A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows

Based upon dynamical systems theory, a fixed point of a vector field such as the wall shear stress (WSS) at the luminal surface of a vessel is a point where the vector field vanishes. Unstable/stable manifolds identify contraction/expansion regions linking fixed points. The significance of such WSS topological features lies in their strong link with “disturbed” flow features like flow stagnation, separation and reversal, deemed responsible for vascular dysfunction initiation and progression. Here, we present a Eulerian method to analyze WSS topological skeleton through the identification and classification of WSS fixed points and manifolds in complex vascular geometries. The method rests on the volume contraction theory and analyzes the WSS topological skeleton through the WSS vector field divergence and Poincare´ index. The method is here applied to computational hemodynamics models of carotid bifurcation and intracranial aneurysm. An in-depth analysis of the time dependence of the WSS topological skeleton along the cardiac cycle is provided, enriching the information obtained from cycle-average WSS. Among the main findings, it emerges that on the carotid bifurcation, instantaneous WSS fixed points co-localize with cycle-average WSS fixed points for a fraction of the cardiac cycle ranging from 0 to 14.5 % ; a persistent instantaneous WSS fixed point confined on the aneurysm dome does not co-localize with the cycle-average low-WSS region. In conclusion, the here presented approach shows the potential to speed up studies on the physiological significance of WSS topological skeleton in cardiovascular flows, ultimately increasing the chance of finding mechanistic explanations to clinical observations

Wall shear stress topological skeleton analysis in cardiovascular flows: Methods and applications

A marked interest has recently emerged regarding the analysis of the wall shear stress (WSS) vector field topological skeleton in cardiovascular flows. Based on dynamical system theory, the WSS topological skeleton is composed of fixed points, i.e., focal points where WSS locally vanishes, and unstable/stable manifolds, consisting of contraction/expansion regions linking fixed points. Such an interest arises from its ability to reflect the presence of near-wall hemodynamic features associated with the onset and progression of vascular diseases. Over the years, Lagrangian-based and Eulerianbased post-processing techniques have been proposed aiming at identifying the topological skeleton features of the WSS. Here, the theoretical and methodological bases supporting the Lagrangian- and Eulerian-based methods currently used in the literature are reported and discussed, highlighting their application to cardiovascular flows. The final aim is to promote the use of WSS topological skeleton analysis in hemodynamic applications and to encourage its application in future mechanobiology studies in order to increase the chance of elucidating the mechanistic links between blood flow disturbances, vascular disease, and clinical observations

Deciphering ascending thoracic aortic aneurysm hemodynamics in relation to biomechanical properties

The degeneration of the arterial wall at the basis of the ascending thoracic aortic aneurysm (ATAA) is a complex multifactorial process, which may lead to clinical complications and, ultimately, death. Individual genetic, biological or hemodynamic factors are inadequate to explain the heterogeneity of ATAA development/progression mechanisms, thus stimulating the analysis of their complex interplay. Here the disruption of the hemodynamic environment in the ATAA is investigated integrating patient-specific computational hemodynamics, CT-based in vivo estimation of local aortic stiffness and advanced fluid mechanics methods of analysis. The final aims are (1) deciphering the ATAA spatiotemporal hemodynamic complexity and its link to near-wall topological features, and (2) identifying the existing links between arterial wall degeneration and hemodynamic insult. Technically, two methodologies are applied to computational hemodynamics data, the wall shear stress (WSS) topological skeleton analysis, and the Complex Networks theory. The same analysis was extended to the healthy aorta. As main findings of the study, we report that: (1) different spatiotemporal heterogeneity characterizes the ATAA and healthy hemodynamics, that markedly reflect on their WSS topological skeleton features; (2) a link (stronger than canonical WSS-based descriptors) emerges between the variation of contraction/expansion action exerted by WSS on the endothelium along the cardiac cycle, and ATAA wall stiffness. The findings of the study suggest the use of advanced methods for a deeper understanding of the hemodynamics disruption in ATAA, and candidate WSS topological skeleton features as promising indicators of local wall degeneration

