The geometric model-based patient-specific simulations of turbulent aortic valve flows

• Autorzy: Stupak E. , Kačianauskas R. , Kačeniauskas A. , Starikovičius V. , Maknickas A. , Pacevič R. , Staškūnienė M. , Davidavičius G. , Aidietis A.
• Języki publikacji: EN

Abstrakty

EN

This paper presents the patient-specific simulations of the aortic valve based on the proposed geometric model. A structural analysis is performed by using the finite element method to determine the stress-strain state of the aortic valve. The study is focused on the investigation of various turbulence models crucial for the appropriate description of the flow in the deceleration phase, following the peak systole. A comparative study of the flow solution without a turbulence model and the numerical results obtained by using various turbulence models is also performed. The results yielded by the shear-stress transport k-ω model supplemented with the intermittency transition equation most closely match those of numerical simulations without a turbulence model.

Słowa kluczowe

EN

geometric model of the aortic valve; pulsatile turbulent flow; shear-stress transport k-ω model; intermittency transition; finite volume method; finite element method

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2017
• Tom: Vol. 69, nr 4-5
• Strony: 317--345
• Opis fizyczny: Bibliogr. 62 poz., rys. kolor.

Twórcy

autor

Stupak E.

• Vilnius Gediminas Technical University Vilnius, Lithuania

autor

Kačianauskas R.

• Vilnius Gediminas Technical University Vilnius, Lithuania

autor

Kačeniauskas A.

• Vilnius Gediminas Technical University Vilnius, Lithuania

autor

Starikovičius V.

• Vilnius Gediminas Technical University Vilnius, Lithuania

autor

Maknickas A.

• Vilnius Gediminas Technical University Vilnius, Lithuania

autor

Pacevič R.

• Vilnius Gediminas Technical University Vilnius, Lithuania

autor

Staškūnienė M.

• Vilnius Gediminas Technical University Vilnius, Lithuania

autor

Davidavičius G.

• Vilnius University Hospital “Santariški¸u Klinikos” Vilnius, Lithuania

autor

Aidietis A.

