## 2 Materials and Methods
\[\frac{dp_{ao}}{dt}=\frac{Q_{av}-Q_{ao}}{C_{ao}} \tag{10}\]  
\[\frac{dQ_{ao}}{dt}=\frac{p_{ao}-p_{as}-R_{ao}Q_{ao}}{L_{ao}} \tag{11}\]  
Here, \(Q_{av}\) and \(p_{as}\) represent aortic valve flow rate and systemic arteriolar pressure; \(C_{ao}\), \(R_{ao}\) and \(L_{ao}\) represent compliance, resistance and inertance in the aorta, respectively. The other compartments in the circulatory system are modelled in the same way using different parameter values. The cardiovascular system model utilised in this study simulates cardiac function for children around 8-12 years of age [15]. Body surface area changes between 0.75 m\({}^{2}\) and 1.3 m\({}^{2}\) around 8-12 years of age [16,17]. Therefore, the body surface area was assumed to be 1.3 m\({}^{2}\) in a 12-year-old child in this study. Detailed information about the cardiovascular system model can be found in [15]. DCM was simulated by modifying the values of the maximal left-ventricular elastance (\(E_{max}\)) (coefficient A in the left ventricle model), left-ventricular zero-pressure volume (\(V_{lv,0}\)) (coefficient K in the left ventricle model) and systemic arteriolar resistance (\(R_{as}\)) in the cardiovascular system model. \(R_{as}\) was set to a healthy value during continuous-flow VAD support as the arterial pressure increased due to heart pump support, and autoregulatory mechanisms regulating the systemic arteriolar resistance accordingly. The parameter values used in the cardiovascular system model simulating healthy and DCM conditions as well as continuous-flow VAD support are presented in Table 1. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline  & **E\({}_{\rm mag}\)** & **E\({}_{\rm mag}\)** & **A** & **B** & **V\({}_{\rm g}\)** & **1** & **K** & **R** & **L** & **C** \\  & **[mmHg/ml.]** & **[mmHg/ml.]** & **[mmHg]** & **[1/ml.]** & **[cm]** & **[cm]** & **[mmHg/ml.]** & **[mmHg/ml.]** & **[cm/mmHg]** \\ \hline LA & 0.4 & 0.2 & - & - & - & 3 & 4.5 & 2.5 & - & - \\ LV & 3.5 (1.3\({}^{\circ}\)) & - & 1 0.085\({}^{\circ}\)) & 0.02 & 10 (17\({}^{\circ}\)) & 7 & 1.5 (1.4\({}^{\circ}\)) & - & - & - \\ RA & 0.4 & 0.2 & - & - & 3 & 4.5 & 2.5 & - & - & - \\ RV & 1.4 & - & 1 & 0.02 & 25 & 7 & 3.25 & - & - & - \\ MV & - & - & - & - & - & - & - & 0.002 & - & - \\ AV & - & - & - & - & - & - & - & 0.002 & - & - \\ TV & - & - & - & - & - & - & - & 0.001 & - & - \\ PV & - & - & - & - & - & - & - & 0.001 & - & - \\ Ao & - & - & - & - & - & - & - & 0.05 & 1E-5 & 0.13 \\ AS & - & - & - & - & - & - & - & 0.95\({}^{\circ}\)(1.4\({}^{\circ}\)) & 1E-5 & 1.13 \\ VS & - & - & - & - & - & - & - & 0.05 & - & 19.35 \\ Po & - & - & - & - & - & - & - & 0.01 & 1E-5 & 3.33 \\ AP & - & - & - & - & - & - & - & 0.15 & 1E-5 & 0.13 \\ VP & - & - & - & - & - & - & - & 0.05 & - & 19.35 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameter values used in the cardiovascular system models. \({}^{\circ}\) Numbers in the brackets were used to simulate DCM and continuous-flow VAD supports. \({}^{\circ}\) R\({}_{\rm ss}\) value used in the cardiovascular system models simulating the healthy condition and continuous-flow VAD support. (LA, left atrium: LV, left ventricle: RA, right atrium: RV, right ventricle: MV, mitral valve, AV, aortic valve TV, tricuspid valve: PV, pulmonary valve, Ao, aorta: AS, systemic arterioles; VS, systemic arterioles; VS, systemic arterioles; PV, pulmonary artery: AP, pulmonary arteries; VP, pulmonary veins, E\({}_{\rm mag}\), maximal distance; E\({}_{\rm mag}\), minimal elastance; A, a parameter used in the ventricle models; B, a parameter used in the ventricle models; V\({}_{\rm o}\) zero-pressure volume; 1, long axis length; K, scaling coefficient used in the heart chamber models; R, resistance; L, interance; C, compliance.). Continuous-flow VAD support was simulated using a model which describes continuous-flow VAD flow rate and the pressure head [18] as given below.