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


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[−(tt0)/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.


  1. Izzo JL Jr, Shykoff BE. Arterial stiffness: clinical relevance, measurement, and treatment. Rev Cardiovasc Med 2001;2:29–34, 37–40.

    Google Scholar 

  2. Izzo JL Jr. Brachial vs. central systolic pressure and pulse wave transmission indicators: a critical analysis. Am J Hypertens 2014;27:1433–42.

    Google Scholar 

  3. Gavish B, Izzo JL Jr. Arterial stiffness: going a step beyond. Am J Hypertens 2016;29:1223–33.

    Google Scholar 

  4. Westerhof N, Elzinga G. Normalized input impedance and arterial decay time over heart period are independent of animal size. Am J Physiol 1991;261:R126–R33.

    Google Scholar 

  5. Finkelstein SM, Cohn JN. First- and third-order models for determining arterial compliance. J Hypertens Suppl 1992;10:S11–S14.

    Google Scholar 

  6. Manning TS, Shykoff BE, Izzo JL Jr. Validity and reliability of diastolic pulse contour analysis (Windkessel model) in humans. Hypertension 2002;39:963–8.

    Google Scholar 

  7. Behnam V, Rong J, Larson MG, Gotal JD, Benjamin EJ, Hamburg NM, et al. Windkessel measures derived from pressure waveforms only: the Framingham Heart Study. J Am Heart Assoc 2019;8:e012300.

  8. Burt VL, Whelton P, Roccella EJ, Brown C, Cutler JA, Higgins M, et al. Prevalence of hypertension in the US adult populatio. Results from the Third National Health and Nutrition Examination Survey, 1988–1991. Hypertension 1995;25:305–13.

    Google Scholar 

  9. Chemla D, Lau EMT, Hervé P, Millasseau S, Brahimi M, Zhu K, et al. Influence of critical closing pressure on systemic vascular resistance and total arterial compliance: a clinical invasive study. Arch Cardiovasc Dis 2017;110:659–66.

    Google Scholar 

  10. Wilkinson IB, Franklin SS, Hall IR, Tyrrell S, Cockcroft JR. Pressure amplification explains why pulse pressure is unrelated to risk in young subjects. Hypertension 2001;38:1461–6.

    Google Scholar 

  11. Sharman JE, McEniery CM, Campbell RI, Coombes JS, Wilkinson IB, Cockcroft JR. The effect of exercise on large artery haemodynamics in healthy young men. Eur J Clin Invest 2005;35:738–44.

    Google Scholar 

  12. Narayan O, Parker KH, Davies JE, Hughes AD, Meredith IT, Cameron JD. Reservoir pressure analysis of aortic blood pressure: an in-vivo study at five locations in humans. J Hypertens 2017;35:2025–33.

    Google Scholar 

  13. O’Rourke MF, Kelly RP. Wave reflection in the systemic circulation and its implications in ventricular function. J Hypertens 1993;11:327–37.

    Google Scholar 

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Correspondence to Joseph Lewis Izzo Jr..

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Peer review under responsibility of the Association for Research into Arterial Structure and Physiology

Data availability statement: The data that support the findings of this study are not publicly available, but remain in the Lab.

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Izzo, J.L., Anwar, M.A., Elsayed, S. et al. Dissociation of Carotid and Forearm Pressure Decay Constants (tau), Windkessel Compliances, and Pulse Wave Velocities: Implications for Circulatory Models. Artery Res 25, 165–169 (2019).

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