Finite Element Modeling Driven by Health Care and Aerospace Applications

This thesis concerns the development, analysis, and computer implementation of mesh generation algorithms encountered in finite element modeling in health care and aerospace. The finite element method can reduce a continuous system to a discrete idealization that can be solved in the same manner as a discrete system, provided the continuum is discretized into a finite number of simple geometric shapes (e.g., triangles in two dimensions or tetrahedrons in three dimensions). In health care, namely anatomic modeling, a discretization of the biological object is essential to compute tissue deformation for physics-based simulations. This thesis proposes an efficient procedure to convert 3-dimensional imaging data into adaptive lattice-based discretizations of well-shaped tetrahedra or mixed elements (i.e., tetrahedra, pentahedra and hexahedra). This method operates directly on segmented images, thus skipping a surface reconstruction that is required by traditional Computer-Aided Design (CAD)-based meshing techniques and is convoluted, especially in complex anatomic geometries. Our approach utilizes proper mesh gradation and tissue-specific multi-resolution, without sacrificing the fidelity and while maintaining a smooth surface to reflect a certain degree of visual reality. Image-to-mesh conversion can facilitate accurate computational modeling for biomechanical registration of Magnetic Resonance Imaging (MRI) in image-guided neurosurgery. Neuronavigation with deformable registration of preoperative MRI to intraoperative MRI allows the surgeon to view the location of surgical tools relative to the preoperative anatomical (MRI) or functional data (DT-MRI, fMRI), thereby avoiding damage to eloquent areas during tumor resection. This thesis presents a deformable registration framework that utilizes multi-tissue mesh adaptation to map preoperative MRI to intraoperative MRI of patients who have undergone a brain tumor resection. Our enhancements with mesh adaptation improve the accuracy of the registration by more than 5 times compared to rigid and traditional physics-based non-rigid registration, and by more than 4 times compared to publicly available B-Spline interpolation methods. The adaptive framework is parallelized for shared memory multiprocessor architectures. Performance analysis shows that this method could be applied, on average, in less than two minutes, achieving desirable speed for use in a clinical setting. The last part of this thesis focuses on finite element modeling of CAD data. This is an integral part of the design and optimization of components and assemblies in industry. We propose a new parallel mesh generator for efficient tetrahedralization of piecewise linear complex domains in aerospace. CAD-based meshing algorithms typically improve the shape of the elements in a post-processing step due to high complexity and cost of the operations involved. On the contrary, our method optimizes the shape of the elements throughout the generation process to obtain a maximum quality and utilizes high performance computing to reduce the overheads and improve end-user productivity. The proposed mesh generation technique is a combination of Advancing Front type point placement, direct point insertion, and parallel multi-threaded connectivity optimization schemes. The mesh optimization is based on a speculative (optimistic) approach that has been proven to perform well on hardware-shared memory. The experimental evaluation indicates that the high quality and performance attributes of this method see substantial improvement over existing state-of-the-art unstructured grid technology currently incorporated in several commercial systems. The proposed mesh generator will be part of an Extreme-Scale Anisotropic Mesh Generation Environment to meet industries expectations and NASA\u27s CFD visio

Reconstruction et description des fonctions de distribution d'orientation en imagerie de diffusion à haute résolution angulaire

