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Computational Mechanics

, Volume 54, Issue 4, pp 1013–1022 | Cite as

A reduced-order model based on the coupled 1D-3D finite element simulations for an efficient analysis of hemodynamics problems

  • Eduardo Soudah
  • Riccardo Rossi
  • Sergio IdelsohnEmail author
  • Eugenio Oñate
Original Paper

Abstract

A reduced-order model for an efficient analysis of cardiovascular hemodynamics problems using multiscale approach is presented in this work. Starting from a patient-specific computational mesh obtained by medical imaging techniques, an analysis methodology based on a two-step automatic procedure is proposed. First a coupled 1D-3D Finite Element Simulation is performed and the results are used to adjust a reduced-order model of the 3D patient-specific area of interest. Then, this reduced-order model is coupled with the 1D model. In this way, three-dimensional effects are accounted for in the 1D model in a cost effective manner, allowing fast computation under different scenarios. The methodology proposed is validated using a patient-specific aortic coarctation model under rest and non-rest conditions.

Keywords

Blood flow Boundary conditions  Reduced-order models and Aortic coarctation 

Notes

Acknowledgments

This research was supported by the HFLUIDS project of the National RTD Plan of the Spanish Ministry of Science and Innovation I+D BIA2010-15880 and by the ERC Advanced Grant projects ”REALTIME”(AdG-2009325) and ”SAFECON”(AdG-267521). We also thank Dr.Pooyan Dadvand for his support on the implementation of the reduced-order model in KRATOS and Mr.Maurizio Bordone for his help during the fitting of the terminal resistances during training and computation phases.

