## 4 Discussion  
Employing the non-linear CHS model enabled an innovative approach to the investigation of cerebral hemodynamics and metabolism during cardiac arrest and CPR, and this yielded notable insights. Using the inverse of the model, we recovered the values of the physiological parameters related to the interplay between neural activity, blood flow dynamics, and oxygenation levels. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter/Analysis** &
\begin{tabular}{c} **Average \(\pm\) Std** \\ **(Baseline)** \\ \end{tabular} & **Reference Range** & **Average Difference** & \(p\)**-Value** \\ \hline \(Fp^{(c)}\) & 0.559 \(\pm\) 0.176 & 0.2–0.8 & \(-\)0.021 & 0.760 \\ \hline \(\boldsymbol{F}^{(d)}\) & **0.705 \(\pm\) 0.089** & **0.6–0.9** & **+0.073** & **0.008** \\ \hline \(\alpha_{o}\) (s\({}^{-1}\)) & 0.762 \(\pm\) 0.115 & 0.6–1.0 & +0.035 & 0.399 \\ \(f\)c\({}^{(c)}\) & 0.460 \(\pm\) 0.102 & 0.1–0.7 & +0.008 & 0.829 \\ \hline \(L^{(c)}\) (mm) & 0.553 \(\pm\) 0.092 & 0.4–0.8 & \(-\)0.041 & 0.368 \\ \hline \(L^{(b)}\) (mm) & 1.012 \(\pm\) 0.028 & 0.5–1.2 & \(-\)0.007 & 0.637 \\ \hline \(p^{(c)}\) (mm/s) & 0.819 \(\pm\) 0.087 & 0.6–1.0 & +0.029 & 0.466 \\ \hline \(\varphi^{(d)}\) & 0.031 \(\pm\) 0.022 & 0.001–0.05 & \(-\)0.009 & 0.177 \\ \hline \(\varphi^{(c)}\) & 0.012 \(\pm\) 0.011 & 0.005–0.05 & +0.002 & 0.438 \\ \hline \(\varphi^{(b)}\) & 0.009 \(\pm\) 0.012 & 0.001–0.05 & +0.002 & 0.561 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 2: The solid lines (blue and red) represent NIRS readings for oxy- and deoxyhemoglobin, respectively. The dotted lines (blue and red) depict the calculated data for oxy- and deoxyhemoglobin, respectively, using the non-linear version of the model. \(R^{2}=0.869\), \(X^{2}=0.131\). The notable consistency between the actual near-infrared spectroscopy measurements and the model's outputs (Figure 2) underscores the accuracy with which the proposed model can capture dynamic shifts in cerebral oxygenation and blood flow. This not only validates the model, but also opens avenues for potential enhancements in resuscitation protocols which have the potential to improve outcomes for CA patients. The reference ranges for the parameters were obtained from the literature. The mean capillary size ranged from 5.9 to 6.5 \(\upmu\)m in diameter and from 0.57 to 0.63 \(\upmu\)m in length [25]. The average capillary blood flow velocity was determined to be 0.85 mm/s, with a coefficient of variation equal to 0.99 [26]. The rate constant for oxygen diffusion into tissue was directly proportional to both the tissue's oxygen solubility and the microvascular partial pressure of oxygen [5]. This partial pressure depends on the metabolic rate of oxygen [27,28]. The blood volume fraction in the brain tissue can vary, with capillaries accounting for approximately 1-1.5%, and the entire microvasculature comprising about 2-4%. These values depend on the depth within the cortex [25,28]. The average baseline values we measured were all within their reference ranges. However, we note a lack of references for the rate of oxygen diffusion from blood to tissue (\(\alpha_{o}\)), which was described only in the works of the group who introduced the CHS model [5,9]. We found significant differences between the baseline and post-CA values for two parameters (\(p\)-value less than 0.05 denoting meaningful distinctions). The average values for \(cHb\) and \(F^{(c)}\) decreased after VF compared to the baseline. Dynamic changes in \(cHb\), both increases and decreases, had been observed previously in human CA patients [29,30]. In [29], the authors suggested that decreased \(cHb\) can be associated with worse neurological outcomes. The authors of [29,30] hypothesized that such changes may reflect the degree of vascular permeability and may be associated with neurologic function after CA. The decrease in the Fahraeus factor is most likely also related to the \(cHb\) change as it quantifies the ratio of \(cHb\) in the capillaries and larger vessels [5,9,31].