A unified variational approach for coupling 3D–1D models and its blood flow applications

Blanco, Pablo; Feijóo, Raúl A.; Urquiza, Santiago

doi:10.1016/j.cma.2007.05.008

Cited by 106 publications

(110 citation statements)

References 29 publications

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“…This flow rate curve corresponds to the result obtained at the proximal point of the axillary artery using an entire model of the cardiovascular system [7].…”

Section: Simulations and Resultsmentioning

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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“…This flow rate curve corresponds to the result obtained at the proximal point of the axillary artery using an entire model of the cardiovascular system [7].…”

Section: Simulations and Resultsmentioning

confidence: 99%

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

2013

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“…This case has been considered in [167]. Instead, for the 3D problem, the Robin/Robin scheme would lead to a defective resistance condition (see (27) and the related paragraph).…”

Section: End Domentioning

confidence: 99%

“…Iterative methods applied directly to the monolithic coupled linearized system have been advocated in [27,29].…”

Section: Further Developments and Commentsmentioning

confidence: 99%

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Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

166

157

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This review paper addresses the so called geometric multiscale approach for the numerical simulation of blood flow problems, from its origin (that we can collocate in the second half of '90s) to our days. By this approach the blood fluid-dynamics in the whole circulatory system is described mathematically by means of heterogeneous featuring different degree of detail and different geometric dimension that interact together through appropriate interface coupling conditions.Our review starts with the introduction of the stand-alone problems, namely the 3D fluidstructure interaction problem, its reduced representation by means of 1D models, and the so-called lumped parameters (aka 0D) models, where only the dependence on time survives. We then address specific methods for stand-alone 3D models when the available boundary data are not enough to ensure the mathematical well posedness. These so-called "defective problems" naturally arise in practical applications of clinical relevance but also because of the interface coupling of heterogeneous problems that are generated by the geometric multiscale process. We also describe specific issues related to the boundary treatment of reduced models, particularly relevant to the geometric multiscale coupling. Next, we detail the most popular numerical algorithms for the solution of the coupled problems. Finally, we review some of the most representative works -from different research groups -which addressed the geometric multiscale approach in the past years.A proper treatment of the different scales relevant to the hemodynamics and their interplay is essential for the accuracy of numerical simulations and eventually for their clinical impact. This paper aims at providing a state-of-the-art picture of these topics, where the gap between theory and practice demands rigorous mathematical models to be reliably filled.

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“…In this sense, geometrical multiscale approaches provide an efficient and reliable way to select the desired level of complexity in each component of the cardiovascular system. 4,14,28,31,37 The main ingredients of a geometrical multiscale model for cardiovascular flows are (i) three-dimensional (3-D) fluid-structure interaction (FSI) models, which are used to represent few specific components of main interest, 3,7,9,13,19,36 (ii) onedimensional (1-D) FSI models, which describe the global blood circulation in the arterial network, 1,5,15,29 and (iii) lumped parameters models, which account for the cumulative effects of all distal vessels, i.e., small arteries, arterioles, and capillaries. 17,35 More generally, from the medical point of view, a 3-D model allows to have a deep insight of a specific region of the cardiovascular system (e.g., the thoracic aorta), whereas the interaction with the global cardiovascular system is modeled by the mean of reduced order models.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of left ventricular assist device implantations: Comparing the ascending and the descending aorta cannulations

Bonnemain

Malossi

Lesinigo

et al. 2013

Medical Engineering & Physics

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A unified variational approach for coupling 3D–1D models and its blood flow applications

Cited by 106 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

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Numerical simulation of left ventricular assist device implantations: Comparing the ascending and the descending aorta cannulations

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