## 3 Results
In most experiments, MATLAB was unable to fit the power law model for \(rCCO\)-related data, resulting in fewer than 10 pigs being represented in Figure 6. Nonetheless, \(R^{2}\) values and the median power law \(\gamma\), along with their standard deviations, are presented in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Relationship/Parameter** & \(\mathbf{R^{2}}\) & \(\gamma\) & \(\boldsymbol{p}\)-Value (\(\gamma\
eq\mathbf{1}\)) \\ \hline \multirow{3}{*}{**Zone I**} & \(CMRO_{2}\) vs. \(rCCO\) & 0.986 \(\pm\) 0.158 & **0.618 \(\pm\) 0.277** & **0.070** \\  & \(CBF\) vs. \(rCCO\) & 0.989 \(\pm\) 0.253 & **0.569 \(\pm\) 0.356** & **0.031** \\  & \(CBF\) vs. \(CMRO_{2}\) & 0.996 \(\pm\) 0.005 & 0.975 \(\pm\) 0.339 & 0.813 \\ \hline \multirow{3}{*}{**Zone II**} & \(CMRO_{2}\) vs. \(rCCO\) & 0.974 \(\pm\) 0.147 & 0.787 \(\pm\) 0.388 & 0.135 \\  & \(CBF\) vs. \(rCCO\) & 0.961 \(\pm\) 0.112 & **0.681 \(\pm\) 0.350** & **0.023** \\ \cline{1-1}  & \(CBF\) vs. \(CMRO_{2}\) & 0.998 \(\pm\) 0.011 & 1.000 \(\pm\) 0.314 & 0.999 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean and standard deviation values of power law exponent \(\gamma\) for \(CMRO_{2}\) vs. \(rCCO\), \(CBF\) vs. \(rCCO\), and \(CBF\) vs. \(CMRO_{2}\) across two ischemic zones during cardiac arrest. Zone I represents \(\approx\)70% reduction in blood flow relative to baseline, while zone II corresponds to 60% to 100% reduction. Bold font indicates statistically significant results (\(p<0.05\)). Figure 6: Scatter plot for 6 pigs (each color represents one pig) from the correlations between \(CMRO_{2}\) and \(rCCO\) during CPR. Table 3 summarizes the \(R^{2}\) values, power law \(\gamma\) means with standard deviations, \(t\)-test \(p\)-values, and statistical powers for each relationship during CPR. From Table 3, one can see that during CPR the interactions involving \(rCCO\) exhibited significant non-linear dynamics with \(\gamma\)>1, underscoring the complexity of cerebral metabolism during cardiac arrest. However, \(p\)-values greater than 0.05 indicated relatively low statistical significance. The statistical power for the values of \(\gamma\) in Table 3 was below 50%. Figure 7 shows \(CBF\) vs. \(CMRO_{2}\), \(CBF\) vs. \(rCCO\), and \(CMRO_{2}\) vs. \(rCCO\) for two of the experiments during which ROSC was achieved, enabling the study of physiological relationships during this phase. Although statistical analysis was not feasible due to the limited sample size, strong non-linear relationships were observed between \(rCCO\) and \(CMRO_{2}\), as well as between \(rCCO\) and \(CBF\). Notable differences compared to the cardiac arrest phase included the emergence of a weak non-linear relationship between \(CBF\) and \(CMRO_{2}\) and a marked change in curvature for the other two relationships (with \(\gamma\) shifting from approximately 0.5 during cardiac arrest to around 3 during ROSC). In addition to the power law exponent \(\gamma\), the intercept \(a\) and the scaling factor \(k\) in Equation (7) were calculated for each relationship during cardiac arrest and CPR. A one-sample \(t\)-test confirmed that \(k\) and \(\gamma\) were positive and significantly different from zero (\(p\) < 0.05) during cardiac arrest, reflecting strong coupling between \(CMRO_{2}\), \(CBF\), and \(rCCO\) under ischemic conditions. The \(p\)-values for \(\gamma\
eq 1\) (non-linearity) and \(\gamma\
eq 0\) (presence of coupling) are presented in Tables 2 and 3, indicating significant deviations from linearity during cardiac arrest (\(p\) < 0.05), except for in the \(CBF\) vs. \(CMRO_{2}\) relationship, where \(\gamma\)\(\approx\)1, suggesting a predominantly linear flow-metabolism coupling. Conversely, during CPR, \(a\) and \(k\) were not significantly different from zero (\(p\) > 0.05) in the \(CBF\) vs. \(rCCO\) and \(CMRO_{2}\) vs. \(rCCO\) relationships, underscoring the absence of meaningful coupling.