Skip to main content
SpringerLink
Log in

Theoretical model for assessing haemodynamics in arterial networks which include bypass grafts

  • Biomechanics
  • Published:
Medical and Biological Engineering and Computing Aims and scope Submit manuscript

Abstract

The paper presents a theoretical model which can be used to simulate a vascular network which includes loops and bypass grafts, a feature not possible with previous models. Using the linearised Navier-Stokes equations, the linearised equation of a uniform thick-walled viscoelastic tube, and the equation of continuity, the model is applied to a vascular network which includes a bypass graft. This method represents each segment of an artery or graft by a four-terminal-network whose A, B, C, D parameters are functions of the frequency and physical characteristics of the segment. The model predicts the flow and pressure waveforms at any point in the human arterial network very accurately when compared with data obtained from normal patients, patients with arterial stenoses and for hypertensive patients. The model also gives results which are in close agreement with hydraulic experimental data for the input impedance of systems with bypass loops.

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

  • Aatre, V. K. (1986)Network theory and filter design. John Wiley & Sons Inc., New York.

    Google Scholar 

  • Avolio, A. P. (1980) Multi-branched model of the human arterial system.Med. & Biol. Eng. & Comput.,18, 709–718.

    Article  Google Scholar 

  • Billet, A., Queral, L., Polito, W. andDagher, F. (1984) The vascular steal phenomenon: an experimental model.Surg.,96, 923–927.

    Google Scholar 

  • Cox, R. H. (1969) Comparison of linearized wave propagation models for arterial blood flow analysis.J. Biomech.,2, 251–265.

    Article  Google Scholar 

  • Gabe, I. T., Karnell, J., Porje, I. G. andRudewald, B. (1964) The measurement of input impedance and apparent phase velocity in the human aorta.Acta. Physiol. Scand.,61, 73–84.

    Google Scholar 

  • How, T. V. andCampbell, H. (1985) Arterial steal phenomenon in femoro-tibial bypass with arterio-venous shunt.J. Biomech.,18, 463–465.

    Article  Google Scholar 

  • Hyman, W. A. andBrewer, M. A. (1980) The hemodynamics of arterial steal.,13, 469–675.

    Google Scholar 

  • Jager, G. N. (1965) Electrical model of the human systemic arterial tree. Ph. D. Thesis. Univ. of Utrecht.

  • Jager, G. N., Westerhof, N. andNoordergraaf, A. (1965) Oscillatory flow impedance in electrical analog of arterial system.Circ. Res.,16, 121–133.

    Google Scholar 

  • Latham, R. D., Westerhof, N., Sipkema, P., Rubal, B. J., Reuderink, P. andMurgo, J. P. (1985) Regional wave travel and reflections along the human aorta: a study with six simultaneous micromanometric pressures.Circ.,72, 1257–1269.

    Google Scholar 

  • Li, J. K.-J. (1987)Arterial system dynamics. New York University Press, New York.

    Google Scholar 

  • Lightner, M. R. andDirector, S. W. (1982) Computer-aided design of electronic circuits. InElectronics engineers' handbook.Fink, D. G. andChristiansen, D. (Eds.), Sec.27, McGraw-Hill, New York.

    Google Scholar 

  • Luchsinger, P. C., Snell, R. E., Patel, D. J. andFry, D. L. (1964) Instantaneous pressure distribution along the human aorta.Circ. Res.,15, 503–510.

    Google Scholar 

  • McDonald, D. A. (1974)Blood flow in arteries. Arnold, London.

    Google Scholar 

  • McHale, P. A., Rembert, J. C. andGreenfield, J. C. (1980) Measurement and significance of aortic pressure-flow relationships in man. InBasic haemodynamics and its role in disease processes.Patel, D. J. andVaishnav, R. N. (Ed.), University Park Press, Baltimore, 363–406.

    Google Scholar 

  • Merillon, J. P., Fontenier, G. J., Lerallut, M. Y., Jaffrin, M. Y., Motte, G. A., Genain, C. P., Gourgon, R. R. (1982) Aortic input impedance in normal man and arterial hypertension: its modification during change in aortic pressure.Cardiovasc. Res.,16, 646–656.

    Google Scholar 

  • Mills, C. J., Gabe, I. T., Gault, J. H., Mason, D. T., Ross, J., Braunwald, E. andShillingford, J. P. (1970) Pressure-flow relationships and vascular impedance in man.,4, 405–417.

    Google Scholar 

  • Milnor, W. R. (1982)Hemodynamics. Williams & Wilkins, Baltimore.

    Google Scholar 

  • Nichols, W. W., Conti, C. R., Walker, W. E. andMilnor, W. R. (1977) Input impedance of the systematic circulation in man.Circ. Res.,40, 451–458.

