Abstract
Blood flows interact inevitably with surrounding elastic tissues. The most general approach to hemodynamic simulations is the solution of fluid–structure interaction (FSI) problems. The numerical solution of 3D FSI problems is computationally expensive and time-consuming, and requires usage of parallel computers. In addition, FSI simulations are hard to personalize since elastic properties of vessels cannot be retrieved in vivo with appropriate accuracy. We address two medical applications which allow us to simulate 3D blood flows with less computational cost than the numerical solution of the 3D FSI problems. The first application is simulation of 3D blood flow in the left ventricle of a patient based on dynamic ceCT medical images. The second application is simulation of 3D blood flow in the aortic bifurcation. We consider mathematical formulations of the models and present numerical results.
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References
Yu. Vassilevski et al. Personalized Computational Hemodynamics: Models, Methods, and Applications for Vascular Surgery and Antitumor Therapy, Academic Press (2020).
G. Kassab. Coronary Circulation: Anatomy, Mechanical Properties, and Biomechanics, Springer International Publishing (2019).
M. Labrosse, Ed. Cardiovascular mechanics, Taylor & Francis Group (2019).
A. Quarteroni et al. Mathematical Modelling of the Human Cardiovascular System: Data, Numerical Approximation, Clinical Applications, Cambridge University Press (2019).
Y. Shi, P. Lawford, R. Hose, Review of zero-D and 1D models of blood flow in the cardiovascular system. Biomed. Eng. Online 10(33) (2011).
N. Bessonov et al., Methods of blood flow modelling. Math. Model. Nat. Phenom. 11 (1) (2016).
A. Danilov et al., A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle. Russian J. Numer. Anal. Math. Modelling 32(4) (2017).
N. Xiao, J. Alastruey-Arimon, C.A. Figueroa, A systematic comparison between 1D and 3D hemodynamics in compliant arterial models. Int. J. Numer. Methods Biomed. Eng. 30 (2) (2014).
A. Lozovskiy, M. Olshanskii, Y. Vassilevski, A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain. Comput. Methods Appl. Mech. Engrg. 333 (2018).
T. Dobroserdova et al., Multiscale models of blood flow in the compliant aortic bifurcation. Appl. Math. Lett. 93C (2019).
J. Hron and S. Turek. A Monolithic FEM/multigrid Solver for an ALE Formulation of Fluid-Structure Interaction with Applications in Biomechanics, Springer Berlin Heidelberg (2006).
A. Lozovskiy et al., An unconditionally stable semi-implicit FSI finite element method. Comput.Methods Appl.Mech.Engrg. 297 (2015).
A. Lozovskiy, M. Olshanskii, Y. Vassilevski, Analysis and assessment of a monolithic FSI finite element method. Computers and Fluids, 179 (2019).
C. Caro et al. The Mechanics of the Circulation, second ed. Cambridge University Press (2012).
Yu. Vassilevski, V. Salamatova and S. Simakov, On the elasticity of blood vessels in one-dimensional problems of hemodynamics. J. Computational Mathematics and Mathematical Physics 55(9) (2015).
T. Dobroserdova, M. Olshanskii and S. Simakov, Multiscale coupling of compliant and rigid walls blood flow models. Int. J. Numer. Methods In Fluids 82 (12) (2016).
A. Kholodov, Some dynamical models of multi-dimensional problems of respiratory and circulatory systems including their interaction and matter transport. In: Computer Models and Medicine Progress, Nauka, Moskva (2001).
K. Magomedov and A. Kholodov, Grid-Characteristics Numerical Methods, second ed. Urait, Moscow (2018).
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The work has been supported by the Russian Science Foundation grant 19-71-10094.
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Vassilevski, Y.V. et al. (2021). Non-FSI 3D Hemodynamic Simulations in Time-Dependent Domains. In: Mondaini, R.P. (eds) Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells. BIOMAT 2020. Springer, Cham. https://doi.org/10.1007/978-3-030-73241-7_16
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