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All issues Volume 56 / No 5 (September-October 2022) ESAIM: M2AN, 56 5 (2022) 1579-1627 References
Open Access
Issue
ESAIM: M2AN
Volume 56, Number 5, September-October 2022
Page(s) 1579 - 1627
DOI https://doi.org/10.1051/m2an/2022052
Published online 20 July 2022
  1. J. Alastruey, K.H. Parker, J. Peiró and S.J. Sherwin, Lumped parameter outflow models for 1-D blood flow simulations: effect on pulse waves and parameter estimation. Commun. Comput. Phys. 4 (2008) 317–336. [MathSciNet] [Google Scholar]
  2. D.S. Berger and J.K.J. Li, Temporal relationship between left ventricular and arterial system elastances. IEEE Trans. Biomed. Eng. 39 (1992) 404–410. [CrossRef] [Google Scholar]
  3. J. Blacher and M.E. Safar, Large-artery stiffness, hypertension and cardiovascular risk in older patients. Nat. Clinical Pract. Cardiovasc. Med. 2 (2005) 450–455. [CrossRef] [PubMed] [Google Scholar]
  4. P.J. Blanco, S.M. Watanabe, E. Dari, M.A.R. Passos and R.A. Feijóo, Blood flow distribution in an anatomically detailed arterial network model: criteria and algorithms. Biomech. Model. Mechanobiol. 13 (2014) 1303–1330. [CrossRef] [PubMed] [Google Scholar]
  5. P.J. Blanco, S. Watanabe, M. Passos, P. Lemos and R.A. Feijóo, An anatomically detailed arterial network model for one-dimensional computational hemodynamics. IEEE Trans. Biomed. Eng. 62 (2015) 736–53. [CrossRef] [PubMed] [Google Scholar]
  6. E. Boileau, P. Nithiarasu, P.J. Blanco, L.O. Müller, F.E. Fossan, L.R. Hellevik, W.P. Donders, W. Huberts, M. Willemet and J. Alastruey, A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling. Int. J. Numer. Methods Biomed. Eng. 31 (2015). [Google Scholar]
  7. A. Cappello, G. Gnudi and C. Lamberti, Identification of the three-element windkessel model incorporating a pressure-dependent compliance. Ann. Biomed. Eng. 23 (2006) 164–177. [Google Scholar]
  8. K. Cruickshank, L. Riste, S.G. Anderson, J.S. Wright, G. Dunn and R.G. Gosling, Aortic pulse-wave velocity and its relationship to mortality in diabetes and glucose intolerance. Circulation 106 (2002) 2085–2090. [CrossRef] [PubMed] [Google Scholar]
  9. S. Epstein, M. Willemet, P.J. Chowienczyk and J. Alastruey, Reducing the number of parameters in 1D arterial blood flow modeling: less is more for patient-specific simulations. Am. J. Physiol. Heart Circulatory Physiol. 309 (2015) H222–H234. [CrossRef] [PubMed] [Google Scholar]
  10. R. Fogliardi, M. Di Donfrancesco and R. Burattini, Comparison of linear and nonlinear formulations of the three-element windkessel model. Am. J. Physiol. Heart Circulatory Physiol. 271 (1996) H2661–H2668. [CrossRef] [Google Scholar]
  11. L. Formaggia and A. Veneziani, Reduced and multiscale models for the human cardiovascular system. Technical report, Politecnico di Milano (October, 2015. [Google Scholar]
  12. L. Formaggia, A. Quarteroni and A. Veneziani, editors. Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System. MS&A: Modeling, Simulation & Applications. Vol. 1. Springer, Milano (2009). [Google Scholar]
  13. F.E. Fossan, J. Mariscal-Harana, J. Alastruey and L.R. Hellevik, Optimization of topological complexity for one-dimensional arterial blood flow models. J. R. Soc. Interface 15 (2018) 20180546. [CrossRef] [PubMed] [Google Scholar]
  14. S. Fujimoto, R. Mizuno, Y. Saito and S. Nakamura, Clinical application of wave intensity for the treatment of essential hypertension. Heart Vessels 19 (2004) 19–22. [CrossRef] [PubMed] [Google Scholar]
  15. Y.C. Fung, Biomechanics: Mechanical Properties of Living Tissues, 2nd edition. Springer (1993). [Google Scholar]
  16. A. Ghigo, Reduced-Order Models for Blood Flow in Networks of Large Arteries. Ph.D thesis, Université Pierre et Marie Curie, Paris (September 2017). [Google Scholar]
  17. J.K. Hale, Ordinary Differential Equations. John Wiley & Sons, Inc. (1969). [Google Scholar]
  18. A. Harten and S. Osher, Uniformly High-order accurate nonoscillatory schemes. I. SIAM J. Numer. Anal. 24 (1987) 279–309. [CrossRef] [MathSciNet] [Google Scholar]
  19. A. Harten, B. Engquist, S. Osher and S.R. Chakravarthy, Uniformly high order accuracy essentially non-oscillatory schemes, III. J. Comput. Phys. 71 (1987) 231–303. [CrossRef] [MathSciNet] [Google Scholar]
  20. P.J. Hunter, Numerical simulation of arterial blood flow. Master’s thesis, The University of Auckland, Auckland (1972). [Google Scholar]
  21. J.K.J. Li, T. Cui and G.M. Drzewiecki, A nonlinear model of the arterial system incorporating a pressure-dependent compliance. IEEE Trans. Biomed. Eng. 37 (1990) 673–678. [CrossRef] [Google Scholar]
