# Time-Domain Near-Infrared Spectroscopy and Imaging: A Review
## 5 Studies toward Clinical Applications of TD-NIRS
### Measuring Optical Properties
#### 5.2.2 Multi-Layered Media  
[PERSON] and [PERSON] [141] used TR reflectance measurements to determine the optical properties of human forearms being assumed as a two-layered media consisting of skin-fat (top: subscript 1) and muscle (bottom: subscript 2) layers. The analytical solutions of the TD-DE for two-layered semi-infinite media were fitted to \(R(\rho,t)\) measured in vivo at two values of \(\rho\) with the wavelength of 830 nm to determine \(\mu_{a1}\), \(\mu_{a2}\), \({\mu_{s1}}^{\prime}\), and \({\mu_{s2}}^{\prime}\) with known thicknesses of the top layer (denoted by \(s_{1}\)) [98]. They concluded that \(\mu_{a2}\) can be determined accurately even if \(s_{1}\) is known only approximately. [PERSON] et al. used the same analytical solutions for two-layered media as [PERSON] and [PERSON] to estimate the intra- and extra-cereb hemoglobin concentrations [141; 142]. The upper layer included the scalp, skull, and CSF, and the lower layer was the brain. They observed noticeable inter-subject variations in the hemoglobin concentrations and constant oxygen saturation of the cerebral hemoglobin. [PERSON] et al. used analytical solutions for the TD-DE using the eigenfunction method for estimating the optical properties of two-layered media [102; 143; 144]. The analytical solutions were fitted to the TR reflectances provided by a MC simulation or phantom and in vivo experiments to estimate \(\mu_{a1}\), \(\mu_{a2}\), \({\mu_{s1}}^{\prime}\), \({\mu_{s2}}^{\prime}\), and \(s_{1}\) accurately [143; 144]. The errors of the estimated \(\mu_{a1}\), \(\mu_{a2}\), and \({\mu_{s1}}^{\prime}\) were small while those of \({\mu_{s2}}^{\prime}\) were large. [PERSON] et al. [145] proposed a method of determining \(\mu_{a2}\) in two-layered semi-infinite media based on the microscopic Beer-Lambert law. Extending this method, a simple algorithm was developed to recover \(\mu_{a1}\) and \(\mu_{a2}\) in a two-layered medium from the TR reflectances measured at two values of \(\rho\) and was verified by numerical simulations and in vivo experiments using human foreheads [146; 147]. [PERSON] et al. [148] reported a method to determine the optical properties of a four-layered human head model using TR reflectance measurements and MC simulations. They used a TRS-10 (Hamamatsu Photonics) to measure the TR reflectances from various head portions of eleven healthy humans with a fixed \(\rho\) of 30 mm. For MC simulations, head models based on MRI scans were constructed as four-layered slabs consisting of the scalp, skull, cerebrospinal fluid (CSF), and brain. By a trial-and-error method, they changed the values of \(\mu_{a}\) and \(\mu_{s}{{}^{\prime}}\) of the four layers to fit the simulated TR reflectances to the measured ones and estimated the partial pathlengths and sensitivities of the four layers. As of the results, they found the followings: (i) the total pathlength ranging from 100 mm to 250 mm was closely related to the thickness of the scalp ranging from 2 mm to 10 mm; (ii) the partial pathlength of the brain ranged from 3% to 13% of the total pathlength; (iii) the brain tissue deeper than 25 mm from the head surface were hardly detected by the near-infrared light; (iv) the scalp tissue at the depth of 4 mm had the highest sensitivity inside the heads; and (v) most of the signals attributed to the brain came from the superficial layer with the thickness of 1 to 2 mm from the brain surface. These findings are important for functional NIRS and could not have been obtained without TD-measurements. [PERSON] and [PERSON] [149] employed a neural network (NN) to estimate \(\mu_{a}\) of the brain (\(\mu_{a,brain}\)) from TR reflectances in the case of five-layered media. Training data of the TR reflectances with a single value of \(\rho\) were generated by the analytical solutions of the TD-DE for five-layered media as well as MC simulations which can model the CSF layer more accurately than the TD-DE [101].