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Large-Eddy Simulation of Turbulence in Cardiovascular Flows

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Book cover Biomedical Technology

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 84))

Abstract

A 4th-order accurate, low dissipative flow solver is used to perform Large-Eddy Simulations of three typical hemodynamic situations: the flow through the idealized medical device proposed by the American Food and Drug Administration; the intracardiac flow within an actual human left heart whose morphology and deformations are deduced from medical imaging; the flow downstream of an artificial aortic valve which arises from the blood-leaflets interaction problem. In all the cases, the \({\varvec{\sigma }}\) subgrid scale model designed to handle wall-bounded transitional flows is successfully used and the numerical simulations compare favourably with the experimental data available. These results illustrate the potential of the Large-Eddy Simulation methodology to properly handle blood flows. They also support the idea that turbulence, even if not fully developed, may be present in cardiovascular flows, including under non pathological conditions.

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References

  1. S. Varghese, S. Frankel, P. Fischer, Direct numerical simulation of stenotic flows. Part 2. Pulsatile flow. J. Fluid Mech. 582, 281 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Les, S. Shadden, C. Figueroa, J. Park, M. Tedesco, R. Herfkens, R. Dalman, C. Taylor, Quantification of hemodynamics in abdominal aortic aneurysms during rest and exercise using magnetic resonance imaging and computational fluid dynamics. Ann. Biomed. Eng. 38(4), 1288–1313 (2010)

    Article  Google Scholar 

  3. K. Valen-Sendstad, M. Piccinelli, D. Steinman, High-resolution computational fluid dynamics detects flow instabilities in the carotid siphon: implications for aneurysm initiation and rupture? J. Biomech. 47(12), 3210–3216 (2014)

    Article  Google Scholar 

  4. J. Mikhal, B. Geurts, Immersed boundary method for pulsatile transitional flow in realistic cerebral aneurysms. Comput. Fluids 91, 144–163 (2014)

    Article  MathSciNet  Google Scholar 

  5. F. Domenichini, G. Querzoli, A. Cenedese, G. Pedrizzetti, Combined experimental and numerical analysis of the flow structure into the left ventricle. J. Biomech. 40, 1988–1994 (2007)

    Google Scholar 

  6. P. Dyverfeldt, J. Kvitting, C. Carlhäll, G. Boano, A. Sigfridsson, U. Hermansson, A. Bolger, J. Enqwall, T. Ebbers, Hemodynamic aspects of mitral regurgitation assessed by generalized phase-contrast MRI. J. Magn. Reson. Imaging 33, 582–588 (2011)

    Article  Google Scholar 

  7. J. Zajac, J. Eriksson, P. Dyverfeldt, A. Bolger, T. Ebbers, C. Carlhäll, Turbulent kinetic energy in normal and myopathic left ventricles. J. Magn. Reson. Imaging 41(4), 1021–1029 (2015)

    Article  Google Scholar 

  8. U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University Press, 1996)

    Google Scholar 

  9. P. Spalart, Progress in aerospace sciences philosophies and fallacies in turbulence modeling. Prog. Aerosp. Sci. 1–15 (2015)

    Google Scholar 

  10. P. Hariharan, M. Giarra, V. Reddy, S. Day, K. Manning, S. Deutsch, S. Stewart, M. Myers, M. Berman, G. Burgreen, E. Paterson, R. Malinauskas, Multilaboratory particle image velocimetry analysis of the FDA benchmark nozzle model to support validation of computational fluid dynamics simulations. J. Biomech. Eng. 133(4), 041002 (2011)

    Google Scholar 

  11. C. Chnafa, S. Mendez, F. Nicoud, Image-based large-eddy simulation in a realistic left heart. Comput. Fluids 94, 173–187 (2014)

    Article  MathSciNet  Google Scholar 

  12. P. Sagaut, Large Eddy Simulation for Incompressible Flows. An Introduction (Springer, Berlin, 2001)

    Book  MATH  Google Scholar 

  13. R. Vichnevetsky, J. Bowles, Fourier Analysis of Numerical Approximations of Hyperbolic Equations, Siam - stu edn. (1982)

