# Assessment of fNIRS Signal Processing Pipelines: Towards Clinical Applications
## 2 Materials and Methods
### Comments on Artifuct Sources  
So far, the MBLL was considered as if the absorbance of tissues other than brain vessels (BVs) was constant and was accordingly omitted in its differential expression (Equation (2)). Conversely, motion dynamics \(m(t)\) cause large changes in the distance \(\Delta\overline{L}_{tissue}\) travelled through a given tissue; hence, measured \(\Delta OD(\lambda,t)\) quantities are strongly affected by underlying tissue distribution. In addition, the traditional fNIRS HRF is highly contaminated by both extracerebral and cerebral components not directly related to evoked brain activity and related to systemic hemodynamics \(s(t)\)[13]. Therefore, these changes in the effective distance of photon travel are multiplied by the relevant linear attenuation \(\mu_{tissue}(\lambda)=\epsilon_{tissue}(\lambda)\cdot\epsilon_{tissue}\), which is here approximately assumed as a constant specific to the tissue concentration, with the only exception of the blood compartment.  
\[\Delta OD(\lambda,t)=DPF(\lambda)\cdot\Delta L_{tissue}\cdot\mu_{tissue}( \lambda)+n(t) \tag{4}\]  
which in turn is subdivided according to tissues encountered along the photon path  
\[\Delta OD(\lambda,t)=DPF(\lambda)\cdot\left\{\begin{array}{c}\Delta L_{BV} \cdot\mu_{BV}(\lambda)+\Delta\overline{L}_{skin}(m(t))\cdot\mu_{skin}( \lambda)\\ \quad\quad\quad+\Delta\overline{L}_{bone}(m(t))\cdot\mu_{bone}(\lambda)\\ \quad\quad\quad+\Delta\overline{L}_{liquor}(m(t))\cdot\mu_{liquor}(\lambda) \\ \quad\quad\quad+\Delta\overline{L}_{cells}(m(t))\cdot\mu_{cells}(\lambda)\\ \quad\quad\quad+\Delta\overline{L}_{blood}(m(t),\;s(t))\cdot\mu_{blood}( \lambda)\end{array}\right\}+n(t) \tag{5}\]  
The high sensitivity of effective distances \(\Delta\overline{L}_{tissue}\) to motion \(m(t)\) relates to geometrical variations in source-detector coupling, even with minimal changes in the relative source-detector distance and orientation. Namely, since absorption variations due to brain perfusion changes are mainly referred to the _BVs_ within the cortical layer, quantification of relative changes in \(HbO_{2}\) and \(HbR\) concentrations can be corrected by introducing a Partial Volume Factor \(PVF(\lambda)\), considering the Partial Pathlength Factor \(PPF(\lambda)=DPF(\lambda)PVF(\lambda)\) to account for variations of optical pathlength over only the cortical layer [30; 31].  
Classically, the source-detector coupling volume is depicted as a photon path whose ends are the source and the detector, while the diffused photons enter the tissues, touching the cortex in its deepest midway region. This schematically, yet clearly, shows the huge weight of tissues other than BVs. Consequently, large unpredictable changes in the presence of head acceleration forces and contraction of cranio-facial muscles can be expected. Furthermore, several elements concur in the amplification of the unwanted artifactual changes vs. the BVs pathways: (i) the effective lengths of surface tissues are heavily weighted by the higher illumination density in external layers compared to the cortex; (ii) among them, bone displays the highest linear attenuation, which is not sufficient to hinder transcranial fNIRS (thanks to the NIR optical window), yet is several times higher than hemoglobin [32].  
As for PCFs, according to Equation (5), the absorbance of blood compartments other than BVs is lumped into a single term, which should mainly include skin and meninge vessels responding to systemic circulation drives \(s(t)\). In addition, the extent of the \(s(t)\) effects on BVs themselves (not shown in Equation (5)) is still an open question. Irrespective of the driving mechanisms, the general criterion to separate PCFs is the hypothesis of a generalized action on all optodes. Hence, all cleaning strategies share the removal of common-mode components (details are provided in Sections 2.5-2.7).