Comparison of Reduced Models for Blood Flow Using Runge-Kutta Discontinuous Galerkin Methods

Overview

Journal Appl Numer Math

Date 2017 Oct 31

PMID 29081563

Citations 2

Authors

Charles Puelz

Suncica canic

Beatrice Riviere

Craig G Rusin

Affiliations

Soon will be listed here.

Abstract

One-dimensional blood flow models take the general form of nonlinear hyperbolic systems but differ in their formulation. One class of models considers the physically conserved quantities of mass and momentum, while another class describes mass and velocity. Further, the averaging process employed in the model derivation requires the specification of the axial velocity profile; this choice differentiates models within each class. Discrepancies among differing models have yet to be investigated. In this paper, we comment on some theoretical differences among models and systematically compare them for physiologically relevant vessel parameters, network topology, and boundary data. In particular, the effect of the velocity profile is investigated in the cases of both smooth and discontinuous solutions, and a recommendation for a physiological model is provided. The models are discretized by a class of Runge-Kutta discontinuous Galerkin methods.

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References

Zhang H, Fujiwara N, Kobayashi M, Yamada S, Liang F, Takagi S . Development of a Numerical Method for Patient-Specific Cerebral Circulation Using 1D-0D Simulation of the Entire Cardiovascular System with SPECT Data. Ann Biomed Eng. 2016; 44(8):2351-2363. DOI: 10.1007/s10439-015-1544-8. View

Azer K, Peskin C . A one-dimensional model of blood flow in arteries with friction and convection based on the Womersley velocity profile. Cardiovasc Eng. 2007; 7(2):51-73. DOI: 10.1007/s10558-007-9031-y. View

Olufsen M, Peskin C, Kim W, Pedersen E, Nadim A, Larsen J . Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions. Ann Biomed Eng. 2001; 28(11):1281-99. DOI: 10.1114/1.1326031. View

Stergiopulos N, Young D, Rogge T . Computer simulation of arterial flow with applications to arterial and aortic stenoses. J Biomech. 1992; 25(12):1477-88. DOI: 10.1016/0021-9290(92)90060-e. View

Xiao N, Alastruey J, Figueroa C . A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models. Int J Numer Method Biomed Eng. 2013; 30(2):204-31. PMC: 4337249. DOI: 10.1002/cnm.2598. View

Politi M, Ghigo A, Fernandez J, Khelifa I, Gaudric J, Fullana J . The dicrotic notch analyzed by a numerical model. Comput Biol Med. 2016; 72:54-64. DOI: 10.1016/j.compbiomed.2016.03.005. View

Barnard A, HUNT W, Timlake W, Varley E . A theory of fluid flow in compliant tubes. Biophys J. 1966; 6(6):717-24. PMC: 1368038. DOI: 10.1016/S0006-3495(66)86690-0. View

Muller L, Blanco P, Watanabe S, Feijoo R . A high-order local time stepping finite volume solver for one-dimensional blood flow simulations: application to the ADAN model. Int J Numer Method Biomed Eng. 2015; 32(10). DOI: 10.1002/cnm.2761. View

Sheng C, Sarwal S, Watts K, Marble A . Computational simulation of blood flow in human systemic circulation incorporating an external force field. Med Biol Eng Comput. 1995; 33(1):8-17. DOI: 10.1007/BF02522938. View

10.

Blanco P, Pivello M, Urquiza S, Feijoo R . On the potentialities of 3D-1D coupled models in hemodynamics simulations. J Biomech. 2009; 42(7):919-30. DOI: 10.1016/j.jbiomech.2009.01.034. View

11.

Lange R, HECHT H . Genesis of pistol-shot and Korotkoff sounds. Circulation. 1958; 18(5):975-8. DOI: 10.1161/01.cir.18.5.975. View

12.

Wang X, Fullana J, Lagree P . Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model. Comput Methods Biomech Biomed Engin. 2014; 18(15):1704-25. DOI: 10.1080/10255842.2014.948428. View

13.

Muller L, Toro E . Well-balanced high-order solver for blood flow in networks of vessels with variable properties. Int J Numer Method Biomed Eng. 2013; 29(12):1388-411. DOI: 10.1002/cnm.2580. View

14.

Acosta S, Puelz C, Riviere B, Penny D, Rusin C . Numerical Method of Characteristics for One-Dimensional Blood Flow. J Comput Phys. 2015; 294:96-109. PMC: 4410450. DOI: 10.1016/j.jcp.2015.03.045. View

15.

Grinberg L, Anor T, Madsen J, Yakhot A, Karniadakis G . Large-scale simulation of the human arterial tree. Clin Exp Pharmacol Physiol. 2008; 36(2):194-205. DOI: 10.1111/j.1440-1681.2008.05010.x. View

16.

Coccarelli A, Boileau E, Parthimos D, Nithiarasu P . An advanced computational bioheat transfer model for a human body with an embedded systemic circulation. Biomech Model Mechanobiol. 2015; 15(5):1173-90. PMC: 5021771. DOI: 10.1007/s10237-015-0751-4. View

17.

Murgo J, Westerhof N, Giolma J, Altobelli S . Aortic input impedance in normal man: relationship to pressure wave forms. Circulation. 1980; 62(1):105-16. DOI: 10.1161/01.cir.62.1.105. View

18.

Marchandise E, Willemet M, Lacroix V . A numerical hemodynamic tool for predictive vascular surgery. Med Eng Phys. 2008; 31(1):131-44. DOI: 10.1016/j.medengphy.2008.04.015. View

19.

Boileau E, Nithiarasu P, Blanco P, Muller L, Fossan F, Hellevik L . A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling. Int J Numer Method Biomed Eng. 2015; 31(10). DOI: 10.1002/cnm.2732. View

20.

REMINGTON J, Wood E . Formation of peripheral pulse contour in man. J Appl Physiol. 1956; 9(3):433-42. DOI: 10.1152/jappl.1956.9.3.433. View