Unstructured hexahedral mesh generation of complex vascular trees using a multi-block grid-based approach

The trend towards realistic numerical models of (pathologic) patient-specific vascular structures brings along larger computational domains and more complex geometries, increasing both the computation time and the operator time. Hexahedral grids effectively lower the computational run time and the required computational infrastructure, but at high cost in terms of operator time and minimal cell quality, especially when the computational analyses are targeting complex geometries such as aneurysm necks, severe stenoses and bifurcations. Moreover, such grids generally do not allow local refinements. As an attempt to overcome these limitations, a novel approach to hexahedral meshing is proposed in this paper, which combines the automated generation of multi-block structures with a grid-based method. The robustness of the novel approach is tested on common complex geometries, such as tree-like structures (including trifurcations), stenoses, and aneurysms. Additionally, the performance of the generated grid is assessed using two numerical examples. In the first example, a grid sensitivity analysis is performed for blood flow simulated in an abdominal mouse aorta and compared to tetrahedral grids with a prismatic boundary layer. In the second example, the fluid-structure interaction in a model of an aorta with aortic coarctation is simulated and the effect of local grid refinement is analyzed

Numerical modelling of the fluid-structure interaction in complex vascular geometries

A complex network of vessels is responsible for the transportation of blood throughout the body and back to the heart. Fluid mechanics and solid mechanics play a fundamental role in this transport phenomenon and are particularly suited for computer simulations. The latter may contribute to a better comprehension of the physiological processes and mechanisms leading to cardiovascular diseases, which are currently the leading cause of death in the western world. In case these computational models include patient-specific geometries and/or the interaction between the blood flow and the arterial wall, they become challenging to develop and to solve, increasing both the operator time and the computational time. This is especially true when the domain of interest involves vascular pathologies such as a local narrowing (stenosis) or a local dilatation (aneurysm) of the arterial wall. To overcome these issues of high operator times and high computational times when addressing the bio(fluid)mechanics of complex geometries, this PhD thesis focuses on the development of computational strategies which improve the generation and the accuracy of image-based, fluid-structure interaction (FSI) models. First, a robust procedure is introduced for the generation of hexahedral grids, which allows for local grid refinements and automation. Secondly, a straightforward algorithm is developed to obtain the prestress which is implicitly present in the arterial wall of a – by the blood pressure – loaded geometry at the moment of medical image acquisition. Both techniques are validated, applied to relevant cases, and finally integrated into a fluid-structure interaction model of an abdominal mouse aorta, based on in vivo measurements

Numerical Insights for AAA Growth Understanding and Predicting: Morphological and Hemodynamic Risk Assessment Features and Transient Coherent Structures Uncovering

Les anévrismes de l'aorte abdominale (AAA) sont des dilatations localisées et fréquentes de l'aorte. En cas de rupture, seul un traitement immédiat peut prévenir la morbidité et la mortalité. Le diamètre maximal AAA ($D_{max}$) et la croissance sont les paramètres actuels pour évaluer le risque associé et planifier l'intervention, avec des seuils inférieurs pour les femmes. Cependant, ces critères ne sont pas personnalisés ; la rupture peut se produire à un diamètre inférieur et les patients vivre avec un AAA important. Si l'on sait que la maladie est associée à une modification de la morphologie et de la circulation sanguine, à un dépôt de thrombus intra-luminal et à des symptômes cliniques, les mécanismes de croissance ne sont pas encore entièrement compris. Dans cette étude longitudinale, une analyse morphologique et des simulations de flux sanguins sont effectuées et comparées aux sujets témoins chez 32 patients ayant reçu un diagnostic clinique d'AAA et au moins 3 tomodensitogrammes de suivi par patient. L'objectif est d'abord d'examiner quels paramètres stratifient les patients entre les groupes sains, à faible risque et à risque élevé. Les corrélations locales entre les paramètres hémodynamiques et la croissance de l'AAA sont également explorées, car la croissance hétérogène de l'AAA n'est actuellement pas comprise. Enfin, les paramètres composites sont construits à partir de données cliniques, morphologiques et hémodynamiques et de leur capacité à prédire si un patient sera soumis à un test de risque. La performance de ces modèles construits à partir de l'apprentissage supervisé est évaluée par les ROC AUC : ils sont respectivement de 0.73 ± 0.09, 0.93 ± 0.08 et 0.96 ± 0.10 . En incorporant tous les paramètres, on obtient une AUC de 0.98 ± 0.06. Pour mieux comprendre les interactions entre la croissance et la topologie de l'écoulement de l'AAA, on propose un worflow spécifique au patient pour calculer les exposants de Lyapunov en temps fini et extraire les structures lagrangiennes-cohérentes (SLC). Ce modèle de calcul a d'abord été comparé à l'imagerie par résonance magnétique (IRM) par contraste de phase 4-D chez 5 patients. Pour mieux comprendre l'impact de la topologie de l'écoulement et du transport sur la croissance de l'AAA, des SLC hyperboliques répulsives ont été calculées chez un patient au cours d'un suivi de 8 ans, avec 9 mesures morphologiques volumétriques de l'AAA par tomographie-angiographie. Les SLC ont défini les frontières du jet entrant dans l'AAA. Les domaines situés entre le SLC et le mur aortique ont été considérés comme des zones de stagnation. Leur évolution a été étudiée lors de la croissance de l'AAA. En plus des SLC hyperboliques (variétés attractives et répulsives) découvertes par FTLE, les SLC elliptiques ont également été considérées. Il s'agit de régions dominées par la rotation, ou tourbillons, qui sont de puissants outils pour comprendre les phénomènes de transport dans les AAA.Abdominal aortic aneurysms (AAA) are localized, commonly-occurring dilations of the aorta. In the event of rupture only immediate treatment can prevent morbidity and mortality. The AAA maximal diameter ($D_{max}$) and growth are the current metrics to evaluate the associated risk and plan intervention, with lower thresholds for women. However, these criteria lack patient specificity; rupture may occur at lower diameter and patients may live with large AAA. If the disease is known to be associated with altered morphology and blood flow, intra-luminal thrombus deposit and clinical symptoms, the growth mechanisms are yet to be fully understood. In this longitudinal study, morphological analysis and blood flow simulations for 32 patients with clinically diagnosed AAA and at least 3 follow-up CT-scans per patient, are performed and compared to control subjects. The aim is first to investigate which metrics stratify patients between healthy, low risk and high risk groups. Local correlations between hemodynamical metrics and AAA growth are also explored, as AAA heterogeneous growth is currently not understood. Finally, composite metrics are built from clinical, morphological, and hemodynamical data, and their ability to predict if a patient will become at risk tested. Performance of these models built from supervised learning is assessed by ROC AUCs: they are respectively, 0.73 ± 0.09, 0.93 ± 0.08 and 0.96 ± 0.10. Mixing all metrics, an AUC of 0.98 ± 0.06 is obtained. For further insights into AAA flow topology/growth interaction, a workout of patient-specific computational flow dynamics (CFD) is proposed to compute finite-time Lyapunov exponents and extract Lagrangian-coherent structures (LCS). This computational model was first compared with 4-D phase-contrast magnetic resonance imaging (MRI) on 5 patients. To better understand the impact of flow topology and transport on AAA growth, hyperbolic, repelling LCS were computed in 1 patient during 8-years follow-up, including 9 volumetric morphologic AAA measures by computed tomography-angiography (CTA). LCS defined barriers to Lagrangian jet cores entering AAA. Domains enclosed between LCS and the aortic wall were considered to be stagnation zones. Their evolution was studied during AAA growth. In addition to hyperbolic (attracting and repelling) LCS uncovered by FTLE, elliptic LCS were also considered. Those encloses rotation-dominated regions, or vortices, which are powerful tools to understand the flow transport in AAA

