Predicting the Location of Glioma Recurrence After a Resection Surgery

International audienceWe propose a method for estimating the location of glioma recurrence after surgical resection. This method consists of a pipeline including the registration of images at different time points, the estimation of the tumor infiltration map, and the prediction of tumor regrowth using a reaction-diffusion model. A data set acquired on a patient with a low-grade glioma and post surgery MRIs is considered to evaluate the accuracy of the estimated recurrence locations found using our method. We observed good agreement in tumor volume prediction and qualitative matching in regrowth locations. Therefore, the proposed method seems adequate for modeling low-grade glioma recurrence. This tool could help clinicians anticipate tumor regrowth and better characterize the radiologically non-visible infiltrative extent of the tumor. Such information could pave the way for model-based personalization of treatment planning in a near future

Tumor Growth Parameters Estimation and Source Localization From a Unique Time Point: Application to Low-grade Gliomas

International audienceCoupling time series of MR Images with reaction-di usion-based models has provided interesting ways to better understand the proliferative-invasive as- pect of glial cells in tumors. In this paper, we address a di erent formulation of the inverse problem: from a single time point image of a non-swollen brain tumor, estimate the tumor source location and the di usivity ratio between white and grey matter, while exploring the possibility to predict the further extent of the observed tumor at later time points in low-grade gliomas. The synthetic and clinical results show the stability of the located source and its varying distance from the tumor barycenter and how the estimated ratio controls the spikiness of the tumor

Geodesic shape regression with multiple geometries and sparse parameters

International audienceMany problems in medicine are inherently dynamic processes which include the aspect of change over time, such as childhood development, aging, and disease progression. From medical images, numerous geometric structures can be extracted with various representations, such as landmarks, point clouds, curves, and surfaces. Different sources of geometry may characterize different aspects of the anatomy, such as fiber tracts from DTI and subcortical shapes from structural MRI, and therefore require a modeling scheme which can include various shape representations in any combination. In this paper, we present a geodesic regression model in the large deformation (LDDMM) framework applicable to multi-object complexes in a variety of shape representations. Our model decouples the deformation parameters from the specific shape representations, allowing the complexity of the model to reflect the nature of the shape changes, rather than the sampling of the data. As a consequence, the sparse representation of diffeomorphic flow allows for the straightforward embedding of a variety of geometry in different combinations, which all contribute towards the estimation of a single deformation of the ambient space. Additionally, the sparse representation along with the geodesic constraint results in a compact statistical model of shape change by a small number of parameters defined by the user. Experimental validation on multi-object complexes demonstrate robust model estimation across a variety of parameter settings. We further demonstrate the utility of our method to support the analysis of derived shape features, such as volume, and explore shape model extrapolation. Our method is freely available in the software package deformetrica which can be downloaded at www.deformetrica.org

Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms

We propose a method to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this trajectory both in terms of geometry and time dynamics. First, we formulate a non-linear mixed-effects statistical model as the combination of a generic statistical model for manifold-valued longitudinal data, a deformation model defining shape trajectories via the action of a finite-dimensional set of diffeomorphisms with a manifold structure, and an efficient numerical scheme to compute parallel transport on this manifold. Second, we introduce a MCMC-SAEM algorithm with a specific approach to shape sampling, an adaptive scheme for proposal variances, and a log-likelihood tempering strategy to estimate our model. Third, we validate our algorithm on 2D simulated data, and then estimate a scenario of alteration of the shape of the hippocampus 3D brain structure during the course of Alzheimer's disease. The method shows for instance that hippocampal atrophy progresses more quickly in female subjects, and occurs earlier in APOE4 mutation carriers. We finally illustrate the potential of our method for classifying pathological trajectories versus normal ageing

Personalized Radiotherapy Planning Based on a Computational Tumor Growth Model

International audienceIn this article, we propose a proof of concept for the automatic planning of personalized radiotherapy for brain tumors. A computational model of glioblastoma growth is combined with an exponential cell survival model to describe the effect of radiotherapy. The model is personalized to the magnetic resonance images (MRIs) of a given patient. It takes into account the uncertainty in the model parameters, together with the uncertainty in the MRI segmentations. The computed probability distribution over tumor cell densities, together with the cell survival model, is used to define the prescription dose distribution, which is the basis for subsequent Intensity Modulated Radiation Therapy (IMRT) planning. Depending on the clinical data available, we compare three different scenarios to personalize the model. First, we consider a single MRI acquisition before therapy, as it would usually be the case in clinical routine. Second, we use two MRI acquisitions at two distinct time points in order to personalize the model and plan radiotherapy. Third, we include the uncertainty in the segmentation process. We present the application of our approach on two patients diagnosed with high grade glioma. We introduce two methods to derive the radiotherapy prescription dose distribution, which are based on minimizing integral tumor cell survival using the maximum a posteriori or the expected tumor cell density. We show how our method allows the user to compute a patient specific radiotherapy planning conformal to the tumor infiltration. We further present extensions of the method in order to spare adjacent organs at risk by redistributing the dose. The presented approach and its proof of concept may help in the future to better target the tumor and spare organs at risk

