Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow

Zhang, Yongjie; Bazilevs, Yuri; Goswami, Sumanta; Bajaj, Chandrajit L.; Hughes, Thomas J.R.

doi:10.1016/j.cma.2007.02.009

Cited by 366 publications

(194 citation statements)

References 40 publications

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“…IGA methodologies have been summarized in the recent book [18] and studied in, e.g., [2,4,9,10,19,23,28,29,11,5,8]. IGA methods are having a growing impact on fields as diverse as fluid dynamics [6,7,40,15,26], structural mechanics [3,1,12,20,30,39], and electromagnetics [17,16].…”

mentioning

confidence: 99%

Overlapping Schwarz Methods for Isogeometric Analysis

Veiga¹,

Cho²,

Pavarino³

et al. 2012

SIAM J. Numer. Anal.

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Abstract. We construct and analyze an overlapping Schwarz preconditioner for elliptic problems discretized with isogeometric analysis. The preconditioner is based on partitioning the domain of the problem into overlapping subdomains, solving local isogeometric problems on these subdomains, and solving an additional coarse isogeometric problem associated with the subdomain mesh. We develop an h-analysis of the preconditioner, showing in particular that the resulting algorithm is scalable and its convergence rate depends linearly on the ratio between subdomain and "overlap sizes" for fixed polynomial degree p and regularity k of the basis functions. Numerical results in two-and three-dimensional tests show the good convergence properties of the preconditioner with respect to the isogeometric discretization parameters h, p, k, number of subdomains N , overlap size, and also jumps in the coefficients of the elliptic operator.Key words. domain decomposition methods, overlapping Schwarz, scalable preconditioners, isogeometric analysis, finite elements, NURBS AMS subject classifications. 65N55, 65N30, 65F10 DOI. 10.1137/110833476 1. Introduction. Isogeometric analysis (IGA) based on NURBS (nonuniform rational B-splines) was introduced by Hughes, Cottrell, and Bazilevs in [27] as an innovative numerical methodology for the analysis of PDE problems, allowing for an exact description of CAD-type geometries. NURBS are a standard in the computeraided design (CAD) community mainly because such spline functions allow excellent representations of free-form surfaces, and there are very efficient algorithms for their evaluation, refinement, and derefinement. In the isogeometric framework, the NURBS basis functions representing the CAD geometry are also used as the basis for the discrete solution space of PDEs, following an isoparametric paradigm. In addition to exact representation of CAD geometries, another advantage of using NURBS basis functions is the higher control on the regularity of the discrete space. For instance, spaces of global C k regularity are easily built, thus allowing for fewer degrees of freedom, better performance in case of vibrations, easier approximation of higher order problems, and other advantages. IGA methodologies have been summarized in the recent book [18] and studied in, e.g., [2,4,9,10,19,23,28,29,11,5,8]. IGA methods are having a growing impact on fields as diverse as fluid dynamics [6,7,40,15,26], structural mechanics [3,1,12,20,30,39], and electromagnetics [17,16].The discrete systems produced by isogeometric methods are better conditioned than the systems produced by standard finite elements or finite differences, but their conditioning can still degenerates rapidly for decreasing mesh size h, increasing poly-

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mentioning

confidence: 99%

Overlapping Schwarz Methods for Isogeometric Analysis

Veiga¹,

Cho²,

Pavarino³

et al. 2012

SIAM J. Numer. Anal.

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“…The target surfaces (the lumen-wall interface) are then extracted by isocontouring the pre-segmented imaging data, followed by the extraction of the vascular skeleton (vessel centrelines) using open-source software [34,35]. Finally, an optimized skeletonbased sweeping method is used to construct hexahedral control meshes employing an in-house numerical code [24] as follows. The geometry is first decomposed into mapped meshable piecewise linear patches.…”

Section: Reconstructing the Patient-specific Vascular Geometrymentioning

confidence: 99%

“…Here, an image-based pipeline, as detailed in [24], is adopted to construct hexahedral solid NURBS meshes for patient-specific vascular geometric models to be used in isogeometric analysis. Briefly, the image quality is first improved by passing the raw imaging data through a preprocessing pipeline for enhancing the contrast, filtering noise, classifying and segmenting regions of various materials.…”

