Modeling Blood Flow Circulation in Intracranial Arterial Networks: A Comparative 3D/1D Simulation Study

Grinberg, Leopold; Cheever, Elizabeth; Anor, Tomer; Madsen, JR; Karniadakis, George Em

doi:10.1007/s10439-010-0132-1

Cited by 133 publications

(92 citation statements)

References 33 publications

(43 reference statements)

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“…This simple law, stating that the membrane radial displacement η r is linearly proportional to the fluid pressure, is successfully considered in many applications, see, e.g., [80,118,181]. Other laws have been proposed to account for other features of the arterial wall.…”

Section: The Euler Model For An Arterial Segmentmentioning

confidence: 99%

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

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

159

155

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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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Section: The Euler Model For An Arterial Segmentmentioning

confidence: 99%

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

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

159

155

View full text Add to dashboard Cite

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“…As a result, after an intrinsic linearization, one obtains a hyperbolic type equation with respect to pressure; or another longitudinal variable. Such models are described in details in [4,13,22,24,25], where one can find a more detailed analysis and references to miscellaneous variants of such models.…”

Section: Introductionmentioning

confidence: 99%

A one-dimensional model of viscous blood flow in an elastic vessel

Berntsson

Karlsson

Kozlov

et al. 2016

Applied Mathematics and Computation

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In this paper we present a one-dimensional model of blood flow in a vessel segment with an elastic wall consisting of several anisotropic layers. The model involves two variables: the radial displacement of the vessel's wall and the pressure, and consists of two coupled equations of parabolic and hyperbolic type. Numerical simulations on a straight segment of a blood vessel demonstrate that the model can produce realistic flow fields that may appear under normal conditions in healthy blood vessels; as well as flow that could appear during abnormal conditions. In particular we show that weakening of the elastic properties of the wall may provoke a reverse blood flow in the vessel.

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“…Clinically, the using of Transcranial Doppler (TCD) [9][10][11][12][13][14][15][16][17][18][19][20], Magnetic Resonance Angiography (MRA) [13,15,17,19,[21][22][23][24][25][26] and Computed Tomography Angiography (CTA) [22,[27][28][29] provide the in-vivo perspective of the role of the CoW in the collateral flow in anatomical variations. Numerically, one-dimensional [30][31][32][33][34][35][36], two-dimensional [37,38] and threedimensional [31,34,[39][40][41][42][43] models of the CoW were developed, flows in the CoW with common anatomical variations were investigated.…”

Section: Introductionmentioning

confidence: 99%