• Vilnius University Hospital “Santariški¸u Klinikos” Vilnius, Lithuania

Bibliografia

• 1. Eurostat, Eurostat regional yearbook 2014, Publications Office of the European Union, 2014; doi: 10.2785/54486.
• 2. A. Tandon, P.A. Grayburn, Imaging of low-gradient severe aortic stenosis, JACC: Cardiovascular Imaging, 6, 184–195, 2013; doi: 10.1016/j.jcmg.2012.11.005.
• 3. S. Orwat, G. Kaleschke, G. Kerckhoff, R. Radke, H. Baumgartner, Low flow, low gradient severe aortic stenosis: diagnosis, treatment and prognosis, EuroIntervention, 9, Suppl: S38–42, 2013; doi: 10.4244/EIJV9SSA8.
• 4. J.G. Dumesnil, P. Pibarot, B. Carabello, Paradoxical low flow and/or low gradient severe aortic stenosis despite preserved left ventricular ejection fraction: implications for diagnosis and treatment, European Heart Journal, 31, 281–289, 2010; doi: 10.1093/eur-heartj/ehp361.
• 5. S. Herrmann, S. Störk, M. Niemann, V. Lange, J.M. Strotmann, S. Frantz, M. Beer, S. Gattenlöhner, W. Voelker, G. Ertl, F. Weidemann, Low-gradient aortic valve stenosis: myocardial fibrosis and its influence on function and outcome, Journal of the American College of Cardiology, 58, 402–412, 2011; doi: 10.1016/j.jacc.2011.02.059.
• 6. E. Sirois, Q.Wang, W. Sun, Fluid simulation of a transcatheter aortic valve deployment into a patient-specific aortic root, Cardiovascular Engineering and Technology, 2, 186–195, 2011; doi:10.1007/s13239-011-0037-7.
• 7. M. Nobili, U. Morbiducci, R. Ponzini, C. Del Gaudio, A. Balducci, M. Grigioni, F. Maria Montevecchi, A. Redaelli, Numerical simulation of the dynamics of a bileaflet prosthetic heart valve using a fluid-structure interaction approach, Journal of Biomechanics, 41, 2539–2550, 2008; doi: 10.1016/j.jbiomech.2008.05.004.
• 8. Z. Malecha, Ł. Mirosław, T. Tomczak, Z. Koza, M. Matyka, W. Tarnawski, D. Szczerba, GPU-based simulation of 3D blood flow in abdominal aorta using Open-FOAM, Archives of Mechanics, 63, 137–161, 2011.
• 9. C. Chnafa, S. Mendez, F. Nicoud, R. Moreno, S. Nottin, I. Schuster, Image-based patient-specific simulation: a computational modelling of the human left heart haemodynamics, Computer Methods in Biomechanics and Biomedical Engineering, 15, 74–75, 2012; doi: 10.1080/10255842.2012.713673.
• 10. C.S. Peskin, Flow patterns around heart valves: A numerical method, Journal of Computational Physics, 10, 252–271, 1972; doi: 10.1016/0021-9991(72)90065-4.
• 11. S.C. Shadden, M. Astorino, J.-F. Gerbeau, Computational analysis of an aortic valve jet with Lagrangian coherent structures, Chaos: An Interdisciplinary Journal of Non-linear Science, 20, 17512-1-17512–10, 2010; doi: 10.1063/1.3272780.
• 12. J. De Hart, G.W.M. Peters. P.J.G. Schreurs, F.P.T. Baaijens, A two-dimensional fluid-structure interaction model of the aortic value, Journal of Biomechanics, 33, 1079–1088, 2000.
• 13. M.A. Nicosia, R. P. Cochran, D.R. Einstein, C. J. Rutland, K.S. Kunzelman, A coupled fluid-structure finite element model of the aortic valve and root, The Journal of Heart Valve Disease, 12, 781–789, 2003.
• 14. B. Su, L. Zhong, X.-K. Wang, J.-M. Zhang, R.S. Tan, J.C. Allen, S.K. Tan, S. Kim, H.L. Leo, Numerical simulation of patient-specific left ventricular model with both mitral and aortic valves by FSI approach, Computer Methods and Programs in Biomedicine, 113, 474–482, 2014; doi: 10.1016/j.cmpb.2013.11.009.
• 15. G.P. Guruswamy, C. Byun, Fluid-structural interactions using Navier-Stokes flow equations coupled with shell finite element structures, AIAA Paper, 93, 3087, 1993; doi: 10.2514/6.1993-3087.
• 16. R. Roszak, P. Posadzy, W. Stankiewicz, M. Morzyński, Fluid-structure interaction for large scale complex geometry and non-linear properties of structure, Archives of Mechanics, 61, 3–27, 2009.
• 17. Y. Bazilevs, J.R. Gohean, T.J.R. Hughes, R.D. Moser, Y. Zhang, Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device, Computer Methods in Applied Mechanics and Engineering, 198, 3534–3550, 2009; doi: 10.1016/j.cma.2009.04.015.
• 18. A. Quarteroni, T. Lassila, S. Rossi, R. Ruiz-Baier, Integrated heart – Coupling multiscale and multiphysics models for the simulation of the cardiac function, Computer Methods in Applied Mechanics and Engineering, 314, 345–407, 2017; doi: 10.1016/j.cma.2016.05.031.
• 19. Y.C. Fung, Biomechanics: Mechanical Properties of Living Tissues, Springer, New York, 1993.
• 20. L. Tumonis, R. Kačianauskas, A. Kačeniauskas, M. Schneider, The transient behavior of rails used in electromagnetic railguns: numerical investigations at constant loading velocities, Journal of Vibroengineering, 9, 15–20, 2007.
