Free Access
Issue
ESAIM: M2AN
Volume 38, Number 4, July-August 2004
Page(s) 613 - 632
DOI https://doi.org/10.1051/m2an:2004036
Published online 15 August 2004
  1. A.P. Avolio, Multibranched model of the human arterial system. Med. Biol. Eng. Comput. 18 (1980) 709–119. [Google Scholar]
  2. B.S. Brook, S.A.E.G. Falle and T.J. Pedley, Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state. J. Fluid Mech. 396 (1999) 223–256. [CrossRef] [MathSciNet] [Google Scholar]
  3. S. Čanić and E.H. Kim, Mathematical analysis of quasilinear effects in a hyperbolic model of blood flow through compliant axi-symmetric vessels. Math. Meth. Appl. Sci. 26 (2003) 1161–1186. [Google Scholar]
  4. S. Čanić and A. Mikelić, Effective equations modeling the flow of a viscous incompressible fluid through a long elastic tube arising in the study of blood flow through small arteries. SIAM J. Appl. Dyn. Sys. 2 (2003) 431–463. [CrossRef] [Google Scholar]
  5. A. Čanić, D. Lamponi, S. Mikelić and J. Tambaca, Self-consistent effective equations modeling blood flow in medium-to-large compliant arteries. SIAM MMS (2004) (to appear). [Google Scholar]
  6. L. de Pater and J.W. van den Berg, An electrical analogue of the entire human circulatory system. Med. Electron. Biol. Engng. 2 (1964) 161–166. [CrossRef] [Google Scholar]
  7. C.A. Desoer and E.S. Kuh, Basic Circuit Theory. McGraw-Hill (1969). [Google Scholar]
  8. L. Formaggia, J.F. Gerbeau, F. Nobile and A. Quarteroni, On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Comput. Methods Appl. Mech. Engrg. 191 (2001) 561–582. [Google Scholar]
  9. L. Formaggia and A. Veneziani, Reduced and multiscale models for the human cardiovascular system. Technical report, PoliMI, Milan (June 2003). Collection of two lecture notes given at the VKI Lecture Series 2003–07, Brussels 2003. [Google Scholar]
  10. E. Godlewski and P.-A. Raviart, Hyperbolic systems of conservation laws. Math. Appl., 3/4. Ellipses, Paris (1991). [Google Scholar]
  11. W.P. Mason, Electromechanical Transducers and Wave Filters (1942). [Google Scholar]
  12. F. Migliavacca, G. Pennati, G. Dubini, R. Fumero, R. Pietrabissa, G. Urcelay, E.L. Bove, T.Y. Hsia and M.R. de Leval, Modeling of the norwood circulation: effects of shunt size, vascular resistances, and heart rate. Am. J. Physiol. Heart Circ. Physiol. 280 (2001) H2076–H2086. [PubMed] [Google Scholar]
  13. V. Milišić and A. Quarteroni, Coupling between linear parabolic and hyperbolic systems of equations for blood flow simulations, in preparation. [Google Scholar]
  14. A. Quarteroni, R. Sacco and F. Saleri, Numerical Mathematics, 37 Texts Appl. Math. Springer-Verlag, New York (2000). [Google Scholar]
  15. V.C. Rideout and D.E. Dick, Difference-differential equations for fluid flow in distensible tubes. IEEE Trans. Biomed. Eng. BME-14 (1967) 171–177. [Google Scholar]
  16. P. Segers, F. Dubois, D. De Wachter and P. Verdonck, Role and relevancy of a cardiovascular simulator. J. Cardiovasc. Eng. 3 (1998) 48–56. [Google Scholar]
  17. S.J. Sherwin, V. Franke, J. Peiro and K. Parker, One-dimensional modelling of a vascular network in space-time variables. J. Engng. Math. 47 (2003) 217–250. [Google Scholar]
  18. N.P. Smith, A.J. Pullan and P.J. Hunter, An anatomically based model of transient coronary blood flow in the heart. SIAM J. Appl. Math. 62 (2001/02) 990–1018 (electronic). [Google Scholar]
  19. J.A. Spaan, J.D. Breuls and N.P. Laird, Diastolic-systolic coronary flow differences are caused by intramyocardial pump action in the anesthetized dog. Circ. Res. 49 (1981) 584–593. [PubMed] [Google Scholar]
  20. N. Stergiopulos, D.F. Young and T.R. Rogge, Computer simulation of arterial flow with applications to arterial and aortic stenoses. J. Biomech. 25 (1992) 1477–1488. [CrossRef] [PubMed] [Google Scholar]
  21. J.C. Strikwerda, Finite difference schemes and partial differential equations. The Wadsworth & Brooks/Cole Mathematics Series. Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA (1989). [Google Scholar]
  22. N. Westerhof, F. Bosman, C.J. De Vries and A. Noordergraaf, Analog studies of the human systemic arterial tree. J. Biomechanics 2 (1969) 121–143. [Google Scholar]
  23. F. White, Viscous Fluid Flow. McGraw-Hill (1986). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you