## 4 Discussion  
In this study, we demonstrate a new way to use high-resolution motion time courses extracted from fMRI to generate acceleration input data for the fNIRS motion correction methods, such as AMARA (acceleration-based movement artifact reduction algorithm) [12] in multimodal fNIRS-fMRI studies. We did so by increasing the effective temporal resolution of acceleration data derived from the fMRI motion measurements, by adapting and expanding a method we developed to extract motion parameters at the slice acquisition time resolution, rather than the volume acquisition time resolution [18]. We call this method AMARA-fMRI. We tested this method on a small number of channels, with a window length and step size representative of concurrent fNIRS/fMRI research datasets (\(\sim\)10 min), rather than the parameters used in the original sleep study on long acquisition times with a window length of 15 min [12]. We found that this high-resolution motion correction method (HighMC) significantly improved the detection of activation in deoxyhemoglobin in comparison to no motion correction (NoMC) in the channels with significant activation (significant channels were only considered significant when both oxyhemoglobin and deoxyhemoglobin were significant for any method--red boxes in Figure 4a) shown in Figure 5d; the method also outperformed simple up-sampled motion traces converted into acceleration data (UpMC) in these channels (Figure 5d). As expected, this was not true for channels showing no activation pattern (defined as channels with neither oxyhemoglobin nor deoxyhemoglobin  
Figure 5: Comparison of motion correction methods. (**a,b**) T-statistics of channels without motion correction (NoMC) and with up-sampled (UpMC) and reconstructed high sample rate motion correction (HighMC) in all non-significant channels (** no significant changes in oxyhemoglobin or deoxyhemoglobin changes with any method, N = 18) and (**c,d**) significant channels (** significant channels were only considered significant when both oxyhemoglobin and deoxyhemoglobin were significant in any method, N = 9), over 10 participants. We only found a significant difference (one-sided \(t\)-test with an alpha of 0.05) in the t-statistics for deoxygenated hemoglobin between NoMC and UpMC in comparison to HighMC (\(p<\) 0.03 and \(p<\) 0.03) in the significant channels. showing significant activation with any method). This fact, in conjunction with the fact that we do not see \"significant activation patterns\" in any of the very small source-detector distances (e.g., channels 3 and 4) which are considered to probe only more superficial layers of the brain (e.g., [30; 31]), is encouraging. This suggests that this motion correction does not simply increase the t-statistics in all the channels it is applied to or introduce patterns resembling activation; rather, it specifically unmasks patterns of underlying neuronal activity, increasing only the t-statistics for these channels. Notably, in most channels AMARA-fMRI performed very well on deoxyhemoglobin measures, even rendering channels significant, which would not have been significant without correction (see Figure 4a, Subject #2, channel 1). Studies have demonstrated that changes in the deoxyhemoglobin concentration detected in fNIRS provide a more accurate reflection of underlying neuronal activation, particularly in the spatial domain. This is in comparison to the calculation of activation maps using oxyhemoglobin. As a result, improving the signal quality of deoxyhemoglobin can greatly enhance the accuracy of fNIRS results [32; 33; 34]. Furthermore, the fNIRS results were mostly in accordance with the underlying pattern of neuronal activity revealed by the fMRI data (Figure 4 and for all subjects Figure 1A), in accordance with previously reported overlaps between both techniques [6; 23; 35; 36; 37; 38]. It also showed that even spatially small activation patterns, in combination with high z-statistics in fMRI, predicted fNIRS activation patterns in the channels above the activation site.