• 21. B.E. Griffith, Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions, International Journal for Numerical Methods in Biomedical Engineering, 28, 317–345, 2012; doi: 10.1002/cnm.2543.
• 22. D. Bluestein, Y.M. Li, I.B. Krukenkamp, Free emboli formation in the wake of bi-leaflet mechanical heart valves and the effects of implantation techniques, Journal of Biomechanics, 35, 1533–1540, 2002; doi: 10.1016/S0021-9290(02)00093-3.
• 23. S. Marquez, R.T. Hon, A.P. Yoganathan, Comparative hydrodynamic evaluation of bioprosthetic heart valves, The Journal of Heart Valve Disease, 10, 802–811, 2001.
• 24. I.R. Ionasec, Patient-specific modeling and quantification of the heart valves from multi-modal cardiac images, PhD thesis, Technische Universität München, Lehrstuhl für Informatikanwendungen in der Medizin, 2010.
• 25. E. Votta, T.B. Le, M. Stevanella, L. Fusini, E.G. Caiani, A. Redaelli, F. Sotiropoulos, Toward patient-specific simulations of cardiac valves: State-of-the-art and future directions, Journal of Biomechanics, 46, 217–228, 2013; doi: 10.1016/j.jbiomech.2012.10.026.
• 26. H. Reul, A. Vahlbruch, M. Giersiepen, Th. Schmitz-Rode, V. Hirtz, S. Effert, The geometry of the aortic root in health, at valve disease and after valve replacement, Journal of Biomechanics, 23, 181–183, 1990; doi: 10.1016/0021-9290(90)90351-3.
• 27. M. Thubrikar, The Aortic Valve, CRC Press, Inc. Boca Raton, 1990.
• 28. M.R. Labrosse, C.J. Beller, F. Robicsek, M.J. Thubrikar, Geometric modeling of functional trileaflet aortic valves: Development and clinical applications, Journal of Biomechanics, 39, 2665–2672, 2006; doi: 10.1016/j.jbiomech.2005.08.012.
• 29. T.E. Claiborne, J. Sheriff, M. Kuetting, U. Steinseifer, M.J. Slepian, D. Bluestein, In vitro evaluation of a novel hemodynamically optimized trileaflet polymeric prosthetic heart valve, Journal of Biomechanical Engineering, 135, 2013; doi: 10.1115/1.4023235.
• 30. J.S. Rankin, A.F. Dalley, P.S. Crooke, R.H. Anderson, A “hemispherical” model of aortic valvar geometry, Journal of Heart Valve Disease, 17, 179–186, 2008.
• 31. R. Haj-Ali, G. Marom, S. Ben Zekry, M. Rosenfeld, E. Raanani, A general three-dimensional parametric geometry of the native aortic valve and root for biomechanical modeling, Journal of Biomechanics, 45, 2392–2397, 2012; doi: 10.1016/j.jbiomech.2012.07.017.
• 32. G. Marom, H.-S. Kim, M. Rosenfeld, E. Raanani, R. Haj-Ali, Fully coupled fluid- structure interaction model of congenital bicuspid aortic valves: effect of asymmetry on hemodynamics, Medical and Biological Engineering and Computing, 51, 839–848, 2013; doi: 10.1007/s11517-013-1055-4.
• 33. D. Bluestein, S. Einav, Techniques in the stability analysis of pulsatile flow through heart valves, [in:] Biomechanical Systems Techniques and Applications, Vol. II: Cardiovascular Techniques, C. Leondes [Ed.], CRC Press, 2000; doi: 10.1201/9781420049534.CH-04.
• 34. C. Kiris, D. Kwak, S. Rogers, I.-D. Chang, Computational approach for probing the flow through artificial heart devices, Journal of Biomechanical Engineering, 119, 452–460, 1997; doi: 10.1115/1.2798293.
• 35. D. Bluestein, E. Rambod, M. Gharib, Vortex shedding as a mechanism for free emboli formation in mechanical heart valves, Journal of Biomechanical Engineering, 122, 125–134, 2000; doi: 10.1115/1.429634.
• 36. E. Tuliszka-Sznitko, K. Kiełczewski, Direct numerical simulation of the Taylor–Couette flow with the asymmetric end-wall boundary conditions, Archives of Mechanics, 68, 395–418, 2016.
• 37. L. Ge, S.C. Jones, F. Sotiropoulos, T.M. Healy, A.P. Yoganathan, Numerical simulation of flow in mechanical heart valves: grid resolution and the assumption of flow symmetry, Journal of Biomechanical Engineering, 125, 709–718, 2003; doi: 10.1115/1.1614817.
• 38. M.D. De Tullio, L. Afferrante, G. Demelio, G. Pascazio, R. Verzicco, Fluid- structure interaction of deformable aortic prostheses with a bileaflet mechanical valve, Journal of Biomechanics, 44, 1684–1690, 2011; doi: 10.1016/j.jbiomech.2011.03.036.
• 39. L.P. Dasi, L. Ge, H.A. Simon, F. Sotiropoulos, A.P. Yoganathan, Vorticity dynamics of a bileaflet mechanical heart valve in an axisymmetric aorta, Physics of Fluids, 19, 2007; doi: 10.1063/1.2743261.
• 40. F. Auricchio, A. Ferrara, S. Morganti, Comparison and critical analysis of invariant-based models with respect to their ability in fitting human aortic valve data, Annals of Solid and Structural Mechanics, 4, 1–14, 2012; doi: 10.1007/s12356-012-0028-x.
• 41. G.A. Holzapfel, R.W. Ogden, Constitutive modelling of arteries, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466, 1551–1597, 2010; doi: 10.1098/rspa.2010.0058.