References

  1. 1.
    Alastruey J, Khir AW, Matthys KS, Segers P, Sherwin SJ, Verdonck PR, Parker KH, Peiró J (2011) Pulse wave propagation in a model human arterial network: assessment of 1-D visco-elastic simulations against in vitro measurements. J Biomech 44(12):2250–2258Google Scholar
  2. 2.
    Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid-structure interaction: methods and applications. ISBN: 978-0-470-97877-1. p 404Google Scholar
  3. 3.
    CFD Challange: Patient-Specific Hemodynamics at Rest and Stress through an Aortic Coarctation. 2013. http://www.vascularmodel.org/miccai2013/
  4. 4.
    Cristiano A, Malossi I, Blanco PJ, 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):474–506CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Dadvand P, Rossi R, Oñate E (2010) An object-oriented environment for developing finite element codes for multi-disciplinary applications. Arch Comput Methods Eng 17:253–297CrossRefzbMATHGoogle Scholar
  6. 6.
    Dadvand P, Rossi R, Gil M, Martorell X, Cotela J, Juanpere E, Idelsohn SR, Oñate E (2013) Migration of a generic multi-physics framework to HPC environments. Comput Fluids 80(10):301–309CrossRefzbMATHGoogle Scholar
  7. 7.
    Formaggia L, Nobile F, Quarteroni A, Veneziani A (1999) Multiscale modelling of the circulatory system: a preliminary analysis. Comput Vis Sci 2:75–83CrossRefzbMATHGoogle Scholar
  8. 8.
    Formaggia L, Lamponi D, Quarteroni A (2003) One dimensional model for blood flow in arteries. J Eng Math 47:251–276CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Formaggia L, Gerbeau JF, Nobile F, Quarteroni A (2001) On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Comput Methods Appl Mech Eng 191:561–582Google Scholar
  10. 10.
    GiD (2011) The personal pre and postprocessor, http://www.gidhome.com CIMNE
  11. 11.
    Ismail M, Wall WA, Gee MG (2013) Adoint-based inverse analysis of windkessel parameters for patient-specific. Vasc Models J Comput Phys 244:113170MathSciNetGoogle Scholar
  12. 12.
    Itu L, Sharma P, Ralovich K, Mihalef V, Ionasec R, Everett A, Ringel R, Kamen A, Comaniciu D (2013) Non-invasive hemodynamic assessment of aortic coarctation: validation with in vivo measurements. Ann Biomed Eng 41:669–681CrossRefGoogle Scholar
  13. 13.
    LaDisa JJ et al (2011) Computational simulations for aortic coarctation: representative results from a sampling of patients. J Biomech Eng 133(9):091008–091017Google Scholar
  14. 14.
    LaDisa JJ, Dholakia RJ, Figueroa CA, Vignon-Clementel IE, Chan FP, Samyn MM, Cava JR, Taylor CA, Feinstein JA (2011) Computational simulations demonstrate altered wall shear stress in aortic coarctation patients treated by resection with end-to-end anastomosis. Congenit Heart Dis 6:432–443CrossRefGoogle Scholar
  15. 15.
    Lantz J, Ebbers T, Engvall J, Karlsson M (2013) Numerical and experimental assessment of turbulent kinetic energy in an aortic coarctation. J Biomech 46(11):1851–1858CrossRefGoogle Scholar
  16. 16.
    Lorensen WE, Cline HE (1987) Marching cubes: a high reso-lution 3d surface construction algorithm. In: Proceedings of SIGGRAPH, pp 163–169Google Scholar
  17. 17.
    Malossi A, Blanco PJ, Crosetto P, Deparis S, Quarteroni A (2013) Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels multiscale modeling. Simulation 11(2):474–506zbMATHMathSciNetGoogle Scholar
  18. 18.
    Manguoglu M, Takizawa K, Sameh AH, Tezduyar TE (2010) Solution of linear systems in arterial fluid mechanics computations with boundary layer mesh refinement. Comput Mech 46:83–89CrossRefzbMATHGoogle Scholar
  19. 19.
    Murray CD (1926) The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proc Natl Acad Sci USA 12(3):207–214CrossRefGoogle Scholar
  20. 20.
    Perdikaris P, Karniadakis GE (2014) Fractional-order viscoelasticity in one-dimensional blood flow models. Ann Biomed Eng, pp 0090–6964Google Scholar
  21. 21.
    Quartapelle L (1993) Numerical solution of the incompressible Navier-Stokes equations. Birkhauser Verlag, BaselCrossRefzbMATHGoogle Scholar
  22. 22.
    Raghu R, Vignon-Clementel IE, Figueroa CA, Taylor CA (2011) Comparative study of viscoelastic arterial wall models in nonlinear one-dimensional finite element simulations of blood flow. J Biomech Eng 133:081003–081011CrossRefGoogle Scholar
  23. 23.
    Ralovich K et al (2012) Hemodynamic assessment of pre-and post-operative aortic coarctation from MRI. In: Ayache N, Delingette H, Golland P, Mori K (eds) MICCAI 2012, Part II, vol 7511., LNCSSpringer, Heidelberg, pp 486–493Google Scholar
  24. 24.
    Reymond P (2011) Pressure and flow wave propagation in patient-specific models of the arterial tree. PhD Thesis, École Polytechnique Fédérale de LausanneGoogle Scholar
  25. 25.
    Reymond P, Merenda F, Perren F, Rafenacht D, Stergiopulos N (2009) Validation of a one-dimensional model of the systemic arterial tree. Am J Physiol Heart Circ Physiol 297(1):H208– H222Google Scholar
  26. 26.
    Sherman TF (1981) On connecting large vessels to small. The meaning of Murray’s law. J Gen Physiol 78(4):431–453Google Scholar
  27. 27.
    Sherwin SJ, Franke V, Peiró J, Parker KH (2003) One-dimensional modelling of a vascular network in space-time variables. J Eng Math 47:217–250CrossRefzbMATHGoogle Scholar
  28. 28.
    Steele BN, Valdez-Jasso D, Haider MA, Olufsen MS (2011) Predicting arterial flow and pressure dynamics using a 1D fluid dynamics model with a viscoelastic wall SIAM. J Appl Math 71(4):1123–1143zbMATHMathSciNetGoogle Scholar
  29. 29.
    Takizawa K, Christopher J, Tezduyar TE, Sathe S (2010) Space-time finite element computation of arterial fluid-structure interactions with patient-specific data. Int J Numer Methods Biomed Eng 26:101–116CrossRefzbMATHGoogle Scholar
  30. 30.
    Takizawa K, Moorman C, Wright S, Purdue J, McPhail T, Chen PR, Warren J, Tezduyar TE (2011) Patient-specific arterial fluid-structure interaction modeling of cerebral aneurysms. Int J Numer Methods Fluids 65:308–323CrossRefzbMATHGoogle Scholar
  31. 31.
    Takizawa K, Moorman C, Wright S, Christopher J, Tezduyar TE (2011) Wall shear stress calculations in space-time finite element computation of arterial fluid-structure interactions. Comput Mech 46:31–41CrossRefMathSciNetGoogle Scholar
  32. 32.
    Tezduyar TE, Takizawa K, Brummer T, Chen PR (2011) Space-time fluid-structure interaction modeling of patient-specific cerebral aneurysms. Int J Numer Methods Biomed Eng 27:665– 1710Google Scholar
  33. 33.
    Torii R, Oshima M, Kobayashi T, Takagi K (2009) Fluid structure interaction modeling of blood flow and cerebral aneurysm. Comput Methods Appl Mech Eng 198:3613–3621CrossRefzbMATHMathSciNetGoogle Scholar
  34. 34.
    Vignon-Clementel IE, Figueroa AC, Jansen KE, Taylor CA (2006) Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput Methods Appl Mech Eng 195(29–32):3776–3796 Google Scholar
  35. 35.
    Wang J, Parker KH (2004) Wave propagation in a model of the arterial circulation. J Biomech 37:457–470CrossRefGoogle Scholar
  36. 36.
    Xiao N, Humphrey JD, Figueroa CA (2013) Multi-scale computational model of three-dimensional hemodynamics within a deformable full-body arterial network. J Comput Phys 244:22–40CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Eduardo Soudah
    • 1
  • Riccardo Rossi
    • 1
  • Sergio Idelsohn
    • 1
    • 2
    Email author
  • Eugenio Oñate
    • 1
  1. 1.International Center for Numerical Methods in Engineering (CIMNE)Technical University of CataloniaBarcelonaSpain
  2. 2.Institució Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain

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