Dissociation of Carotid and Forearm Pressure Decay Constants (tau), Windkessel Compliances, and Pulse Wave Velocities: Implications for Circulatory Models

Abstract

Windkessel (WK) models have often been used to simulate the arterial circulation. We studied a critical characteristic of WK function, the arterial pressure-decay constant tau, to test whether all arterial regions share the same WK characteristics, which should theoretically be related to arterial stiffness. We performed carotid and forearm arterial tonometry (Sphygmocor) and modeled arterial pressure (P) as A + (SBP − A)·exp[−(t − t₀)/tau], where A = minimum pressure, SBP = systolic BP, t = time, t₀ = start of decay). Model validity was supported by strong between-site correlations for t₀ and A. We also measured central and peripheral Pulse Wave Velocity (PWV, Colin VP1000) and calculated arterial compliances (1/PWV²) in the heart-femoral (hf) and femoral-ankle (fa) regions. For the full cohort [n = 98, mean (SD): age 50 (20) years, weight 81 (17) kg, BP 135/77 (17/12) mmHg, 38% female], carotid and forearm taus were different [283 (126) vs. 199 (88) ms, p < 0.000] and uncorrelated (r² = 0.01). Although hf and fa arterial compliances were well correlated (p < 0.000), neither was closely correlated with carotid or forearm tau (r² < 0.06). In a subset (n = 22), carotid and brachial blood flow (Ultramark 9) were measured and regional WK compliances were calculated (= tau/regional resistance). Carotid blood flow [571 (216) vs. 117 (84) mL/min, p < 0.000] and WK compliance [0.031 (0.017) vs. 0.004 (0.004) mL/mmHg, p < 0.000] were much higher than corresponding forearm values. We conclude that: (1) tau and WK compliance are regional, not systemic indicators, (2) neither carotid nor forearm tau reflects large artery stiffness, and (3) a single WK model cannot adequately describe the arterial circulation.