Complexity Analysis of Cortical Surface Detects Changes in Future Alzheimer’s Disease Converters

Alzheimer’s disease (AD) is a neurological disorder that creates neurodegenerative changes at several structural and functional levels in human brain tissue. The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of the human brain. In this study we investigate spherical harmonic-based FD (SHFD), thickness and local gyrification index (LGI) to assess whether they identify cortical surface abnormalities toward the conversion to AD. We study 33 AD patients, 122 mild cognitive impairment (MCI) patients (50 MCI-converters and 29 MCI-non converters) and 32 healthy controls (HC). SHFD, thickness and LGI methodology allowed us to perform not only global but also local level assessments in each cortical surface vertex. First, we found that global SHFD decreased in AD and future MCI-converters compared to HC, and in MCI-converters compared to MCI-non-converters. Second, we found that local white matter SHFD was reduced in AD compared to HC and MCI mainly in medial temporal lobe. Third, local white matter SHFD was significantly reduced in MCI-converters compared to MCI-non-converters in distributed areas, including the medial frontal lobe. Thickness and LGI metrics presented a reduction in AD compared to HC. Thickness was significantly reduced in MCI-converters compared to healthy controls in entorhinal cortex and lateral temporal. In summary, SHFD was the only surface measure showing differences between MCI individuals that will convert or remain stable in the next four years. We suggest that SHFD may be an optimal complement to thickness loss analysis in monitoring longitudinal changes in preclinical and clinical stages of AD

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Geometric modeling and optimization over regular domains for graphics and visual computing

The effective construction of parametric representation of complicated geometric objects can facilitate many design, analysis, and simulation tasks in Computer-Aided Design (CAD), Computer-Aided Manufacturing (CAM), and Computer-Aided Engineering (CAE). Given a 3D shape, the procedure of finding such a parametric representation upon a canonical domain is called geometric parameterization. Regular geometric regions, such as polycubes and spheres, are desirable domains for parameterization. Parametric representations defined upon regular geometric domains have many desirable mathematical properties and can facilitate or simplify various surface/solid modeling and processing computation. This dissertation studies the construction of parameterization on regular geometric domains and explores their applications in shape modeling and computer-aided design. Specifically, we studies (1) the surface parameterization on the spherical domain for closed genus-zero surfaces; (2) the surface parameterization on the polycube domain for general closed surfaces; and (3) the volumetric parameterization for 3D-manifolds embedded in 3D Euclidean space. We propose novel computational models to solve these geometric problems. Our computational models reduce to nonlinear optimizations with various geometric constraints. Hence, we also need to explore effective optimization algorithms. The main contributions of this dissertation are three-folded. (1) We developed an effective progressive spherical parameterization algorithm, with an efficient nonlinear optimization scheme subject to the spherical constraint. Compared with the state-of-the-art spherical mapping algorithms, our algorithm demonstrates the advantages of great efficiency, lower distortion, and guaranteed bijectiveness, and we show its applications in spherical harmonic decomposition and shape analysis. (2) We propose a first topology-preserving polycube domain optimization algorithm that simultaneously optimizes polycube domain together with the parameterization to balance the mapping distortion and domain simplicity. We develop effective nonlinear geometric optimization algorithms dealing with variables with and without derivatives. This polycube parameterization algorithm can benefit the regular quadrilateral mesh generation and cross-surface parameterization. (3) We develop a novel quaternion-based optimization framework for 3D frame field construction and volumetric parameterization computation. We demonstrate our constructed 3D frame field has better smoothness, compared with state-of-the-art algorithms, and is effective in guiding low-distortion volumetric parameterization and high-quality hexahedral mesh generation

Wavelet Analysis on the Sphere

The goal of this monograph is to develop the theory of wavelet harmonic analysis on the sphere. By starting with orthogonal polynomials and functional Hilbert spaces on the sphere, the foundations are laid for the study of spherical harmonics such as zonal functions. The book also discusses the construction of wavelet bases using special functions, especially Bessel, Hermite, Tchebychev, and Gegenbauer polynomials

Registration of magnetic resonance and ultrasound images for guiding prostate cancer interventions

Prostate cancer is a major international health problem with a large and rising incidence in many parts of the world. Transrectal ultrasound (TRUS) imaging is used routinely to guide surgical procedures, such as needle biopsy and a number of minimally-invasive therapies, but its limited ability to visualise prostate cancer is widely recognised. Magnetic resonance (MR) imaging techniques, on the other hand, have recently been developed that can provide clinically useful diagnostic information. Registration (or alignment) of MR and TRUS images during TRUS-guided surgical interventions potentially provides a cost-effective approach to augment TRUS images with clinically useful, MR-derived information (for example, tumour location, shape and size). This thesis describes a deformable image registration framework that enables automatic and/or semi-automatic alignment of MR and 3D TRUS images of the prostate gland. The method combines two technical developments in the field: First, a method for constructing patient-specific statistical shape models of prostate motion/deformation, based on learning from finite element simulations of gland motion using geometric data from a preoperative MR image, is proposed. Second, a novel “model-to-image” registration framework is developed to register this statistical shape model automatically to an intraoperative TRUS image. This registration approach is implemented using a novel model-to-image vector alignment (MIVA) algorithm, which maximises the likelihood of a particular instance of a statistical shape model given a voxel-intensity-based feature vector that represents an estimate of the surface normal vectors at the boundary of the organ in question. Using real patient data, the MR-TRUS registration accuracy of the new algorithm is validated using intra-prostatic anatomical landmarks. A rigorous and extensive validation analysis is also provided for assessing the image registration experiments. The final target registration error after performing 100 MR–TRUS registrations for each patient have a median of 2.40 mm, meaning that over 93% registrations may successfully hit the target representing a clinically significant lesion. The implemented registration algorithms took less than 30 seconds and 2 minutes for manually defined point- and normal vector features, respectively. The thesis concludes with a summary of potential applications and future research directions

