## 4 Discussion
### Inclusion of Systemic Data in fNIRS Functional Connectivity Analysis  
The contribution of non-neuronal physiological changes to the fNIRS signal have been widely investigated over the past years. Previous studies [10; 29; 59; 60] have found that excluding the impact of systemic confounders leads to discrepancies in the connectivity maps. On the other hand, taking physiological interferences into consideration will likely increase the number of the overall connections. Consequently, this can reduce (in average) the length of functional paths between two any nodes. However, not accounting for them might lead to a misleading interpretation due to the appearance of spurious associations. This risk can be reduced by simultaneously measuring physiological data alongside fNIRS, performing digital filtering as a preprocessing step, or including systemic confounders when modelling the fNIRS signal reconstruction, processing and analysis to compute relative changes in Hb species [19; 61; 62; 63]. However, to date, only few researchers have considered the inclusion of physiological measurements when dealing with fNIRS FC analysis [10; 64; 60]. Here, we investigated the possibility of including systemic data (heart rate and breathing rate) in the FC analysis in order to obtain a more accurate representation of the symmetry between FC networks. In general, we found structural variations within FC networks and we observed changes in HbO\({}_{2}\) and HHb connectivity density and symmetry when systemic data were included. Based on our group-level results presented in Figure 7, we showed that the addition of systemic information tends to change both integrational and segregational characteristic measures of the networks.  
Concerning the integration, a decrease in the global efficiency was observed in four out of five networks corresponding to the baseline, social prospective memory, non-social prospective memory, and ongoing contaminated conditions, in both Hb-derived networks. By contrast, only during the ongoing task the HbO\({}_{2}\) network seems to increase the global efficiency. This could be caused by the inclusion of confounding variables that removes spurious relationships and generate a re-route of the functional paths between regions, resulting in a larger one. On the other hand, the segregational measure, the modularity, presents the opposite pattern in respect to the global efficiency. The modularity of both Hb networks increases when non-neuronal signals are taken into account. The inclusion of physiological variables is performed by considering them as nodes.  
These systemic nodes become mediators between channel nodes, creating new paths and producing a reorganization of groups of nodes (community structure). Here, we found that the 80% of the functional networks are above 0.3 modularity, a value from which a network is considered to have a significant community structure.  
The experimental results presented here are preliminary and are based on data from a small sample size. Although the statistical results shown here are strong, we will further validate the proposed method on bigger data sets. In addition, we have included the contribution of only heart and breathing rate and evaluated their effect on 16 fNIRS channels recorded on the prefrontal cortex during a prospective memory task. In our future studies, we will enrich our investigations with a wider set of physiological variables (e.g., galvanic skin response, blood pressure). It would also be interesting to investigate how the symmetry between HbO\({}_{2}\) and HHb connectivity networks varies in case of different cognitive tasks and task designs (e.g., block, event-related, continuous), and across different brain regions, and with less/more dense channels configurations.