    Google Scholar 

  14. Y. Morinishi, T. Lund, O. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow. J. Comput. Phys. 143(1), 90–124 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  15. R. Mittal, P. Moin, Suitability of upwind-biased finite differance schemes for large eddy simulation of turbulent flows. AIAA J. 35(8), 1415–1417 (1997)

    Article  MATH  Google Scholar 

  16. N. Park, J. Yoo, H. Choi, Discretization errors in large eddy simulation: on the suitability of centered and upwind-biased compact difference schemes. J. Comput. Phys. 198(2), 580–616 (2004)

    Article  MATH  Google Scholar 

  17. A. Chorin, Numerical solution of the Navier-Stokes equations. Math. Comput. 22, 745–762 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Williamson, Low-storage Runge-Kutta schemes. J. Comput. Phys. 35(1), 48–56 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  19. V. Moureau, P. Domingo, L. Vervisch, Design of a massively parallel CFD code for complex geometries. Comptes Rendus Mécanique 339(2–3), 141–148 (2011)

    Article  MATH  Google Scholar 

  20. M. Malandain, N. Maheu, V. Moureau, Optimization of the deflated Conjugate Gradient algorithm for the solving of elliptic equations on massively parallel machines. J. Comput. Phys. 238, 32–47 (2013)

    Article  MathSciNet  Google Scholar 

  21. F. Nicoud, H. Baya Toda, O. Cabrit, S. Bose, J. Lee, Using singular values to build a subgrid-scale model for large eddy simulations. Phys. Fluids 23(8), 085106 (2011)

    Google Scholar 

  22. H. Baya Toda, O. Cabrit, K. Truffin, G. Bruneaux, F. Nicoud, Assessment of subgrid-scale models with a large-eddy simulation-dedicated experimental database: the pulsatile impinging jet in turbulent cross-flow. Phys. Fluids 26(7), 075108 (2014)

    Google Scholar 

  23. M. Germano, U. Piomelli, P. Moin, W. Cabot, A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1766 (1991)

    Article  MATH  Google Scholar 

  24. S. Stewart, E. Paterson, G. Burgreen, P. Hariharan, M. Giarra, V. Reddy, S. Day, K. Manning, S. Deutsch, M. Berman, M. Myers, R. Malinauskas, M. Berman, R. Malinauskas, Assessment of CFD performance in simulations of an idealized medical device: results of FDA’s first computational interlaboratory study. Cardiovasc. Eng. Technol. 3(2), 139–160 (2012)

    Article  Google Scholar 

  25. A. Marsden, Y. Bazilevs, C. Long, M. Behr, Recent advances in computational methodology for simulation of mechanical circulatory assist devices. WIREs Syst. BiolMed. 6, 169–188 (2014)

    Article  Google Scholar 

  26. S. Mendez, V. Zmijanovic, E. Gibaud, J. Siguenza, F. Nicoud, Assessing macroscopic models for hemolysis from fully resolved simulations, in 4th International Conference on Computational and Mathematical Biomedical Engineering, CMBE2015 Proceedings, ed. by P. Nithiarasu, E. Budyn (ENS Cachan, France, 2015), pp. 575–578

    Google Scholar 

  27. T. Passerini, A. Quaini, U. Villa, A. Veneziani, S. Canic, Validation of an open source framework for the simulation of blood flow in rigid and deformable vessels. Int. J. Numer. Methods Biomed. Eng. 29(11), 1192–1213 (2013)

    Google Scholar 

  28. Y. Delorme, K. Anupindi, S. Frankel, Large eddy simulation of FDA’s idealized medical device. Cardiovasc. Eng. Technol. 4(4), 392–407 (2013)

    Article  Google Scholar 

  29. S. Bhushan, D. Walters, G. Burgreen, Laminar, turbulent, and transitional simulations in benchmark cases with cardiovascular device features. Cardiovasc. Eng. Technol. 4(4), 408–426 (2013)

    Article  Google Scholar 

  30. G. Janiga, Large eddy simulation of the FDA benchmark nozzle for a Reynolds number of 6500. Comput. Biol. Med. 47(April), 113–119 (2014)

