The 3D version of this simulator lets you drag pressure directly along the static sigmoid — an open-loop, instantaneous view. This 2D version instead runs the closed feedback loop forward in time: pressure is a real dynamical state that the baroreflex actively pulls back toward its set-point after a disturbance, exactly like the real cardiovascular control system.
F(P) = 100 / (1 + e^(−G·(P−P0))) afferent firing rate, %
HR(P) = HRmax − (HRmax−HRmin)·F(P)/100 heart rate, bpm
dP/dt = Drive(t) − K·(F(P) − 50) / 50 closed-loop pressure dynamics
dHR/dt = (HR_target(F(P)) − HR) / τ_HR lagged autonomic HR response
K = loop authority (mmHg/s), τ_HR ≈ 1.5 s vagal response lag
Because F(P) is a monotonic sigmoid centred on P0, the restoring term −K·(F(P)−50)/50 is always negative above P0 and positive below it — a genuine negative-feedback control law, not just a lookup. With no sustained drive the only stable point is P = P0. A sustained external drive (this is a proportional-only controller, like the real reflex) is only partially buffered: pressure settles to a new steady-state offset from P0, found by inverting the sigmoid — exactly the physiological phenomenon of a baroreflex that dampens but cannot fully cancel a persistent pressor stimulus.
- Haemorrhage bolus — an instantaneous −20 mmHg step (acute blood loss); watch the trajectory spiral back toward P0 along the sigmoid, with the recovery speed set by gain × loop authority.
- Stand up — a transient, decaying disturbance (venous pooling on standing) that fades over a few seconds even as the reflex simultaneously fights it — the two effects are the real, competing dynamics behind why standing quickly still causes a brief pressure dip.
- Gain / set-point sliders — as in the 3D model: gain steepens the sigmoid (faster, tighter correction — higher local dF/dP), and set-point resetting shifts the whole equilibrium, modelling chronic hypertension re-centring the reflex around a higher "normal".
- Firing / heart-rate curve toggle — switches which output the top sigmoid plots; the trailing dot shows the operating point's actual time history, not just its current position.
Real-world relevance: framing the baroreflex as a control loop with time-domain step-responses is exactly how autonomic function is tested clinically (Valsalva manoeuvre, active stand test, neck-chamber pressure steps) — the recovery half-time and the residual steady-state offset are the same quantities cardiologists read off a beat-to-beat blood-pressure trace.