Abstract
Quantification of 3-D intravascular flow is valuable for studying arterial wall diseases but currently there is a lack of effective clinical tools for this purpose. Divergence-free interpolation (DFI) using radial basis function (RBF) is an emerging approach for full-field flow reconstruction using experimental sparse flow field samples. Previous DFI reconstructs full-field flow from scattered 3-D velocity input obtained using phase-contrast magnetic resonance imaging with low temporal resolution. In this study, a new DFI algorithm is proposed to reconstruct full-field flow from scattered 2-D in-plane velocity vectors obtained using ultrafast contrast-enhanced ultrasound (>1000 fps) and particle imaging velocimetry. The full 3-D flow field is represented by a sum of weighted divergence-free RBFs in space. Because the acquired velocity vectors are only in 2-D and hence the problem is ill-conditioned, a regularized solution of the RBF weighting is achieved through singular value decomposition (SVD) and the L-curve method. The effectiveness of the algorithm is determined via numerical experiments for Poiseuille flow and helical flow with added noise, and it is found that an accuracy as high as 95.6% can be achieved for Poiseuille flow (with 5% input noise). Experimental feasibility is also determined by reconstructing full-field 3-D flow from experimental 2-D ultrasound image velocimetry measurements in a carotid bifurcation phantom. The method is typically faster for a range of problems compared with computational fluid dynamics, and has been found to be effective for the three flow cases.
Highlights
Atherosclerosis, caused by the buildup of atheromas in the lining of artery walls and narrowing arteries, can affect any artery in the body, causing diseases such as angina, stroke, heart attack and peripheral artery disease
Development of atherosclerosis is associated with bends and bifurcations in vessel geometry, and it has been hypothesized that flow patterns related to differences in geometry and wall shear stress are involved in the selective localization of atherosclerosis (Glagov et al 1988; Ku et al 1985; Zarins et al 1983)
High-fidelity Computational fluid dynamics (CFD) requires (i) accurate flow domain geometry, which poses a challenge for lumen surface reconstruction from noisy and scattered imaging input, because in many cases imaging input includes missing boundary data with holes resulting from the accessibility limitation of imaging scanners; (ii) reliable 3-D boundary/initial conditions and fluid properties (Johnston et al 2004; Yilmaz and Gundogdu 2008)
Summary
Atherosclerosis, caused by the buildup of atheromas in the lining of artery walls and narrowing arteries, can affect any artery in the body, causing diseases such as angina, stroke, heart attack and peripheral artery disease. We proposed a new 3-D flow reconstruction method using 2-D in-plane projected vectorial data, taking advantage of ultrafast plane wave UIV at a high frame rate (>1000 fps) and divergence-free RBF. B is the planar projection of true 3-D flow vector on two imaging planes, that is, velocity from UIV measurement.
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