    Article  Google Scholar 

  31. F. Sotiropoulos, Computational fluid dynamics for medical device design and evaluation: are we there yet? Cardiovasc. Eng. Technol. 3(2), 137–138 (2012)

    Google Scholar 

  32. V. Zmijanovic, S. Mendez, V. Moureau, F. Nicoud, About the numerical robustness of biomedical benchmark cases: Interlaboratory FDA’s idealized medical device. Int. J. Numer. Methods Biomed. Eng. (2016). doi:10.1002/cnm.2789

  33. X. Wu, P. Moin, R. Adrian, J. Baltzer, Osborne Reynolds pipe flow: direct simulation from laminar through gradual transition to fully developed turbulence. Proc. Natl. Acad. Sci. 112(26), 7920–7924 (2015)

    Article  Google Scholar 

  34. K. Avila, D. Moxey, A. de Lozar, M. Avila, D. Barkley, B. Hof, The onset of turbulence in pipe flow. Science 333, 192–196 (2011)

    Article  Google Scholar 

  35. A. Kheradvar, M. Gharib, On mitral valve dynamics and its connection to early diastolic flow. Ann. Biomed. Eng. 37(1) (2009)

    Google Scholar 

  36. G. Pedrizzetti, F. Domenichini, G. Tonti, On the left ventricular vortex reversal after mitral valve replacement. Ann. Biomed. Eng. 38(3), 769–773 (2010)

    Article  Google Scholar 

  37. P. Davies, A. Remuzzi, E. Gordon, C. Dewey, M. Gimbrone, Turbulent fluid shear stress induces vascular endothelial cell turnover in vitro. Proc. Natl. Acad. Sci. 83(7), 2114–2117 (1986)

    Article  Google Scholar 

  38. S. Olesen, D. Clapham, P. Davies, Haemodynamic shear stress activates a K\(+\) current in vascular endothelial cells. Nature 331(6152), 168–170 (1988)

    Article  Google Scholar 

  39. A. Pasipoularides, Mechanotransduction mechanisms for intraventricular diastolic vortex forces and myocardial deformations: Part 1. J. Cardiovasc. Transl. Res. 8(1), 76–87 (2015)

    Google Scholar 

  40. F. Domenichini, G. Pedrizzetti, B. Baccani, Three-dimensional filling flow into a model left ventricle. J. Fluid Mech. 539, 179–198 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  41. C. Chnafa, S. Mendez, F. Nicoud, Image-based simulations show important flow fluctuations in a normal left ventricle: what could be the implications? Ann. Biomed. Eng. (2016). doi:10.1007/s10439-016-1614-6

  42. T. Le, F. Sotiropoulos, On the three-dimensional vortical structure of early diastolic flow in a patient-specific left ventricle. Eur. J. Mech. B/Fluids 35, 20–24 (2012)

    Article  Google Scholar 

  43. C. Chnafa, S. Mendez, R. Moreno, F. Nicoud, Using image-based CFD to investigate the intracardiac turbulence, in Modeling the Heart and the Circulatory System, ed. by A. Quarteroni (Springer International Publishing, New York, 2015), pp. 97–117

    Google Scholar 

  44. P. Kilner, G. Yang, J. Wilkes, R. Mohiaddin, D. Firmin, M. Yacoub, Asymmetric redirection of flow through the heart. Nature 404(6779), 759–761 (2000)

    Article  Google Scholar 

  45. V. Mihalef, R. Ionasec, P. Sharma, B. Georgescu, I. Voigt, M. Suehling, D. Comaniciu, Patient-specific modelling of whole heart anatomy, dynamics and haemodynamics from four-dimensional cardiac CT images. Interface Focus 1(3), 286–296 (2011)

    Article  Google Scholar 

  46. A. Falahatpisheh, A. Kheradvar, High-speed particle image velocimetry to assess cardiac fluid dynamics in vitro: From performance to validation. Eur. J. Mech. B/Fluids 35, 2–8 (2012)