  22. K.S. Matthys, J. Alastruey, J. Peiró, A.W. Khir, P. Segers, P.R. Verdonck, K.H. Parker and S.J. Sherwin, Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements. J. Biomech. 40 (2007) 3476–3486. [CrossRef] [Google Scholar]
  23. V. Milišić and A. Quarteroni, Analysis of lumped parameter models for blood flow simulations and their relation with 1D models. ESAIM: Math. Model. Numer. Anal. 38 (2004) 613–632. [CrossRef] [EDP Sciences] [Google Scholar]
  24. M. Mirramezani and S.C. Shadden, A distributed lumped parameter model of blood flow. Ann. Biomed. Eng. 48 (2020) 2870–2886. [CrossRef] [PubMed] [Google Scholar]
  25. L.O. Müller and E.F. Toro, A global multiscale mathematical model for the human circulation with emphasis on the venous system. Int. J. Numer. Methods Biomed. Eng. 30 (2014) 681–725. [CrossRef] [MathSciNet] [Google Scholar]
  26. L.O. Müller and E.F. Toro, Enhanced global mathematical model for studying cerebral venous blood flow. J. Biomech. 47 (2014) 3361–3372. [CrossRef] [Google Scholar]
  27. J.P. Murgo, N. Westerhof, J.P. Giolma and S.A. Altobelli, Aortic input impedance in normal man: relationship to pressure wave forms. Circulation 62 (1980) 105–116. [CrossRef] [PubMed] [Google Scholar]
  28. J.P. Mynard, Computer modelling and wave intensity analysis of perinatal cardiovascular function and dysfunction, Ph.D. thesis, Department of Paediatrics, The University of Melbourne (August, 2011). [Google Scholar]
  29. J.P. Mynard and J.J. Smolich, One-dimensional haemodynamic modeling and wave dynamics in the entire adult circulation. Ann. Biomed. Eng. 43 (2015) 1443–1460. [CrossRef] [PubMed] [Google Scholar]
  30. S. Safaei, P.J. Blanco, L.O. Müller, F.E. Fossan, L.R. Hellevik and P.J. Hunter, Bond graph model of cerebral circulation: toward clinically feasible systemic blood flow simulations. Front. Physiol. 9 (2018) 148. [CrossRef] [Google Scholar]
  31. K. Sagawa, R.K. Lie and J. Schaefer, Translation of Otto Frank’s paper “Die Grundform des Arteriellen Pulses” Zeitschrift für Biologie 37: 483–526 (1899). J. Mol. Cell. Cardiol. 22 (1990) 253–254. [CrossRef] [Google Scholar]
  32. M. Saito, Y. Ikenaga, M. Matsukawa, Y. Watanabe, T. Asada and P.-Y. Lagrée, One-dimensional model for propagation of a pressure wave in a model of the human arterial network: comparison of theoretical and experimental results. J. Biomech. Eng. 133 (2011) 121005. [CrossRef] [PubMed] [Google Scholar]
  33. D.A. Sánchez, Ordinary Differential Equations and Stability Theory. Dover Publications, Inc. (1968). [Google Scholar]
  34. S.J. Sherwin, V. Franke, J. Peiró and K.H. Parker, One-dimensional modelling of a vascular network in space-time variables. J. Eng. Math. 47 (2003) 217–250. [CrossRef] [Google Scholar]
  35. Y. Shi, P. Lawford and R. Hose, Review of zero-D and 1-D models of blood flow in the cardiovascular system. BioMed. Eng. OnLine 10 (2011) 33. [CrossRef] [Google Scholar]
  36. A. Spilimbergo, E.F. Toro and L.O. Müller, One-dimensional blood flow with discontinuous properties and transport: mathematical analysis and numerical schemes. Commun. Comput. Phys. 29 (2021) 649–697. [CrossRef] [MathSciNet] [Google Scholar]
  37. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, 3rd edition. Springer-Verlag, Berlin Heidelberg (2009). [Google Scholar]
  38. E.F. Toro, Brain venous haemodynamics, neurological diseases and mathematical modelling: a review. Appl. Math. Comput. 272 (2016) 542–579. [MathSciNet] [Google Scholar]
  39. E.F. Toro, R.C. Millington and L.A.M. Nejad, Towards very high-order godunov schemes. In: Godunov Methods: Theory and Applications, Edited Review, edited by E.F. Toro. Kluwer Academic/Plenum Publishers (2001) 905–937. [Google Scholar]
  40. M. Ursino, A mathematical model of the carotid baroregulation in pulsating conditions. IEEE Trans. Biomed. Eng. 46 (1999) 382–392. [CrossRef] [Google Scholar]
  41. M. Ursino and C.A. Lodi, A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics. J. Appl. Physiol. 82 (1997) 1256–1269. [CrossRef] [PubMed] [Google Scholar]
  42. M. Ursino, A. Fiorenzi and E. Belardinelli, The role of pressure pulsatility in the carotid baroreflex control: a computer simulation study. Comput. Biol. Med. 26 (1996) 297–314. [CrossRef] [Google Scholar]
  43. B. van Leer, On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe. SIAM J. Sci. Stat. Comput. 5 (1985) 1–20. [Google Scholar]
  44. N. Xiao, J. Alastruey and C.A. Figueroa, A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models. Int. J. Numer. Methods Biomed. Eng. 30 (2014) 204–231. [CrossRef] [MathSciNet] [Google Scholar]

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