## 4 Discussion
The relationships between \(CBF\) and \(rCCO\) (\(p=0.023\)) showed significant deviations from linearity, reflecting increased variability in mitochondrial responses under severe ischemia. These findings contrast with the linearity observed during moderate occlusion in [12] and emphasize the need for non-linear modeling to fully capture metabolic dynamics during extreme reductions in blood flow. The comparison between zone I and zone II highlights the shift from linear to non-linear behavior as ischemia deepens. While prior studies concentrated on milder ischemic conditions, our data illustrate the breakdown of linear relationships during extreme drops in blood flow, emphasizing the need for non-linear modeling to fully capture the metabolic dynamics of CA and CPR. Motion artifacts from mechanical chest compressions during CPR pose challenges to accurate data recording. In our study, we minimized these effects by invasively placing LDF probes and hNIRS optodes on the dura mater through cranial drilling and securing them with sutures, providing an ideal setup for data acquisition. However, in real-life clinical scenarios, non-invasive sensor placements would be more affected by motion. Future research should explore modeling techniques, such as advanced signal processing or machine learning, to mitigate motion artifacts and improve the reliability of cerebral oxygen monitoring in practical applications. Unfortunately, our study observed only two ROSC cases out of a total of ten experiments. During ROSC, the non-linear relationship between \(CMRO_{2}\) and \(rCCO\) persisted but exhibited a significant shift, with \(\gamma\) values increasing to approximately 3. This sharp contrast to the values of \(\gamma\) observed during CA suggests dynamic changes in mitochondrial activity and oxygen utilization as circulation is restored. The observed non-linearity may reflect the brain's attempt to rapidly restore homeostasis following prolonged ischemia. However, the differences in metabolic and mitochondrial responses between CA, CPR, and ROSC phases warrant further investigation in larger cohorts. Additionally, in this study we focused on the relative changes in \(rCCO\) rather than on the absolute values, as we did not have baseline measurements of oxidized and reduced \(CCO\) concentrations. This limitation should be considered when interpreting the results, as absolute values would provide a more comprehensive understanding of the physiological changes occurring during CA and CPR. To advance our understanding, leveraging mathematical models presents several advantages. By identifying and quantifying the mathematical relationships between physiological variables, we can predict one variable based on measurements of another. This approach becomes particularly valuable in situations where advanced measurement technologies are unavailable or impractical. Mathematical models can provide meaningful insights and predictions in such contexts. In our future research, we will focus on evaluating the validity and applicability of existing hemometabolic models to describe the mathematical relationships between \(rCCO\), \(CMRO_{2}\), and \(CBF\). A key part of this effort will involve applying the _BrainSignal_ model [34], which provides a comprehensive framework for analyzing these interactions. Unlike CHS, which lacks the capacity to calculate \(rCCO\), _BrainSignal_ incorporates mitochondrial metabolism, allowing for the quantification of \(rCCO\). In this study, the availability of hNIRS enabled us to directly measure \(rCCO\), offering insights into mitochondrial function during CA and CPR. Moving forward, we aim to apply the _BrainSignal_ model to mathematically estimate \(rCCO\) in contexts where direct measurements are not feasible. By integrating this model with our experimental data, we seek to uncover more precise correlations between \(rCCO\), \(CMRO_{2}\), and \(CBF\) under various physiological conditions.