Skip to main content
SpringerLink
Log in

Arterial windkessel parameter estimation: A new time-domain method

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

We developed and validated a new, more accurate, and easily applied method for calculating the parameters of the three-element Windkessel to quantitate arterial properties and to investigate ventriculoarterial coupling. This method is based on integrating the governing differential equation of the three-element Windkessel and solving for arterial compliance. It accounts for the interaction between characteristic impedance and compliance, an important phenomenon that has been ignored by previously implemented methods. The new integral method was compared with four previously published methods as well as a new independent linear least-squares analysis, using ascending aortic micromanometric and volumetric flow measurements from eight dogs. The parameters calculated by the new integral method were found to be significantly different from those obtained by the previous methods but did not differ significantly from maximum likelihood estimators obtained by a linear leastsquares approach. To assess the accuracy of parameter estimation, pressure and flow waveforms were reconstructed in the time domain by numerically solving the governing differential equation of the three-element Windkessel model. Standard deviations of reconstructed waveforms from the experimental ensemble-averaged waveforms, which solely reflect the relative accuracy of the Windkessel parameters given by the various methods, were calculated. The new integral method invariably yielded the smallest error. These results demonstrate the improved accuracy of our new integral method in estimating arterial parameters of the three-element Windkessel.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Burkhoff, D.; Alexander, J. Jr.; Schipke, J. Assessment of Windkessel as a model of aortic input impedance. Am. J. Physiol. 255:H742-H753; 1988.

    CAS  PubMed  Google Scholar 

  2. Campbell, K.B.; Lee, L.C.; Frasch, H.F.: Noordergraaf, A. Pulse reflection sites and effective length of the arterial system. Am. J. Physiol. 256:H1684-H1689; 1989.

    CAS  PubMed  Google Scholar 

  3. Dujardin, J.P.L.; Stone, D.N.: Characteristic impedance of the proximal aorta determined in the time and frequency domain: a comparison. Med. Biol. Eng. Comp. 19:565–568; 1981.

    CAS  Google Scholar 

  4. Finkelstein, S.M.; Collins, V.R.. Vascular hemodynamic impedance measurement. Prog. Cardiovasc. Dis. 24:401–418; 1982.

    CAS  PubMed  Google Scholar 

  5. Frank, O.. Die Grundform des arteriellen pulses. Z. Biol. 37:483–526; 1899.

    Google Scholar 

  6. Laskey, W.K.; Parker, H.G.; Ferrari, V.A.; Kussmaul, W.G.; Noordergraaf, A. Estimation of total systemic arterial compliance in humans. J. Appl. Physiol. 69:112–119; 1990.

    CAS  PubMed  Google Scholar 

  7. Li, J.K.J. Time domain resolution of forward and reflected waves in the aorta. IEEE Trans. Biomed. Eng. 33:783–785; 1986.

    CAS  PubMed  Google Scholar 

  8. Lucas, C.L.; Wilcox, B.R.; Ha, B.; Henry, G.W. Comparison of time domain algorithms for estimating aortic characteristic impedance in humans. IEEE Trans. Biomed. Eng. 35:62–68; 1988.

    Article  CAS  PubMed  Google Scholar 

  9. McDonald, D.A. Blood flow in arteries. Baltimore: Williams & Wilkins; 1974: pp. 315–322.

    Google Scholar 

  10. Milnor, W.R. Hemodynamics, ed 2. Baltimore: Williams & Wilkins; 1989: pp. 170–179.

    Google Scholar 

  11. Murgo, J.P.; Westerhof, N.; Giolma, J.P.; Altobelli, S.A. Aortic input impedance in normal man: relationship to pressure wave forms. Circulation 62:105–116; 1980.

    CAS  PubMed  Google Scholar 

  12. Murgo, J.P.; Westerhof, N.; Giolma, J.P.; Altobelli, S.A. Manipulation of ascending aortic pressure and flow wave reflections with the Valsalva maneuver: relationship to input impedance. Circulation 63:122–132; 1981.

    CAS  PubMed  Google Scholar 

  13. Nichols, W.W.; O'Rourke, M.F.; Avolio, A.P.; Yaginuma, T.; Murgo, J.P.; Pepine, C.J.; Conti, C.R. Effects of age on ventriculo-vascular coupling. Am. J. Cardiol. 55:1179–1184; 1985.

    CAS  PubMed  Google Scholar 

  14. O'Rourke, M.F. Vascular impedance in studies of arterial and cardiac function. Physiol. Rev. 62:570–623; 1982.

    PubMed  Google Scholar 

  15. Pasipoularides, A. Clinical assessment of ventricular ejection dynamics with and without outflow obstruction. J. Am. Coll. Cardiol. 15:859–882; 1990.

