Non-rigid registration of serial intra-operative images for automatic brain shift estimation

Measurement of intra-operative brain motion is important to provide boundary conditions to physics-based deformation models that can be used to register pre- and intra-operative information. In this paper we present and test a technique that can be used to measure brain surface motion automatically. This method relies on a tracked laser range scanner (LRS) that can acquire simultaneously a picture and the 3D physical coordinates of objects within its field of view. This reduces the 3D tracking problem to a 2D non-rigid registration problem which we solve with a Mutual Information-based algorithm. Results obtained on images of a phantom and on images acquired intra-operatively that demonstrate the feasibility of the method are presented

Dense deformation field estimation for atlas registration using the active contour framework

A key research area in computer vision is image segmentation. Image segmentation aims at extracting objects of interest in images or video sequences. These objects contain relevant information for a given application. For example, a video surveillance application generally requires to extract moving objects (vehicles, persons or animals) from a sequence of images in order to check that their path stays conformed to the regulation rules set for the observed scene. Image segmentation is not an easy task. In many applications, the contours of the objects of interest are difficult to delineate, even manually. The problems linked to segmentation are often due to low contrast, fuzzy contours or too similar intensities with adjacent objects. In some cases, the objects to be extracted have no real contours in the image. This kind of objects is called virtual objects. Virtual objects appear especially in medical applications. To draw them, medical experts usually estimate their position from surrounding objects. The problems related to image segmentation can be greatly simplified with information known in advance on the objects to be extracted (the prior knowledge). A widely used method consists to extract the needed prior knowledge from a reference image often called atlas. The goal of the atlas is to describe the image to be segmented like a map would describe the components of a geographical area. An atlas can contain three types of information on each object being part of the image: an estimation of its position in the image, a description of its shape and texture, and the features of its adjacent objects. The atlas-based segmentation method is rather used when the atlas can characterize a range of images. This method is thus especially adapted to medical images due to the existing consistency between anatomical structures of same type. There exist two types of atlas: the determinist atlas and the statistical atlas. The determinist atlas is an image which has been selected or computed, to be the most representative of an image category to be segmented. This image is called intensity atlas. The contours of the objects of interest (the objects to be extracted in images of the same type) have been traced manually on the intensity atlas, or by using a semi-automatic method. A label is often attributed to each one of these objects in order to differentiate them. In this way, we obtain a labeled version of the atlas called labeled atlas. The statistical atlas is an atlas created from a database of images in order to be the most representative of a certain type of images to be segmented. In this atlas, the position and the features of the objects of interest depend on statistical measures. In this thesis, we are focused on the use of determinist atlases for image segmentation. The segmentation process with a determinist atlas consists to deform the objects delineated in the atlas in order to better align them with their corresponding objects in the image to be segmented. To perform this task, we have distinguished two types of approaches in the literature. The first approach consists to reduce the segmentation problem in an image registration problem. First of all, a dense deformation field that registers (i.e. puts in point-to-point spatial correspondence) the atlas to the image to be segmented, is explicitly computed. Then, this transformation is used to project the assigned labels onto each atlas structure on the image to be segmented. The advantage of this approach is that the deformation field computed from the registration of visible contours allows to easily estimate the position of virtual objects or objects with fuzzy contours. However, the methods currently used for the atlas registration are often only based on the intensity atlas. That means that they do not exploit the object-based information that can be obtained by combining the intensity atlas with its labeled version. In the second approach, the atlas contours selected by the labeled atlas are directly deformed without using a geometrical deformation. For that, this approach is based on matching contour techniques, generally called deformable models. In this thesis, we are interested to a particular type of deformable models, which are the active contour segmentation models. The advantage of the active contour method is that this segmentation technique has been designed to exploit the image information directly linked to the object to be delineated. By using object-based information, active contour models are frequently able to extract regions where the atlas-based segmentation method by registration fails. On the other hand, the result of this local segmentation method is very sensitive to the initial atlas contour position regarding to the target contours. On the other hand, this local segmentation method is very sensitive to the initial position of the atlas contours: the closer they are to the contours to be detected, the more robust the active contour-based segmentation will be. Besides, this segmentation technique needs prior shape models to be able to estimate the position of virtual objects. The main objective of this thesis is to design an algorithm for atlas-based segmentation which combines the advantages of the dense deformation field computed by the registration algorithms, with local segmentation constraints coming from the active contour framework. This implies to design a model where the registration and segmentation by active contours are jointly performed. The atlas registration algorithm that we propose is based on a formulation allowing the integration of any segmentation or contour regularization forces derived from the theory of the active contours in a non parametric registration process. Our algorithm led us to introduce the concept of hierarchical atlas registration. Its principle is that the registration of the main image objects helps the registration of depending objects. This allows to bring progressively the atlas contours closer to their target and thus, to limit the risk to be stuck in a local minimum. Our model had been designed to be easily adaptable to various types of segmentation problems. At the end of the thesis, we present several examples of atlas registration applications in medical imaging. These applications highlight the integration of manual constraints in an atlas registration process, the modeling of a tumor growth in the atlas, the labelization of the thalamus for a statistical study on neuronal connections, the localization of the subthalamic nucleus (STN) for deep brain stimulation (DBS) and the compensation of intra-operative brain shift for neuronavigation systems

