Arterial Windkessel Pressure Simulator

Cardiac & Vascular Parameters

Heart rate 72 bpm

Stroke volume 70 mL

Peripheral resistance R 1.00

Arterial compliance C 1.50

Live Arterial Pressure

--/--
systolic / diastolic, mmHg

Mean arterial P

-- mmHg

Pulse pressure

-- mmHg

Cardiac output

-- L/min

Outflow now

-- mL/s

How it works

The two-element Windkessel model treats the systemic arteries as one elastic reservoir (compliance C) draining through the small vessels (resistance R). Conservation of volume gives a single first-order ODE for arterial pressure P(t):

C · dP/dt = Q_in(t) − P / R

Q_in(t) = pulsatile ejection from the left ventricle
          (half-sine pulse each systole, 0 during diastole)
Q_out(t) = P(t) / R   (continuous run-off through the periphery)

Each heartbeat injects a stroke volume of blood over the systolic fraction of the cycle. Because the compliant vessel wall stretches, pressure keeps rising through systole even as some blood is already draining out, then decays smoothly through diastole as C discharges through R — an RC-circuit exponential decay, P(t) = P₀·e^(−t/RC).

Heart rate / stroke volume — set how much blood is ejected and how often; their product is cardiac output.
Resistance R — mainly the arterioles. Raising it (vasoconstriction) raises mean and diastolic pressure and slows the diastolic decay.
Compliance C — how stretchy the large arteries are. Lower C (stiffer vessels, as in aging) makes the same stroke volume produce a much bigger pulse pressure — the same mechanism behind isolated systolic hypertension.

Clinical relevance: this exact model underlies bedside estimates of arterial compliance and is the textbook explanation for why arterial stiffening, not just resistance, drives high pulse pressure in older or hypertensive patients.

Compliant reservoir (aorta) Ventricular inflow Peripheral outflow

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