Cardiac Pressure-Volume Loop Simulator

Left Ventricle

Contractility (Ees) 2.5 mmHg/mL

Preload (venous pressure) 10 mmHg

Afterload (arterial resistance) 1.20

Heart rate 72 bpm

Vitals

Stroke vol.

–

Eject. fraction

–

Card. output

–

How it works

The left ventricle is modelled as a time-varying elastance chamber, exactly the mechanism cardiac physiologists use to explain the pressure-volume (PV) loop. Instantaneous ventricular pressure blends a passive filling curve with an active contraction curve, weighted by an activation function e(t) that rises and falls once per heartbeat:

P(t) = e(t)·Ees·(V-V0) + (1-e(t))·Ped(V)
Ped(V) = P0·(e^(k(V-V0)) - 1)        [EDPVR, passive filling]
Pes(V) = Ees·(V-V0)                  [ESPVR, contractility line]

Two diode-like valves gate flow: the mitral valve opens only while venous pressure exceeds ventricular pressure (filling), the aortic valve opens only while ventricular pressure exceeds arterial pressure (ejection). Between those two windows both valves are shut and volume cannot change at all — that is what produces the loop's two vertical, isovolumic sides; they are not drawn in, they fall out of the valve equations on their own.

Q_mv = max(0, Pven-P)/Rmv     dV/dt = Q_mv - Q_av
Q_av = max(0, P-Pao)/Rav      dPao/dt = (Q_av - Pao/Rsys)/Cart

Contractility (Ees) — the slope of the end-systolic PV relation; a stiffer, steeper ESPVR means the ventricle reaches a higher pressure at any given volume, ejecting further before pressure and afterload force the aortic valve shut.
Preload — venous/atrial filling pressure. Raising it fills the ventricle to a larger end-diastolic volume before contraction begins, the Frank-Starling mechanism: more stretch, more stroke volume, with no change in the muscle itself.
Afterload — systemic arterial resistance the ventricle must eject against. Raising it slows outflow and raises end-systolic volume, shrinking the loop's width (stroke volume) even though preload and contractility are unchanged.
Heart rate — cycles per minute; faster rates shorten the diastolic filling window, which can itself reduce end-diastolic volume if filling doesn't have time to complete.

Real-world relevance: this exact PV-loop construction is what a cardiologist reads off a conductance catheter during a cath-lab study — loop width is stroke volume, loop area is stroke work, and how the loop's top-right corner shifts along the ESPVR line versus the EDPVR curve is precisely how systolic versus diastolic heart failure are told apart.

Volume (mL) → ← Pressure (mmHg)

PV loop (live) ESPVR (contractility) EDPVR (passive filling) Mitral / Aortic valve — open

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Cardiac Pressure-Volume Loop Simulator

🔬 What It Demonstrates

🎮 How to Use

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