Application of the lattice Boltzmann model to simulated stenosis growth in a two-dimensional carotid artery

Boyd, J.; Buick, James; Cosgrove, J. A.; Stansell, Paul

doi:10.1088/0031-9155/50/20/003

Cited by 47 publications

(37 citation statements)

References 34 publications

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“…We note that LB may be adapted to Stokes flow, in which the fluid inertia is ignored in a regime of very small Re [15], but its simplest and most effective form lies in approximating the full Navier-Stokes equations. LB has previously been used to simulate blood flow (i) at the macroscopic, arterial level [23][24][25], (ii) at the microscopic level [16,26], and (iii) to simulate many deformable droplets in flow [27].…”

Section: B Fluid Dynamics: Lattice Boltzmann (Lb)mentioning

confidence: 99%

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Modeling the flow of dense suspensions of deformable particles in three dimensions

et al. 2007

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We describe here a rigorous and accurate model for the simulation of three-dimensional deformable particles (DPs). The method is very versatile, easily simulating various types of deformable particles such as vesicles, capsules, and biological cells. Each DP is resolved explicitly and advects within the surrounding Newtonian fluid. The DPs have a preferred rest shape (e.g., spherical for vesicles, or biconcave for red blood cells). The model uses a classic hybrid system: an Eulerian approach is used for the Navier-Stokes solver (the lattice Boltzmann method) and a Lagrangian approach for the evolution of the DP mesh. Coupling is accomplished through the lattice Boltzmann velocity field, which transmits force to the membranes of the DPs. The novelty of this method resides in its ability (by design) to simulate a large number of DPs within the bounds of current computational limitations: our simple and efficient approach is to (i) use the lattice Boltzmann method because of its acknowledged efficiency at low Reynolds number and its ease of parallelization, and (ii) model the DP dynamics using a coarse mesh (approximately 500 nodes) and a spring model constraining (if necessary) local area, total area, cell volume, local curvature, and local primary stresses. We show that this approach is comparable to the more common-yet numerically expensive-approach of membrane potential function, through a series of quantitative comparisons. To demonstrate the capabilities of the model, we simulate the flow of 200 densely packed red blood cells-a computationally challenging task. The model is very efficient, requiring of the order of minutes for a single DP in a 50 μm×40 μm×40 μm simulation domain and only hours for 200 DPs in 80 μm×30 μm×30 μm. Moreover, the model is highly scalable and efficient compared to other models of blood cells in flow, making it an ideal and unique tool for studying blood flow in microvessels or vesicle or capsule flow (or a mixture of different particles). In addition to directly predicting fluid dynamics in complex suspension in any geometry, the model allows determination of accurate, empirical rules which may improve existing macroscopic, continuum models.

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Section: B Fluid Dynamics: Lattice Boltzmann (Lb)mentioning

confidence: 99%

“…Viscoelasticity may, however, be easily incorporated, following Bagchi's simple and elegant approach [13], by adding ( 25 ) to the total force on the DP membrane.…”

Section: Coupling Of Dp and Fluid Dynamicsmentioning

confidence: 99%

Modeling the flow of dense suspensions of deformable particles in three dimensions

et al. 2007

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“…These US images could, possibly, also be used to derive growth patterns of the individual AACs, but in the current study we have focused on the X-ray images. Previously conducted studies from CT and X-rays have focused on growth models based on arterial geometry, blood rate, and kinematics of finite growth combined with open system thermodynamics [30,31,11,4,10,32,33]. These studies have been based on cross-sectional data or a simulation model with a relative small population size (n \ 10).…”

Section: Longitudinal Studymentioning

confidence: 99%

Growth patterns of abdominal atherosclerotic calcified deposits from lumbar lateral X-rays

Lillemark

Ganz

Barascuk

et al. 2010

Int J Cardiovasc Imaging

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The aim of this study is to investigate new methods for describing the progression of atherosclerosis based on novel information of the growth patterns of individual abdominal aortic calcifications (AACs) over time. Lateral X-ray images were used due to their low cost, fast examination time, and wide-spread use, which facilitates a large statistical model (n > 100) based on longitudinal data. The examined cohort consisted of 103 post-menopausal women aged 62.4 years (± 7.0 years) with an average number of AACs of (4.7 ± 8.0) at baseline. The subjects had X-ray images taken in 1992-1993 (baseline) and again in 2000-2001 (follow-up). The growth patterns of the individual AACs were derived based on registered baseline and follow-up images. Area, height, width, centre of mass position, and movement of the centre of mass, and upper and lower boundary of the matched AACs were measured. The AACs occurred first, mainly, on the posterior aortic wall. The AACs grew on average 41 in the longitudinal direction and 21 in the radial direction. A correlation of 0.48 (P < 0.001) between growth in width and height of the AACs was present. The centre of mass of the AACs moved 0.60 mm (P < 0.001) downstream in the aorta, on average. The growth patterns of AACs may give new insights into the progression of atherosclerosis. The downstream asymmetry in the growth patterns indicates variability in microscopic environments around the AACs.

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“…The LB method is chosen as it has been used previously to capture both blood flow [17][18][19][20] and fluid-structure interactions [21][22][23][24][25][26]. Only a brief description of the LB method is given here and the reader is referred to the works of Verberg and Ladd [27,28], Frisch et al [29], He and Luo [30,31], and d'Humières et al [32] for a more complete description.…”

Section: Fluid Dynamicsmentioning

confidence: 99%

Computational Phlebology: The Simulation of a Vein Valve

Buxton

Clarke

2006

J Biol Phys

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We present a three-dimensional computer simulation of the dynamics of a vein valve. In particular, we couple the solid mechanics of the vein wall and valve leaflets with the fluid dynamics of the blood flow in the valve. Our model captures the unidirectional nature of blood flow in vein valves; blood is allowed to flow proximally back to the heart, while retrograde blood flow is prohibited through the occlusion of the vein by the valve cusps. Furthermore, we investigate the dynamics of the valve opening area and the blood flow rate through the valve, gaining new insights into the physics of vein valve operation. It is anticipated that through computer simulations we can help raise our understanding of venous hemodynamics and various forms of venous dysfunction.

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Application of the lattice Boltzmann model to simulated stenosis growth in a two-dimensional carotid artery

Cited by 47 publications

References 34 publications

Modeling the flow of dense suspensions of deformable particles in three dimensions

Modeling the flow of dense suspensions of deformable particles in three dimensions

Growth patterns of abdominal atherosclerotic calcified deposits from lumbar lateral X-rays

Computational Phlebology: The Simulation of a Vein Valve

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