Black-box decomposition approach for computational hemodynamics: One-dimensional models

Blanco, Pablo; Leiva, Jorge S.; Feijóo, Raúl A.; Buscaglia, Gustavo C.

doi:10.1016/j.cma.2010.12.006

Cited by 24 publications

(33 citation statements)

References 29 publications

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“…Regarding the description of the numerical methodologies to address the solution of the 3D Navier-Stokes equations in compliant domains and its coupling with the 1D model the reader is referred to [7,8,29]. Here we provide a brief account of the domain decomposition strategy employed to iteratively couple the 1D and 3D models.…”

Section: Dimensionally-heterogeneous Modelingmentioning

confidence: 99%

Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

2013

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Abstract.A distributed-parameter (one-dimensional) anatomically detailed model for the arterial network of the arm is developed in order to carry out hemodynamics simulations. This work focuses on the specific aspects related to the model set-up. In this regard, stringent anatomical and physiological considerations have been pursued in order to construct the arterial topology and to provide a systematic estimation of the involved parameters. The model comprises 108 arterial segments, with 64 main arteries and 44 perforator arteries, with lumen radii ranging from 0.24 cm -axillary artery-to 0.018 cmperforator arteries. The modeling of blood flow in deformable vessels is governed by a well-known set of hyperbolic partial differential equations that accounts for mass and momentum conservation and a constitutive equation for the arterial wall. The variational formulation used to solve the problem and the related numerical approach are described. The model rendered consistent pressure and flow rate outputs when compared with patient records already published in the literature. In addition, an application to dimensionally-heterogeneous modeling is presented in which the developed arterial network is employed as an underlying model for a three-dimensional geometry of a branching point to be embedded in order to perform local analyses.Mathematics Subject Classification. 76Z05, 92C10, 92C30.

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Section: Dimensionally-heterogeneous Modelingmentioning

confidence: 99%

Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

2013

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“…This is done by using the methodology described in [32, section 3.2.1], which is devised for the most general case. Then, during the second step, the matrix entries can be either computed by solving the tangent problems associated with the coupled models [31,32], or approximated by using a simpler finite difference approach, which may lead to a good approximation at a reasonable cost [4,31]. We further discuss this topic in section 3.3.…”

Section: Numerical Approachmentioning

confidence: 99%

“…Modeling the corresponding fluid-structure interaction (FSI) can be achieved in several ways, e.g., using a one-dimensional (1-D) model that integrates the blood and the arterial wall (see, e.g., [4,6,17,42]); performing a three-dimensional (3-D) simulation for the fluid inside the deformable lumen, where the deformation of the wall is accounted for at the variational level by a proper boundary condition on the endothelial wall (see, e.g., [26,35,44]); or considering the full interaction between the 3-D blood flow and a 3-D vessel wall by coupling the equations for the fluid flow with those for a solid structure (see [2,10,12,27,33,43] and the references therein).…”

mentioning

confidence: 99%

Implicit Coupling of One-Dimensional and Three-Dimensional Blood Flow Models with Compliant Vessels

Malossi

Blanco

Crosetto

et al. 2013

Multiscale Model. Simul.

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Abstract. The blood flow in arterial trees in the cardiovascular system can be simulated with the help of different models, depending on the outputs of interest and the desired degree of accuracy. In particular, one-dimensional fluid-structure interaction models for arteries are very effective in reproducing physiological pressure wave propagation and in providing quantities like pressure and velocity, averaged on the cross section of the arterial lumen. In locations where onedimensional models cannot capture the complete flow dynamics, e.g., in the presence of stenoses and aneurysms or other strong geometric perturbations, three-dimensional coupled fluid-structure interaction models are necessary to evaluate more accurately, for instance, critical factors responsible for pathologies which are associated with hemodynamics, such as wall shear stress. In this work we formalize and investigate the geometrical multiscale problem, where heterogeneous fluid-structure interaction models for arteries are implicitly coupled. We introduce new coupling algorithms, describe their implementation, and investigate on simple geometries the numerical reflections that occur at the interface between the heterogeneous models. We also simulate on a supercomputer a threedimensional abdominal aorta under physiological conditions, coupled with up to six one-dimensional models representing the surrounding arterial branches. Finally, we compare CPU times and number of coupling iterations for different algorithms and time discretizations.

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“…One of the remedies recommended is a two time step method in which the first time step corresponds to the stability limit of an explicit configuration of each segment (local time step), and the global time step is for the branching sites (Malossi et al, 2012). A similar technique was also used by (Blanco et al, 2011) to overcome difficulties of using two different time steps, and to avoid previous time step information. As a result of the implicit treatment in the reported works, the time step restriction associated with the explicit treatment was reduced.…”

Section: Introductionmentioning

confidence: 99%

Robust Finite Element Approaches to Systemic Circulation Using the Locally Conservative Galerkin (LCG) Method

Hasan¹,

Nithiarasu

2016

Proceedings of the Indian National Science Academy

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In this paper novel finite element algorithms for robustly solving flow equations of a systemic circulation are presented and compared. A novel, Locally Conservative Galerkin (LCG) method is developed by adopting semi-and fully-implicit time discretisations to address the behavior of blood flow in the human circulatory system. These techniques are efficient for nonlinear system of equations used in blood flow models and achieve rapid convergence. Several comparisons are made between the methods to demonstrate the validity and stability of the current numerical models to solve the blood flow characteristics in a human body.

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Black-box decomposition approach for computational hemodynamics: One-dimensional models

Cited by 24 publications

References 29 publications

Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

Implicit Coupling of One-Dimensional and Three-Dimensional Blood Flow Models with Compliant Vessels

Robust Finite Element Approaches to Systemic Circulation Using the Locally Conservative Galerkin (LCG) Method

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