    CAS  PubMed  Google Scholar 

  16. Pasipoularides, A. Cardiac mechanics: basic and clinical contemporary research. Ann. Biomed. Eng. 20:3–17; 1992.

    CAS  PubMed  Google Scholar 

  17. Pasipoularides, A.; Murgo, J.P.; Miller, J.W.; Craig, W.E. Nonobstructive left ventricular ejection pressure gradients in man. Circ. Res. 61:220–227; 1987.

    CAS  PubMed  Google Scholar 

  18. Pepine, C.J.; Nichols, W.W.; Conti, C.R. Aortic input impedance in heart failure. Circulation 58:460–465; 1978.

    CAS  PubMed  Google Scholar 

  19. Press, W.H.; Flannery, B.P.; Teukolsky, S.A.; Vetterling, W.T. Numerical recipes. New York: Cambridge University Press; 1986: pp. 509–520, 547–554.

    Google Scholar 

  20. Randall, O.S.; Esler, M.D.; Calfee, R.V.; Bulloch, G.F.; Maisel A.S.; Culp B. Arterial compliance in hypertension. Aust. NZJ. Med. 6(suppl):49–59; 1976.

    Google Scholar 

  21. Shim, Y.; Hampton, T.G.; Straley, C.A.; Harrison, J.K.; Spero, L.A.; Bashore, T.M.; Pasipoularides, A.D. Ejection load changes in aortic stenosis: observations made after balloon aortic valvuloplasty. Circ. Res. 71:1174–1184; 1992.

    CAS  PubMed  Google Scholar 

  22. Shoukas, A.A.; Sagawa, K. Control of total systemic vascular capacity by the carotid sinus baroreceptor reflex. Circ. Res. 33:22–32; 1973.

    CAS  PubMed  Google Scholar 

  23. Sunagawa, K.; Burkhoff, D.; Lim, K.O.; Sagawa, K. Impedance loading servo pump system for excised canine ventricle. Am. J. Physiol. 243:H346-H350; 1982.

    CAS  PubMed  Google Scholar 

  24. Toorop, G.P.; Westerhof, N.; Elzinga, G. Beat-to-beat estimation of peripheral resistance and arterial compliance during pressure transients. Am. J. Physiol. 252:H1275-H1283; 1987.

    CAS  PubMed  Google Scholar 

  25. Toy, S.M.; Melbin, J.; Noordergraaf, A. Reduced models of arterial systems. IEEE Trans. Biomed. Eng. 32:172–174; 1985.

    Google Scholar 

  26. Westerhof, N.; Bosman, F.; De Vries, C.J.; Noordergraaf, A. Analog studies of the human systemic arterial tree. J. Biomech. 2:121–143; 1969.

    Article  CAS  PubMed  Google Scholar 

  27. Westerhof, N.; Elzinga, G.; Sipkema, P. An artificial arterial system for pumping hearts. J. Appl. Physiol. 31:776–781; 1971.

    CAS  PubMed  Google Scholar 

  28. Westerhof, N.; Noordergraaf, A. Arterial viscoelasticity: a generalized model. J. Biomech. 3:357–379; 1970.

    CAS  PubMed  Google Scholar 

  29. Westerhof, N.; Sipkema, P.; Van den Bos, G.C.; Elzinga, G. Forward and backward waves in the arterial system. Cardiovasc. Res. 6:648–656; 1972.

    CAS  PubMed  Google Scholar 

  30. Yin, F.C.P.; Zhaorong, L.; Brin, K.P. Estimation of arterial compliance. In: Yin, F.C.P., ed. Ventricular/vascular coupling. New York: Springer-Verlag; 1987: pp. 384–398.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Biomedical Engineering, Duke University, Durham, NC

    Youngtack Shim, Ares Pasipoularides, Craig A. Straley, Thomas G. Hampton & Donald D. Glower

  2. Department of Surgery, Duke University Medical Center, Durham, NC

    Pablo F. Soto, Clarence H. Owen & James W. Davis

Authors
  1. Youngtack Shim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ares Pasipoularides
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Craig A. Straley
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thomas G. Hampton
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Pablo F. Soto
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Clarence H. Owen
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. James W. Davis
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Donald D. Glower
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shim, Y., Pasipoularides, A., Straley, C.A. et al. Arterial windkessel parameter estimation: A new time-domain method. Ann Biomed Eng 22, 66–77 (1994). https://doi.org/10.1007/BF02368223

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02368223

Keywords

Search

Navigation