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A note on the solution of the one-dimensional unsteady equations of arterial blood flow by the method of characteristics

Published online by Cambridge University Press:  17 February 2009

L. K. Forbes
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, South Australia 5000
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Abstract

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The “Hartree hybrid method” has recently been employed in one-dimensional non-linear aortic blood-flow models, and the results obtained appear to indicate that shock-waves could only form in distances which exceed physiologically meaningful values. However, when the same method is applied with greater numerical accuracy to these models, the existence of a shock-wave in the vicinity of the heart is predicted. This appears to be contrary to present belief.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Anliker, M., Rockwell, R. L. and Ogden, E., “Nonlinear analysis of flow pulses and shock waves in arteries”, Z. angew. Math. Phys. 22 (1971), 217 and 563.CrossRefGoogle Scholar
[2]Jones, E., “A mathematical model for nonlinear analysis of flow pulses utilizing an integral technique”, Z. angew. Math. Phys. 24 (1973), 565.CrossRefGoogle Scholar
[3]Lambert, J. W., “On the nonlinearities of fluid flow in nonrigid tubes”, J. Franklin Inst. 266 (1958), 83.CrossRefGoogle Scholar
[4]Lister, M., “The numerical solution of hyperbolic differential equations by the method of characteristics”, in Mathematics for digital computers (New York: Wiley, 1960).Google Scholar
[5]Rumberger, J. A. and Nerem, R. M., “A method-of-characteristics calculation of coronary blood flow”, J. Fluid Mech. 82 (1977), 429.CrossRefGoogle Scholar
[6]Streeter, V. L., Keitzer, W. F. and Bohr, D. F., “Pulsatile pressure and flow through distensible vessels”, Circulation Res. 13 (1963), 3.CrossRefGoogle ScholarPubMed
[7]Streeter, V. L., Keitzer, W. F. and Bohr, D. F., “Energy dissipation in pulsatile flow through distensible tapered vessels”, in Pulsatile blood flows (ed. Attinger, E. O.) (New York: McGraw-Hill, 1964).Google Scholar