Spatio-temporal Modeling and Analysis of Brain Development

The incidence of preterm birth is increasing and has emerged as a leading cause of neurodevelopmental impairment in childhood. In early development, defined here as the period before and around birth, the brain undergoes significant morphological, functional and appearance changes. The scope and rate of change is arguably greater than at any other time in life, but quantitative markers of this period of development are limited. Improved understanding of cerebral changes during this critical period is important for mapping normal growth, and for investigating mechanisms of injury associated with risk factors for maldevelopment such as premature birth. The objective of this thesis is the development of methods for spatio-temporal modeling and quantitative measures of brain development that can assist understanding the patterns of normal growth and can guide interventions designed to reduce the burden of preterm brain injury. An approach for constructing high-definition spatio-temporal atlases of the developing brain is introduced. A novelty in the proposed approach is the use of a time-varying kernel width, to overcome the variations in the distribution of subjects at different ages. This leads to an atlas that retains a consistent level of detail at every time-point. The resulting 4D fetal and neonatal average atlases have greater anatomic definition than currently available 4D atlases, an important factor in improving registrations between the atlas and individual subjects with clear anatomical structures and atlas-based automatic segmentation. The fetal atlas provides a natural benchmark for assessing preterm born neonates and gives some insight into differences between the groups. Also, a novel framework for longitudinal registration which can accommodate large intra-subject anatomical variations is introduced. The framework exploits previously developed spatio-temporal atlases, which can aid the longitudinal registration process as it provides prior information about the missing anatomical evolution between two scans taken over large time-interval. Finally, a voxel-wise analysis framework is proposed which complements the analysis of changes in brain morphology by the study of spatio-temporal signal intensity changes in multi-modal MRI, which can offer a useful marker of neurodevelopmental changes

Méthodes mathématiques d’analyse d’image pour les études de population transversales et longitudinales

In medicine, large scale population analysis aim to obtain statistical information in order to understand better diseases, identify their risk factors, develop preventive and curative treatments and improve the quality of life of the patients.In this thesis, we first introduce the medical context of Alzheimer’s disease, recall some concepts of statistical learning and the challenges that typically occurwhen applied in medical imaging. The second part focus on cross-sectional studies,i.e. at a single time point. We present an efficient method to classify white matter lesions based on support vector machines. Then we discuss the use of manifoldlearning techniques for image and shape analysis. Finally, we present extensions ofLaplacian eigenmaps to improve the low-dimension representations of patients usingthe combination of imaging and clinical data. The third part focus on longitudinalstudies, i.e. between several time points. We quantify the hippocampus deformations of patients via the large deformation diffeomorphic metric mapping frameworkto build disease progression classifiers. We introduce novel strategies and spatialregularizations for the classification and identification of biomarkers.En médecine, les analyses de population à grande échelle ont pour but d’obtenir des informations statistiques pour mieux comprendre des maladies, identifier leurs facteurs de risque, développer des traitements préventifs et curatifs et améliorer la qualité de vie des patients.Dans cette thèse, nous présentons d’abord le contexte médical de la maladie d’Alzheimer, rappelons certains concepts d’apprentissage statistique et difficultés rencontrées lors de l’application en imagerie médicale. Dans la deuxième partie,nous nous intéressons aux analyses transversales, c-a-d ayant un seul point temporel.Nous présentons une méthode efficace basée sur les séparateurs à vaste marge (SVM)permettant de classifier des lésions dans la matière blanche. Ensuite, nous étudions les techniques d’apprentissage de variétés pour l’analyse de formes et d’images, et présentons deux extensions des Laplacian eigenmaps améliorant la représentation de patients en faible dimension grâce à la combinaison de données d’imagerie et cliniques. Dans la troisième partie, nous nous intéressons aux analyses longitudinales, c-a-d entre plusieurs points temporels. Nous quantifions les déformations des hippocampus de patients via le modèle des larges déformations par difféomorphismes pour classifier les évolutions de la maladie. Nous introduisons de nouvelles stratégies et des régularisations spatiales pour la classification et l’identification de marqueurs biologiques

The TPS Direct Transport: a new method for transporting deformations in the Size-and-shape Space

Modern shape analysis allows the fine comparison of shape changes occurring between different objects. Very often the classic machineries of Generalized Procrustes Analysis and Principal Component Analysis are used in order to contrast the shape change occurring among configurations represented by homologous landmarks. However, if size and shape data are structured in different groups thus constituting different morphological trajectories, a data centering is needed if one wants to compare solely the deformation representing the trajectories. To do that, inter-individual variation must be filtered out. This maneuver is rarely applied in studies using simulated or real data. A geometrical procedure named Parallel Transport, that can be based on various connection types, is necessary to perform such kind of data centering. Usually, the Levi Civita connection is used for interpolation of curves in a Riemannian space. It can also be used to transport a deformation. We demonstrate that this procedure does not preserve some important characters of the deformation, even in the affine case. We propose a novel procedure called `TPS Direct Transport' which is able to perfectly transport deformation in the affine case and to better approximate non affine deformation in comparison to existing tools. We recommend to center shape data using the methods described here when the differences in deformation rather than in shape are under study

Proceedings of the Fourth International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Biological Shape Variability Modeling (MFCA 2013), Nagoya, Japan

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the first edition of this workshop in 2006, second edition in New-York in 2008, the third edition in Toronto in 2011, the forth edition was held in Nagoya Japan on September 22 2013