## 3 Results  
Figure 3 presents representative time traces of [_tHB_], _rCCO_, _CMRO_2, and _CBF_ for one of the pigs, serving as an example of absolute value calculations as well as the normalized _CBF_, _rCCO_, and _CMRO_2 in pairs. The top two plots show [_tHB_] versus _CBF_ and _rCCO_ versus _CMRO_2 in absolute values. [_tHB_] and _rCCO_ values are given in \(\mu M\), while _CBF_ and _CMRO_2 are expressed in mL blood/100 g tissue/min and mL \(O_{2}\)/100 g tissue/min, respectively. Figure 4 illustrates these relationships during cardiac arrest, with each dataset normalized to its maximum value for comparability. Each relationship is represented by a unique color, with median lines shown as solid lines and data ranges depicted by shaded areas. These plots highlight the linear and non-linear dynamics between \(rCCO\), \(CMRO_{2}\), and \(CBF\) under the extreme physiological conditions of cardiac arrest. Figure 4: Scatter plots for all the pigs (each color represents one pig) during cardiac arrest for the correlations between (**a**) \(rCCO\) and \(CMRO_{2}\), (**b**) \(CBF\) and \(rCCO\), and (**c**) \(CBF\) and \(CMRO_{2}\). Table 1 presents the values of the power law fit \(R^{2}\), power law \(\gamma\) means \(\pm\) standard deviations, \(t\)-test \(p\)-values, and statistical power corresponding to Figure 4. From Table 1, one can see that for the \(\mathit{CMRO_{2}}\) vs. \(\mathit{rCCO}\)_and CBF vs. \(\mathit{rCCO}\)_(Figures 4a and 4b, respectively) the \"square-root\" type of relationship (\(\gamma\)\(\approx\) 0.5) was established with high statistical significance and power, despite a relatively low sample size of 10. To further analyze the data shown in Figure 5 and to compare them to similar studies reporting approximately 60-70% reductions from the baseline, the data obtained were investigated by dividing them into two zones. During cardiac arrest, zone I represents the period from the baseline to a 70% drop relative to the baseline, while zone II corresponds to a 60% to 100% drop (complete cessation of blood flow). The results indicate that as the blood flow approached zero, the parameters exhibited increasingly random behavior. This is reflected in the standard deviation of the power law \(\gamma\) values, with \(\mathit{CMRO_{2}}\) vs. \(\mathit{rCCO}\) showing a standard deviation of 0.388, _CBF_ vs. \(\mathit{rCCO}\) of 0.350, and _CBF_ vs. \(\mathit{CMRO_{2}}\) of 0.314. These findings highlight the variability and instability of physiological responses during severe reductions in perfusion. This suggests that during severe ischemia, the relationships between these parameters become less predictable, reflecting the breakdown of normal regulatory mechanisms. While variability at this level is expected under extreme conditions, it highlights the need for careful interpretation and potentially more complex modeling to accurately capture metabolic dynamics during CA. Table 2 provides the median and standard deviation values for \(\gamma\) across both zones and for all three relationships. Figure 5: Correlation plots for all pigs (each color represents one relationship) during cardiac arrest, divided into two zones. Zone I represents the period from baseline to \(\approx\)70% _CBF_ drop relative to baseline,  
while zone II corresponds to 60% to 100% drop (complete cessation of blood flow): (red) \(CMRO_{2}\) vs. \(rCCO\) during cardiac arrest; (blue) \(CBF\) vs. \(rCCO\); (green) \(CBF\) vs. \(CMRO_{2}\). Due to the volatile conditions during CPR, characterized by intense movements and mechanical compressions, analyzing physiological markers was challenging compared to doing so for stable periods for most experiments. As a result, no clear relationships between \(rCCO\) and other variables were observed, and the data appeared random. This is reflected in the low \(R^{2}\) values for the power law fits. Figure 6 shows a scatter plot of \(CMRO_{2}\) vs. \(rCCO\), illustrating this lack of a correlation. However, as expected, \(CBF\) and \(CMRO_{2}\) maintained a strong linear relationship.