Learning disease progression models with longitudinal data and missing values

International audienceStatistical methods have been developed for the analysis of longitudinal data in neurodegenerative diseases. To cope with the lack of temporal markers-i.e. to account for subject-specific disease progression in regard to age-a common strategy consists in realigning the individual sequence data in time. Patient's specific trajectories can indeed be seen as spatiotemporal perturbations of the same normative disease trajectory. However, these models do not easily allow one to account for multimodal data, which more than often include missing values. Indeed, it is rare that imaging and clinical examinations for instance are performed at the same frequency in clinical protocols. Multimodal models also need to allow a different profile of progression for data with different structure and representation. We propose to use a generative mixed effect model that considers the progression trajectories as curves on a Rieman-nian Manifold. We use the concept of product manifold to handle multimodal data, and leverage the generative aspect of our model to handle missing values. We assess the robuste-ness of our methods toward missing values frequency on both synthetic and real data. Finally we apply our model on a real-world dataset to model Parkinson's disease progression from data derived from clinical examination and imaging

Learning disease progression models with longitudinal data and missing values

International audienceStatistical methods have been developed for the analysis of longitudinal data in neurodegenerative diseases. To cope with the lack of temporal markers-i.e. to account for subject-specific disease progression in regard to age-a common strategy consists in realigning the individual sequence data in time. Patient's specific trajectories can indeed be seen as spatiotemporal perturbations of the same normative disease trajectory. However, these models do not easily allow one to account for multimodal data, which more than often include missing values. Indeed, it is rare that imaging and clinical examinations for instance are performed at the same frequency in clinical protocols. Multimodal models also need to allow a different profile of progression for data with different structure and representation. We propose to use a generative mixed effect model that considers the progression trajectories as curves on a Rieman-nian Manifold. We use the concept of product manifold to handle multimodal data, and leverage the generative aspect of our model to handle missing values. We assess the robuste-ness of our methods toward missing values frequency on both synthetic and real data. Finally we apply our model on a real-world dataset to model Parkinson's disease progression from data derived from clinical examination and imaging

Introducing Soft Topology Constraints in Deep Learning-based Segmentation using Projected Pooling Loss

International audienceDeep learning methods have achieved impressive results for 3D medical image segmentation. However, when the network is only guided by voxel-level information, it may provide anatomically aberrant segmentations. When performing manual segmentations, experts heavily rely on prior anatomical knowledge. Topology is an important prior information due to its stability across patients. Recently, several losses based on persistent homology were proposed to constrain topology. Persistent homology offers a principled way to control topology. However, it is computationally expensive and complex to implement, in particular in 3D. In this paper, we propose a novel loss function to introduce topological priors in deep learning-based segmentation, which is fast to compute and easy to implement. The loss performs a projected pooling within two steps. We first focus on errors from a global perspective by using 3D MaxPooling to obtain projections of 3D data onto three planes: axial, coronal and sagittal. Then, 2D MaxPooling layers with different kernel sizes are used to extract topological features from the multi-view projections. These two steps are combined using only MaxPooling, thus ensuring the efficiency of the loss function. Our approach was evaluated in several medical image datasets (spleen, heart, hippocampus, red nucleus). It allowed reducing topological errors and, in some cases, improving voxel-level accuracy

Multi-Spherical Diffusion MRI: An in-vivo Test- Retest Study of Time-Dependent q-space Indices

International audienceWe assess the test-retest reproducibility of time-dependent q-space indices (qτ-indices) in three C57Bl6 wild-type mice. To estimate qτ-indices from the four-dimensional qτ diffusion signal - varying over 3D q-space and diffusion time - we use our recent Multi-Spherical Diffusion MRI (MS-dMRI) method. Using MS-dMRI we could reliably estimate qτ-indices for two out of three subjects, where acquisition artifacts caused the offsets of the last subject

Multi-Spherical Diffusion MRI: Exploring Diffusion Time Using Signal Sparsity

International audienceEffective representation of the diffusion signal's dependence on diffusion time is a sought-after, yet still unsolved, challenge in diffusion MRI (dMRI). We propose a functional basis approach that is specifically designed to represent the dMRI signal in this four-dimensional space – varying over gradient strength, direction and diffusion time. In particular , we provide regularization tools imposing signal sparsity and signal smoothness to drastically reduce the number of measurements we need to probe the properties of this multi-spherical space. We illustrate a novel application of our approach, which is the estimation of time-dependent q-space indices, on both synthetic data generated using Monte-Carlo simulations and in vivo data acquired from a C57Bl6 wild-type mouse. In both cases, we find that our regularization approach stabilizes the signal fit and index estimation as we remove samples, which may bring multi-spherical diffusion MRI within the reach of clinical application

Multi-Spherical MRI: Breaking the Boundaries of Diffusion Time

International audienceEffective representation of the diffusion signal’s dependence on diffusion time is a sought-after, yet still unsolved challenge in diffusion MRI (dMRI). We propose a functional basis approach that is specifically designed to represent the dMRI signal in this four-dimensional space – varying over gradient strength, direction and diffusion time – that we call the multi-spherical space. In particular, we provide regularization tools imposing signal sparsity and signal smoothness to drastically reduce the number of measurements we need to probe the properties of this multi-spherical space