Contribution à la prévision de l'érosion de cavitation à partir de simulations numériques : proposition d'un modèle à deux échelles pour l'estimation du chargement imposé en paroi par le fluide

During the life's cycle of a hydraulic installation, the occurrence of cavitation can cause significant damages on the material's surface. The quantification of the cavitation intensity in different geometry can be useful to get better designs for new installations, but also to improve the operating and to optimize maintenance of existing equipments. The development of universal laws of similarity from experiments is difficult due to the large number of parameters governing cavitating flows. With the increase of computational performance, numerical simulations offer the opportunity to study this phenomenon in various geometries. The main difficulty of this approach is the scale's difference existing between the numerical simulations U-RANS used to calculate the cavitating flow and mechanisms of bubble's collapse held responsible for damages on the solid. The proposed method in this thesis is based on a textbf{post-treatment} of the textbf{U-RANS} simulations to characterize a distribution of bubbles and to simulate their behavior at lower spatial and temporal scales. Our first objective is to make explicit a system of equations corresponding to phenomena occurring locally in the two-phase flow. This work leads to the development of mixture variables taking into account the presence of non-condensable gases in the fluid. Assumptions are taken to make the system, after using the Reynolds averaging procedure, equivalent to those, using a homogeneous approach, implemented in the unsteady cavitating flows solvers previously developed in the laboratory. The characterization of bubbles made by this post-treatment takes into account both the surface tension and the presence of non-condensable gases. The development of a solver for the simulation of the dynamic of a bubble cloud is started. It aims to take into account both the interactions between bubbles and non-spherical deformations with a potential method. First results of these simulations are presented and small non-spherical deformations occurring during the collapse can be observed. Finally, we propose a chained method between these two systems initializing the bubble dynamic solver with results of U-RANS simulations. The energy emitted during the implosion of bubbles impacting the solid surface is calculated. So the aggressiveness of the flow on the material can be characterized. We apply this method on different flows to compare numerical and experimental results.Lors du fonctionnement d'une installation hydraulique, l'apparition de zone de cavitation dans l'écoulement peut entraîner un endommagement important sur la surface des matériaux. La quantification de l'intensité de cavitation sur les composants hydrauliques serait utile à la fois pour mieux concevoir les nouveaux équipements en projet, mais aussi pour améliorer la conduite et optimiser la maintenance des matériels existants. Au vu du grand nombre de paramètres régissant les écoulements cavitants, l'élaboration de lois de similitudes universelles à partir d'expériences est délicate. Avec l'augmentation des moyens de calculs, la simulation numérique est un outil pour étudier ce phénomène sur des géométries variées. La principale difficulté de cette démarche réside dans la différence d'échelles existant entre les simulations numériques U-RANS servant à simuler l'écoulement cavitant et les mécanismes d'implosion de bulles jugés responsables de l'endommagement sur le solide. La méthode proposée dans ce manuscrit s'appuie sur un post-traitement des simulations U-RANS afin de caractériser une distribution de bulles et de simuler leurs comportements à de plus petites échelles spatiales et temporelles. Dans un premier temps, notre travail consiste à expliciter les équations locales de conservation de masse, de quantité de mouvement et d'énergie pour un écoulement liquide/gaz comprenant deux espèces eau/air. Ce travail mène à l'élaboration de grandeurs de mélange prenant notamment en compte la présence de gaz incondensables au sein du fluide. Des hypothèses permettent de rendre ce système équivalent à ceux, utilisant une approche homogène, implémentés dans les codes de simulations d'écoulements cavitants instationnaires développés précédemment au laboratoire. La caractérisation des populations de bulles effectuée par le post-traitement prend ainsi en considération à la fois la tension superficielle et la présence de gaz incondensables. Dans un deuxième temps, l'élaboration d'un code de calcul permettant la simulation de la dynamique d'un nuage de bulles est débutée. Ce dernier a pour ambition de tenir compte à la fois des interactions entre les bulles et des déformations non sphériques que celles-ci peuvent subir à l'aide d'une méthode potentielle. Des premiers résultats de simulations sont présentés dans ce manuscrit et permettent de tenir compte de faibles déformations des bulles. La dernière étape de ce travail consiste à proposer une méthode de chaînage entre ces deux échelles en initialisant le calcul de dynamique de bulles à l'aide des résultats du calcul U-RANS. L'énergie émise lors de l'implosion des bulles et impactant la surface solide est ainsi calculée, caractérisant de ce fait le chargement imposé par l'écoulement sur le matériau. Cette méthode est par la suite appliquée sur différentes géométries en comparant à chaque fois les résultats obtenus à des expériences. Nous comparons également nos résultats à des méthodes précédemment établies au sein du laboratoire afin d'évaluer la pertinence de cette approche