Higher-order block-structured hex meshing of tubular structures

Numerical simulations of the cardiovascular system are growing in popularity due to the increasing availability of computational power, and their proven contribution to the understanding of pathodynamics and validation of medical devices with in-silico trials as a potential future breakthrough. Such simulations are performed on volumetric meshes reconstructed from patient-specific imaging data. These meshes are most often unstructured, and result in a brutally large amount of elements, significantly increasing the computational complexity of the simulations, whilst potentially adversely affecting their accuracy. To reduce such complexity, we introduce a new approach for fully automatic generation of higher-order, structured hexahedral meshes of tubular structures, with a focus on healthy blood vessels. The structures are modeled as skeleton-based convolution surfaces. From the same skeleton, the topology is captured by a block-structure, and the geometry by a higher-order surface mesh. Grading may be induced to obtain tailored refinement, thus resolving, e.g., boundary layers. The volumetric meshing is then performed via transfinite mappings. The resulting meshes are of arbitrary order, their elements are of good quality, while the spatial resolution may be as coarse as needed, greatly reducing computing time. Their suitability for practical applications is showcased by a simulation of physiological blood flow modelled by a generalised Newtonian fluid in the human aorta

A computational framework for generating patient-specific vascular models and assessing uncertainty from medical images

Patient-specific computational modeling is a popular, non-invasive method to answer medical questions. Medical images are used to extract geometric domains necessary to create these models, providing a predictive tool for clinicians. However, in vivo imaging is subject to uncertainty, impacting vessel dimensions essential to the mathematical modeling process. While there are numerous programs available to provide information about vessel length, radii, and position, there is currently no exact way to determine and calibrate these features. This raises the question, if we are building patient-specific models based on uncertain measurements, how accurate are the geometries we extract and how can we best represent a patient's vasculature? In this study, we develop a novel framework to determine vessel dimensions using change points. We explore the impact of uncertainty in the network extraction process on hemodynamics by varying vessel dimensions and segmenting the same images multiple times. Our analyses reveal that image segmentation, network size, and minor changes in radius and length have significant impacts on pressure and flow dynamics in rapidly branching structures and tapering vessels. Accordingly, we conclude that it is critical to understand how uncertainty in network geometry propagates to fluid dynamics, especially in clinical applications.Comment: 21 pages, 9 figure

Vascular Modeling from Volumetric Diagnostic Data: A Review

Reconstruction of vascular trees from digital diagnostic images is a challenging task in the development of tools for simulation and procedural planning for clinical use. Improvements in quality and resolution of acquisition modalities are constantly increasing the fields of application of computer assisted techniques for vascular modeling and a lot of Computer Vision and Computer Graphics research groups are currently active in the field, developing methodologies, algorithms and software prototypes able to recover models of branches of human vascular system from different kinds of input images. Reconstruction methods can be extremely different according to image type, accuracy requirements and level of automation. Some technologies have been validated and are available on medical workstation, others have still to be validated in clinical environments. It is difficult, therefore, to give a complete overview of the different approach used and results obtained, this paper just presents a short review including some examples of the principal reconstruction approaches proposed for vascular reconstruction, showing also the contribution given to the field by the Medical Application Area of CRS4, where methods to recover vascular models have been implemented and used for blood flow analysis, quantitative diagnosis and surgical planning tools based on Virtual Reality