Frontotemporal dementia and amyotrophic lateral sclerosis are rare neurodegenerative diseases with no effective treatment. The development of biomarkers allowing an accurate assessment of disease progression is crucial for evaluating new therapies. Concretely, neuroimaging and transcriptomic (microRNA) data have been shown useful in tracking their progression. However, no single biomarker can accurately measure progression in these complex diseases. Additionally, large samples are not available for such rare disorders. It is thus essential to develop methods that can model disease progression by combining multiple biomarkers from small samples. In this paper, we propose a new framework for computing a disease progression score (DPS) from cross-sectional multimodal data. Specifically, we introduce a supervised multimodal variational autoencoder that can infer a meaningful latent space, where latent representations are placed along a disease trajectory. A score is computed by orthogonal projections onto this path. We evaluate our framework with multiple synthetic datasets and with a real dataset containing 14 patients, 40 presymptomatic genetic mutation carriers and 37 controls from the PREV-DEMALS study. There is no ground truth for the DPS in real-world scenarios, therefore we use the area under the ROC curve (AUC) as a proxy metric. Results with the synthetic datasets support this choice, since the higher the AUC, the more accurate the predicted simulated DPS. Experiments with the real dataset demonstrate better performance in comparison with state-of-the-art approaches. The proposed framework thus leverages cross-sectional multimodal datasets with small sample sizes to objectively measure disease progression, with potential application in clinical trials.

This paper introduces a framework for disease prediction from multimodal genetic and imaging data. We propose a multilevel survival model which allows predicting the time of occurrence of a future disease state in patients initially exhibiting mild symptoms. This new multilevel setting allows modeling the interactions between genetic and imaging variables. This is in contrast with classical additive models which treat all modalities in the same manner and can result in undesirable elimination of specific modalities when their contributions are unbalanced. Moreover, the use of a survival model allows overcoming the limitations of previous approaches based on classification which consider a fixed time frame. Furthermore, we introduce specific penalties taking into account the structure of the different types of data, such as a group lasso penalty over the genetic modality and a$\ell _2$-penalty over the imaging modality. Finally, we propose a fast optimization algorithm, based on a proximal gradient method. The approach was applied to the prediction of Alzheimer’s disease (AD) among patients with mild cognitive impairment (MCI) based on genetic (single nucleotide polymorphisms - SNP) and imaging (anatomical MRI measures) data from the ADNI database. The experiments demonstrate the effectiveness of the method for predicting the time of conversion to AD. It revealed how genetic variants and brain imaging alterations interact in the prediction of future disease status. The approach is generic and could potentially be useful for the prediction of other diseases.

In order to reach precision medicine and improve patients' quality of life, machine learning is increasingly used in medicine. Brain disorders are often complex and heterogeneous, and several modalities such as demographic, clinical, imaging, genetics and environmental data have been studied to improve their understanding. Deep learning, a subpart of machine learning, provides complex algorithms that can learn from such various data. It has become state of the art in numerous fields, including computer vision and natural language processing, and is also growingly applied in medicine. In this article, we review the use of deep learning for brain disorders. More specifically, we identify the main applications, the concerned disorders and the types of architectures and data used. Finally, we provide guidelines to bridge the gap between research studies and clinical routine.

Gaussian graphical models (GGM) are often used to describe the conditional correlations between the components of a random vector. In this article, we compare two families of GGM inference methods: the nodewise approach and the penalised likelihood maximisation. We demonstrate on synthetic data that, when the sample size is small, the two methods produce graphs with either too few or too many edges when compared to the real one. As a result, we propose a composite procedure that explores a family of graphs with a nodewise numerical scheme and selects a candidate among them with an overall likelihood criterion. We demonstrate that, when the number of observations is small, this selection method yields graphs closer to the truth and corresponding to distributions with better KL divergence with regards to the real distribution than the other two. Finally, we show the interest of our algorithm on two concrete cases: first on brain imaging data, then on biological nephrology data. In both cases our results are more in line with current knowledge in each field.

Numerous machine learning (ML) approaches have been proposed for automatic classification of Alzheimer's disease (AD) from brain imaging data. In particular, over 30 papers have proposed to use convolutional neural networks (CNN) for AD classification from anatomical MRI. However, the classification performance is difficult to compare across studies due to variations in components such as participant selection, image preprocessing or validation procedure. Moreover, these studies are hardly reproducible because their frameworks are not publicly accessible and because implementation details are lacking. Lastly, some of these papers may report a biased performance due to inadequate or unclear validation or model selection procedures. In the present work, we aim to address these limitations through three main contributions. First, we performed a systematic literature review. We identified four main types of approaches: i) 2D slice-level, ii) 3D patch-level, iii) ROI-based and iv) 3D subject-level CNN. Moreover, we found that more than half of the surveyed papers may have suffered from data leakage and thus reported biased performance. Our second contribution is the extension of our open-source framework for classification of AD using CNN and T1-weighted MRI. The framework comprises previously developed tools to automatically convert ADNI, AIBL and OASIS data into the BIDS standard, and a modular set of image preprocessing procedures, classification architectures and evaluation procedures dedicated to deep learning. Finally, we used this framework to rigorously compare different CNN architectures. The data was split into training/validation/test sets at the very beginning and only the training/validation sets were used for model selection. To avoid any overfitting, the test sets were left untouched until the end of the peer-review process. Overall, the different 3D approaches (3D-subject, 3D-ROI, 3D-patch) achieved similar performances while that of the 2D slice approach was lower. Of note, the different CNN approaches did not perform better than a SVM with voxel-based features. The different approaches generalized well to similar populations but not to datasets with different inclusion criteria or demographical characteristics. All the code of the framework and the experiments is publicly available: general-purpose tools have been integrated into the Clinica software (www.clinica.run) and the paper-specific code is available at: https://github.com/aramis-lab/AD-DL.

