# Clinical Brain Monitoring with Time Domain NIRS: A Review and Future Perspectives
## 2 Basics of NIRS
### TD-NIRS Methodology  
In TD-NIRS an ultra-short light impulse (typically in the picosecond range) illuminates the tissue. Tissue has the effect of attenuating and broadening the re-emitted pulse (the resulting pulse-width is typically few nanoseconds wide). The measured signal is typically called a temporal point spread function (TPSF) or distribution of time of flights (DTOFs) of photons. Indeed, the measurand here is the histogram of the arrival time of photons. Thus, the amount of information acquired by time resolved systems outstrips the two previous techniques since they only acquire intensity (CW-NIRS) or intensity and phase (FD-NIRS) dimensions. The DTOF acquired by the TD-NIRS systems contains information on the optical properties of the tissue and enables various data processing workflows to be used. Each method has its own strengths and drawbacks, in terms of computational cost accuracy, or need for a priori, as depicted in Figure 2. There are three main approaches for the data processing of TD-NIRS: the fitting approach, the moment calculation approach, and the gating approach (also called time gating or time windowing). _The fitting approach._ This approach was the first to be used to process TPSF data [38]. It consists of minimising the different between an analytical solution of the DE for a particular geometry, and the measured TPSF. Typically, a non-linear fitting procedure based on the classical Levenberg-Marquardt approach is used in order to determine tissue \(\mu_{a}\) and \(\mu^{\prime}\)s [39]. Different geometry can be assumed, the most commonly used being the homogeneous semi-infinite one, notably for its simplicity [38]. However, assuming that the head is completely homogeneous might appear an over simplification. More accurate tissue geometries can be considered, such as the multi-layered geometry, that represents more accurately the brain geometry [40]. For example, one could considerer an extra-cerebral and an intra-cerebral layer. As mentioned earlier, FEM and MC methods can also be used to model-specific anatomies which provides the best accuracy. Once the absorption coefficient is known at several wavelengths, the absolute concentration of each chromophore considered can be calculated using the Beer-Lambert Law. Typically, the considered chromophores are HbO\({}_{2}\), HHb and water. The water content is usually set to 80% and the free fitting parameters are [HbO\({}_{2}\)] and [HHb] [41]. The tissue saturation can then be extracted from those concentrations. It worth mentioning that no assumption of \(\mu^{\prime}\)s is needed here as it is calculated. It worth mentioning that in all TD-NIRS measurements, the contribution of the instrument to the DTOF has to be taken into account by measuring what is called the instrument response function (IRF). The ability to deconvolute the IRF from the tissue response function is crucial in order to retrieve  
Figure 2: Schematic of the three-data processing approach in TD-NIRS. accurate data [42]. This deconvolution step is non-trivial and the standard approach when fitting the data is to minimise the error between the TPSF and the model convoluted by the IRF [43]. _The moments calculation._ This approach reduces the amount of information contained in the entire DTOF by calculating 3 metrics, the 0 th order moment corresponding to the total number of photons (equivalent to CW), the 1 st order moment corresponding to the mean arrival time of photon (i.e., used to calculate the DPF (see refs. [26; 44])), and the second-order moment corresponding to the variance of the TPSF [45]. Thus, it reduces the computational cost of the calculation. Moreover, the deconvolution of the TPSF is made easier since the deconvolution process only requires subtraction of the moments of the IRF from the moments of the TPSF. Analytical expressions based on these moments are available in order to determine the absorption and scattering coefficients [45].