Fourier Disentangled Multimodal Prior Knowledge Fusion for Red Nucleus Segmentation in Brain MRI

Early and accurate diagnosis of parkinsonian syndromes is critical to provide appropriate care to patients and for inclusion in therapeutic trials. The red nucleus is a structure of the midbrain that plays an important role in these disorders. It can be visualized using iron-sensitive magnetic resonance imaging (MRI) sequences. Different iron-sensitive contrasts can be produced with MRI. Combining such multimodal data has the potential to improve segmentation of the red nucleus. Current multimodal segmentation algorithms are computationally consuming, cannot deal with missing modalities and need annotations for all modalities. In this paper, we propose a new model that integrates prior knowledge from different contrasts for red nucleus segmentation. The method consists of three main stages. First, it disentangles the image into high-level information representing the brain structure, and low-frequency information representing the contrast. The high-frequency information is then fed into a network to learn anatomical features, while the list of multimodal low-frequency information is processed by another module. Finally, feature fusion is performed to complete the segmentation task. The proposed method was used with several iron-sensitive contrasts (iMag, QSM, R2*, SWI). Experiments demonstrate that our proposed model substantially outperforms a baseline UNet model when the training set size is very small

Spatio-Temporal dMRI Acquisition Design: Reducing the Number of Samples

International audienceSynopsis Acquisition time is a major limitation in recovering brain white matter microstructure with diffusion magnetic resonance imaging. Finding a sampling scheme that maximizes signal quality and satisfies given time constraints is NP-hard. Therefore, we propose a heuristic method based on genetic algorithm that finds sub-optimal solutions in reasonable time. Our diffusion model is defined in the qτ-space, so that it captures both spacial and temporal phenomena. The experiments on synthetic data and in-vivo diffusion images of the C57Bl6 wild-type mouse corpus callosum reveal superiority of our approach over random sampling and even distribution in the qτ-space. Introduction Brain white matter (WM) microstructure recovery with diffusion Magnetic Resonance Imaging (dMRI) requires lengthy acquisition which is unattainable in clinical practice. Dense scanning schemes studied by researchers [1-5] typically take few hours of imaging time, whereas human subjects can tolerate a little more than one hour [6, 7]. Nonetheless, recent in vivo studies of the WM microstructure [7-9] call for more fine-grained investigation of both space-and time-dependent diffusion. In this work, we aim at bridging the gap between growing demands on spatio-temporal (qτ) probing of dMRI signal [10] and acquisition time limitations. To this end, we propose an acquisition design that reduces the number of samples under adjustable quality loss. Most of the current acquisition schemes assume the fixed τ case, focusing on a dense sampling of the q-space instead [3-5]. However, a pronounced time-dependence in dMRI was recently reported by De Santis et al. [9], Burcaw et al. [11], and Novikov et al. [12]. Their results incline towards paying more attention to temporal phenomena in dMRI signal by incorporating multiple τ variants into acquisition schemes. Methods The main goal of our study is to find a qτ-indexed sampling scheme that best preserves the dMRI signal while satisfying given acquisition time limits [10,13]. We formulate the acquisition design task as an optimization problem. Furthermore, we want our approach to be applicable for real data. To this end, we discretize the spatio-temporal search space by performing a state-of-the-art dense pre-acquisition of dMRI signal. The problem thus boils down to selecting an optimal subset of Diffusion Weighted Images (DWIs), which is NP-hard [13]. Taking into account that the time complexity of our problem grows exponentially with the size of domain, such that global optima cannot be found deterministically within few hours or even few days, we apply a stochastic search engine instead. We use Standard Genetic Algorithm (SGA) [14] for this purpose due to its fast convergence rate, ability to avoid local optima, and the fact that it is based on the mathematically profound Markov Chain model [15]. Experiments For evaluation of our approach, we used both synthetic diffusion data and in vivo dMRI images of the C57Bl6 wild-type mouse. The dense pre-acquisition of signals covered 40 shells, each of which comprised 20 directions and one b 0-image, i.e. 40 × 20 = 800 DWIs plus 40 non-weighted images. We used combinations of 5 separation times Δ ∈ {10.8, 13.1, 15.4, 17.7, 20.0} [ms] and 8 gradient strengths G ∈ {50, 100, 150, 200, 250, 300, 350, 400} [mT/m]. The gradient duration δ = 5 ms remained constant throughout the experiments. We considered four variants of time limits expressed as budget sizes n max = {100, 200, 300, 400} out of 800 DWIs. We compared our method with two alternative sampling schemes. One of them, called random, used the uniform random distribution of qτ samples in the index space {1, …, N}. In the second one, referred to as even, we picked each i-th sample for i = ⌊kN / n max ⌋ and k = 1,. .. , n max. Discussion As Figure 1 shows, our method outperformed the other two in all analyzed cases, assuring lowest mean squared errors (MSEs) and standard deviations (STDs). We verified statistical significance of the results with the two-sample Student's t level α = 10 −