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Modeling Approaches for the Macrocirculation

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Dimension Reduced Modeling of Blood Flow in Large Arteries

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Abstract

As we noted in the previous chapter, the human vascular system consists of a huge number of vessels with different diameters, lengths and wall thicknesses. In both the venous and arterial vessel trees, subnetworks with different length scales can be identified. There are essentially three different types of length scales: Macrocirculation, mesoscale and microcirculation [1, Chap. 1].

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References

  1. Ambrosi D, Quarteroni A, Rozza G (eds) (2012) Modeling of physiological flows, vol 5. Springer Science & Business Media

    Google Scholar 

  2. Blanco P, Feijóo R et al (2010) A 3D-1D-0D Computational model for the entire cardiovascular system. In: Dvorking E, Goldschmit M, Storti M (eds) Computational Mechanics, vol 29, pp 5887–5911

    Google Scholar 

  3. Blanco P, Feijóo R (2013) A dimensionally-heterogeneous closed-loop model for the cardiovascular system and its applications. Med Eng Phys 35(5):652–667. Elsevier

    Google Scholar 

  4. Blanco P, Feijóo R, Urquiza S (2007) A unified variational approach for coupling 3D–1D models and its blood flow applications. Comput Methods Appl Mech Eng 196(41–44):4391–4410. Elsevier

    Google Scholar 

  5. Deuflhard P, Weiser M (2012) Adaptive numerical solution of PDEs. de Gruyter, Adaptive Numerical Solution of PDEs

    Book  MATH  Google Scholar 

  6. Stergiopulos N, Young D, Rogge T (1992) Computer simulation of arterial flow with applications to arterial and aortic stenoses. J Biomech 25(12):1477–1488. Elsevier

    Google Scholar 

  7. Reichold J, Stampanoni M, Keller A, Buck A, Jenny P, Weber B (2009) Vascular graph model to simulate the cerebral blood flow in realistic vascular networks. J Cereb Blood Flow Metab 29(8):1429–1443. SAGE Publications Sage, London, England

    Google Scholar 

  8. Formaggia L, Quarteroni A, Veneziani A (eds) (2010) Cardiovascular mathematics: modeling and simulation of the circulatory system, vol 1. Springer Science & Business Media

    Google Scholar 

  9. Wick T (2011) Adaptive finite element simulation of fluid-structure interaction with application to heart-valve dynamics

    Google Scholar 

  10. Quarteroni A, Manzoni A, Vergara C (2017) The cardiovascular system: mathematical modelling, numerical algorithms and clinical applications. Acta Numerica 26:365–590. Cambridge University Press

    Google Scholar 

  11. D’Apice C, D’Arienzo M, Kogut P, Manzo R (2018) On boundary optimal control problem for an arterial system: Existence of feasible solutions. J Evol Eqn 1–42. Springer

    Google Scholar 

  12. Marsden A (2014) Optimization in cardiovascular modeling. Ann Rev Fluid Mech 46:519–546. Annual Reviews

    Google Scholar 

  13. Lantz J, Renner J, Karlsson M (2011) Wall shear stress in a subject specific human aorta–influence of fluid-structure interaction. Int J Appl Mech 3(04):759–778. World Scientific

    Google Scholar 

  14. Malossi A, Blanco P, Crosetto P, Deparis S, Quarteroni A (2013) Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels. Multiscale Model Simul 11(2):474–506. SIAM

    Google Scholar 

  15. Marsden A, Esmaily-Moghadam M (2015) Multiscale modeling of cardiovascular flows for clinical decision support. Appl Mech Rev 67(3):030804. American Society of Mechanical Engineers

    Google Scholar 

  16. Passerini T, De Luca M, Formaggia L, Quarteroni A, Veneziani A (2009) A 3D/1D geometrical multiscale model of cerebral vasculature. J Eng Math 64(4):319. Springer

    Google Scholar 

  17. Urquiza S, Blanco P, Vénere M, Feijóo R (2006) Multidimensional modelling for the carotid artery blood flow. Comput Methods Appl Mech Eng 195(33–36):4002–4017. Elsevier

    Google Scholar 

  18. Čanić S, Kim E (2003) Mathematical analysis of the quasilinear effects in a hyperbolic model blood flow through compliant axi-symmetric vessels. Math Methods Appl Sci 26(14):1161–1186. Wiley Online Library

    Google Scholar 

  19. Payne S (2004) Analysis of the effects of gravity and wall thickness in a model of blood flow through axisymmetric vessels. Med Biol Eng Comput 42(6):799–806. Springer

    Google Scholar 

  20. Alastruey J, Parker K, Peiró J, Sherwin S (2008) Lumped parameter outflow models for 1-D blood flow simulations: Effect on pulse waves and parameter estimation. Commun Comput Phys 4(2):317–336

    MathSciNet  MATH  Google Scholar 

  21. Canuto D, Chong K, Bowles C, Dutson E, Eldredge J, Benharash P (2018) A regulated multiscale closed-loop cardiovascular model, with applications to hemorrhage and hypertension. Int J Numer Methods Biomed Eng e2975. Wiley Online Library

    Google Scholar 

  22. Shi Y, Lawford P, Hose R (2011) Review of zero-D and 1-D models of blood flow in the cardiovascular system. Biomed Eng 10(1):33. BioMed Central

    Google Scholar 

  23. Liang F, Oshima M, Huang H, Liu H, Takagi S (2015) Numerical study of cerebroarterial hemodynamic changes following carotid artery operation: A comparison between multiscale modeling and stand-alone three-dimensional modeling. J Biomech Eng 137(10):101011. American Society of Mechanical Engineers

    Google Scholar 

  24. Mynard J, Smolich J (2015) One-dimensional haemodynamic modeling and wave dynamics in the entire adult circulation. Ann Biomed Eng 43(6):1443–146. Springer

    Google Scholar 

  25. Acosta S, Puelz C, Rivière B, Penny D, Brady K, Rusin C (2017) Cardiovascular mechanics in the early stages of pulmonary hypertension: A computational study. Biomech Model Mechanobiol 16(6):2093–2112. Springer

    Google Scholar 

  26. Liang F, Liu H (2005) A closed-loop lumped parameter computational model for human cardiovascular system. JSME Int J Ser C Mech Syst Mach Elem Manufac 48(4):484–493. The Japan Society of Mechanical Engineers

    Google Scholar 

  27. Liang F, Liu H (2006) Simulation of hemodynamic responses to the Valsalva maneuver: An integrative computational model of the cardiovascular system and the autonomic nervous system. J Physiol Sci 56(1):45–65. Physiological Society of Japan

    Google Scholar 

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Correspondence to Tobias Köppl .

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Köppl, T., Helmig, R. (2023). Modeling Approaches for the Macrocirculation. In: Dimension Reduced Modeling of Blood Flow in Large Arteries. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-33087-2_2

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  • DOI: https://doi.org/10.1007/978-3-031-33087-2_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-33086-5

  • Online ISBN: 978-3-031-33087-2

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