# Clinical Brain Monitoring with Time Domain NIRS: A Review and Future Perspectives
## 2 Basics of NIRS  
In the wavelength range used in NIRS (i.e., 600-1000 nm), two main physical phenomena affect the photon trajectory in tissues: scattering and absorption [17]. The scattering is the dominant effect in biological tissue and is caused by microscopic refractive index changes inside the tissue. The resulting effect is that the initial trajectory of the photon is lost, and the photon is deviated to another direction. In NIRS, this quantity is represented by the reduced scattering coefficient \(\mu^{\prime}s\), which represents the scattering probability per unit length together with the average scattering direction. This parameter can give an insight to the tissue structure [18]. On the other hand, the absorption is the consequence of the loss of a photon which is due to the presence of particular chromophores inside the tissue that convert light intensity into other kinds of energy, either radiative (i.e., fluorescence) or nonradiative (i.e., vibrational). In NIRS, this quantity is represented by the absorption coefficient \(\mu_{a}\), which represents the absorption probability per unit length. As each chromophore has a specific spectral shape, they will each contribute differently to the overall absorption. Then, using a multiwavelength light source with well-chosen wavelengths s us to separate the contribution of each chromophore in order to quantify its concentration. A more detailed explanation of those processes can be found in [17; 19]. The effects of absorption and scattering contribute non-linearly to the global attenuation of the light by the tissue. Hence, it is not straightforward to disentangle them. Indeed, an inverse problem must be solved in order to have access to the absorption and scattering independently [20]. Basically, light transport in tissue can be modelled accurately by the radiative transport equation (RTE) or by the simpler diffusion equation (DE), which is derived from the RTE given certain assumptions [19]. Usually, the RTE is solved numerically using Monte Carlo (MC) approaches and gives the most accurate description of light propagation. This accuracy comes at the cost of long calculation time [21]. The DE can also be solved numerically, by using the finite element method (FEM). Software platforms are available to facilitate this process include TOAST++ and NIRFAST [22; 23]. However, the real strength of the DE is that it can be solved analytically in various simple geometries [17]. Thus, the calculation time is fast, and real-time methods can be implemented. As mentioned in the introduction, data acquisition can be performed in three modes: CW, FD, and TD. The principle of those acquisition modes is summarized in Figure 1. Below we describe the basics of each technique, so the reader can appreciate their advantages and disadvantages. For further, more detailed information we refer the reader to [24]. In all the three modes, the basic idea is to shine light onto the tissue, and to collect the transmitted/reflected light few centimetres away from the source point. The single point CW technique is the simplest one; a continuous light is emitted onto the tissue, and the transmitted attenuated light is collected few centimetres away. CW- NIRS only measures the changes in light attenuation, which is defined as the variation and reduction of the transmitted/reflected light intensity from the emitted light. Indeed, using the change in light attenuation at several wavelengths and assuming that light scattering has not changed between measurement time points, CW-NIRS can calculate, using the modified Beer-Lambert law (MBLL) [25], the changes in [HbO\({}_{2}\)] and [HHb] concentrations, which are assumed to be the sole chromophores that contributes to the contrast. The MBLL considers the extra path length between the source and the detector due to the scattering with a parameter named the differential path length factor (DPF).