    Article  Google Scholar 

  47. G. Querzoli, S. Fortini, A. Cenedese, Effect of the prosthetic mitral valve on vortex dynamics and turbulence of the left ventricular flow. Phys. Fluids 22, 1–10 (2010)

    Google Scholar 

  48. I. Celik, Z. Cehreli, I. Yavuz, Index of resolution quality for large eddy simulations. J. Fluid Eng. 127(5), 949–958 (2005)

    Article  Google Scholar 

  49. S. Pope, Turbulent Flows (Cambridge University Press, 2000)

    Google Scholar 

  50. S. Pope, Ten questions concerning the large-eddy simulation of turbulent flows. New J. Phys. 6 (2004)

    Google Scholar 

  51. P. Stein, H. Sabbah, Measured turbulence and its effect on thrombus formation. Circ. Res. 35, 608–614 (1974)

    Article  Google Scholar 

  52. A. Yoganathan, Z. He, S. Jones, Fluid mechanics of heart valves. Annu. Rev. Biomed. Eng. 6, 331–362 (2004)

    Article  Google Scholar 

  53. D. Pott, J. Sigüenza, S. Sonntag, U. Steinseifer, S. Mendez, F. Nicoud, Dynamics of artificial aortic valves: a combined experimental and numerical study, in 42th ESAO meeting, Leuven (2015)

    Google Scholar 

  54. J. Sigüenza, S. Mendez, D. Ambard, F. Dubois, F. Jourdan, R. Mozul, F. Nicoud, Validation of an immersed thick boundary method for simulating fluid-structure interactions of deformable membranes. J. Comput. Phys. 322, 723–746 (2016). doi:10.1016/j.jcp.2016.06.041, http://dx.doi.org/10.1016/j.jcp.2016.06.041

  55. C. Peskin, The immersed boundary method. Acta Numerica 11, 479–517 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  56. S. Mendez, E. Gibaud, F. Nicoud, An unstructured solver for simulations of deformable particles in flows at arbitrary Reynolds numbers. J. Computat. Phys. 256, 465–483 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  57. A. Pinelli, I. Naqavi, U. Piomelli, J. Favier, Immersed-boundary methods for general finite-difference and finite-volume Navier-Stokes solvers. J. Comput. Phys. 229, 9073–9091 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  58. F. Radjai, F. Dubois, Discrete Numerical Modeling of Granular Materials (Wiley-ISTE, 2011)

    Google Scholar 

  59. H. Reul, A. Vahlbruch, M. Giersiepen, T. Schmitz-Rode, V. Hirtz, S. Effert, The geometry of the aortic root in health, at valve disease and after valve replacement. J. Biomech. 23(2), 181–191 (1990)

    Article  Google Scholar 

  60. A. Robertson, A. Sequeira, R. Owens, Rheological models for blood, in Cardiovascular Mathematics. Modeling and Simulation of the Circulatory System (Springer, 2009), pp. 211–241

    Google Scholar 

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Acknowledgements

The authors thank ANR and BPI for their supports through the Laboratory of Excellence NUMEV (ANR-10-LABX-20), the FORCE (ANR-11-JS09-0011) and the DAT@DIAG (ISI-I1112018W) project. Dr S. Sonntag and PhD student D. Pott from the Helmholtz Institute of Aachen are gratefully acknowledged for providing the details of their experimental test rig about the aortic valve dynamics. CC also thanks CNRS for funding his thesis. Dr. V. Moureau is gratefully acknowledged for giving access to the YALES2 solver. This work was performed using HPC resources from GENCI-CINES (Grants 2014-, 2015- and 2016-c2015037194) and the HPC@LR Center.

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Nicoud, F., Chnafa, C., Siguenza, J., Zmijanovic, V., Mendez, S. (2018). Large-Eddy Simulation of Turbulence in Cardiovascular Flows. In: Wriggers, P., Lenarz, T. (eds) Biomedical Technology. Lecture Notes in Applied and Computational Mechanics, vol 84. Springer, Cham. https://doi.org/10.1007/978-3-319-59548-1_9

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  • DOI: https://doi.org/10.1007/978-3-319-59548-1_9

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