Cardiovascular Engineering

, Volume 7, Issue 1, pp 1–6 | Cite as

Application of the Method of Characteristics for the Study of Shock Waves in Models of Blood Flow in the Aorta

Original Paper


Numerical algorithms are presented for the numerical solution of the one-dimensional model of blood flow in the aorta. The pertinent hyperbolic equations are written using Riemann invariants, which are integrated along the characteristics using two efficient algorithms. Because of the hyperbolic nature of the equations shock waves are to be expected, and their occurrence is discussed.


  1. Anliker M, Rockweel RL, Ogden E. Nonlinear analysis of flow pulses and shock waves in arteries, Part I. Zeit Angew Math Phys 1971;22:217–46; Part II. Zeit Angew Math Phys 1971;22:563–81Google Scholar
  2. Jones CJH, Parher KH, Hughes R, Sheridan DJ. Nonlinearity of the human arterial pulse wave transmission. J Biomech Eng 1992;114:10–4PubMedGoogle Scholar
  3. Lanoye LL, Vierendeels JA, Segers P, Verdonck PR. Wave intensity analysis of ventricular filling. J Biomech Eng 2005;127:862–7CrossRefGoogle Scholar
  4. MacRae JM, Sun Y-H, Isaac DL, Dobson GM, Cheng C-P, Little WC, Parker KH, Tyberg KH. Wave-intensity analysis: a new approach to left ventricular filling dynamics. Heart Vessels 1997;12:53–9PubMedGoogle Scholar
  5. Niederer PF. Damping mechanisms and shock-like transitions in the human arterial tree. Zeit Angew Math Phys 1985;36:205–18Google Scholar
  6. Parker KH, Jones CJH. Forward and backward running waves in the arteries: analysis using the method of characteristics. J Biomech Eng 1990;112:322–6PubMedGoogle Scholar
  7. Pohn E, Shoucri MM, Kamelander G. The eulerian Vlasov codes. Comp Phys Comm 2005;166:81–93CrossRefGoogle Scholar
  8. Rudinger G. Shock waves in mathematical models of the aorta. J Appl Mech 1970;37:34–7CrossRefGoogle Scholar
  9. Shoucri MM. Numerical calculations of discontinuities by shape preserving splines. J Comp Phys 1983;49:334–8CrossRefGoogle Scholar
  10. Shoucri MM, Gagné R. Splitting schemes for the the numerical solution of a two-dimensional Vlasov equation. J Comp Phys 1978;27:315–22CrossRefGoogle Scholar
  11. Toro EF. Riemann solvers and numerical methods for fluid dynamics. 2nd ed. Berlin: Springer; 1999Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Royal Military College of CanadaKingstonCanada
  2. 2.Institut de Recherche d’Hydro-Québec (IREQ)VarennesCanada

Personalised recommendations