3-D lung deformation and function from respiratory-gated 4-D x-ray CT images : application to radiation treatment planning.

Many lung diseases or injuries can cause biomechanical or material property changes that can alter lung function. While the mechanical changes associated with the change of the material properties originate at a regional level, they remain largely asymptomatic and are invisible to global measures of lung function until they have advanced significantly and have aggregated. In the realm of external beam radiation therapy of patients suffering from lung cancer, determination of patterns of pre- and post-treatment motion, and measures of regional and global lung elasticity and function are clinically relevant. In this dissertation, we demonstrate that 4-D CT derived ventilation images, including mechanical strain, provide an accurate and physiologically relevant assessment of regional pulmonary function which may be incorporated into the treatment planning process. Our contributions are as follows: (i) A new volumetric deformable image registration technique based on 3-D optical flow (MOFID) has been designed and implemented which permits the possibility of enforcing physical constraints on the numerical solutions for computing motion field from respiratory-gated 4-D CT thoracic images. The proposed optical flow framework is an accurate motion model for the thoracic CT registration problem. (ii) A large displacement landmark-base elastic registration method has been devised for thoracic CT volumetric image sets containing large deformations or changes, as encountered for example in registration of pre-treatment and post-treatment images or multi-modality registration. (iii) Based on deformation maps from MOFIO, a novel framework for regional quantification of mechanical strain as an index of lung functionality has been formulated for measurement of regional pulmonary function. (iv) In a cohort consisting of seven patients with non-small cell lung cancer, validation of physiologic accuracy of the 4-0 CT derived quantitative images including Jacobian metric of ventilation, Vjac, and principal strains, (V?1, V?2, V?3, has been performed through correlation of the derived measures with SPECT ventilation and perfusion scans. The statistical correlations with SPECT have shown that the maximum principal strain pulmonary function map derived from MOFIO, outperforms all previously established ventilation metrics from 40-CT. It is hypothesized that use of CT -derived ventilation images in the treatment planning process will help predict and prevent pulmonary toxicity due to radiation treatment. It is also hypothesized that measures of regional and global lung elasticity and function obtained during the course of treatment may be used to adapt radiation treatment. Having objective methods with which to assess pre-treatment global and regional lung function and biomechanical properties, the radiation treatment dose can potentially be escalated to improve tumor response and local control

Respiratory Motion Correction on 3D Positron Emission Tomography Images

PET/CT Gräte erlauben gleichzeitige morphologische und anatomische Bildaufnahme des Körpers. Die Aufnahmemodalitäten bedingen, dass bei der Positronen-Emissions-Tomographie (PET) der Patient weiter Atmet. Bei der Computer Tomographie (CT) dagegen, die nur wenige Sekunden dauert, hält er seinen Atem. Aufgrund der Diskrepanz zwischen den Aufnahmen kommt es zu Artefakten bei der Gewichtung der PET-Daten durch die CT-Daten. Diese Gewichtung ist aber für Quantitative PET-Daten notwendig. Des Weiteren können kleine Tumore durch die Verschmierung der Daten im Rauschen untergehen. In dieser Arbeit wird eine Lösung des Problems vorgeschlagen die auf zwei Schritte beruht. Zunächst werden die PET-Daten in verschiedene Atemphasen unterteilt. Im zweiten Schritt werden die Daten verschiedener Phasen mit einer Zielphase in Übereinstimmung gebracht. Hierzu wird eine Optical Flow Methode benutzt. Die Ergebnisse auf Phantom und auf Patientendaten zeigen, dass das Problem erfolgreich gelöst worden ist

Résolution du problème de transfert de chaleur par une approche TAC : application au traitement et à l'analyse des images

Nous proposons une alternative aux équations aux dérivées partielles (EDP) en vue de solutionner certains problèmes en traitement d'images qui sont basés sur un modèle de transfert de chaleur. Traditionnellement , la démarche pour solutionner de tels problèmes basés sur un modèle de champs physiques est de discrétiser et de solutionner une EDP par un procédé purement mathématique. Au lieu de l'EDP, nous proposons d'utiliser une approche qui consiste à décomposer en lois de base, le principe global de conservation de chaleur. Nous montrons que certaines de ces lois admettent une version globale et exacte puisqu'elles proviennent de principes conservateurs. Nous montrons également que les hypothèses sur les autres lois de base peuvent être faites de façon avisée, en tenant compte de certaines connaissances sur le problème et le domaine. Nous utilisons un modèle d'images basé sur la topologie algébrique calculatoire qui nous permet d'encoder simplement les lois de conservation en liant une valeur globale sur un domaine avec des valeurs sur les frontières de ce domaine. Le schéma numérique est dérivé directement du problème modélisé. Ce procédé fournit une explication physique de chaque étape de la résolution. Nous appliquons ce schéma à plusieurs problèmes de traitement d'images qui sont tous régis par le transfert de chaleur : la reconstruction d'images à partir du Laplacien, le calcul du flot optique, le débruitage par diffusion des niveaux de gris et des couleurs ainsi que la retouche d'images ( «inpainting» ).Abstract: This thesis proposes an alternative to partial differential equations (PDEs) for the solution of some problems in computer vision based on the heat transfer equation. Traditionally, the method for solving such physics-based problems is to discretize and solve a PDE by a purely mathematical process. Instead of using the PDE, we propose to use the global heat equation and to decompose it into basic laws. We show that some of these laws admit an exact global version since they arise from balance principles. We also show that the assumptions made on the other basic laws can be made wisely, taking into account knowledge about the problem and the domain. We use a computational algebraic topology-based image model which allows us to encode a physical conservative law by linking a global value on a domain with values on its boundary. The numerical scheme is derived in a straightforward way from the problem modeled. It thus provides a physical explanation of each solving step in the solution. We apply the scheme to various applications: image reconstruction from the Laplacian, optical flow computation, denoising by graylevel and multispectral diffusion and inpainting which are all modeled with the heat transfer equation