Doctor of Philosophy

dissertationHigh arterial tortuosity, or twistedness, is a sign of many vascular diseases. Some ocular diseases are clinically diagnosed in part by assessment of increased tortuosity of ocular blood vessels. Increased arterial tortuosity is seen in other vascular diseases but is not commonly used for clinical diagnosis. This study develops the use of existing magnetic resonance angiography (MRA) image data to study arterial tortuosity in a range of arteries of hypertensive and intracranial aneurysm patients. The accuracy of several centerline extraction algorithms based on Dijkstra's algorithm was measured in numeric phantoms. The stability of the algorithms was measured in brain arteries. A centerline extraction algorithm was selected based on its accuracy. A centerline tortuosity metric was developed using a curve of tortuosity scores. This tortuosity metric was tested on phantoms and compared to observer-based tortuosity rankings on a test data set. The tortuosity metric was then used to measure and compare with negative controls the tortuosity of brain arteries from intracranial aneurysm and hypertension patients. A Dijkstra based centerline extraction algorithm employing a distance-from-edge weighted center of mass (DFE-COM) cost function of the segmented arteries was selected based on generating 15/16 anatomically correct centerlines in a looping artery iv compared to 15/16 for the center of mass (COM) cost function and 7/16 for the inverse modified distance from edge cost function. The DFE-COM cost function had a lower root mean square error in a lopsided phantom (0.413) than the COM cost function (0.879). The tortuosity metric successfully ordered electronic phantoms of arteries by tortuosity. The tortuosity metric detected an increase in arterial tortuosity in hypertensive patients in 13/13 (10/13 significant at α = 0.05). The metric detected increased tortuosity in a subset of the aneurysm patients with Loeys-Dietz syndrome (LDS) in 7/7 (three significant at α = 0.001). The tortuosity measurement combination of the centerline algorithm and the distance factor metric tortuosity curve was able to detect increases in arterial tortuosity in hypertensives and LDS patients. Therefore the methods validated here can be used to study arterial tortuosity in other hypertensive population samples and in genetic subsets related to LDS

Automatic segmentation of coronary angiograms based on fuzzy inferring and probabilistic tracking

<p>Abstract</p> <p>Background</p> <p>Segmentation of the coronary angiogram is important in computer-assisted artery motion analysis or reconstruction of 3D vascular structures from a single-plan or biplane angiographic system. Developing fully automated and accurate vessel segmentation algorithms is highly challenging, especially when extracting vascular structures with large variations in image intensities and noise, as well as with variable cross-sections or vascular lesions.</p> <p>Methods</p> <p>This paper presents a novel tracking method for automatic segmentation of the coronary artery tree in X-ray angiographic images, based on probabilistic vessel tracking and fuzzy structure pattern inferring. The method is composed of two main steps: preprocessing and tracking. In preprocessing, multiscale Gabor filtering and Hessian matrix analysis were used to enhance and extract vessel features from the original angiographic image, leading to a vessel feature map as well as a vessel direction map. In tracking, a seed point was first automatically detected by analyzing the vessel feature map. Subsequently, two operators [e.g., a probabilistic tracking operator (PTO) and a vessel structure pattern detector (SPD)] worked together based on the detected seed point to extract vessel segments or branches one at a time. The local structure pattern was inferred by a multi-feature based fuzzy inferring function employed in the SPD. The identified structure pattern, such as crossing or bifurcation, was used to control the tracking process, for example, to keep tracking the current segment or start tracking a new one, depending on the detected pattern.</p> <p>Results</p> <p>By appropriate integration of these advanced preprocessing and tracking steps, our tracking algorithm is able to extract both vessel axis lines and edge points, as well as measure the arterial diameters in various complicated cases. For example, it can walk across gaps along the longitudinal vessel direction, manage varying vessel curvatures, and adapt to varying vessel widths in situations with arterial stenoses and aneurysms.</p> <p>Conclusions</p> <p>Our algorithm performs well in terms of robustness, automation, adaptability, and applicability. In particular, the successful development of two novel operators, namely, PTO and SPD, ensures the performance of our algorithm in vessel tracking.</p

