This is the first study reporting the reconstruction of the spatial distribution of \(\mu_{a}\) and \(\text{StO}_{2}\) in the whole human thyroid with DOT. The neck is composed of various organs, and the refractive index inside the neck is heterogeneous. Notably, between the tissue and the trachea, there is a strong refractive index mismatch. To date, whether the thyroid can be imaged accurately by DOT has been regarded as a seriously nontrivial question, but in this paper, we have shown that the whole shape of the thyroid can be reconstructed if the grid for the calculations excludes the trachea void region. However, the reentrance of light, which propagates through the trachea, was not taken into account in the present study. It is expected that reconstructed images will be improved if the reentrant light is taken into account [23]. In this paper, the thyroid was reconstructed at a position closer to the skin than its actual position. This can be understood from the structure of the objective function used in our numerical reconstruction. Since the diffuse fluence of near-infrared light decays exponentially with increased depth in biological tissue, measurement sensitivity decreases along the depth direction. Spatially variant regularization has been proposed to compensate for this [33; 34]. However, we did not employ depth-dependent regularization, which is one reason why the position of the reconstructed thyroid shifted slightly towards the skin. The obtained \(\mu_{a}\) values in the present study were much larger than the published values that have been obtained with time-domain measurements. In a study preceding this, the \(\mu_{a}\) values were estimated by fitting the TOF distribution derived from the analytical solution of the DE for a semi-infinite homogeneous medium to the measured TOF distribution [14]. However, it cannot be assumed that the human neck is homogeneous, and as the thyroid is covered by muscles, it is likely that the published \(\mu_{a}\) values should be partly attributed to the \(\mu_{a}\) of muscle tissue. Here, the present study indicates the possibility of selectively measuring the \(\mu_{a}\) of the thyroid, and the \(\mu_{a}\) values in the present paper may also be assumed to deviate from the true situation to some extent, because the reduced scattering coefficient was not updated during the iterations of the nonlinear conjugate gradient method. An accurate quantification of \(\mu_{a}\) requires the simultaneous reconstruction of both \(\mu_{a}\) and \(\mu_{s}\)' [35], which are subjected to artifacts caused by cross-talk between the two parameters. To suppress cross-talk artifacts, the use of multiple datasets for the objective functions, such as a combination of skew and Laplace transform of the TOF distribution (Equation (3)), has been proposed [36]. The present DOT is still insufficient for the quantitative measurement of optical properties and Hb concentrations; however, the map of \(\text{StO}_{2}\) (Figure 5) indicates that the thyroid is distinguishable from the background tissue (muscles): the \(\text{StO}_{2}\) of the thyroid was around 90%, while that of the muscles was around 65%. A high \(\text{StO}_{2}\) is the more favorable option for detecting cancer hypoxia, because the difference in \(\text{StO}_{2}\) between normal and cancerous tissue is thought to be larger than that when the \(\text{StO}_{2}\) of the thyroid is lower. Cytochrome c oxidase is a more sensitive indicator of cell hypoxia than \(\text{StO}_{2}\)[17]. However, TRS-80 with three wavelengths cannot measure the redox state of cyt. ox., and an instrument with four or more wavelengths is required. Regarding treatment of thyroid diseases, it is important that the shape and size of the thyroid are tracked over time, which can be conducted with ultrasound scanning. Hence, several 2D segmentation algorithms for thyroid ultrasound images have been developed, and 3D segmentation is now possible [37; 38].