## 3 Results
Maximum points varied between different variants, although all were within 110 to 130 bpm. Variant 3 is notable in that there is no count drop off at 130 bpm as there is in all other variants. Overall, all variants exhibit similar behavior, increasing count with bpm, up to a maximum around 120 bpm. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Output Name** & \multicolumn{2}{c}{**Output Values**} \\ \hline  & **NSR** & **AF** \\ \hline P\({}_{\text{a,sys}}\) (mmHg) & 117.44 \(\pm\) 21.35 & 119.51 \(\pm\) 17.45 \\ P\({}_{\text{a,dias}}\) (mmHg) & 77.81 \(\pm\) 15.85 & 78.95 \(\pm\) 16.64 \\ Q\({}_{\text{ACA}}\) (ml s\({}^{-1}\)) & 0.99 \(\pm\) 0.37 & 0.95 \(\pm\) 0.45 \\ Q\({}_{\text{MACA}}\) (ml s\({}^{-1}\)) & 3.68 \(\pm\) 1.21 & 3.64 \(\pm\) 1.37 \\ Q\({}_{\text{PCA}}\) (ml s\({}^{-1}\)) & 1.47 \(\pm\) 0.52 & 1.44 \(\pm\) 0.59 \\ CBF (ml s\({}^{-1}\)) & 12.54 \(\pm\) 4.24 & 12.31 \(\pm\) 4.78 \\ \hline \hline \end{tabular} Model output statistics for a simulation run with CoW variant 1 (complete CoW), at an HR of 80 BPM under AF and NSR conditions. Systemic pressure and cerebral blood flow statistics are shown to be similar in both NSR and AF cases. Values are shown as median \(\pm\) standard deviation. P\({}_{\text{a,sys}}\): Arterial systolic pressure; P\({}_{\text{a,dias}}\): Arterial diastolic pressure; Q\({}_{\text{ACA}}\): Anterior cerebral artery flow rate; Q\({}_{\text{MACA}}\): Middle cerebral artery flow rate; Q\({}_{\text{PCA}}\): Posterior cerebral artery flow rate; CBF: Cerebral blood flow.  
\end{table} 
Table 2: Model outputs under NSR conditions. Figure 5: Hemodynamic outputs of a simulation of AF (red) and NSR (blue) at 70 bpm in the normal CoW. (**A**) Aortic blood pressures. (**B**) Blood flow through the left middle distal artery with hypoperfusion events shown in black. Figure 7 illustrates alterations in cerebral blood flow heterogeneity between the six variants. Under AF conditions, the left middle, left anterior, and left posterior regions experience a balanced outflow in variants 1 through 4 (Figure 7A-D), indicating virtually uniform cerebral perfusion. Alternatively, variants 5 and 6 show flow patterns that are more irregular. Both these variants also have either out-of-phase or negative-flow amplitude in the LP region relative to the other two regions shown. Additionally, flow oscillations in the LP region for these two variants have much larger amplitudes than flow to the other regions and compared to all flow in the other variants. As illustrated in Figure 8, the maximal PRCC values regarding hypoperfusion count are the intrinsic heart rate (HR\({}_{0}\)), E\({}_{\text{disrav}}\), E\({}_{\text{sysrv}}\), G\({}_{\text{aut}}\), and E\({}_{\text{disra}}\). Notably, HR\({}_{0}\) ranked the highest for each variant, with varying amplitudes across the variants. Additionally, mechanical characteristics of the right ventricle and atria have high PRCC values, i.e., E\({}_{\text{disrav}}\), E\({}_{\text{sysrv}}\), E\({}_{\text{disra}}\), and E\({}_{\text{sysra}}\). G\({}_{\text{aut}}\) and \({\text{tauaint}}\), which are both parameters that play a role in the cerebral autoregulation mechanism, also have high PRCC values for all variants. Figure 6: Absolute frequencies of hypoperfusion events in the distal cerebral circulations at varying heart rates under AF conditions. Count is the sum of all hypoperfusion events in each of the six distal circulation regions over a 5000 heart-beat simulation. Each panel shows hypoperfusion counts for heart rates from 50 bpm to 130 bpm for a particular CoW variant. (**A**) Complete CoW. (**B**) Missing PCoA. (**C**) Missing both PCoA. (**D**) Missing ACA. (**E**) Missing PCA. (**F**) Missing PCoA and PCA. Figure 8: PRCCs for hypoperfusion count for each of the six considered CoW variants. The 10 PRCC values with the greatest magnitude are shown for each case and are ordered from greatest to least magnitude. Symbols are described in Table 1. Each panel illustrates PRCC analysis for a particular CoW variant. (**A**) Complete CoW. (**B**) Missing PCoA.