Coupling schemes and inexact Newton for multi-physics and coupled optimization problems

This work targets mathematical solutions and software for complex numerical simulation and optimization problems. Characteristics are the combination of different models and software modules and the need for massively parallel execution on supercomputers. We consider two different types of multi-component problems in Part I and Part II of the thesis: (i) Surface coupled fluid- structure interactions and (ii) analysis of medical MR imaging data of brain tumor patients. In (i), we establish highly accurate simulations by combining different aspects such as fluid flow and arterial wall deformation in hemodynamics simulations or fluid flow, heat transfer and mechanical stresses in cooling systems. For (ii), we focus on (a) facilitating the transfer of information such as functional brain regions from a statistical healthy atlas brain to the individual patient brain (which is topologically different due to the tumor), and (b) to allow for patient specific tumor progression simulations based on the estimation of biophysical parameters via inverse tumor growth simulation (given a single snapshot in time, only). Applications and specific characteristics of both problems are very distinct, yet both are hallmarked by strong inter-component relations and result in formidable, very large, coupled systems of partial differential equations. Part I targets robust and efficient quasi-Newton methods for black-box surface-coupling of parti- tioned fluid-structure interaction simulations. The partitioned approach allows for great flexibility and exchangeable of sub-components. However, breaking up multi-physics into single components requires advanced coupling strategies to ensure correct inter-component relations and effectively tackle instabilities. Due to the black-box paradigm, solver internals are hidden and information exchange is reduced to input/output relations. We develop advanced quasi-Newton methods that effectively establish the equation coupling of two (or more) solvers based on solving a non-linear fixed-point equation at the interface. Established state of the art methods fall short by either requiring costly tuning of problem dependent parameters, or becoming infeasible for large scale problems. In developing parameter-free, linear-complexity alternatives, we lift the robustness and parallel scalability of quasi-Newton methods for partitioned surface-coupled multi-physics simulations to a new level. The developed methods are implemented in the parallel, general purpose coupling tool preCICE. Part II targets MR image analysis of glioblastoma multiforme pathologies and patient specific simulation of brain tumor progression. We apply a joint medical image registration and biophysical inversion strategy, targeting at facilitating diagnosis, aiding and supporting surgical planning, and improving the efficacy of brain tumor therapy. We propose two problem formulations and decompose the resulting large-scale, highly non-linear and non-convex PDE-constrained optimization problem into two tightly coupled problems: inverse tumor simulation and medical image registration. We deduce a novel, modular Picard iteration-type solution strategy. We are the first to successfully solve the inverse tumor-growth problem based on a single patient snapshot with a gradient-based approach. We present the joint inversion framework SIBIA, which scales to very high image resolutions and parallel execution on tens of thousands of cores. We apply our methodology to synthetic and actual clinical data sets and achieve excellent normal-to-abnormal registration quality and present a proof of concept for a very promising strategy to obtain clinically relevant biophysical information. Advanced inexact-Newton methods are an essential tool for both parts. We connect the two parts by pointing out commonalities and differences of variants used in the two communities in unified notation