## 2 Materials and Methods
### Analysis Methods  
The data analysis was conducted using MATLAB R2023a (MathWorks, Natick, MA, USA). We analyzed data during periods of cardiac arrest or ventricular fibrillation (VF), CPR, and, in cases where it occurred, ROSC. Each of these phases was examined individually to assess physiological responses under different conditions. Outliers were systematically identified and excluded to ensure the accuracy and reliability of the results.  
Figure 2: Overview of the experimental workflow.  
The analysis included the use of hNIRS diffusion modeling [15; 16; 17; 18; 19; 20] to assess the cerebral oxygenation, deoxygenation, and \(rCCO\) levels.  
The absolute values of \(CBF\) and \(CMRO_{2}\) were calculated using the non-linear version of the Coherent Hemodynamic Spectroscopy (CHS) model [21]. This approach integrates experimental data obtained from hNIRS and LDF, allowing for accurate assessment during significant physiological perturbations, such as cardiac arrest and CPR [22].  
_CBF_ was derived from the model's fitted capillary blood flow factor (\(cBF\)) and \(CBFi\) measured using LDF. The time-dependent velocity of the capillary blood flow \(c^{(c)}(t)\) was calculated as  
\[c^{(c)}\ (t)\left(\frac{mm}{s}\right)=cBF\left(\frac{mm}{s}\right).\ CBFi(t). \tag{3}\]  
Using the capillary cross-sectional area (3.85\(\times\)10\({}^{-7}\) cm\({}^{2}\)), the brain tissue density (1.081 g/mL) and the total volume of capillaries in the brain tissue (2.7%), the absolute \(CBF\) per 100 g of brain tissue was computed as  
\[CBF(t)\left(\frac{ml\ blood}{100\ g\ tissue.min}\right)=18.75\ \left(\frac{s.cm^{2}}{100\ g\ tissue.min}\right)\times c^{(c)}(t)\left( \frac{mm}{s}\right). \tag{4}\]  
This value falls within accepted ranges reported in similar studies, supporting its validity. However, further validation is part of our ongoing work [23; 24; 25; 26].  
_CMRO\({}_{2}\)_ was calculated using the equation called \"the Fick's principle\" [27]:  
\[\begin{array}{c}CMRO_{2}\ (t)\left(\frac{ml\ O_{2}}{100\ g\ tissue\ min}\right)=k \left(\frac{ml\ O_{2}}{g\ Hb}\right)\\ \times\ [tHb](\frac{s}{1})\times CBF(t)\left(\frac{ml\ blood}{100\ g\ tissue\ min} \right)\times(S^{a}(t)-S^{v}(t)),\end{array} \tag{5}\]  
where \(S^{a}(t)\) and \(S^{v}(t)\) represent the time-dependent arterial and venous oxygen saturations, respectively, and \(k\) is a factor describing the amount of \(O_{2}\) bound to hemoglobin when completely saturated (1.39 mL of \(O_{2}\) per g of \(Hb\)). \(CMRO_{2}\) is expressed in units of mL \(O_{2}/100\) g/min.  
The venous oxygen saturation was calculated using the CHS model [28]. To do so, the non-linear version of this model was used [21; 22]. The results closely matched the equations suggested by the authors [27]:  
\[S^{v}(t)=\frac{4}{3}\text{tSO}_{2}t\ \ \frac{1}{3}S^{a}(t), \tag{6}\]  
where \(tSO_{2}\) is the tissue oxygen saturation measured by hNIRS.  
Possible non-linearities among the variables of interest, \(rCCO\) and \(CMRO_{2}\), \(rCCO\) and \(CBF\), and \(CMRO_{2}\) and \(CBF\), were investigated by fitting the relationships with the power law:  
\[Y(X)=a+kX^{\gamma}, \tag{7}\]  
where \(k\) is a scaling factor, \(\gamma>0\) is the power exponent, and \(X\) and \(Y\) are the change in either the \(CMRO_{2}\), \(CBF\), or \(rCCO\). In the cases of non-linear relationships, \(\gamma\) was significantly different from 1.