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.

The brain is composed of several neural circuits which may be seen as anatomical complexes composed of grey matter structures interconnected by white matter tracts. Grey and white matter components may be modeled as 3-D surfaces and curves, respectively. Neurodevelopmental disorders involve morphological and organizational alterations which cannot be jointly captured by usual shape analysis techniques based on single diffeomorphisms. We propose a new deformation scheme, called double diffeomorphism, which is a combination of two diffeomorphisms. The first one captures changes in structural connectivity, whereas the second one recovers the global morphological variations of both grey and white matter structures. This deformation model is integrated into a Bayesian framework for atlas construction. We evaluate it on a data-set of 3-D structures representing the neural circuits of patients with Gilles de la Tourette syndrome (GTS). We show that this approach makes it possible to localise, quantify, and easily visualise the pathological anomalies altering the morphology and organization of the neural circuits. Furthermore, results also indicate that the proposed deformation model better discriminates between controls and GTS patients than a single diffeomorphism.

We propose a generic Bayesian mixed-effects model to estimate the temporal progression of a biological phenomenon from observations obtained at multiple time points for a group of individuals. The progression is modeled by continuous trajectories in the space of measurements. Individual trajectories of progression result from spatiotemporal transformations of an average trajectory. These transformations allow for the quantification of changes in direction and pace at which the trajectories are followed. The framework of Riemannian geometry allows the model to be used with any kind of measurements with smooth constraints. A stochastic version of the Expectation-Maximization algorithm is used to produce maximum a posteriori estimates of the parameters. We evaluated our method using a series of neuropsychological test scores from patients with mild cognitive impairments, later diagnosed with Alzheimer's disease, and simulated evolutions of symmetric positive definite matrices. The data-driven model of impairment of cognitive functions illustrated the variability in the ordering and timing of the decline of these functions in the population. We showed that the estimated spatiotemporal transformations effectively put into correspondence significant events in the progression of individuals.

Fiber bundles stemming from tractography algorithms contain many streamlines. They require therefore a great amount of computer memory and computational resources to be stored, visualised and processed. We propose an approximation scheme for fiber bundles which results in a parsimonious representation of weighted prototypes. Prototypes are chosen among the streamlines and they represent groups of similar streamlines. Their weight is related to the number of approximated streamlines. Both streamlines and prototypes are modelled as weighted currents. This computational model does not need point-to-point correspondences and two streamlines are considered similar if their endpoints are close to each other and if their pathways follow similar trajectories. Moreover, the space of weighted currents is a vector space with a closed-form metric. This permits easy computation of the approximation error and the selection of the prototypes is based on the minimisation of this error. We propose an iterative algorithm which approximates independently and simultaneously all the fascicles of the bundle in a fast and accurate way. We show that the resulting representation preserves the shape of the bundle and it can be used to accurately reconstruct the original structural connectivity. We evaluate our algorithm on bundles obtained from both deterministic and probabilistic tractography algorithms. The resulting approximations use on average only 2% of the original streamlines as prototypes. This drastically reduces the computational burden of the processes where the geometry of the streamlines is considered. We demonstrate its effectiveness using as example the registration between two fiber bundles.

We propose a Bayesian mixed-effects model to learn typical scenarios of changes from longitudinal manifold-valued data, namely repeated measurements of the same objects or individuals at several points in time. The model allows to estimate a group-average trajectory in the space of measurements. Random variations of this trajectory result from spatiotemporal transformations, which allow changes in the direction of the trajectory and in the pace at which trajectories are followed. The use of the tools of Riemannian geometry allows to derive a generic algorithm for any kind of data with smooth constraints, which lie therefore on a Riemannian manifold. Stochastic approximations of the Expectation-Maximization algorithm is used to estimate the model parameters in this highly non-linear setting.The method is used to estimate a data-driven model of the progressive impairments of cognitive functions during the onset of Alzheimer's disease. Experimental results show that the model correctly put into correspondence the age at which each individual was diagnosed with the disease, thus validating the fact that it effectively estimated a normative scenario of disease progression. Random effects provide unique insights into the variations in the ordering and timing of the succession of cognitive impairments across different individuals.