• 42. A. Gilmanov, H. Stolarski, F. Sotiropoulos, Non-linear rotation-free shell finite- element models for aortic heart valves, Journal of Biomechanics, 50, 56–62, 2017; doi: 10.1016/j.jbiomech.2016.11.031.
• 43. G. Marom, M. Peleg, R. Halevi, M. Rosenfeld, E. Raanani, A. Hamdan, R. Haj-Ali, Fluid-structure interaction model of aortic valve with porcine-specific collagen fiber alignment in the cusps, Journal of Biomechanical Engineering, 135, 2013.
• 44. K. Cao, M. Bukač, P. Sucosky, Three-dimensional macro-scale assessment of regional and temporal wall shear stress characteristics on aortic valve leaflets, Computer Methods in Biomechanics and Biomedical Engineering, 19, 603–613, 2016; doi: http://dx.doi.org/10.1080/10255842.2015.1052419.
• 45. A. Joda, Z. Jin, A. Haverich, J. Summers, S. Korossis, Multiphysics simulation of the effect of leaflet thickness inhomogeneity and material anisotropy on the stress-strain distribution on the aortic valve, Journal of Biomechanics, 49, 2502–2512, 2016; doi: 10.1016/j.jbiomech.2016.02.041.
• 46. D.J. Acheson, Elementary Fluid Dynamics, Oxford University Press, 1990.
• 47. A. Kačeniauskas, Development of efficient interface sharpening procedure for viscous incompressible flows, Informatica, 19, 487–504, 2008.
• 48. W. Nichols, M. O’Rourke, C. Vlachopoulos [Eds.], [with a contribution from] A. Hoeks, R. Reneman, McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles, 6th Edition, CRC Press, Taylor & Francis Group, 2011.
• 49. F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA Journal, 32, 1598–1605, 1994; doi: 10.2514/3.12149.
• 50. F.R. Menter, P.E. Smirnov, T. Liu, R. Avancha, A one-equation local correlation-based transition model, Flow, Turbulence and Combustion, 95, 583–619, 2015; doi: 10.1007/s10494-015-9622-4.
• 51. R.B. Langtry, F.R. Menter, Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes, AIAA Journal, 47, 2894–2906, 2009; doi: 10.2514/1.42362.
• 52. M. Kato, B.E. Launder, The modeling of turbulent flow around stationary and vibrating square cylinders, Ninth Symposium on Turbulent Shear Flows, August 16–18, pp. 10.4.1– 10.4.6, 1993; doi: 10.1007/s13398-014-0173-7.2.
• 53. S. Skatulla, C. Sansour, On a path-following method for non-linear solid mechanics with applications to structural and cardiac mechanics subject to arbitrary loading scenarios, International Journal of Solids and Structures, 96, 181–191, 2016; doi: 10.1016/j.ijsolstr.2016.06.009.
• 54. D. Maleike, M. Nolden, H.-P. Meinzer, I. Wolf, Interactive segmentation frame work of the Medical Imaging Interaction Toolkit, Computer Methods and Programs in Biomedicine, 96, 72–83, 2009; doi: 10.1016/j.cmpb.2009.04.004.
• 55. Z. Šír, B. Bastl, M. Lávička, Hermite interpolation by hypocycloids and epicycloids with rational offsets, Computer Aided Geometric Design, 27, 405–417, 2010; doi: 10.1016/j.cagd.2010.02.001.
• 56. S.N. Krivoshapko, V.N. Ivanov, Encyclopedia of Analytical Surfaces, Springer International Publishing, 2015; doi: 10.1007/978-3-319-11773-7.
• 57. T. Stolarski, Y. Nakasone, S. Yoshimoto, Engineering Analysis with ANSYS Software, Elsevier Butterworth-Heinemann, 2007.
• 58. M.R. Labrosse, K. Lobo, C.J. Beller, Structural analysis of the natural aortic valve in dynamics: from unpressurized to physiologically loaded, Journal of Biomechanics, 43, 1916–1922, 2010; doi: 10.1016/j.jbiomech.2010.03.020.
• 59. A. Kačeniauskas, R. Pacevič, V. Starikovičius, A. Maknickas, M. Stašku¯niene˙ , G. Davidavičius, Development of cloud services for patient-specific simulations of blood flows through aortic valves, Advances in Engineering Software, 103, 57–64, 2017; doi: 10.1016/j.advengsoft.2016.01.013.
• 60. A. Kačeniauskas, R. Pacevič, M. Stašku¯niene˙ , D. Šešok, D. Rusakevičius, A. Aidietis, G. Davidavičius, Private cloud infrastructure for applications of mechanical and dedical engineering, Information Technology and Control, 44, 254–261, 2015; doi: http://www.itc.ktu.lt/index.php/ITC/article/view/7379.
• 61. R. Pacevič, A. Kačeniauskas, The development of VisLT visualization service in Openstack cloud infrastructure, Advances in Engineering Software, 103, 46–56, 2017; doi: 10.1016/j.advengsoft.2016.06.012.
• 62. F. Sturla, E. Votta, M. Stevanella, C.A. Conti, A. Redaelli, Impact of modeling fluid-structure interaction in the computational analysis of aortic root biomechanics, Medical Engineering and Physics, 35, 1721–1730, 2013; doi: 10.1016/j.medengphy.2013.07.015.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).