## 3 Results  
We calculated high temporal resolution motion parameters by dividing the original multiband fMRI brain images, taken with TR of 0.72 s, into the 9 sets, or'stacks', of simultaneously acquired images acquired within each TR at 9 \"slice times\" (72 slices with a multiband factor of 8 corresponds to 9 sets of slices acquired at 9 different slice or acquisition times), and merging the resulting time course of the 9 stacks for each motion parameter (total 6) according to the slice timing (Figure 2) [18]. This resulted in an effective sample rate of 12.5 Hz. Notably, even by using initial motion traces with a sample time of 0.72 s (1.4 Hz sampling rate, with a Nyquist frequency of 0.7 Hz), for which the cardiac signal at \(\sim\)1 Hz could not be resolved, we could now resolve the cardiac signal (Figure 2). Figure 3 shows an example of the resulting fNIRS time course with and without motion correction (Figure 3b-d) as well as an example an fMRI time course in the sensitive region of the fNIRS probe (Figure 3a). We also compared our fNIRS results to the fMRI data (Figure 4 and for all subjects see Figure A1) including the z-statistics in the photon probability path underneath the channels (Figure 4b) as well as the overlap between the photon probability path and the significantly activated voxels seen in fMRI (Figure 4c) for three contrasts of the N-back task (1 st contrast: 2-back = 1, 3-back = 1; 2 nd contrast: 2-back = 1, 3-back = 0; 3 rd contrast: 2-back = 0, 3-back = 1). We found a high consensus in most subjects with high z-statistics (z \(>\) 10) in areas with even a small percentage overlap with fMRI (\(\sim\)above 5%) when taking both oxyhemoglobin and deoxyhemoglobin into account (red boxes around channels below the \(x\)-axis in Figure 4a), except in subject #4 and #5. Subject 5 was especially affected by motion which may explain the improved t-statistics with motion correction (for deoxyhemoglobin). However, even though t-statistics were high for both oxyhemoglobin and deoxyhemoglobin for Subject 5 channel 6, the significance threshold was not reached when multiple comparison correction was applied (blue box around channel in which significance was reached without multiple comparison correction). Changes in the t-statistics of the task response with motion correction (with up-sampled (UpMC) and reconstructed high sample rate (HighMC) motion parameters) in comparison to without motion correction (NoMC) were compared in all 10 subjects both for oxyhemoglobin and deoxyhemoglobin. For this evaluation, we considered the 18 non-significant channels (no significant changes in oxyhemoglobin or deoxyhemoglobin changes with any method, Figure 5a,b) and the 9 significant channels (both significant oxyhemoglobin and deoxyhemoglobin changes, Figure 5c,d) separately and disregarded channels in which only oxyhemoglobin or deoxyhemoglobin showed significant activation with any method. Non-significant channels (N = 18) for oxyhemoglobin in the NoMc and UpMC condition did not differ significantly from HighMC (one-sided \(t\)-test, \(p\)\(<\) 0.09 and \(p\)\(<\) 0.48, respectively) (Figure 5a) and neither did non-significant channels for deoxyhemoglobin (one-sided \(t\)-test, \(p\)\(<\) 0.56 and \(p\)\(<\) 0.11, respectively) (Figure 5b). Mean +/ - Std t-statistics for non-significant oxyhemoglobin channels in all three motion correction methods were 0.54 +/ - 1.0 (NoMC), 0.81 +/ - 1.0 (UpMC), and 0.81 +/ - 1.0 (HighMC) (Figure 5a) and for non-significant deoxyhemoglobin channels \(-\)0.17 +/ - 1.1 (NoMC), \(-\)0.11 +/ - 1.4 (UpMC), and \(-\)0.15 +/ - 1.4 (HighMC) (Figure 5b). Significant channels (N = 9) for oxyhemoglobin in the NoMc and UpMC condition did not differ significantly from HighMC (one-sided \(t\)-test, \(p\)\(<\) 0.51 and \(p\)\(<\) 0.87, respectively) (Figure 5c); however, significant channels for deoxyhemoglobin did (one-sided \(t\)-test, \(p\)\(<\) 0.03 and \(p\)\(<\) 0.03, respectively) (Figure 5d).