This paper presents a framework to introduce spatial and anatomical priors in SVM for brain image analysis based on regularization operators. A notion of proximity based on prior anatomical knowledge between the image points is defined by a graph (e.g., brain connectivity graph) or a metric (e.g., Fisher metric on statistical manifolds). A regularization operator is then defined from the graph Laplacian, in the discrete case, or from the Laplace-Beltrami operator, in the continuous case. The regularization operator is then introduced into the SVM, which exponentially penalizes high-frequency components with respect to the graph or to the metric and thus constrains the classification function to be smooth with respect to the prior. It yields a new SVM optimization problem whose kernel is a heat kernel on graphs or on manifolds. We then present different types of priors and provide efficient computations of the Gram matrix. The proposed framework is finally applied to the classification of brain Magnetic Resonance (MR) images (based on Gray Matter (GM) concentration maps and cortical thickness measures) from 137 patients with Alzheimer's Disease (AD) and 162 elderly controls. The results demonstrate that the proposed classifier generates less-noisy and consequently more interpretable feature maps with high classification performances.

The alignment and normalization of individual brain structures is a prerequisite for group-level analyses of structural and functional neuroimaging data. The techniques currently available are either based on volume and/or surface attributes, with limited insight regarding the consistent alignment of anatomical landmarks across individuals. This article details a global, geometric approach that performs the alignment of the exhaustive sulcal imprints (cortical folding patterns) across individuals. This DIffeomorphic Sulcal-based COrtical (DISCO) technique proceeds to the automatic extraction, identification and simplification of sulcal features from T1-weighted Magnetic Resonance Image (MRI) series. These features are then used as control measures for fully-3-D diffeomorphic deformations. Quantitative and qualitative evaluations show that DISCO correctly aligns the sulcal folds and gray and white matter volumes across individuals. The comparison with a recent, iconic diffeomorphic approach (DARTEL) highlights how the absence of explicit cortical landmarks may lead to the misalignment of cortical sulci. We also feature DISCO in the automatic design of an empirical sulcal template from group data. We also demonstrate how DISCO can efficiently be combined with an image-based deformation (DARTEL) to further improve the consistency and accuracy of alignment performances. Finally, we illustrate how the optimized alignment of cortical folds across subjects improves sensitivity in the detection of functional activations in a group-level analysis of neuroimaging data.

Support vector machines (SVM) are increasingly used in brain image analyses since they allow capturing complex multivariate relationships in the data. Moreover, when the kernel is linear, SVMs can be used to localize spatial patterns of discrimination between two groups of subjects. However, the features' spatial distribution is not taken into account. As a consequence, the optimal margin hyperplane is often scattered and lacks spatial coherence, making its anatomical interpretation difficult. This paper introduces a framework to spatially regularize SVM for brain image analysis. We show that Laplacian regularization provides a flexible framework to integrate various types of constraints and can be applied to both cortical surfaces and 3D brain images. The proposed framework is applied to the classification of MR images based on gray matter concentration maps and cortical thickness measures from 30 patients with Alzheimer's disease and 30 elderly controls. The results demonstrate that the proposed method enables natural spatial and anatomical regularization of the classifier.

The aim of this paper is to develop a registration methodology in order to combine anatomical and functional information provided by thoracic/abdominal computed tomography (CT) and whole-body positron emission tomography (PET) images. The proposed procedure is based on the incorporation of prior anatomical information in an intensity-based nonrigid registration algorithm. This incorporation is achieved in an explicit way, initializing the intensity-based registration stage with the solution obtained by a nonrigid registration of corresponding anatomical structures. A segmentation algorithm based on a hierarchically ordered set of anatomy-specific rules is used to obtain anatomical structures in CT and emission PET scans. Nonrigid deformations are modeled in both registration stages by means of free-form deformations, the optimization of the control points being achieved by means of an original vector field-based approach instead of the classical gradient-based techniques, considerably reducing the computational time of the structure registration stage. We have applied the proposed methodology to 38 sets of images (33 provided by standalone machines and five by hybrid systems) and an assessment protocol has been developed to furnish a qualitative evaluation of the algorithm performance.

The spatial relation "between" is a notion which is intrinsically both fuzzy and contextual, and depends, in particular, on the shape of the objects. The literature is quite poor on this and the few existing definitions do not take into account these aspects. In particular, an object B that is in a concavity of an object A1 not visible from an object A2 is considered between A1 and A2 for most definitions, which is counter intuitive. Also, none of the definitions deal with cases where one object is much more elongated than the other. Here, we propose definitions which are based on convexity, morphological operators, and separation tools, and a fuzzy notion of visibility. They correspond to the main intuitive exceptions of the relation. We distinguish between cases where objects have similar spatial extensions and cases where one object is much more extended than the other. Extensions to cases where objects, themselves, are fuzzy and to three-dimensional space are proposed as well. The original work proposed in this paper covers the main classes of situations and overcomes the limits of existing approaches, particularly concerning nonvisible concavities and extended objects. Moreover, the definitions capture the intrinsic imprecision attached to this relation. The main proposed definitions are illustrated on real data from medical images.