Proceedings of the FEniCS Conference 2017

Proceedings of the FEniCS Conference 2017 that took place 12-14 June 2017 at the University of Luxembourg, Luxembourg

Advanced Algorithms for 3D Medical Image Data Fusion in Specific Medical Problems

Fúze obrazu je dnes jednou z nejběžnějších avšak stále velmi diskutovanou oblastí v lékařském zobrazování a hraje důležitou roli ve všech oblastech lékařské péče jako je diagnóza, léčba a chirurgie. V této dizertační práci jsou představeny tři projekty, které jsou velmi úzce spojeny s oblastí fúze medicínských dat. První projekt pojednává o 3D CT subtrakční angiografii dolních končetin. V práci je využito kombinace kontrastních a nekontrastních dat pro získání kompletního cévního stromu. Druhý projekt se zabývá fúzí DTI a T1 váhovaných MRI dat mozku. Cílem tohoto projektu je zkombinovat stukturální a funkční informace, které umožňují zlepšit znalosti konektivity v mozkové tkáni. Třetí projekt se zabývá metastázemi v CT časových datech páteře. Tento projekt je zaměřen na studium vývoje metastáz uvnitř obratlů ve fúzované časové řadě snímků. Tato dizertační práce představuje novou metodologii pro klasifikaci těchto metastáz. Všechny projekty zmíněné v této dizertační práci byly řešeny v rámci pracovní skupiny zabývající se analýzou lékařských dat, kterou vedl pan Prof. Jiří Jan. Tato dizertační práce obsahuje registrační část prvního a klasifikační část třetího projektu. Druhý projekt je představen kompletně. Další část prvního a třetího projektu, obsahující specifické předzpracování dat, jsou obsaženy v disertační práci mého kolegy Ing. Romana Petera.Image fusion is one of today´s most common and still challenging tasks in medical imaging and it plays crucial role in all areas of medical care such as diagnosis, treatment and surgery. Three projects crucially dependent on image fusion are introduced in this thesis. The first project deals with the 3D CT subtraction angiography of lower limbs. It combines pre-contrast and contrast enhanced data to extract the blood vessel tree. The second project fuses the DTI and T1-weighted MRI brain data. The aim of this project is to combine the brain structural and functional information that purvey improved knowledge about intrinsic brain connectivity. The third project deals with the time series of CT spine data where the metastases occur. In this project the progression of metastases within the vertebrae is studied based on fusion of the successive elements of the image series. This thesis introduces new methodology of classifying metastatic tissue. All the projects mentioned in this thesis have been solved by the medical image analysis group led by Prof. Jiří Jan. This dissertation concerns primarily the registration part of the first project and the classification part of the third project. The second project is described completely. The other parts of the first and third project, including the specific preprocessing of the data, are introduced in detail in the dissertation thesis of my colleague Roman Peter, M.Sc.

Deformable Medical Image Registration: A Survey

Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: i) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; ii) longitudinal studies, where temporal structural or anatomical changes are investigated; and iii) population modeling and statistical atlases used to study normal anatomical variability. In this technical report, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this technical report is to provide an extensive account of registration techniques in a systematic manner.Le recalage déformable d'images est une des tâches les plus fondamentales dans l'imagerie médicale. Parmi ses applications les plus importantes, on compte: i) la fusion d' information provenant des différents types de modalités a n de faciliter le diagnostic et la planification du traitement; ii) les études longitudinales, oú des changements structurels ou anatomiques sont étudiées en fonction du temps; et iii) la modélisation de la variabilité anatomique normale d'une population et les atlas statistiques. Dans ce rapport de recherche, nous essayons de donner un aperçu des différentes méthodes du recalage déformables, en mettant l'accent sur les avancées les plus récentes du domaine. Nous avons particulièrement insisté sur les techniques appliquées aux images médicales. A n d'étudier les méthodes du recalage d'images, leurs composants principales sont d'abord identifiés puis étudiées de manière indépendante, les techniques les plus récentes étant classifiées en suivant un schéma logique déterminé. La contribution de ce rapport de recherche est de fournir un compte rendu détaillé des techniques de recalage d'une manière systématique

Towards Robust and Accurate Image Registration by Incorporating Anatomical and Appearance Priors

