## 3 Results
Therefore, after the regression the HbO\({}_{2}\) changes should have smaller magnitudes than the HHb and rCCO responses. Figure 6: Cross-subject average correlation and standard deviation spectra of signals from the 3 cm and 4 cm channels after regressing out changes measured at the 1 cm channel. In Figure 7 the green and blue curves show the cross-subject averaged changes in HbO\({}_{2}\), HHb, tHB, and rCCO calculated by applying the spectral-domain regression to the residuals after regressing out the in time-domain the changes measured at the 1 cm channel from the signals measured at the 3 cm and 4 cm channels, respectively. The tHB changes were computed by averaging changes in the 5 nm waveband around 800 nm where the HHb- and HbO\({}_{2}\)-specific absorptions were equal. Note that the changes in Figure 7 show the differences in the time-courses of changes in the deep and superficial tissues. (Note that signals measured at different channels never changed in opposite directions, which follows from the correlation analysis shown in Figure 3 and explained above.) In particular, the rising slopes seen on the curves in Figure 7 correspond to the time intervals when changes measured at 3 or 4 cm increased faster than changes measured at 1 cm. Conversely, the curves in Figure 6 show negative slopes during the times when changes measured at long-distance channels decreased faster than changes measured at the 1 cm channel. The fact that the HbO\({}_{2}\) responses to BHs were not very clear means that the time-courses of [HbO\({}_{2}\)] changes in the superficial and cerebral tissues were similar. (The \"noise\" seen in Figure 7 was mostly due to the respiratory sinus arrhythmia between BHs). In Figure 7 one can also see that the peak times of [HHb], [tHB], and [rCCO] responses during all three BH episodes were between 15 and 25 s after the BH onsets, which was similar to the peak times of rCCO responses shown in Figure 4, but very different from the peak times of HbO\({}_{2}\) and HHb responses shown in Figure 4, which never occurred earlier than 26 s from the beginning of a BH episode (see also Table 1). Some details of the HHb, tHB, and rCCO responses in Figure 7 were quite different. In particular, during BH episodes, the HHb curves showed initial dips during the first 10-15 s turning into the fast increases after that. During the same initial periods of BHs the tHB curves showed steady positive changes, while rCCO curves showed almost no changes during the first 10 s. These differences indicated that the responses to BHs in Figure 7 indeed corresponded to different chromophores and did not result from a crosstalk between different NIR wavelengths. The fact that in Figure 7 the curves corresponding to the 4 cm channel showed similar changes to the curves corresponding to the 3 cm channel but with much smaller magnitudes was due to the overall smaller magnitudes of changes at 4 cm as shown in Figure 3 and explained above. In addition, the red curves in Figure 7 correspond to regressing out the 3 cm changes from the 4 cm changes. The fact that these curves show almost no changes means that after regressing out the changes due to the contribution from the superficial tissues, the time-courses of changes at all wavelengths in both 3 cm and 4 cm channels were very similar, which was also in agreement with the high correlation between signals from these channels at all wavelengths as shown in Figure 6.  
Table 2 shows that HHb-, tHb-, and rCCO-specific cerebral responses to each individual BH were significant at both 3 cm and at 4 cm. rCCO responses showed highest significance (\(p<0.03\)) among all chromophores. HbO\({}_{2}\)-specific cerebral responses to individual BHs were not significant at 3 cm or at 4 cm. RM ANOVA analysis did not reveal statistical significance of differences in responses to different BH trials.