Every view is generated from one time-varying elastance model with a linear ESPVR, a Klotz-normalised EDPVR and a Windkessel-derived arterial pressure. Values are physiologically calibrated but idealised — they illustrate direction and magnitude of change, not a specific patient. Timings follow standard relations (Weissler for ejection time, Gorlin for valve gradients, Klotz for the filling curve). The sound is synthesised from the model, not recorded: murmur envelopes are the computed flow and gradient traces, so loudness tracks severity. It is a schematic and should not be used as an auscultation reference — where a murmur is loudest follows conventional teaching rather than anything in the physics.
Where the numbers come from
Published relations, implemented in their standard form.
Time-varying elastance and the ESPVR — Suga & Sagawa, Circ Res 1974; Burkhoff, Mirsky & Suga,
Am J Physiol 2005;289:H501. Single-beat EDPVR — Klotz et al., Am J Physiol 2006.
Venous return and cardiac function curves — Guyton, Physiol Rev 1955;35:123.
Valve area and gradient — Gorlin. Ejection time — Weissler. Subendocardial supply and
demand — Buckberg (DPTI/SPTI). Pressure–volume analysis of mechanical support —
Burkhoff et al., JACC 2015;66:2663.
Constants fitted, not derived. Several coefficients were tuned so that a normal adult
lands at roughly 111/77 mmHg, EF 57%, Ea/Ees 0.61 — among
them the Ea scaling, the transpulmonary offset, the resistance to venous return and the
Klotz size mapping. They reproduce normal physiology; they are not measurements.
Drug and device effects are illustrative. Directions and relative magnitudes follow the
literature — Guarracino & Monge García, Ann Transl Med 2020 (noradrenaline
raises Ea without a matching rise in Ees and worsens coupling; dobutamine does
the reverse); Lyhne et al., Pulm Circ 2021 (inodilators lower end-systolic pressure without
raising PVA, dobutamine raises both); and for the devices the in-vitro cardiogenic-shock
measurements of Yahagi et al., Sci Rep 2024;14:14125, against which the Impella, VA-ECMO and
ECPELLA behaviour here was checked. The individual multipliers are the author’s
construction. No number this tool gives for a drug or a device should be quoted.
The reflex layer is illustrative throughout. Nine mechanisms — four neural arcs, two
offered but off by default, and three intrinsic to myocardium — are wrapped as a damped outer loop
around the same steady-state solver. Sensors, directions and saturation shapes follow the standard
physiology; every coefficient was chosen to place the saturations where they are clinically
recognisable and is fitted to no dataset. Reflex gains are far softer in the literature than
Ees or Ea, so read those modules for behaviour rather than magnitude, and
quote no number from them. Reflex exhaustion is deliberately not modelled, and neither is renal or
RAAS control: the kidney owns arterial pressure over days, and mixing that time domain with this one
is misleading. Modules before the reflex section stay open-loop on purpose, because that is the
condition under which Ees, Ea and the EDPVR are defined.
Known limits. Away from the reflex modules, systemic resistance stays wherever you set it.
The circulation is a single compartment: the pulmonary circuit appears only as an
offset, which is why left-sided filling pressure on VA ECMO needs an explicit term rather than
emerging. Impella is modelled as volume withdrawn during the isovolumic phases, not as a pump on its
own pressure–flow curve. Dopamine is given one profile when its clinical character is
dose-dependence. The heart sounds are synthesised and schematic. At a handful of physiologically
incoherent settings — a barely contracting ventricle driven fast against a tight mitral valve with a
pump across the aortic one — the closed loop has no steady state at all; the tool detects this and
reports the mean of the cycle rather than an arbitrary point on it.