## 3 Results
In contrast, at 4 cm the rCCO responses were very clear (Figures 4 and 5c), which also might indicate that these responses belonged solely to the cerebral tissue. Each rCCO fall after the end of BH was quickly followed by a rebound which also could be a result of the faster restoration of the oxygen supply in the brain than in other tissues. Note that rCCO peak changes had about 10 times smaller magnitudes than HbO\({}_{2}\) and HHb changes (Table 1), which was in agreement with the fact that the concentration of CCO in the brain is approximately 10 times smaller than the concentration of hemoglobin. Figure 4: Cross-subject averaged changes in [HBO2], [HHb], and [rCCO], and regional SO2 measured at 1 cm, 3 cm, and 4 cm using the homogeneous tissue model and 750–900 nm waveband. Blue color shows the cross-subject standard deviations. Figure 5: Cross-subject averaged temporal traces of [HbO2] (**a**), [HHb] (**b**), and [rCCO] (**c**) showing a comparison of 1 cm and 4 cm time-courses and a return to the baseline 4 min after BHs. In Figure 4 the SO\({}_{2}\) time-course at 4 cm was also very different from those at 1 cm and 3 cm, which were very similar to each other by showing SO\({}_{2}\) increases characteristic for the scalp tissue. However, the quick SO\({}_{2}\) falls at 4 cm at the end of each BH should not be interpreted as the failure of cerebral autoregulation but rather, these falls resulted from the smaller magnitude of the HbO\({}_{2}\) increase than of the HHb increase due to the difference in the partial volume of the skull interrogated by light at shorter and longer wavelengths. From Table 1 one can see that the magnitudes of HbO\({}_{2}\) and HHb responses to BHs decreased with the distance. The reason for this was the application of the homogeneous model to the measurements of the inhomogeneous tissue, which included bone, where almost no blood was present. With the increase of the distance the partial volume of the bone increased leading to the underestimation of the magnitudes of HbO\({}_{2}\) and HHb responses to BHs at 3 cm and 4 cm. The cumulative \(p\)-values in Table 1 show that all included responses were statistically significant at \(p<0.05\) when the results of all three BHs were combined. HbO\({}_{2}\) and HHb responses to each individual BH were significant at 1 cm and at 3 cm. Unlike HbO\({}_{2}\) and HHb, at 4 cm, rCCO responses to each individual BH were statistically significant. Although the average peak values for different BHs in Table 1 were different, RM ANOVA analysis did not show statistical significance of these differences. As explained above, in order to reveal differences between responses to BHs measured in different channels we performed time-spectral linear regression analysis. For the regression analysis the range of wavelengths was limited to 750-900 nm where the highest correlation between different channels was detected (see Figure 3). Figure 6 shows the cross-subject average correlation and standard deviations spectra of signals from the 3 cm and 4 cm channels after regressing out changes measured at the 1 cm channel. One could see that the correlation coefficient for all wavelengths in both channels was greater than 0.6 between 750 nm and 900 nm. The correlation coefficient for the same wavelengths in both channels (corresponding to the diagonal of the correlation map in Figure 6) was particularly high for all wavelengths. This high correlation indicated that after regressing out the superficial changes, both 3 cm and 4 cm channels exhibited very similar time-courses at all wavelengths. Also in Figure 6 one can see that the spectra of average amplitudes of changes (measured by SDs) were similar in shape to those before regression (shown in Figure 3). They showed peaks at the HHb and rCCO absorption maxima around 760 nm and 830 nm, respectively, (compare with Figure 2), and decreased at wavelengths longer than 870 nm, corresponding to maximum HbO\({}_{2}\) absorption.