Three-compartment ventricular circulation model
= 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>.