## 2 Methods
### Model Circulation. Figure 1: The modelled lumped parameter coronary vasculature tree network. (**A**) Closed loop vascular structure including tree network and functional components. See Table 1 for vessel names. \(Z_{i}\) (\(i=1\) to \(9\)) represent terminal vessel impedances. Vessels as well as impedances shown in red were used in the simulation experiments. (**B**) Typical blood vessel represented by a resistance (R\({}_{\text{n}}\)), inductance (L\({}_{\text{n}}\)), and a capacitance (C\({}_{\text{n}}\)). P\({}_{\text{n}-1}\): vessel inlet pressure; Q\({}_{\text{n}}\): flow through vessel; P\({}_{\text{n}}\): pressure in vessel; Q\({}_{\text{o}}\): outlet flow; P\({}_{\text{n}+1}\): outlet pressure, or pressure in distal vessel. (**C**) Symbols used in panels (**A**, **B**), and elsewhere in this work. Using the parameters given in Tables 1 and 2, summarized from the parent model [27] and microvascular impedances calculated using Equation (1), pressure at each node of the model (Figure 1) was computed as  
\[\frac{dP_{n}}{dt}=\frac{Q_{n}-Q_{0}}{C_{n}} \tag{2}\]  
and the flow through each vessel (resistance) was calculated as  
\[\frac{dQ_{n}}{dt}=\frac{P_{n-1}-P_{n}-R_{n}Q_{n}}{L_{n}} \tag{3}\]  
Further, the flow through each of the terminals was calculated as  
\[Q_{z,n}=\frac{P_{n-1}-P_{n}}{Z_{n}} \tag{4}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Vessel**} & **R** & **C** & **L** \\  & **(mmHg-s/mL)** & **(ml/mmHg \(\times\) 10\({}^{-3}\))** & **(mmHg-s/2/mL)** \\ \hline
**LMCA** & 0.2299 & 2.9 & 0.00228 \\
**LAD** & 0.4662 & 1.6 & 0.0298 \\
**LAD1** & 0.5729 & 1.6 & 0.0342 \\
**LAD2** & 1.7077 & 3.4 & 0.0916 \\
**LAD3** & 3.7484 & 1.3 & 0.1115 \\
**LAD4** & 3.2930 & 0.4 & 0.0716 \\
**LCX** & 0.3929 & 1.2 & 0.0241 \\
**LCX1** & 0.4730 & 0.7 & 0.0231 \\
**LCX2** & 1.0264 & 0.7 & 0.0380 \\
**LCX3** & 3.2342 & 1.1 & 0.0944 \\
**MARG1** & 1.7351 & 1.2 & 0.0655 \\
**MARG2** & 2.9195 & 0.8 & 0.0787 \\
**MARG3** & 3.0683 & 1 & 0.0896 \\
**RCA** & 1.8302 & 6.3 & 0.1171 \\
**PLA** & 2.4412 & 1.1 & 0.0799 \\
**PDA** & 1.2571 & 1.8 & 0.0596 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model parameter values. See Figure 1 for vessel connectivity. The rows are colour-coded to suggest the major epicardial coronaries, either LAD, LCX, or RCA. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Z (Figure 1).**} & **Root Vessel Radius,** & \multirow{2}{*}{**N.**} & **Control Z Values** \\  & **r\({}_{0}\) (mm).** & & **(mmHg-s/mL).** \\ \hline \(Z_{1}\) & PDA & 0.108 & 19 & 134.100 \\ \(Z_{2}\) & PLA & 0.130 & 20 & 083.710 \\ \(Z_{3}\) & LAD1 & 0.146 & 20 & 059.095 \\ \(Z_{4}\) & LAD3 & 0.103 & 19 & 154.592 \\ \(Z_{5}\) & LAD4 & 0.088 & 18 & 227.185 \\ \(Z_{6}\) & MARG1 & 0.116 & 19 & 108.224 \\ \(Z_{7}\) & MARG2 & 0.098 & 19 & 179.482 \\ \(Z_{8}\) & MARG3 & 0.102 & 19 & 159.184 \\ \(Z_{9}\) & LCX3 & 0.102 & 19 & 159.184 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters used to compute microvascular impedances. Simulation experiments: In all simulations, fractional flow reserve (FFR) was computed as the average of the ratio of the time-dependent distal pressure, \(P_{d}\) (pressure downstream from stenosis) to the time-dependent proximal (aortic) pressure, \(P_{a}\):  
\[FFR_{vessel}=\frac{1}{M}\sum_{n=1}^{n=M}\frac{P_{vessel,n}}{P_{aorta,n}} \tag{5}\]  
where \(M\) represents the total number of fractions over a given time \(T\), which consisted of \(M\) time step recordings. \(T\) was taken to be 100 heart beats and the final 20 were analyzed. Simulations were designed to explore the effects of stenosis severity in the largest epicardial vessels (either LAD, LCX, or RCA; see Figure 1) or microvascular disease, or both. A sensitivity analysis was performed as described below. Stenosis in three large vessels, namely the left anterior descending artery (LAD), the left circumflex artery (LCX), and the right coronary artery (RCA), was investigated. Simulations were performed by imposing focal or diffuse stenosis in a given large vessel.