Registration and analysis of dynamic magnetic resonance image series

Cystic fibrosis (CF) is an autosomal-recessive inherited metabolic disorder that affects all organs in the human body. Patients affected with CF suffer particularly from chronic inflammation and obstruction of the airways. Through early detection, continuous monitoring methods, and new treatments, the life expectancy of patients with CF has been increased drastically in the last decades. However, continuous monitoring of the disease progression is essential for a successful treatment. The current state-of-the-art method for lung disease detection and monitoring is computed tomography (CT) or X-ray. These techniques are ill-suited for the monitoring of disease progressions because of the ionizing radiation the patient is exposed during the examination. Through the development of new magnetic resonance imaging (MRI) sequences and evaluation methods, MRI is able to measure physiological changes in the lungs. The process to create physiological maps, i.e. ventilation and perfusion maps, of the lungs using MRI can be split up into three parts: MR-acquisition, image registration, and image analysis. In this work, we present different methods for the image registration part and the image analysis part. We developed a graph-based registration method for 2D dynamic MR image series of the lungs in order to overcome the problem of sliding motion at organ boundaries. Furthermore, we developed a human-inspired learning-based registration method. Here, the registration is defined as a sequence of local transformations. The sequence-based approach combines the advantage of dense transformation models, i.e. large space of transformations, and the advantage of interpolating transformation models, i.e. smooth local transformations. We also developed a general registration framework called Autograd Image Registration Laboratory (AIRLab), which performs automatic calculation of the gradients for the registration process. This allows rapid prototyping and an easy implementation of existing registration algorithms. For the image analysis part, we developed a deep-learning approach based on gated recurrent units that are able to calculate ventilation maps with less than a third of the number of images of the current method. Automatic defect detection in the estimated MRI ventilation and perfusion maps is essential for the clinical routine to automatically evaluate the treatment progression. We developed a weakly supervised method that is able to infer a pixel-wise defect segmentation by using only a continuous global label during training. In this case, we directly use the lung clearance index (LCI) as a global weak label, without any further manual annotations. The LCI is a global measure to describe ventilation inhomogeneities of the lungs and is obtained by a multiple breath washout test

Proceedings of the First International Workshop on Mathematical Foundations of Computational Anatomy (MFCA'06) - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceNon-linear registration and shape analysis are well developed research topic in the medical image analysis community. There is nowadays a growing number of methods that can faithfully deal with the underlying biomechanical behaviour of intra-subject shape deformations. However, it is more difficult to relate the anatomical shape of different subjects. The goal of computational anatomy is to analyse and to statistically model this specific type of geometrical information. In the absence of any justified physical model, a natural attitude is to explore very general mathematical methods, for instance diffeomorphisms. However, working with such infinite dimensional space raises some deep computational and mathematical problems. In particular, one of the key problem is to do statistics. Likewise, modelling the variability of surfaces leads to rely on shape spaces that are much more complex than for curves. To cope with these, different methodological and computational frameworks have been proposed. The goal of the workshop was to foster interactions between researchers investigating the combination of geometry and statistics for modelling biological shape variability from image and surfaces. A special emphasis was put on theoretical developments, applications and results being welcomed as illustrations. Contributions were solicited in the following areas: * Riemannian and group theoretical methods on non-linear transformation spaces * Advanced statistics on deformations and shapes * Metrics for computational anatomy * Geometry and statistics of surfaces 26 submissions of very high quality were recieved and were reviewed by two members of the programm committee. 12 papers were finally selected for oral presentations and 8 for poster presentations. 16 of these papers are published in these proceedings, and 4 papers are published in the proceedings of MICCAI'06 (for copyright reasons, only extended abstracts are provided here)

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described