= Solution
Let $p_a,p_v,p_{LV}$ be pressures in the <arterial reservoir>, <venous reservoir> and <left ventricle>. Constant <vascular compliances> $C_a,C_v$ relate volume changes to <pressure> changes. The <ventricular elastance> relation is
$$
V_{LV}=V_0+\frac{p_{LV}}{E_{LV}(t)},
$$
where $V_0$ is the unstressed ventricular volume and $E_{LV}(t)>0$ is the time-dependent inverse compliance. Define the positive part $[x]_+=\max(x,0)$. The systemic, aortic-valve and mitral-valve flows are
$$
Q_c=\frac{p_a-p_v}{R_c},\qquad Q_a=\frac{[p_{LV}-p_a]_+}{R_a},\qquad Q_v=\frac{[p_v-p_{LV}]_+}{R_v}.
$$
Each $R$ is a positive <hydraulic resistance>. The <aortic valve> permits outflow only when ventricular <pressure> exceeds arterial <pressure>, and the <mitral valve> permits filling only when venous <pressure> exceeds ventricular <pressure>.
<Mass conservation>, with <blood> treated as incompressible, gives
$$
C_a\dot p_a=Q_a-Q_c,\qquad C_v\dot p_v=Q_c-Q_v,\qquad\frac{d}{dt}\left(\frac{p_{LV}}{E_{LV}}\right)=Q_v-Q_a.
$$
Substitution and multiplication of the first two equations by $R_c$ give exactly
$$
\boxed{\begin{aligned}
R_cC_a\dot p_a&=-(p_a-p_v)+\frac{R_c}{R_a}[p_{LV}-p_a]_+,\\
R_cC_v\dot p_v&=(p_a-p_v)-\frac{R_c}{R_v}[p_v-p_{LV}]_+,\\
\frac{d}{dt}(p_{LV}/E_{LV})&=\frac{[p_v-p_{LV}]_+}{R_v}-\frac{[p_{LV}-p_a]_+}{R_a}.
\end{aligned}}
$$
Adding the three original balances gives zero total volume change. This is a <three-compartment ventricular circulation model>.
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