An optimal reconstruction of the human arterial tree from doppler echotracking measurements

Dumas, Laurent; Boutouyrie, Pierre; Bozec, Erwan

doi:10.1145/2330784.2330866

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…They can be used, for example, as stand‐alone tools or combined with multidimensional fluid–structure interaction models in a multiscale framework. One‐dimensional models can also be used to solve inverse problems to compute patient‐specific cardiovascular network characteristics, as performed recently in . It is reasonable to assume that for the foreseeable future, one‐dimensional models will play a crucial role in any attempt to construct closed, global models for the human circulation system.…”

Section: Introductionmentioning

confidence: 99%

Well‐balanced high‐order solver for blood flow in networks of vessels with variable properties

Müller

Toro

2013

Numer Methods Biomed Eng

100

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We present a well-balanced, high-order non-linear numerical scheme for solving a hyperbolic system that models one-dimensional flow in blood vessels with variable mechanical and geometrical properties along their length. Using a suitable set of test problems with exact solution, we rigorously assess the performance of the scheme. In particular, we assess the well-balanced property and the effective order of accuracy through an empirical convergence rate study. Schemes of up to fifth order of accuracy in both space and time are implemented and assessed. The numerical methodology is then extended to realistic networks of elastic vessels and is validated against published state-of-the-art numerical solutions and experimental measurements. It is envisaged that the present scheme will constitute the building block for a closed, global model for the human circulation system involving arteries, veins, capillaries and cerebrospinal fluid.

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Section: Introductionmentioning

confidence: 99%

Well‐balanced high‐order solver for blood flow in networks of vessels with variable properties

Müller

Toro

2013

Numer Methods Biomed Eng

100

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“…They have proved to be valuable and efficient tools to capture pulse wave propagation in large network simulations and obtain satisfactory evaluations of average quantities such as the cross-sectional area (A), the flow rate (Q) or the pressure (P ) [2,49]. In recent works, 1D models have also been used to compute inverse problems to obtain patient specific parameters [34,38,23]. Due to their simplicity, efficiency and the reduced number of parameters they require, we hope that in the near future these 1D models will be intensively used by medical practitioners to make pre-and-post operative diagnosis and perform patient specific simulations of surgeries.…”

Section: Introductionmentioning

confidence: 99%

Low-Shapiro hydrostatic reconstruction technique for blood flow simulation in large arteries with varying geometrical and mechanical properties

Ghigo

Delestre

Fullana

et al. 2017

Journal of Computational Physics

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The purpose of this work is to construct a simple, efficient and accurate well-balanced numerical scheme for one-dimensional (1D) blood flow in large arteries with varying geometrical and mechanical properties. As the steady states at rest are not relevant for blood flow, we construct two well-balanced hydrostatic reconstruction techniques designed to preserve low-Shapiro number steady states that may occur in large network simulations. The Shapiro number S h = u/c is the equivalent of the Froude number for shallow water equations and the Mach number for compressible Euler equations. The first is the low-Shapiro hydrostatic reconstruction (HR-LS), which is a simple and efficient method, inspired from the hydrostatic reconstruction technique (HR). The second is the subsonic hydrostatic reconstruction (HR-S), adapted here to blood flow and designed to exactly preserve all subcritical steady states. We systematically compare HR, HR-LS and HR-S in a series of single artery and arterial network numerical tests designed to evaluate their well-balanced and wave-capturing properties. The results indicate that HR is not adapted to compute blood flow in large arteries as it is unable to capture wave reflections and transmissions when large variations of the arteries' geometrical and mechanical properties are considered. On the contrary, HR-S is exactly well-balanced and is the most accurate hydrostatic reconstruction technique. However, HR-LS is able to compute low-Shapiro number steady states as well as wave reflections and transmissions with satisfying accuracy and is simpler and computationally less expensive than HR-S. We therefore recommend using HR-LS for 1D blood flow simulations in large arterial network simulations. arXiv -HALPublished in the Journal of Computational Physics. http://dx

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An optimal reconstruction of the human arterial tree from doppler echotracking measurements

Cited by 2 publications

References 7 publications

Well‐balanced high‐order solver for blood flow in networks of vessels with variable properties

Well‐balanced high‐order solver for blood flow in networks of vessels with variable properties

Low-Shapiro hydrostatic reconstruction technique for blood flow simulation in large arteries with varying geometrical and mechanical properties

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