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During this stage of the cardiac cycle, the ventricular inlet and outlet valves are both closed. Ventricular volume is fixed at its end-filling value $V^{+}$, while increasing ventricular elastance raises pressure as $p_{LV}=E_{LV}(t)(V^{+}-V_0)$. Arterial and venous pressures remain approximately fixed when the stage is short relative to their systemic resistance–compliance times.

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 iswhere $V_0$ 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 areEach $R$ 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, givesSubstitution and multiplication of the first two equations by $R_c$ give exactlyAdding the three original balances gives zero total volume change. This is a three-compartment ventricular circulation model.

Systole is ventricular contraction and ejection; diastole includes ventricular relaxation and filling. Let $V_a,V_v,V_{LV}$ denote arterial, venous and left-ventricular blood volumes. Let $Q^{+}$ flow through the aortic valve into the arteries, $Q_c$ through the peripheral circulation, and $Q^{-}$ through the mitral valve into the ventricle. Conservation of volume givesThe same $Q_c$ leaves arteries and enters veins because the capillary compartment has no changing stored volume in this approximation. Adding the equations conserves total modeled blood volume.

Use constant vascular compliances $C_a,C_v$, with ${\dot{V}}_a=C_a{\dot{p}}_a$ and ${\dot{V}}_v=C_v{\dot{p}}_v$, and ventricular elastance $p_{LV}=E_{LV}(t)(V_{LV}-V_0)$. The hydraulic resistances and ideal one-way valves givewhere $[z{]}^{+}=\max (z,0)$. Substitution into the conservation equations gives the two stated arterial/venous pressure equations. Since $V_{LV}-V_0=p_{LV}/E_{LV}$, differentiating this identity gives the third equation. The positive parts encode valve closure against a reverse pressure difference.

During isovolumetric contraction both valves are closed. Let $V^{+}$ be the end-diastolic ventricular volume, $V_0$ its unstressed reference volume, and $p_a^{+}$ arterial pressure before ejection. The rapidly raised elastance generates $E_s(V^{+}-V_0)$, so the aortic valve opens if $\boxed{E_s(V^{+}-V_0)>p_a^{+}}$.

During ejection, $R_a/R_c\ll 1$ makes the open-valve pressure drop small on the peripheral drainage time scale, so $p_{LV}\approx p_a$. The mitral valve is closed, and adding arterial and ventricular volume balances eliminates $Q^{+}$. With $p_v\ll p_a$ this givesFor approximately constant systolic elastance, set $C_s=1/E_s$ and reset time to the start of the slow ejection phase. ThenHere ${\hat{p}}_a$ is the matched pressure at that start. If peripheral outflow is negligible during the preceding rapid artery-ventricle pressure equilibration, conservation gives the more explicit ${\hat{p}}_a=[C_a{p}_a^{+}+V^{+}-V_0]/(C_a+C_s)$.

After aortic closure the ventricular volume is fixed at the end-systolic value $V^{-}$. Relaxation decreases $E_{LV}$ until the mitral valve opens at $p_{LV}=p_v$, hence $\boxed{E_{LV}\sim p_v/(V^{-}-V_0)}$, with $p_v$ the venous filling pressure at opening. During filling the aortic valve is closed, so $R_c{C}_a{\dot{p}}_a=-(p_a-p_v)\approx -p_a$. With $p_a^{-}$ the arterial pressure at the start of filling and time reset there,The change from $C_a+C_s$ to $C_a$ is physical: the ejecting ventricle shares the arterial pressure during systole, whereas a closed aortic valve disconnects it during filling.

If an open aortic valve equilibrates pressure much faster than peripheral outflow, the arteries and ventricle share a common pressure while their combined blood volume is conserved during the short adjustment. Let arterial vascular compliance be $C_a$ and systolic ventricular elastance be $E_s$. Equating the initial and final arterial-plus-ventricular stored volumes gives the displayed pressure. Subsequent peripheral drainage sees the combined compliance $C_a+1/E_s$; during filling a closed aortic valve removes the ventricular contribution.

Stroke volume is the volume expelled by a ventricle in one contraction. In a time-dependent ventricular elastance model, if end-ejection pressure is $p$ and systolic compliance is $C_s$, the remaining ventricular volume is $V_0+C_{s}p$. Subtracting that from the end-filling volume gives the ejected volume.