Windkessel diastolic decay τ = R × C

The two-element Windkessel makes aortic pressure decay exponentially in diastole with time constant τ = R × C. The engine measures τ ≈ 1.54 s by a log-linear fit of the diastolic segment, matching the analytic R×C product (1.54 s) and the cited human aortic value (~1.5 s). Compliance buffers pulsatile flow into perfusion. Grade [consistency]/[L].

In diastole the valve is shut and the compliant aorta discharges through the peripheral resistance, so pressure decays as P(t) = P₀ e^(−t/RC). The measured decay constant τ ≈ 1.54 s equals the R×C product 1.54 s.

Compliance turns pulses into flow

The Windkessel adds one element to the resistive network: a compliance C in parallel with the peripheral resistance R. During diastole the stored volume discharges and pressure relaxes exponentially.

Fitting the log of the diastolic pressure segment recovers τ ≈ 1.54 s, exactly the analytic R×C = 1.54 s, and within the cited aortic range. This is why arterial pressure never collapses to zero between beats: the compliance buffers the pump into near-steady organ perfusion.

The fitted τ equalling R×C is a [consistency] check (the fit recovers the model's own constant); 1.54 s is a [code output] of the input R and C. [observation] Diastolic aortic pressure decay constants of about 1.5–2 s are reported in humans (Westerhof, Lankhaar & Westerhof 2009, Med. Biol. Eng. Comput. 47:131).