## 3 Results  
Model output statistics are presented from a single simulation instance with CoW variant 1 (complete CoW) at 80 bpm in Table 2. The statistics from the AF case are shown to be similar to those in the NSR case. Median systemic blood pressures of 117.44/77.81 mmHg (systolic/diastolic) for NSR and 119.51/78.95 mmHg for AF are shown to be similar to physiological levels. Additionally, total cerebral blood flow is 12.54 mL s\({}^{-1}\) for the NSR case and 12.31 mL s\({}^{-1}\) for the AF case. The model has demonstrated that large variations in blood pressure are propagated through the large arterial circulation and have a high impact on small vessels in the distal cerebral circulation, annotated as RA, LA, RM, LM, RP, and LP in Figure 2. This effect is demonstrated in Figure 5 where a drop in aortic blood pressure due to a long RR interval is associated with two consecutive hypoperfusion events. The example shows aortic blood pressure and simultaneous blood flow into the LM in a control and AF case, colored in blue and red, respectively. On panel A, the dip in blood pressure can be seen in the AF case between seconds 1 and 3. Corresponding with this dip, two hypoperfusion events are annotated with black in panel B, with horizontal lines indicating the mean blood flow value during the heartbeat to show that it is indeed below the fifth percentile of normal blood flow. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Baseline Value** \\ \hline \multicolumn{3}{c}{Whole-body circulation} \\ \hline HR\({}_{0}\) & Intrinsic heart rate & 75 bpm \\ Ediasrv & Right ventricular diastolic elastance. & 0.07 (mmHg ml\({}^{-1}\)) \\ Esysrv & Right ventricular systolic elastance. & 1.3 (mmHg ml\({}^{-1}\)) \\ Esysra & Right atrial systolic elastance. & 0.74 (mmHg ml\({}^{-1}\)) \\ Ediasra & Right atrial diastolic elastance. & 0.3 (mmHg ml\({}^{-1}\)) \\ Ediaslv & Left ventricular diastolic elastance. & 0.13 (mmHg ml\({}^{-1}\)) \\ Rpv & Pulmonary venous resistance. & 0.01 (mmHg s ml\({}^{-1}\)) \\ \hline \multicolumn{3}{c}{Cerebral circulation} \\ \hline Gaut & Autoregulation function gain. & 0.9 (unitless) \\ tauaut & Autoregulation function time constant. & 20 (s) \\ Cd & Distal cerebral arterial compliance. & 200 (ml mmHg\({}^{-1}\)) \\ kR & Distal cerebral resistance scaling term. & 13,100 (mmHg\({}^{-3}\) s ml\({}^{-1}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Relevant model parameters. The heart rate and vascular geometry dependence of hypoperfusion events is illustrated in Figure 6. For each of the six common variants of the CoW, total hypoperfusion event counts are shown for simulations at imposed heart rates ranging from 50 to 130 bpm. All variants displayed similar behavior within the range of heart rates examined, with some differences in the number of counts, as well as the point at which they have the highest hypoperfusion count. Variant 1, with a complete CoW, is represented in Figure 6A. This variant had a minimum count occurring at a heart rate of 50 bpm with 178 total events, and a maximum count at 120 bpm with 2048 total events. Variant two, with a missing PCa, is represented in Figure 6B. This variant had a minimum count at 50 bpm with 264 events, and a maximum count at 120 bpm with 2248 events. Variant number three, with both PCa missing, is shown in Figure 6C. It had a minimum count at 50 bpm with 268 events, and a maximum count at 130 bpm with 2120 events. Variant four, with a missing ACA1, is represented in Figure 6D. This variant had a minimum count at 50 bpm with 675 events, and a maximum count at 110 bpm with 2861 events. Variant five, with a missing PCA1, is represented in Figure 6E. This variant had a minimum count at 50 bpm with 211 events, and a maximum count at 120 bpm with 2458 events. Variant six, with a missing PCa and contralateral PCA1, is represented in Figure 6F. This variant had a minimum count at 50 bpm with 97 events, and a maximum count at 110 bpm with 2386 events. All variants had minimum counts at a 50 bpm heart rate.