## 4 Discussion
The relationship between _CBF_ and _CMRO_2 consistently showed a \(p>0.05\) (\(p=0.428\) during CA and \(p=0.831\) during CPR), indicating that the coupling between oxygen delivery andconsumption persisted even during mechanical compressions. Conversely, the relationships involving \(rCCO\) demonstrated a \(p<0.05\) for \(\gamma\
eq 1\) during CA and ROSC (\(p=0.000\) and \(p=0.015\), respectively), reflecting significant deviations from linearity. This suggests that mitochondrial function follows non-linear behavior under ischemic and reperfusion conditions. During CPR, the relationships between \(rCCO\) and \(CMRO_{2}\) or \(CBF\) weakened, as indicated by a \(p>0.05\), which may reflect the hemodynamic instability introduced by chest compressions. Despite this, \(p\)-values for \(\gamma\
eq 0\) remained highly significant (\(p<0.001\)), highlighting the ongoing metabolic contribution of \(rCCO\) even during turbulent periods. The scaling factor \(k\), which represents the proportional relationship between the variables of interest, was consistently positive and statistically significant across all phases of the study (CA, CPR, and ROSC). This finding aligns with physiological expectations, suggesting that even during severe reductions in the cerebral blood flow, a positive relationship between \(CMRO_{2}\), \(CBF\), and \(rCCO\) persists, reflecting the brain's ongoing metabolic activity and mitochondrial function. The significance of \(k\) during CPR highlights the resilience of cerebral metabolism, even under the dynamic and mechanically unstable conditions introduced by chest compressions. This reinforces the importance of preserving mitochondrial function during resuscitation efforts, as it may play a critical role in improving neurological outcomes post-ROSC. To further analyze these relationships, we separated the data obtained during CA into two zones: zone I (baseline to a \(\approx\)70% drop) and zone II (60% to 100% drop in the blood flow). The results revealed increasing randomness in physiological responses as the blood flow approached zero, with greater variability in the power law \(\gamma\) values observed in zone II. The standard deviations of \(\gamma\) for \(CMRO_{2}\) vs. \(rCCO\) (0.388), \(CBF\) vs. \(rCCO\) (0.350), and the \(CBF\) vs. \(CMRO_{2}\) (0.314) suggest heightened instability in mitochondrial and metabolic responses near the complete cessation of perfusion. The segmentation of the data into zone I and zone II enabled a more detailed analysis of metabolic responses. This division allowed for a direct comparison with prior non-invasive studies in small piglets by [PERSON] et al. [12], which focused on smaller perturbations in \(CBF\) from the baseline values. In zone I, for the \(CMRO_{2}\) vs. \(rCCO\) relationship, \(p=0.07\), suggesting near-linearity. This result corresponds closely to those of [12], where the relationship between \(rCCO\) and \(CMRO_{2}\) was found to be not significantly different from one. The relationship between \(CMRO_{2}\) and \(CBF\) remained linear with \(\gamma=0.975\pm 0.339\) and \(p=0.813\) for \(\gamma\
eq 1\), indicating that oxygen delivery and consumption are tightly coupled under moderate reductions in blood flow. Interestingly, this result contrasts with the findings of [12], where the same relationship exhibited mild non-linearity (\(\gamma=1.39\pm 0.31\)) during carotid occlusion. One possible explanation for this difference is the nature of the ischemic event. In [PERSON] et al. [12], ischemia was induced gradually under anesthesia, which may have allowed for compensatory mechanisms that introduced non-linearity. In contrast, our study involved CA, characterized by a rapid and complete cessation of blood flow, likely overwhelming autoregulatory mechanisms and preserving a direct linear relationship between \(CBF\) and \(CMRO_{2}\) during the initial phase of ischemia. However, in zone II, as the blood flow approached zero, non-linear responses emerged.