This thesis concerns the reconstruction and description of orientation distribution functions (ODFs) in high angular resolution diffusion imaging (HARDI) such as q-ball imaging (QBI). QBI is used to analyze more accurately fiber structures (crossing, bending, fanning, etc.) in a voxel. In this field, the ODF reconstructed from QBI is widely used for resolving complex intravoxel fiber configuration problem. However, until now, the assessment of the characteristics or quality of ODFs remains mainly visual and qualitative, although the use of a few objective quality metrics is also reported that are directly borrowed from classical signal and image processing theory. At the same time, although some metrics such as generalized anisotropy (GA) and generalized fractional anisotropy (GFA) have been proposed for classifying intravoxel fiber configurations, the classification of the latters is still a problem. On the other hand, QBI often needs an important number of acquisitions (usually more than 60 directions) to compute accurately ODFs. So, reducing the quantity of QBI data (i.e. shortening acquisition time) while maintaining ODF quality is a real challenge. In this context, we have addressed the problems of how to reconstruct high-quality ODFs and assess their characteristics. We have proposed a new paradigm allowing describing the characteristics of ODFs more quantitatively. It consists of regarding an ODF as a general three-dimensional (3D) point cloud, projecting a 3D point cloud onto an angle-distance map (ADM), constructing an angle-distance matrix (ADMAT), and calculating morphological characteristics of the ODF such as length ratio, separability and uncertainty. In particular, a new metric, called PEAM (PEAnut Metric), which is based on computing the deviation of ODFs from a single fiber ODF represented by a peanut, was proposed and used to classify intravoxel fiber configurations. Several ODF reconstruction methods have also been compared using the proposed metrics. The results showed that the characteristics of 3D point clouds can be well assessed in a relatively complete and quantitative manner. Concerning the reconstruction of high-quality ODFs with reduced data, we have proposed two methods. The first method is based on interpolation by Delaunay triangulation and imposing constraints in both q-space and spatial space. The second method combines random gradient diffusion direction sampling, compressed sensing, resampling density increasing, and missing diffusion signal recovering. The results showed that the proposed missing diffusion signal recovering approaches enable us to obtain accurate ODFs with relatively fewer number of diffusion signals.Ce travail de thèse porte sur la reconstruction et la description des fonctions de distribution d'orientation (ODF) en imagerie de diffusion à haute résolution angulaire (HARDI) telle que l’imagerie par q-ball (QBI). Dans ce domaine, la fonction de distribution d’orientation (ODF) en QBI est largement utilisée pour étudier le problème de configuration complexe des fibres. Toutefois, jusqu’à présent, l’évaluation des caractéristiques ou de la qualité des ODFs reste essentiellement visuelle et qualitative, bien que l’utilisation de quelques mesures objectives de qualité ait également été reportée dans la littérature, qui sont directement empruntées de la théorie classique de traitement du signal et de l’image. En même temps, l’utilisation appropriée de ces mesures pour la classification des configurations des fibres reste toujours un problème. D'autre part, le QBI a souvent besoin d'un nombre important d’acquisitions pour calculer avec précision les ODFs. Ainsi, la réduction du temps d’acquisition des données QBI est un véritable défi. Dans ce contexte, nous avons abordé les problèmes de comment reconstruire des ODFs de haute qualité et évaluer leurs caractéristiques. Nous avons proposé un nouveau paradigme permettant de décrire les caractéristiques des ODFs de manière plus quantitative. Il consiste à regarder un ODF comme un nuage général de points tridimensionnels (3D), projeter ce nuage de points 3D sur un plan angle-distance (ADM), construire une matrice angle-distance (ADMAT), et calculer des caractéristiques morphologiques de l'ODF telles que le rapport de longueurs, la séparabilité et l'incertitude. En particulier, une nouvelle métrique, appelé PEAM (PEAnut Metric) et qui est basée sur le calcul de l'écart des ODFs par rapport à l’ODF (représenté par une forme arachide) d’une seule fibre, a été proposée et utilisée pour classifier des configurations intravoxel des fibres. Plusieurs méthodes de reconstruction des ODFs ont également été comparées en utilisant les paramètres proposés. Les résultats ont montré que les caractéristiques du nuage de points 3D peuvent être évaluées d'une manière relativement complète et quantitative. En ce qui concerne la reconstruction de l'ODF de haute qualité avec des données réduites, nous avons proposé deux méthodes. La première est basée sur une interpolation par triangulation de Delaunay et sur des contraintes imposées à la fois dans l’espace-q et dans l'espace spatial. La deuxième méthode combine l’échantillonnage aléatoire des directions de gradient de diffusion, le compressed sensing, l’augmentation de la densité de ré-échantillonnage, et la reconstruction des signaux de diffusion manquants. Les résultats ont montré que les approches de reconstruction des signaux de diffusion manquants proposées nous permettent d'obtenir des ODFs précis à partir d’un nombre relativement faible de signaux de diffusion

HYDI-DSI revisited: Constrained non-parametric EAP imaging without q-space re-gridding

Producción CientíficaHybrid Diffusion Imaging (HYDI) was one of the first attempts to use multi-shell samplings of the q-space to infer diffusion properties beyond Diffusion Tensor Imaging (DTI) or High Angular Resolution Diffusion Imaging (HARDI). HYDI was intended as a flexible protocol embedding both DTI (for lower -values) and HARDI (for higher -values) processing, as well as Diffusion Spectrum Imaging (DSI) when the entire data set was exploited. In the latter case, the spherical sampling of the q-space is re-gridded by interpolation to a Cartesian lattice whose extent covers the range of acquired b-values, hence being acquisition-dependent. The Discrete Fourier Transform (DFT) is afterwards used to compute the corresponding Cartesian sampling of the Ensemble Average Propagator (EAP) in an entirely non-parametric way. From this lattice, diffusion markers such as the Return To Origin Probability (RTOP) or the Mean Squared Displacement (MSD) can be numerically estimated. We aim at re-formulating this scheme by means of a Fourier Transform encoding matrix that eliminates the need for q-space re-gridding at the same time it preserves the non-parametric nature of HYDI-DSI. The encoding matrix is adaptively designed at each voxel according to the underlying DTI approximation, so that an optimal sampling of the EAP can be pursued without being conditioned by the particular acquisition protocol. The estimation of the EAP is afterwards carried out as a regularized Quadratic Programming (QP) problem, which allows to impose positivity constraints that cannot be trivially embedded within the conventional HYDI-DSI. We demonstrate that the definition of the encoding matrix in the adaptive space allows to analytically (as opposed to numerically) compute several popular descriptors of diffusion with the unique source of error being the cropping of high frequency harmonics in the Fourier analysis of the attenuation signal. They include not only RTOP and MSD, but also Return to Axis/Plane Probabilities (RTAP/RTPP), which are defined in terms of specific spatial directions and are not available with the former HYDI-DSI. We report extensive experiments that suggest the benefits of our proposal in terms of accuracy, robustness and computational efficiency, especially when only standard, non-dedicated q-space samplings are available.Ministerio de Ciencia e Innovación (PID2021-124407NB-I00 and TED2021-130758B-I00)Ministry of Science and Higher Education (Poland) (PPN/BEK/ 2019/1/00421