Coronary Artery Stenting Affects Wall Shear Stress Topological Skeleton

Despite the important advancements in the stent technology for the treatment of diseased coronary arteries, major complications still affect the postoperative long-term outcome. The stent-induced flow disturbances, and especially the altered wall shear stress (WSS) profile at the strut level, play an important role in the pathophysiological mechanisms leading to stent thrombosis (ST) and in-stent restenosis (ISR). In this context, the analysis of the WSS topological skeleton is gaining more and more interest by extending the current understanding of the association between local hemodynamics and vascular diseases. This study aims to analyze the impact that a deployed coronary stent has on the WSS topological skeleton. Computational fluid dynamics (CFD) simulations were performed in three stented human coronary artery geometries reconstructed from clinical images. The selected cases presented stents with different designs (i.e., two contemporary drug-eluting stents and one bioresorbable scaffold) and included regions with stent malapposition or overlapping. A recently proposed Eulerian-based approach was applied to analyze the WSS topological skeleton features. The results highlighted that the presence of single or multiple stents within a coronary artery markedly impacts the WSS topological skeleton. In particular, repetitive patterns of WSS divergence were observed at the luminal surface, highlighting a WSS contraction action exerted proximal to the stent struts and a WSS expansion action distal to the stent struts. This WSS action pattern was independent from the stent design. In conclusion, these findings could contribute to a deeper understanding of the hemodynamics-driven processes underlying ST and ISR

Aneurysm Identification in Cerebral Models with Multiview Convolutional Neural Network

Stroke is the third most common cause of death and a major contributor to long-term disability worldwide. Severe stroke is most often caused by the rupture of a cerebral aneurysm, a weakened area in a blood vessel. The detection and quantification of cerebral aneurysms are essential for the prevention and treatment of aneurysmal rupture and cerebral infarction. Here, we propose a novel aneurysm detection method in a three-dimensional (3D) cerebrovascular model based on convolutional neural networks (CNNs). The multiview method is used to obtain a sequence of 2D images on the cerebral vessel branch model. The pretrained CNN is used with transfer learning to overcome the small training sample problem. The data augmentation strategy with rotation, mirroring and flipping helps improve the performance dramatically, particularly on our small datasets. The hyperparameter of the view number is determined in the task. We have applied the labeling task on 56 3D mesh models with aneurysms (positive) and 65 models without aneurysms (negative). The average accuracy of individual projected images is 87.86%, while that of the model is 93.4% with the best view number. The framework is highly effective with quick training efficiency that can be widely extended to detect other organ anomalies

A framework for intracranial saccular aneurysm detection and quantification using morphological analysis of cerebral angiograms

Reliable early prediction of aneurysm rupture can greatly help neurosurgeons to treat aneurysms at the right time, thus saving lives as well as providing significant cost reduction. Most of the research efforts in this respect involve statistical analysis of collected data or simulation of hemodynamic factors to predict the risk of aneurysmal rupture. Whereas, morphological analysis of cerebral angiogram images for locating and estimating unruptured aneurysms is rarely considered. Since digital subtraction angiography (DSA) is regarded as a standard test by the American Stroke Association and American College of Radiology for identification of aneurysm, this paper aims to perform morphological analysis of DSA to accurately detect saccular aneurysms, precisely determine their sizes, and estimate the probability of their ruptures. The proposed diagnostic framework, intracranial saccular aneurysm detection and quantification, first extracts cerebrovascular structures by denoising angiogram images and delineates regions of interest (ROIs) by using watershed segmentation and distance transformation. Then, it identifies saccular aneurysms among segmented ROIs using multilayer perceptron neural network trained upon robust Haralick texture features, and finally quantifies aneurysm rupture by geometrical analysis of identified aneurysmic ROI. De-identified data set of 59 angiograms is used to evaluate the performance of algorithms for aneurysm detection and risk of rupture quantification. The proposed framework achieves high accuracy of 98% and 86% for aneurysm classification and quantification, respectively