    Google Scholar 

  • Noordergraff, A. (1969) Hemodynamics. InBiological engineering.Schwan, H. P. (Ed.), McGraw-Hill, New York, 391–545.

    Google Scholar 

  • Noordergraff, A. (1978)Circulatory system dynamics. Academic Press, New York.

    Google Scholar 

  • O'Rourke, M. F., Blazek, J. V., Morreels C. L. Jr. andKrovetz, L. G. (1968) Pressure wave transmission along the human aorta.Circ. Res.,23, 567–579.

    Google Scholar 

  • O'Rourke, M. F. (1970) Arterial hemodynamics in hypertension., Suppl. II,16 and17, 123–133.

    Google Scholar 

  • O'Rourke, M. F. (1976) Pulsatile arterial hemodynamics in hypertension.Austr. N. Z. J. Med., Suppl.II,6, 40–48.

    Google Scholar 

  • Patel, D. J., Greenfield, J. C., Austen, W. G., Morrow, A. G. andFry, D. L. (1965) Pressure-flow relationships in the ascending aorta and femoral artery of man.J. Appl. Physiol.,20, 459–463.

    Google Scholar 

  • Rittgers, S. E., Karayannacos, P. E., Guy, J. F., Nerem, R. M., Shaw, G. M., Hostetler, J. R. andVasko, J. S. (1978) Velocity distribution and intimal proliferation in autologous vein grafts in dogs.Circ. Res.,42, 792–801.

    Google Scholar 

  • Roller, M. L. andClark, M. E. (1969) Precursor cerebral circulation models.J. Biomech.,2, 241–250.

    Article  Google Scholar 

  • Sunagawa, K., Maughan, W. L. andSagawa, K. (1985) Stroke volume effect of changing arterial input impedance over selected frequency ranges.Am. J. Physiol.,17, H477-H484.

    Google Scholar 

  • Taylor, M. G. (1966a) The input impedance of an assembly of randomly branching elastic tubes.Biophys. J.,6, 29–51.

    Google Scholar 

  • Taylor, M. G. (1966b) Wave transmission through an assembly of randomly branching elastic tubes.,6, 697–716.

    Article  Google Scholar 

  • Ting, C. T., Brin, K. P., Lin, S. J., Wang, S. P., Chang, M. S., Chiang, B. N. andYin, F. C. P. (1985) Arterial hemodynamics in human hypertension.J. Clin. Invest.,78, 1462–1471.

    Article  Google Scholar 

  • Tukmachi, E. S. A. andTaylor, D. E. M. (1985) Method of assessing the contribution of components of an anastomosing vascular network to total vascular impedance.J. Biomed. Eng.,7, 105–112.

    Google Scholar 

  • Westerhof, N., Elzinga, G. andVan den Bos, G. C. (1973) Influence of central and peripheral changes on the hydraulic input impedance of the systemic arterial tree.Med. & Biol. Eng.,11, 710–723.

    Google Scholar 

  • Westerhof, N., Murgo, J. P., Sipkema, P., Giolma, J. P. andElzinga, G. (1979) Arterial impedance. InQuantitative cardiovascular studies.Hwang, N. H. C., Gross, D. R. andPatel, D. J. (Eds.), University Park Press, Balitmore, 111.

    Google Scholar 

  • Wiener, F., Morkin, E., Skalak, R. andFishman, A. P. (1966) Wave propagation in the pulmonary circulation.Circ. Res.,19, 834–850.

    Google Scholar 

  • Womersley, J. R. (1957a) The mathematical analysis of the arterial circulation in a state of oscillatory motion. Wright Air Development Center, Technical Report WADC-TR56-614.

  • Womersley, J. R. (1957b) Oscillatory flow in arteries: the constrained elastic tube as a model of arterial flow and pulse transmission.Phys. Med. Biol.,2, 178–187.

    Article  Google Scholar 

  • Wylie, B. E. andStreeter, V. (1977)Fluid transients. McGraw-Hill, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Technical University of Nova Scotia, PO Box 1000, B3J 2X4, Halifax, Nova Scotia, Canada

    M. A. Helai & K. C. Watts

  2. Department of Electrical Engineering, Technical University of Nova Scotia, PO Box 1000, B3J 2X4, Halifax, Nova Scotia, Canada

    A. E. Marble

  3. Department of Applied Mathematics, Technical University of Nova Scotia, PO Box 1000, B3J 2X4, Halifax, Nova Scotia, Canada

    S. N. Sarwal

Authors
  1. M. A. Helai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. C. Watts
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. E. Marble
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. N. Sarwal
    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

Helai, M.A., Watts, K.C., Marble, A.E. et al. Theoretical model for assessing haemodynamics in arterial networks which include bypass grafts. Med. Biol. Eng. Comput. 28, 465–473 (1990). https://doi.org/10.1007/BF02441970

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02441970

Keywords

Search

Navigation