Investigation of intraoperative accelerometer data recording for safer and improved target selection for deep brain stimulation

Background: Deep Brain Stimulation (DBS) is a well established surgical treatment for Parkinson’s Disease (PD) and Essential Tremor (ET). Electrical leads are surgically implanted in the deeply seated structures in the brain and chronically stimulated. The location of the lead with respect to the anatomy is very important for optimal treatment. Therefore, clinicians carefully plan the surgery, record electrophysiological signals from the region of interest and perform stimulation tests to identify the best location to permanently place the leads. Nevertheless, there are certain aspects of the surgery that can still be improved. Firstly, therapeutic effects of stimulation are estimated by visually evaluating changes in tremor or passively moving patient's limb to evaluate changes in rigidity. These methods are subjective and depend heavily on the experience of the evaluator. Secondly, a significant amount of patient data is collected before and during the surgery like various CT and MR images, surgical planning information, electrophysiological recordings and results of stimulation tests. These are not fully utilized at the time of choosing the position for lead placement as they are either not available or acquired on separate systems or in the form of paper notes only. Thirdly, studies have shown that the current target structures to implant the leads (Subthalamic Nucleus (STN) for PD and Ventral Intermediate Nucleus (VIM) for ET) may not be the only ones responsible for the therapeutic effects. The objective of this doctoral work is to develop new methods that help clinicians subdue the above limitations which could in the long term improve the DBS therapy. Method: After a thorough review of the existing literature, specifically customized solutions were designed for the shortcomings described above. A new method to quantitatively evaluate tremor during DBS surgery using acceleration sensor was developed. The method was then adapted to measure acceleration of passive movements and to evaluate changes in rigidity through it. Data from 30 DBS surgeries was collected by applying these methods in two clinical studies: one in Centre Hospitalier Universitaire, Clermont-Ferrand, France and another multi-center study in Universitäspital Basel and Inselspital Bern in Switzerland. To study the role of different anatomical structures in the therapeutic and adverse effects of stimulation, the data collected during the study was analysed using two methods. The first classical approach was to classify the data based on the anatomical structure in which the stimulating contact of the electrode was located. The second advanced approach was to use patient-specific Finite Element Method (FEM) simulations of the Electric Field (EF) to estimate the spatial distribution of stimulation in the structures surrounding the electrode. Such simulations of the adverse effect inducing stimulation current amplitudes are used to visualize the boundaries of safe stimulation and identify structures that could be responsible for these effects. In addition, the patient-specific simulations are also used to develop a new method called "Improvement Maps" to generate 2D and 3D visualization of intraoperative stimulation test results with the patient images and surgical planning. This visualization summarized the stimulation test results by dividing the explored area into multiple regions based on the improvement in symptoms as measured by the accelerometric methods. Results: The accelerometric method successfully measured changes in tremor and rigidity. Standard deviation, signal energy and spectral amplitude of dominant frequency correlated with changes in the symptoms. Symptom suppressing stimulation current amplitudes identified through quantitative methods were lower than those identified through the subjective methods. Comparison of anatomical targets using the accelerometric data showed that to suppress rigidity in PD patients, stimulation current needed was marginally higher for Fields of Forel (FF) and Zona Incerta (ZI) compared to STN. On the other hand, the adverse effect occurrence rate was significantly lower in ZI and FF, indicating them to be better targets compared to STN. Similarly, for ET patients, other thalamic nuclei like the Intermediolateral (InL) and Ventro-Oral (VO) as well as the Pre-Lemniscal Radiations (PLR) are as efficient in suppressing tremor as the VIM but have lower occurrence of adverse effects. Volumetric analysis of spatial distribution of stimulation agreed with these results suggesting that the structures other than the VIM could also play a role in therapeutic effects of stimulation. The visualization of the adverse effect simulations clearly show the structures which could be responsible for such effects e.g. stimulation in the internal capsula induced pyramidal effects. These findings concur with the published literature. With regard to the improvement maps, the clinicians found them intuitive and easy to use to identify the optimal position for lead placement. If the maps were available during the surgery, the clinicians' choice of lead placement would have been different. Conclusion: This doctoral work has shown that modern techniques like quantitative symptom evaluation and electric field simulations can suppress the existing drawbacks of the DBS surgery. Furthermore, these methods along with 3D visualization of data can simplify tasks for clinicians of optimizing lead placement. Better placement of the DBS lead can potentially reduce adverse effects and increase battery life of implanted pulse generator, resulting in better therapy for patients