## 2 Methods
### Model Components  
The 0D model is a composite model that consists of whole-body circulation, a blood-pressure modulated baroreflex control mechanism, and detailed cerebral circulation with an autoregulation function. All model parameters were inherited from the literature values, unless otherwise stated. The whole-body circulation model was adapted from the model published by [PERSON] (1976). It consists of a network of blood containing elastic Windkessel compartments, which represent individual, or networks of, blood vessels. The time-dependent change in pressure within each compartment is a function of the change in volume (i.e., flow in or out) divided by the compliance of the compartment shown by the equation:  
\[\frac{dP}{dt}=\frac{q_{in}-q_{out}}{C}, \tag{1}\]  
Figure 1: Caricature of the whole-body blood flow model. The cerebral model (black box, bold, top) is expanded in Figure 2.  
Figure 2: Cerebral arterial architecture consisting of all Circle of Willis arteries. RA: Right anterior artery; LA: Left anterior artery; RM: Right middle artery; LM: Left middle artery; RP: Right posterior artery; LP: Left posterior artery; ACA1: Pre-communicating anterior cerebral artery; PCoA: Posterior communicating artery; and PCA1: Pre-communicating posterior cerebral artery. where \(P\) denotes compartment pressure, \(t\) denotes time, \(q\) denotes flow, and \(C\) denotes compliance. The flow between connected compartments is calculated using the following equation:  
\[q=\frac{P_{p}-P_{d}}{R}, \tag{2}\]  
where \(P_{p}\) and \(P_{d}\) denote proximal and distal pressure, respectively, and \(R\) denotes resistance. The pumping heart is represented as four compartments with variable elastance (inverse of compliance), representing the four chambers of the heart. The time-dependent elastances of ventricles and atria were calculated using activation terms. The equation for atrial activation is:  
\[0<t_{loc}\leq t_{\text{asys}}: act_{a}=1-\cos\Bigl{(}\pi\frac{t_{loc}}{t_{\text{asys}}} \Bigr{)},\] \[t_{\text{asys}}<t_{loc}\leq 1.5t_{\text{asys}}: act_{a}=1+\cos\Bigl{(}2\pi\frac{t_{loc}-t_{\text{asys}}}{t_{\text{asys}}} \Bigr{)} \tag{3}\] \[\text{otherwise}: act_{a}=0\]  
in which \(act_{a}\) is the activation term, \(t_{loc}\) is the time since the initiation of the cardiac cycle, and \(t_{\text{asys}}\) is a contraction timing parameter. Similarly, ventricular activation is calculated using:  
\[t_{av}<t_{loc}\leq t_{av}+t_{s}: act_{v}=1-\cos\Bigl{(}\pi\frac{t_{loc}-t_{av}}{t_{s}}\Bigr{)}\] \[t_{av}+t_{s}<t_{loc}\leq t_{av}+1.5t_{s}: act_{v}=1+\cos\Bigl{(}2\pi\frac{t_{av}-t_{av}-t_{s}}{t_{s}}\Bigr{)} \tag{4}\] Figure 1:0  
where \(t_{av}\) is the atrioventricular time delay and \(t_{s}\) is a contraction timing parameter. The activation constants are applied to each heart compartment using the equation:  
Figure 1:1  
where \(E_{\text{{sys}}}\) and \(E_{\text{{diss}}}\) are systolic and diastolic elastances, respectively. Additionally, backflow is prevented in the heart and systemic veins by setting flow between compartments equal to 0 if distal pressure is greater than proximal pressure. A simplified caricature of the circulation model is presented in Figure 1, in which compartments are represented by boxes, and connections are indicated by arrows. It should be noted that the boxes labeled \"cereb\" and \"lower body\" each represents multiple compartments. The baroreflex is a feedback mechanism, which works to maintain hemodynamic homeostasis. It modulates peripheral vascular resistance, heart rate, and heart contractility to maintain systemic blood pressure and flow at healthy levels. The baroreceptor mechanism is implemented according to the model proposed by [PERSON] et al. [15]. The model dynamically calculates sympathetic nervous activity (SNA) and parasympathetic nervous activity (PNA) based on the mean arterial pressure, as well as arterial PCO\({}_{2}\), which is assigned a constant value of 40 mmHg.