## 2 Materials and Methods
### Near-Infrared Time-Resolved Spectroscopy  
We used a portable three-wavelength near-infrared TRS system (TRS-21, Hamamatsu Photonics K.K., Hamamatsu, Japan). This system uses a time-correlated single-photon counting technique for detection. The system was controlled by a computer through a digital I/O interface that consisted of a three-wavelength (762, 800, and 836 nm) picosecond light pulser (PLP) as the pulse light source, a photon-counting head for single-photon detection, and signal-processing circuits for time-resolved measurement. The PLP emitted near-infrared light with a pulse duration of approximately 100 ps, a mean power of at least 200 uWat each wavelength, and pulse repetitions at a frequency of 5 MHz. The input light power to the patient was approximately 300 uW. The light from the PLP was sent to a patient from a source fiber with a length of 3 m, and the photon re-emitted from the patient was collected simultaneously by a detector fiber bundle with a length of 3 m. We obtained a set of histograms that displayed the photon flight time or re-emission profile. In this study, the emerging light was collected over a period of 1 s to exceed a photon count of at least 1000 in the peak channel of the re-emission profiles. The re-emission profiles observed at each measurement point were fitted by the time-resolved reflectance derived from the analytical solution of the PDE proposed by [PERSON] et al. [PERSON] et al. (1988); [PERSON] et al. (1988), which is convoluted with the instrumental response function, to calculate the \(\mu_{\text{a}}\) and \(\mu_{\text{s}}\)' values of the head at wavelengths of 762, 800, and 836 nm. In each iterative calculation, the analytical solution of the PDE was calculated in reflectance mode; it was then fitted to the observed re-emission profile. After determination of the \(\mu_{\text{a}}\) and \(\mu_{\text{s}}\)' values at three wavelengths, the oxyHb and deoxyHb concentrations were calculated from the extinction coefficients of oxyHb and deoxyHb with the following equations, based on the assumption that the background absorption was due to 85% (by volume) water. \[\mu_{\text{a 762 nm}}\ =\ \varepsilon_{\text{762 nm}}^{\text{oxyHb}}[\text{oxyHb}]\ +\ \varepsilon_{\text{762 nm}}^{\text{deoxyHb}}[\text{deoxyHb}]\ +\ \varepsilon_{\text{762 nm}}^{\text{water}}[\text{water volume fraction}] \tag{1}\]  
Figure 1: Photograph showing the actual near-infrared time-resolved spectroscopy (TRS) setting. \[\mu_{\text{a 800 nm}} = \varepsilon_{\text{800 nm}}^{\text{oxyHb}}[\text{oxyHb}]\ +\ \varepsilon_{\text{800 nm}}^{\text{deoxyHb}}[\text{deoxyHb}]\ +\ \varepsilon_{\text{800 nm}}^{\text{water}}[\text{water volume fraction}] \tag{2}\] \[\mu_{\text{a 836 nm}} = \varepsilon_{\text{836 nm}}^{\text{oxyHb}}[\text{oxyHb}]\ +\ \varepsilon_{\text{836 nm}}^{\text{deoxyHb}}[\text{deoxyHb}]\ +\ \varepsilon_{\text{836 nm}}^{\text{water volume fraction}}] \tag{3}\]  
where \(\varepsilon_{\text{\lambda nm}}\) is the extinction coefficient at the wavelength of \(\lambda\) nm and [oxyHb] and [deoxyHb] are the concentrations of oxyHb and deoxyHb, respectively. First, water absorption was subtracted from \(\mu_{\text{a}}\) at each of the three wavelengths and then the concentrations of oxyHb and deoxyHb were estimated by applying the least-squares fitting method. The extinction coefficients for oxyHb, deoxyHb, and water shown in Table 1 were used. The ratio of the optical pathlength to the interoptode distance was defined as the DPF. We used the prism-type probe. The source and detector optodes were positioned on the frontal region at a 30 mm interoptode distance.