# Using Coherent Hemodynamic Spectroscopy Model to Investigate Cardiac Arrest
## 3 Results
#### 3.2.1 Recovering the Fixed Values of Model Parameters  
Figure 3 shows changes in the physiological variables measured and computed using our algorithm during a cardiac arrest experiment on a pig, which resulted in the death of the animal during the CPR epoch (no return to spontaneous circulation). A total of 37 pigs were used in the experiments, but data from only 21 were usable. The remaining cases were excluded due to issues such as unsuccessful cardiac arrest induction, animal shivering, or excessive cranial bleeding. The fitting was performed for the entire 18 min time interval shown on Figure 3. The recovered values of the model parameters are presented in Table 2. The run time on a PC with AMD Ryzen 5 3600X 6-core processor (AMD, Santa Clara, CA, USA) was 8.1 min.  
The application of the pacing AC voltage caused instability in _CBF_ during the \"pacing\" epoch and a complete stop of _CBF_ during the CA epoch. In Figures 3 and 4, the heart pacing, cardiac arrest, and CPR epochs are shown by the vertical lines. Figure 3a shows the measured and fitted traces of oxy- and deoxyhemoglobin. This causes instability and a change in [_HbO_2] and [_HHb_] concentrations (Figure 3a). One can see a good correlation between the fitted and measured hemoglobin traces (\(R^{2}\) = 0.96).  
In Figure 3b, one can see that while _CBF_ goes to zero at the end of the CA epoch (i.e., the blood flow stops), the total hemoglobin increases. This is a typical behavior of [_tHb_] due to vasodilation [17].  
Figure 3c shows the computed changes in the capillary (\(\langle S^{(c)}\rangle(t)\)) and venule (\(\langle S^{(v)}\rangle(t)\)) oxygen saturations. The curves in this subplot exhibit features similar to the corresponding simulated curves in Figure 2d: during CA, the capillary oxygen saturation \(\langle S^{(c)}\rangle(t)\) (blue curve in Figure 3c) drops to 0%. Unlike \(\langle S^{(c)}\rangle(t)\), the venule oxygen saturation \(\langle S^{(v)}\rangle(t)\) computed using the CHS model (red curve in Figure 3c) drops only slightly during CA and more significantly during CPR, when the deoxygenated blood arrives to the venules from the capillaries due to the restoration of _CBF_. The green-dotted curve in Figure 3c shows that Equation (10) gives higher values for venule saturation \(\langle S^{(v)}\rangle(t)\) compared with the values resulting from the CHS model (red curve).  
While the capillary saturation \(\langle S^{(c)}\rangle(t)\) decreases to zero during CA, (blue curve in Figure 3c), the minimum values of the measured tissue oxygen saturation \(S_{1}O_{2}\) (blue curve in Figure 3d) do not drop below 40%. The fact that the values of \(S_{1}O_{2}\) computed using the CHS model (red curve in Figure 3d) remain close to the measured \(S_{1}O_{2}\) values proves that CHS correctly predicts the main features of \(S_{1}O_{2}\) during the pacing, CA, and CPR epochs. Figure 2e shows that \(\mathit{CMRO_{2}}\) drops to zero during CA. Overestimation of the venule saturation results in the underestimation of \(\mathit{CMRO_{2}}\) (green-dotted curve in Figure 2e). In Figure 2e, one can also see a good correlation between the time courses of the computed \(\mathit{CMRO_{2}}\) and redox cytochrome C oxidase (\(rCCO\)), which is the intracellular molecular marker of the oxygen metabolism [18].