Abstract
The paper presents a numerical simulation for fluid-structure interaction (FSI) of unsteady blood flow interacting with the vessel wall. The present work aims to provide a simple approach for very large deformation of the wall. The implementation of the method is straightforward and can be employed for a large scale problem with a cheap computational cost. The classical finite element discretization is adopted both for fluid and solid domains on tetrahedral elements. The monolithic scheme is used for the strong coupling of fluid and structure to satisfy kinematic and dynamic equilibrium conditions at the interface. The Navier-Stokes equations of an incompressible flow are solved by using the integrated method based on the Arbitrary Lagrangian-Eulerian (ALE) formula for the moving grid, and the total Lagrangian formulation is used for the non-linear hyper-elastic material of the vessel wall with the Mooney-Rivlin material model adopted as a constitutive equation for the solid domain. The numerical solutions for the FSI of blood vessel problem are quite similar to the experimental data. After validation the code, two problems of the blood vessel walls are considered: The carotid bifurcation and the aortic valve problems. The simulation results can be used for predicting the risk of cardiovascular diseases.
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References
Jeannette, H.S., Johan, J., Niclas, J., Johan, H.: 3D fluid-structure interaction simulation of aortic valves using a unified continuum ALE FEM model. Front. Physiol. 9, 363 (2018)
Ha, S.T., Choi, H.G.: Investigation on the effect of density ratio on the convergence behavior of partitioned method for fluid–structure interaction simulation. J. Fluids Struct. 96, 103050 (2020)
Ha, S.T., Ngo, L.C., Saeed, M., Jeon, B.J., Choi, H.G.: A comparative study between partitioned and monolithic methods for the problems with 3D fluid–structure interaction of blood vessels. J. Mech. Sci. Technol. 31, 281–287 (2017)
Kang, S., Choi, H.G., Yoo, J.Y.: Investigation of fluid–structure interactions using a velocity-linked P2/P1 finite element method and the generalized-α method. Internat. J. Numer. Methods Eng. 90, 1529–1548 (2012)
Ha, S.T., Choi, H.G.: Simulation of the motion of a carotid artery interacting with blood flow by using a partitioned semi-implicit algorithm. Korean Soc. Comput. Fluids Eng. (2019)
Vu, T.H., Phung, V.P., Nguyen, X.H., Wahab, M.A.: A polytree-based adaptive polygonal finite element method for topology optimization of fluid-submerged breakwater interaction. Comput. Math. Appl. 76(5), 1198–1218 (2018)
Yao, J., Liu, G.R., Narmoneva, D.A., Hinton, R.B., Zhang, Z.Q.: Immersed smoothed finite element method for fluid–structure interaction simulation of aortic valves. Comput. Mech. 50(6), 789–804 (2012)
Vu, T.H., Le, T.C., Nguyen, X.H., Abdel, M.A.: An equal-order mixed polygonal finite element for two-dimensional incompressible stokes flows. Eur. J. Mech.-B/Fluids 79, 92–108 (2020)
Vu, T.H., Le, T.C., Nguyen, X.H., Abdel, M.A.: A high-order mixed polygonal finite element for incompressible Stokes flow analysis. Comput. Methods Appl. Mech. Eng. 356, 175–198 (2019)
Holzapfel, G.A.: Nonlinear solid mechanics: a continuum approach for engineering science. Meccanica 37, 489–490 (2002)
Nobuko, K., Joji, A., Chen, X., Hisada, T.: Multiphysics simulation of blood flow and LDL transport in a porohyperelastic arterial wall model. J. Biomech. Eng. 129(3), 374–385 (2007)
Eken, A., Sahin, M.: A parallel monolithic algorithm for the numerical simulation of large-scale fluid structure interaction problems. Int. J. Numer. Methods Fluids 80, 687–714 (2016)
Yeom, E., Nam, K.H., Jin, C., Paeng, D.G., Lee, S.J.: 3D reconstruction of a carotid bifurcation from 2D transversal ultrasound images. Ultrasonics 54(8), 2184–2192 (2014)
Jingliang, D., Zhonghua, S., Kiao, I., Jiyuan, T.: Fluid–structure interaction analysis of the left coronary artery with variable angulation. Comput. Methods Biomech. Biomed. Engin. 18(14), 1500–1508 (2015)
Ha, S.T.: Development of a new geometric multi-grid finite element method and a semi-implicit partitioned algorithm for fluid-structure interaction simulation. Ph.D. Dissertation, Seoultech (2019)
Ryo, T., et al.: Fluid–structure interaction analysis of a patient-specific right coronary artery with physiological velocity and pressure waveforms. Commun. Numer. Meth. Eng. 25, 565–580 (2009)
Einstein, D.R., Reinhall, P., Nicosia, M., Cochran, R.P., Kunzelman, K.: Dynamic finite element implementation of nonlinear, anisotropic hyperelastic biological membranes. Comput. Methods Biomech. Biomed. Eng. 6(1), 33–44 (2003)
Ranga, A., Mongrain, R., Biadilah, Y., Cartier, R.: A compliant dynamic FEA model of the aortic valve. In: 12th IFToMM World Congress, Besançon, France, pp. 1–6 (2007)
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Ha, S.T., Nguyen, T.D., Vu, V.C., Nguyen, M.H., Nguyen, M.D. (2022). A Study of Fluid-Structure Interaction of Unsteady Flow in the Blood Vessel Using Finite Element Method. In: Tien Khiem, N., Van Lien, T., Xuan Hung, N. (eds) Modern Mechanics and Applications. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-3239-6_85
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