Section: Reconstructing the Patient-specific Vascular Geometrymentioning

confidence: 99%

“…The isogeometric framework uses geometric primitives (NURBS: non-uniform rational B-splines) developed in computer-aided design and computational geometry, which allows us to represent geometrical objects with a higher degree of precision and smoothness (higher order basis functions with continuous derivatives) than piecewise polynomials (continuous, but not smooth, basis functions) commonly used in finite-element analysis [24]. The ability of NURBS to accurately represent smooth exact geometries (i.e.…”

Section: Introductionmentioning

confidence: 99%

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Magnetic resonance imaging-based computational modelling of blood flow and nanomedicine deposition in patients with peripheral arterial disease

Hossain

Zhang

et al. 2015

J. R. Soc. Interface.

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Peripheral arterial disease (PAD) is generally attributed to the progressive vascular accumulation of lipoproteins and circulating monocytes in the vessel walls leading to the formation of atherosclerotic plaques. This is known to be regulated by the local vascular geometry, haemodynamics and biophysical conditions. Here, an isogeometric analysis framework is proposed to analyse the blood flow and vascular deposition of circulating nanoparticles (NPs) into the superficial femoral artery (SFA) of a PAD patient. The local geometry of the blood vessel and the haemodynamic conditions are derived from magnetic resonance imaging (MRI), performed at baseline and at 24 months post intervention. A dramatic improvement in blood flow dynamics is observed post intervention. A 500% increase in peak flow rate is measured in vivo as a consequence of luminal enlargement. Furthermore, blood flow simulations reveal a 32% drop in the mean oscillatory shear index, indicating reduced disturbed flow post intervention. The same patient information (vascular geometry and blood flow) is used to predict in silico in a simulation of the vascular deposition of systemically injected nanomedicines. NPs, targeted to inflammatory vascular molecules including VCAM-1, E-selectin and ICAM-1, are predicted to preferentially accumulate near the stenosis in the baseline configuration, with VCAM-1 providing the highest accumulation (approx. 1.33 and 1.50 times higher concentration than that of ICAM-1 and E-selectin, respectively). Such selective deposition of NPs within the stenosis could be effectively used for the detection and treatment of plaques forming in the SFA. The presented MRI-based computational protocol can be used to analyse data from clinical trials to explore possible correlations between haemodynamics and disease progression in PAD patients, and potentially predict disease occurrence as well as the outcome of an intervention.

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“…The range of applications in which curve-skeletons are used is wide and comprises computer animation [3], shape matching [4], modelling [5], remeshing and quad layout extraction [6], polycube [7], and hexahedral mesh construction [8]. Since each of these applications requires skeletons with different properties, further processing is often required in order to obtain optimal results in the pipeline in which they will be used.…”

Section: Introductionmentioning

confidence: 99%

An interactive editor for curve-skeletons: SkeletonLab

Barbieri

Meloni

Usai

et al. 2016

Computers & Graphics

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Curve-skeletons are powerful shape descriptors able to provide higher level information on topology, structure and semantics of a given digital object. Their range of application is wide and encompasses computer animation, shape matching, modelling and remeshing. While a universally accepted definition of curve-skeleton is still lacking, there are currently many algorithms for the curve-skeleton computation (or skeletonization) as well as different techniques for building a mesh around a given curve-skeleton (inverse skeletonization). Despite their widespread use, automatically extracted skeletons usually need to be processed in order to be used in further stages of any pipeline, due to different requirements. We present here an advanced tool, named SkeletonLab, that provides simple interactive techniques to rapidly and automatically edit and repair curve skeletons generated using different techniques proposed in literature, as well as handcrafting them. The aim of the tool is to allow trained practitioners to manipulate the curve-skeletons obtained with skeletonization algorithms in order to fit their specific pipelines or to explore the requirements of newly developed techniques.

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Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow

Cited by 366 publications

References 40 publications

Overlapping Schwarz Methods for Isogeometric Analysis

Overlapping Schwarz Methods for Isogeometric Analysis

Magnetic resonance imaging-based computational modelling of blood flow and nanomedicine deposition in patients with peripheral arterial disease

An interactive editor for curve-skeletons: SkeletonLab

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