Ph.DDOCTOR OF PHILOSOPH

A high-performance boundary element method and its applications in engineering

As a semi-numerical and semi-analytical method, owing to the inherent advantage, of boundary-only discretisation, the boundary element method (BEM) has been widely applied to problems with complicated geometries, stress concentration problems, infinite domain problems, and many others. However, domain integrals and non-symmetrical and dense matrix systems are two obstacles for BEM which have hindered the its further development and application. This thesis is aimed at proposing a high-performance BEM to tackle the above two drawbacks and broaden the application scope of BEM. In this thesis, a detailed introduction to the traditional BEM is given and several popular algorithms are introduced or proposed to enhance the performance of BEM. Numerical examples in heat conduction analysis, thermoelastic analysis and thermoelastic fracture problems are performed to assess the efficiency and correction of the algorithms. In addition, necessary theoretical derivations are embraced for establishing novel boundary integral equations (BIEs) for specific engineering problems. The following three parts are the main content of this thesis. (1) The first part (Part II consisting of two chapters) is aimed at heat conduction analysis by BEM. The coefficient matrix of equations formed by BEM in solving problems is fully-populated which occupy large computer memory. To deal with that, the fast multipole method (FMM) is introduced to energize the line integration boundary element method (LIBEM) to performs better in efficiency. In addition, to compute domain integrals with known or unknown integrand functions which are caused by heat sources or heterogeneity, a novel BEM, the adaptive orthogonal interpolation moving least squares (AOIMLS) method enhanced LIBEM, which also inherits the advantage of boundary-only discretisation, is proposed. Unlike LIBEM, which is an accurate and stable method for computing domain integrals, but only works when the mathematical expression of integral function in domain integrals is known, the AOIMLS enhanced LIBEM can compute domain integrals with known or unknown integral functions, which ensures all the nonlinear and nonhomogeneous problems can be solved without domain discretisation. In addition, the AOIMLS can adaptively avoid singular or ill-conditioned moment matrices, thus ensuring the stability of the calculation results. (2) In the second part (Part III consisting of four chapters), the thermoelastic problems and fracture problems are the main objectives. Due to considering thermal loads, domain integrals appear in the BIEs of the thermoelastic problems, and the expression of integrand functions is known or not depending on the temperature distribution given or not, the AOIMLS enhanced LIBEM is introduced to conduct thermoelasticity analysis thereby. Besides, a series of novel unified boundary integral equations based on BEM and DDM are derived for solving fracture problems and thermoelastic fracture problems in finite and infinite domains. Two sets of unified BIEs are derived for fracture problems in finite and infinite domains based on the direct BEM and DDM respectively, which can provide accurate and stable results. Another two sets of BIEs are addressed by employing indirect BEM and DDM, which cannot ensure a stable result, thereby a modified indirect BEM is proposed which performs much more stable. Moreover, a set of novel BIEs based on the direct BEM and DDM for cracked domains under thermal stress is proposed. (3) In the third part (Part IV consisting of one chapter), a high-efficiency combined BEM and discrete element method (DEM) is proposed to compute the inner stress distribution and particle breakage of particle assemblies based on the solution mapping scheme. For the stress field computation of particles with similar geometry, a template particle is used as the representative particle, so that only the related coefficient matrices of one template particle in the local coordinate system are needed to be calculated, while the coefficient matrices of the other particles, can be obtained by mapping between the local and global coordinate systems. Thus, the combined BEM and DEM is much more effective when modelling a large-scale particle system with a small number of distinct possible particle shapes. Furthermore, with the help of the Hoek-Brown criterion, the possible cracks or breakage paths of a particle can be obtained

Methods based on B-splines for model representation, numerical analysis and image registration

The thesis consists of inter-connected parts for modeling and analysis using newly developed isogeometric methods. The main parts are reproducing kernel triangular B-splines, extended isogeometric analysis for solving weakly discontinuous problems, collocation methods using superconvergent points, and B-spline basis in image registration applications. Each topic is oriented towards application of isogeometric analysis basis functions to ease the process of integrating the modeling and analysis phases of simulation. First, we develop reproducing a kernel triangular B-spline-based FEM for solving PDEs. We review the triangular B-splines and their properties. By definition, the triangular basis function is very flexible in modeling complicated domains. However, instability results when it is applied for analysis. We modify the triangular B-spline by a reproducing kernel technique, calculating a correction term for the triangular kernel function from the chosen surrounding basis. The improved triangular basis is capable to obtain the results with higher accuracy and almost optimal convergence rates. Second, we propose an extended isogeometric analysis for dealing with weakly discontinuous problems such as material interfaces. The original IGA is combined with XFEM-like enrichments which are continuous functions themselves but with discontinuous derivatives. Consequently, the resulting solution space can approximate solutions with weak discontinuities. The method is also applied to curved material interfaces, where the inverse mapping and the curved triangular elements are considered. Third, we develop an IGA collocation method using superconvergent points. The collocation methods are efficient because no numerical integration is needed. In particular when higher polynomial basis applied, the method has a lower computational cost than Galerkin methods. However, the positions of the collocation points are crucial for the accuracy of the method, as they affect the convergent rate significantly. The proposed IGA collocation method uses superconvergent points instead of the traditional Greville abscissae points. The numerical results show the proposed method can have better accuracy and optimal convergence rates, while the traditional IGA collocation has optimal convergence only for even polynomial degrees. Lastly, we propose a novel dynamic multilevel technique for handling image registration. It is application of the B-spline functions in image processing. The procedure considered aims to align a target image from a reference image by a spatial transformation. The method starts with an energy function which is the same as a FEM-based image registration. However, we simplify the solving procedure, working on the energy function directly. We dynamically solve for control points which are coefficients of B-spline basis functions. The new approach is more simple and fast. Moreover, it is also enhanced by a multilevel technique in order to prevent instabilities. The numerical testing consists of two artificial images, four real bio-medical MRI brain and CT heart images, and they show our registration method is accurate, fast and efficient, especially for large deformation problems