Three-compartment ventricular circulation model

An arterial reservoir, venous reservoir and a left ventricle exchange flows $Q_a,Q_v,Q_c$. Their volume balances are $C_a{\dot{p}}_a=Q_a-Q_c$, $C_v{\dot{p}}_v=Q_c-Q_v$, and $d(p_{LV}/E_{LV})/dt=Q_v-Q_a$. Ideal one-way valves give $Q_a=[p_{LV}-p_a{]}_{+}/R_a$, $Q_v=[p_v-p_{LV}{]}_{+}/R_v$; systemic resistance gives $Q_c=(p_a-p_v)/R_c$. Summing the three equations verifies total mass conservation for incompressible blood.