# Time-Domain Near-Infrared Spectroscopy and Imaging: A Review
## 5 Studies toward Clinical Applications of TD-NIRS
### Time-Domain Diffuse Optical Tomography (TD-DOT)
#### 5.3.2 Modified Generalized Pulse Spectrum Technique for TD-DOT  
[PERSON] et al. [171] proposed a modified generalized pulse spectrum technique (GPST) for image reconstruction of TD-DOT. The modified GPST is based on the Laplace transformed RTE and employs a ratio of the Laplace transformed signals at two Laplace parameters (denoted \(p_{1}\) and \(p_{2}\)), \(R=\Gamma(p_{2})/\Gamma(p_{1})\), as the featured TD data. Then, with some assumptions, the sensitivities of \(R\) to the changes both in \(\mu_{a}\) and in \(\mu_{s}\)\({}^{\prime}\) are expressed using the product of the Green's functions of the Laplace transformed fluence rate and flux as follows,  
\[W_{a}^{(R)}(\mathbf{r}_{d},\mathbf{r}_{s},t)=\int_{V_{p}}G^{(R)}(r_{d},r,p)G( rt,r_{s},p)dr, \tag{53}\]  
\[W_{s}^{(R)}(\mathbf{r}_{d},\mathbf{r}_{s},t)=\frac{\mu_{a}+p}{\mu_{s}{}^{ \prime}}W_{a}^{(R)}(\mathbf{r}_{d},\mathbf{r}_{s},t). \tag{54}\]  
Note that the sensitivity to change in \(\mu_{s}\)\({}^{\prime}\), \(W_{s}^{(R)}(\mathbf{r}_{d},\mathbf{r}_{s},t)\), is easily calculated while the sensitivities of other featured TD data to the change in \(\mu_{s}\)\({}^{\prime}\) are usually expressed by the spatial gradients of both the Green's functions of the fluence rate and flux as Equation (18), which makes computation ineffective and leads to crosstalk between \(\mu_{a}\) and \(\mu_{s}\)\({}^{\prime}\) images. This difference in calculating the sensitivity to the change in \(\mu_{s}\)\({}^{\prime}\) is the biggest advantage of the modified GPST over the other featured TD data approaches. In addition, taking positive and negative Laplace parameters for \(p_{1}\) and \(p_{2}\) is interpreted as weighting the early and late times in the TOF distributions, thus covering the key features of the TOF distributions. With these advantages, the modified GPST makes the simultaneous reconstruction of \(\mu_{a}\) and \(\mu_{s}\)\({}^{\prime}\) images possible with less crosstalk between them. \(\mu_{s}\)\({}^{\prime}\) images provide anatomical information while \(\mu_{a}\) images provide physiological information. The modified GPST was successfully extended from a 2D case to a semi-3D case with numerical simulations and phantom experiments [171; 172; 173].  
A numerical simulation and phantom experimental studies using the modified GPST were performed for imaging brain activation from TR reflectance measurements in a two-layered model [174]. Comparisons of the reconstructed images among various featured data types such as \(E\), \(<\)\(t\)\(>\), \(<\)\(t\)\(>\) + \(c2\), \(E+<\)\(t\)\(>\), modified GPST and full TOF distributions were made, and it was found that the full TOF distributions provided the best images at the cost of long computation times [175].  
Figure 16: Effects of the type of featured data on the quality of the reconstructed DOT images of \(\mu_{a}\). (**a**) Geometry of a 2D object; reconstructed DOT images using (**b**) \(E\) (CW), (**c**) \(<\)\(t\)\(>\), and (**d**) full TOF-distributions normalized by \(E\). The 2D object has a diameter of 80 mm and contains two small absorbers with a diameter of 10 mm and a separation of 16 mm. Modified from Reference [170].