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Hodge decomposition of wall shear stress vector fields characterizing biological flows.

ABSTRACT: A discrete boundary-sensitive Hodge decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results for the smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into five components: gradient (curl-free), co-gradient (divergence-free) and three harmonic fields induced from the boundary, which are called the centre, Neumann and Dirichlet fields. First, an analysis of WSS in several simulated simplified phantom geometries (duct and idealized aorta) was performed in order to understand the nature of the five components. It was shown that the decomposition is able to distinguish harmonic blood flow arising from the inlet from harmonic circulations induced by the interior topology of the geometry. Finally, a comparative analysis of 11 patients with coarctation of the aorta (CoA) before and after treatment as well as 10 control patients was done. The study shows a significant difference between the CoA patients before and after the treatment, and the healthy controls. This means a global difference between aortic shapes of diseased and healthy subjects, thus leading to a new type of WSS-based analysis and classification of pathological and physiological blood flow.

SUBMITTER: Razafindrazaka FH

PROVIDER: S-EPMC6408383 | biostudies-literature | 2019 Feb

REPOSITORIES: biostudies-literature

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Hodge decomposition of wall shear stress vector fields characterizing biological flows.

Razafindrazaka Faniry H FH Yevtushenko Pavlo P Poelke Konstantin K Polthier Konrad K Goubergrits Leonid L

Royal Society open science 20190206 2

A discrete boundary-sensitive Hodge decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results for the smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into five components: gradient (curl-free), co-gradient (divergence-free) and three harmonic fields induced from the boundary, which are called the centre, Neumann and Diric ...[more]

PMID: 30891301

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Project description:AimsAtherosclerotic plaque development has been associated with wall shear stress (WSS). However, the multidirectionality of blood flow, and thus of WSS, is rarely taken into account. The purpose of this study was to comprehensively compare five metrics that describe (multidirectional) WSS behaviour and assess how WSS multidirectionality affects coronary plaque initiation and progression.Methods and resultsAdult familial hypercholesterolaemic pigs (n = 10) that were fed a high-fat diet, underwent imaging of the three main coronary arteries at three-time points [3 (T1), 9 (T2), and 10-12 (T3) months]. Three-dimensional geometry of the arterial lumen, in combination with local flow velocity measurements, was used to calculate WSS at T1 and T2. For analysis, arteries were divided into 3 mm/45° sectors (n = 3648). Changes in wall thickness and final plaque composition were assessed with near-infrared spectroscopy-intravascular ultrasound, optical coherence tomography imaging, and histology. Both in pigs with advanced and mild disease, the highest plaque progression rate was exclusively found at low time-averaged WSS (TAWSS) or high multidirectional WSS regions at both T1 and T2. However, the eventually largest plaque growth was located in regions with initial low TAWSS or high multidirectional WSS that, over time, became exposed to high TAWSS or low multidirectional WSS at T2. Besides plaque size, also the presence of vulnerable plaque components at the last time point was related to low and multidirectional WSS. Almost all WSS metrics had good predictive values for the development of plaque (47-50%) and advanced fibrous cap atheroma (FCA) development (59-61%).ConclusionThis study demonstrates that low and multidirectional WSS promote both initiation and progression of coronary atherosclerotic plaques. The high-predictive values of the multidirectional WSS metrics for FCA development indicate their potential as an additional clinical marker for the vulnerable disease.

Project description:BackgroundBlood flowing in the arterial lumen acts on the surface of the vessel wall to form wall shear stress (WSS). To date, there has been limited research on the utility of non-invasive technology in the accurate quantification of carotid WSS in patients with hypertension (HP).ObjectiveThe present study aimed to explore the usage of vascular vector flow mapping (VFM) in the quantitative assessment of carotid WSS in hypertensive patients at an early stage and to validate its clinical utility.MethodsA total of 50 individuals confirmed without carotid plaques were grouped into a HP group (n = 25) and a control (CON) group (n = 25) according to blood pressure. An ALOKA LISENDO 880 Color Doppler Ultrasound with a L441 3-15 MHZ probe was used to obtain a longitudinal section scan to determine the regions of interests (ROIs) of the common carotid artery. VFM-based WSS measurements were obtained by selecting the ROI with optimal image quality from three full cardiac cycles. WSS-derived measurements, including WSSmax, WSSmin, and WSSmean, were analyzed and compared between the HP and CON groups. In addition, the correlations between WSS-derived measurements and the carotid artery intima-media thickness (IMT) were also analyzed.ResultsThere were significant statistical differences in WSSmax and WSSmean between patients in the HP and CON groups. Specifically, the HP group had significantly decreased WSSmax and WSSmean compared to the CON group (WSSmax: 1.781 ± 0.305 Pa vs. 2.286 ± 0.257 Pa; WSSmean: 1.276 ± 0.333 Pa vs. 1.599 ± 0.293 Pa, both p < 0.001). However, there was no statistical difference in WSSmin between the groups (0.79 ± 0.36 vs. 0.99 ± 0.42, p = 0.080). Additionally, Spearman's correlation analysis indicated that the WSS-derived parameters were negatively correlated with the IMT (p < 0.001).ConclusionVascular VFM technology shows promising results in the quantitative assessment of difference in hemodynamics of the vascular flow field between patients with HP and normal controls. Difference in WSS may serve as a potential predictor for the development of arteriosclerosis risks.

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Hodge decomposition of wall shear stress vector fields characterizing biological flows.

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Hodge decomposition of wall shear stress vector fields characterizing biological flows.

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