Advertisement

Journal of Engineering Mathematics

, Volume 47, Issue 3–4, pp 185–199 | Cite as

Systemic and pulmonary hemodynamics assessed with a lumped-parameter heart-arterial interaction model

  • Patrick Segers
  • Nikos Stergiopulos
  • Nico Westerhof
  • Patrick Wouters
  • Philippe Kolh
  • Pascal Verdonck
Article

Abstract

Arterial pressure and flow result from the interaction between the (actively) ejecting ventricle and the (passive) arterial circulation. The main objective was to construct a model, accounting for this interaction, that is simple enough so that (i) model parameters can be derived from data measured in experimental and/or clinical conditions, and (ii) the model can be applied to support the analysis and interpretation of these data. It is demonstrated how an established conceptual model of ventricular function (the time-varying elastance) can be coupled to a four-element windkessel model of the arterial system to yield an elegant model of heart-arterial interaction. The coupling leads to a set of three ordinary differential equations. The model allows the study of the effect of changes in cardiac and/or arterial properties on arterial pressure and flow. As an illustration, cardiac and arterial model parameters are derived from measured experimental data in the systemic circulation of a pig and in the pulmonary circulation of a dog. It is evaluated how well measured cardiac and arterial function actually adhere to their assumed theoretical models (time-varying elastance and four-element windkessel model). It is further assessed how well the simple model of heart-arterial interaction describes systemic and pulmonary hemodynamics by comparing simulated and measured experimental data. The limitations and pitfalls of the model, as well as possible applications in the clinical field, are discussed.

