Left-ventricular pressure gradients: a computer-model simulation

  • P. Verdonck
  • J. Vierendeels
  • K. Riemslagh
  • E. Dick


Both invasive left-ventricular pressure measurements and non-invasive colour M-mode echographic measurements have shown the existence of intraventricular pressure gradients (IVPGs) during early filling. The mechanisms responsible for these IVPG cannot be completely explained by the experiments. Therefore a one-dimensional numerical model is developed and validated. The model describes filling (both velocities and pressures) along a left ventricular (LV) base-apex axis. Blood-wall interaction in the left ventricle with moving boundaries is taken into account. The computational results for a canine heart indicate that the observed IVPGs during filling are the consequence of a complex interaction between, on the one hand, pressure waves travelling in the LV and, on the other hand, LV geometry, relaxation and compliance. The computational results indicate the pressure dependency of wavespeed (0.77–1.90 m−1 s) for different mean intraventricular pressures (0.88–5.00 mmHg) and IVPGs up to 2 mmHg, independent of the ratio of end systolic volume and equilibrium volume. Increasing relaxation rate not only decreases minimum basal pressure (2.8 instead of 3.6 mmHg) but also has a strong influence on the time delay between the minimum basal and apical pressures (14 ms instead of 49 ms). The results sustain the hypothesis that pressure-wave propagation determines IVPGs and that IVPGs are no proof of elastic recoil.


Intraventricular pressure gradients Elastic recoil Diastolic filling Computer model Blood-wall interaction 


  1. Bloom, W.L. (1955): ‘Diastolic filling of the beating excised heart’,Am. J. Physiol.,187, pp. 143–44Google Scholar
  2. Courtois, M., Kovacs, S.J., andLudbrook, P.A. (1988): ‘Transmitral pressure-flow velocity relation. Importance of regional pressure gradients in the left ventricle during diastole’,Circulation,78, pp. 661–671Google Scholar
  3. Davie, A., Francis, C., Carnana, L., Sutherland, andG., McMurray, J. (1977): ‘The prevalence of left ventricular diastolic filling abnormalities in patients with suspected heart failure’,Eur. Heart J.,18, (6), pp. 981–984Google Scholar
  4. Gilbert, J.C., andGlantz, S.A. (1989): ‘Determinants of left ventricular filling and the diastolic pressure-volume relation’,Circ. Res.,64, p. 827Google Scholar
  5. Greenberg, N.L., Vandervoort, P.M., andThomas, J.D. (1996): ‘Estimation of instantaneous transmitral pressure difference from color Doppler M-mode echocardiography’,Am. J. Physiol.,271, (Heart Circ. Physiol.) pp. H1267–1276Google Scholar
  6. Ling, D., Rankin, J.S., Edwards, C.H., McHale, P.A., andAnderson, R.W. (1979): ‘Regional diastolic mechanics of the left ventricle in the conscious dog’,Am. J. Physiol.,236, pp. 323–330Google Scholar
  7. Mirsky, I. (1973): ‘Ventricular and arterial wall stresses based on large deformation analysis’,Biophys. J.,13, pp. 1141–1159CrossRefMathSciNetGoogle Scholar
  8. Nikolic, S., Fenely, M., Pajaeo, O., Scott Rankin, J., andYellin, E. (1995): ‘Origin of regional pressure gradients in the left ventricle during early diastole’,Am. J. Physiol.,268, pp. 550–557Google Scholar
  9. Nishimura, R., Abel, M., Hatle, M., Tajik, A. (1990): ‘Relation of pulmonary vein to mitral flow velocities by transesophageal Doppler echocardiography. Effect of different loading conditions’,Circulation,81, p. 1488Google Scholar
  10. Owen, A. (1993): ‘A numerical model of early diastolic filling: importance of intraventricular pressure wave propagation’,Cardiovas. Res.,27, pp. 255–261CrossRefGoogle Scholar
  11. Pai, R., andBuech, G. (1996): ‘New Doppler measures of left ventricular dysfunction’,Clin. Cardiol.,19,(4), pp. 277–88CrossRefGoogle Scholar
  12. Pasipoularides, A., Murgo, J., Miller, J., andCraiga, W. (1987): ‘Nonobstructive left ventricular ejection pressure gradients in man’,Circ. Res.,61, (2), pp. 220–227Google Scholar
  13. Peskin, C., andMcQueen, D. (1989): ‘A three-dimensional computational method for blood flow in the heart. Immersed elastic fibers in a viscous incompressible fluid’,J. Comput. Phys.,81, pp 372–405MATHCrossRefMathSciNetGoogle Scholar
  14. Redaelli, A., andMontevecchi, F. (1996): ‘Computational evaluation of intraventricular pressure gradients based on a fluid-structure approach’,J. Biomed. Eng,118, (4), pp. 529–537Google Scholar
  15. Stugaard, M., Smiseth, O., Risae, C., andIhlen, H. (1995): ‘Intraventricular early diastolic velocity profile during acute myocardial ischemia: a color M-mode Doppler echocardiography study’,J. Am. Soc. Echocardiogr.,8,(3), pp. 270–279CrossRefGoogle Scholar
  16. Tyberg, J.V., Keon, W.J., Sonnenblick, E.H., andUrschel, C.W. (1970): ‘Mechanics of ventricular diastole’,Cardiovasc. Res.,4, pp. 423–28CrossRefGoogle Scholar
  17. Vierendeels, J., Verdonck, P., andDick, E. (1997): ‘Assessment of intraventricular pressure gradients during diastole with a 1D moving fluid-structure interaction model’. Proc. ASME Summer Meeting, FEDSM97-3 428.Google Scholar
  18. Yellin, E.L., Hori, M., Yoran, C., Sonnenblick, E.H., Gabbay, S., andFrater, R.W.M. (1986): ‘Left ventricular relaxation in the filling and nonfilling intact canine heart’,Am. J. Physiol.,250, pp. H620-H629Google Scholar
  19. Yellin, E.L., Nikolic, S., andFrater, R.W. (1990): ‘Left ventricular filling dynamics and diastolic function’,Prog. Cardiovasc. Dis.,32, p. 242CrossRefGoogle Scholar

Copyright information

© IFMBE 1999

Authors and Affiliations

  • P. Verdonck
    • 1
  • J. Vierendeels
    • 1
  • K. Riemslagh
    • 1
  • E. Dick
    • 1
  1. 1.Institute of Biomedical TechnologyUniversity of GentGentBelgium

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