## 2 Materials and Methods
### Statistical Analysis  
In the individual subject data the peak magnitudes of responses in \(\Delta[\text{Hb}]\), \(\Delta[\text{HbO}_{\text{2}}]\), and \(\Delta[\text{CCO}]\), and in \(\delta[\text{Hb}]\), \(\delta[\text{HbO}_{\text{2}}]\), and \(\delta[\text{CCO}]\) were measured as the difference between the time average over \(\pm\)5 s around each peak time (see Table 1) and the average over 20 s just before BHs. These samples were checked for normality (positively) and further tested by the one-sample \(t\)-test (_ttest_ MATLAB function) and \(p\)-values reported in Tables 1 and 2. In addition, the differences in response magnitudes among three BH episodes were analyzed using _ranova_ MATLAB function (repeated measures analysis of variance, RM ANOVA). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **HbO\({}_{2}\): Peak, \(p\)-Value, and Peak Times** & & \\ \hline \multirow{4}{*}{1 cm} & \(\Delta\)(\(\mu\)M) & 5.7 \(\pm\) 1.4, 0.01 & 6.3 \(\pm\) 1.5, 0.02 & 3.7 \(\pm\) 0.9, 0.001 & 5.2 \(\pm\) 0.8, 0.00002 \\  & \(t\)(s) & 25.4 \(\pm\) 3.5 & 28.6 \(\pm\) 3.7 & 30.5 \(\pm\) 4.3 & 28.2 \(\pm\) 2.3 \\  & \(\Delta\)(\(\mu\)M) & 2.8 \(\pm\) 0.6, 0.04 & 2.9 \(\pm\) 0.6, 0.01 & 2.1 \(\pm\) 0.5, 0.01 & 2.6 \(\pm\) 0.3, 0.00002 \\  & \(t\)(s) & 33.6 \(\pm\) 3.6 & 29.6 \(\pm\) 2.8 & 31.6 \(\pm\) 3.3 & 31.6 \(\pm\) 1.9 \\  & \(\Delta\)(\(\mu\)M) & 0.2 \(\pm\) 0.06 & 0.2 \(\pm\) 0.1, 0.01 & 0.2 \(\pm\) 0.1, 0.3 & 0.2 \(\pm\) 0.07, 0.001 \\  & \(t\)(s) & 28.0 \(\pm\) 5.4 & 28.8 \(\pm\) 4.1 & 26.6 \(\pm\) 4.3 & 27.9 \(\pm\) 1.3 \\ \hline \multicolumn{6}{c}{**rCCO: Peak, \(p\)-Value, and Peak Times**} \\ \hline \multirow{4}{*}{4 cm} & \multirow{2}{*}{\(\Delta^{\star}10^{-2}\)} & **1 st BH** & **2 nd BH** & **3 rd BH** & **Cumulative** \\  & & 1.1 \(\pm\) 0.2, 0.01 & 0.9 \(\pm\) 0.1, 0.05 & 0.8 \(\pm\) 0.2, 0.04 & 0.9 \(\pm\) 0.1, 0.00007 \\  & \(t\)(s) & 24.4 \(\pm\) 3.9 & 29.4 \(\pm\) 5.4 & 27.6 \(\pm\) 4.7 & 27.1 \(\pm\) 2.5 \\ \hline \multicolumn{6}{c}{**HHb: Peak, \(p\)-Value, and Peak Times**} \\ \hline \multirow{4}{*}{1 cm} & \multirow{2}{*}{\(\Delta\)(\(\mu\)M)} & **1 st BH** & **2 nd BH** & **3 rd BH** & **Cumulative** \\  & & 1.9 \(\pm\) 0.4, 0.017 & 2.1 \(\pm\) 0.4, 0.015 & 1.9 \(\pm\) 0.3, 0.002 & 2.0 \(\pm\) 0.2, 0.00001 \\  & \(t\)(s) & 35.0 \(\pm\) 3.8 & 36.5 \(\pm\) 4.1 & 42.5 \(\pm\) 3.8 & 38.5 \(\pm\) 4.0 \\  & \(\Delta\)(\(\mu\)M) & 0.7 \(\pm\) 0.3, 0.02 & 0.6 \(\pm\) 0.2, 0.01 & 0.6 \(\pm\) 0.2, 0.04 & 0.6 \(\pm\) 0.06, 0.0003 \\  & \(t\)(s) & 33.0 \(\pm\) 4.3 & 32.5 \(\pm\) 4.6 & 34.5 \(\pm\) 5.1 & 33.3 \(\pm\) 1.3 \\  & \(\Delta\)(\(\mu\)M) & 0.4 \(\pm\) 0.1, 0.02 & 0.3 \(\pm\) 0.1, 0.6 & 0.4 \(\pm\) 0.1, 0.04 & 0.4 \(\pm\) 0.06, 0.008 \\  & \(t\)(s) & 32.2 \(\pm\) 5.7 & 31.7 \(\pm\) 6.3 & 34.3 \(\pm\) 4.9 & 32.7 \(\pm\) 3.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cross-subject average peak magnitudes, \(p\)-values, and peak times obtained from the homogeneous semi-infinite diffusion analysis. The peak magnitudes were measured from the 20 s averaged values before BHs. The peak times measured from the beginning of BHs were found in the averaged traces shown in Figure 4 with the errors estimated as the mean absolute deviation from the individual data.