hemodynamics lumped-parameter model modeling time-varying elastance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Elzinga and N. Westerhof, Pressure and flow generated by the left ventricle against different impedances. Circ. Res. 32 (1973) 178–186.Google Scholar
  2. 2.
    H. Suga, K. Sagawa and A. A. Shoukas, Load independence of the instantaneous pressure-volume ratio of the canine left ventricle and effects of epinephrine and heart rate on the ratio. Circ. Res. 32 (1973) 314–322.Google Scholar
  3. 3.
    H. Suga and K. Sagawa, Instantaneous pressure-volume relationships and their ratio in the excised, supported canine left ventricle. Circ. Res. 35 (1974) 117–126.Google Scholar
  4. 4.
    H. Senzaki, C.-H. Chen and D. A. Kass, Single-beat estimation of end-systolic pressure-volume relation in humans. A new method with the potential for noninvasive application. Circulation 94 (1996) 2497–2506.Google Scholar
  5. 5.
    N. Westerhof and N. Stergiopulos, Models of the arterial tree. Stud. Health Technol. Inform. 71 (2000) 65–77.Google Scholar
  6. 6.
    O. Frank, Die Grundform des arteriellen Pulses. Erste Abhandlung. Mathematische Analyse. Zeitschr. Biol. 37 (1899) 483–526.Google Scholar
  7. 7.
    P. Segers and P. Verdonck, Principles of vascular physiology. In: P. Lanzer and E. Topol (eds.), PanVascular Medicine. Integrated Clinical Management Springer (2002) pp. 116–137.Google Scholar
  8. 8.
    S. Toy, J. Melbin and A. Noordergraaf, Reduced models of arterial systems. IEEE Trans Biomed. Eng. 32 (1985) 174–176.Google Scholar
  9. 9.
    N. Westerhof, G. Elzinga and P. Sipkema, An artificial arterial system for pumping hearts. J. Appl. Physiol. 31 (1971) 776–781.Google Scholar
  10. 10.
    N. Stergiopulos, J. Meister and N. Westerhof, Evaluation of methods for estimation of total arterial compliance. Am. J. Physiol. 268 (1995) H1540-H1548.Google Scholar
  11. 11.
    N. Westerhof (1968). Analog Studies of Human Systemic Arterial Hemodynamics. PhD thesis. University of Pennsylvania. Dept. Biomed. Engng. (1968) 242 pp.Google Scholar
  12. 12.
    N. Stergiopulos, B. Westerhof and N. Westerhof, Total arterial inertance as the fourth element of the windkessel model. Am. J. Physiol. 276 (1999) H81-H88.Google Scholar
  13. 13.
    P. Segers, V. Tchana-Sato, H. Leather, B. Lambermont, A. Ghuysen, J.-M. Dogne, P. Benoit, P. Morimont, P. Wouters, P. Verdonck and P. Kolh, Determinants of left ventricular preload-adjusted maximal power. Am. J. Physiol. 284 (2003) 2295–2301.Google Scholar
  14. 14.
    P. Segers, H. A. Leather, P. Verdonck, Y.-Y. Sun and P. Wouters, Preload adjusted maximal power for the right ventricle: contribution of end-systolic P-V relation intercept. Am. J. Physiol. 283 (2002) H1681-H1687.Google Scholar
  15. 15.
    P. Segers, N. Stergiopulos, J. Schreuder, B. Westerhof and N. Westerhof, Systolic and diastolic wall stress normalize in the chronic pressure overloaded heart. A mathematical model study. Am. J. Physiol. 279 (2000) H1120-H1127.Google Scholar
  16. 16.
    P. Segers, P. Steendijk, N. Stergiopulos and N. Westerhof, Predicting systolic and diastolic aortic pressure and stroke volume in the intact sheep. J. Biomech. 34 (2001) 41–50.Google Scholar
  17. 17.
    L. Dell'Italia and R. Walsh, Application of a time varying elastance model to right ventricular performance in man. Cardiovasc. Res. 22 (1988) 864–874.Google Scholar
  18. 18.
    W. Maughan, A. Shoukas, K. Sagawa and M. Weisfeldt, Instantaneous pressure-volume relationship of the canine right ventricle. Circ. Res. 44 (1979) 309–315.Google Scholar
  19. 19.
    N. Stergiopulos, J. J. Meister and N. Westerhof, Determinants of stroke volume and systolic and diastolic pressure. Am. J. Physiol. 270 (1996) H2050-H2059.Google Scholar
  20. 20.
    R. Kelly, C. Ting, T. Yang, C. Liu, W. Lowell, M. Chang and D. Kass, Effective arterial elastance as index of arterial vascular load in humans. Circulation 86 (1992) 513–521.Google Scholar
  21. 21.
    P. Segers, N. Stergiopulos and N. Westerhof, Relation of effective arterial elastance to arterial system properties. Am. J. Physiol. 282 (2002) H1041-H1046.Google Scholar
  22. 22.
    P. Segers, P. Morimont, P. Kolh, N. Stergiopulos, N. Westerhof and P. Verdonck, Arterial elastance and heart-arterial coupling in aortic regurgitation are determined by aortic leak severity. Am. Heart J. 144 (2002) 568–576.Google Scholar
  23. 23.
    S. Vandenberghe, P. Segers, B. Meyns and P. Verdonck, Effect of rotary blood pump failure on left ventricular energetics assessed by mathematical modeling. Artif Organs 26 (2002) 1032–1039.Google Scholar
  24. 24.
    P. Segers, N. Stergiopulos and N. Westerhof, Quantifying the contribution of cardiac and arterial remodeling to hypertension. Hypertension 36 (2000) 760–765.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Patrick Segers
    • 1
  • Nikos Stergiopulos
    • 2
  • Nico Westerhof
    • 3
  • Patrick Wouters
    • 4
  • Philippe Kolh
    • 5
  • Pascal Verdonck
    • 1
  1. 1.Hydraulics Laboratory, Institute of Biomedical TechnologyRUG Ghent UniversityGentBelgium
  2. 2.Laboratory of Hemodynamics and Cardiovascular TechnologyEPFLLausanneSwitzerland
  3. 3.Laboratory for Physiology, Institute for Cardiovascular ResearchVU University Medical CenterAmsterdamThe Netherlands
  4. 4.Centre for Experimental Surgery and Anaesthesiology, KULeuvenBelgium
  5. 5.Hemodynamic Research CenterUniversity of LiegeBelgium

Personalised recommendations