CoBCoM 2021 Lectures

Overview and introductory presentation coming soon.

The CoBCoM 2021 Lectures:

Rotation Invariant Features for Diffusion MRI

We present a novel computational framework for analytically generating a complete set of algebraically independent Rotation Invariant Features (RIF) given the Laplace-series expansion of a spherical function. Our computational framework provides a closed-form solution for these new invariants, which are the natural expansion of the well known spherical mean, power-spectrum and bispectrum invariants. We highlight the maximal number of algebraically independent invariants which can be obtained from a truncated Spherical Harmonic (SH) representation of a spherical function and show that most of these new invariants can be linked to statistical and geometrical measures of spherical functions, such as the mean, the variance and the volume of the spherical signal. Moreover, we demonstrate their application to dMRI signal modeling including the Apparent Diffusion Coefficient (ADC), the diffusion signal and the fiber Orientation Distribution Function (fODF). In addition, using both synthetic and real data, we test the ability of our invariants to estimate brain tissue microstructure in healthy subjects and show that our framework provides more flexibility and open up new opportunities for innovative development in the domain of microstructure recovery from diffusion MRI.

Adaptive Phase Correction for Diffusion Weighted Images

Phase correction (PC) is a preprocessing technique that exploits the phase of images acquired in Magnetic Resonance Imaging (MRI) to obtain real-valued images containing tissue contrast with additive Gaussian noise, as opposed to magnitude images which follow a non-Gaussian distribution, e.g. Rician. PC finds its natural application to diffusion-weighted images (DWIs) due to their inherent low signal-to-noise ratio and consequent non-Gaussianity that induces a signal overestimation bias that propagates to the calculated diffusion indices. PC effectiveness depends upon the quality of the phase estimation, which is often performed via a regularization procedure. We show that a suboptimal regularization can produce alterations of the true image contrast in the real-valued phase-corrected images. We propose adaptive phase correction (APC), a method where the phase is estimated by using MRI noise information to perform a complex-valued image regularization that accounts for the local variance of the noise. We show, on synthetic and acquired data, that APC leads to phase-corrected real-valued DWIs that present a reduced number of alterations and a reduced bias. The substantial absence of parameters for which human input is required favors a straightforward integration of APC in MRI processing pipelines.

Spherical Convolutional Neural Networks for Diffusion MRI Analysis

Diffusion Magnetic Resonance Imaging (dMRI) is an imaging technique which enables analysis of the brain tissue at a microscopic scale, particularly the analysis of white matter. Given a high enough angular resolution, a common way to explain the measured signal is via fiber orientation distribution function (fODF). This function describes the orientation and volume fraction of axon bundles within each voxel and is an essential ingredient of tractography. In this work, we have investigated a deep learning approach for the fODF estimation. U-nets enable fast and high resolution inference by combining multi-scale features from contracting and expanding parts of the network. As dMRI signals are most commonly acquired on spheres, we propose a spherical U-net which is adjusted to the properties of the dMRI data, namely its real nature, antipodal symmetry, uniform sampling and axial symmetry of the signals corresponding to individual fibers. We compared our model with another deep learning approach based on a 3D convolutional neural network and a state-of-the-art approach-multi-shell multi-tissue constrained spherical deconvolution, on real data from Human Connectome Project and synthetic data generated using ball and stick model. The methods are compared in terms of mean square error and mean angular error for dMRI signals of different angular resolutions. Provided quantitative analyses show improved performance with our approach even with significantly reduced number of parameters and results obtained on synthetic data indicate its robustness with respect to noise. Qualitative results illustrating the performance of the methods are also presented.

Brain Network Alignment and Similarity

An important part of our current understanding of the structure of the human brain relies on the concept of brain network, which is obtained by looking at how different brain regions are connected with each other. In this work we present a strategy for choosing a suitable parcellation of the brain for structural connectivity studies by making use of the concepts of network alignment and similarity. To do so, we design a novel similarity measure between weighted networks called graph Jaccard index, and a new network alignment technique called WL-align. By assessing the possibility to retrieve graph matchings that provide highly similar graphs, we show that morphology- and structure-based atlases define brain networks that are more topologically robust across a wide range of resolutions.

A Unified Framework for Structure-Function Mapping Based on Eigenmodes

Characterizing the connection between brain structure and brain function is essential for understanding how behaviour emerges from the underlying anatomy. A number of studies have shown that the network structure of the white matter shapes functional connectivity. Therefore, it should be possible to predict, at least partially, functional connectivity given the structural network. Many structure–function mappings have been proposed in the literature, including several direct mappings between the structural and functional connectivity matrices. However, the current literature is fragmented and does not provide a uniform treatment of current methods based on eigendecompositions. In particular, existing methods have never been compared to each other and their relationship explicitly derived in the context of brain structure–function mapping. In this lecture, we propose a unified computational framework that generalizes recently proposed structure–function mappings based on eigenmodes. Using this unified framework, we highlight the link between existing models and show how they can be obtained by specific choices of the parameters of our framework. By applying our framework to 50 subjects of the Human Connectome Project, we reproduce 6 recently published results, devise two new models and provide a direct comparison between all mappings. Finally, we show that a glass ceiling on the performance of mappings based on eigenmodes seems to be reached and conclude with possible approaches to break this performance limit.

The following publications are related to structure-function mapping:

Paradigm Free Regularization for fMRI Brain Activation Recovery

The advent of new brain imaging techniques such as resting-state functional MRI (fMRI), has led to the need for new approaches to recover brain functional activations without a prior knowledge on the experimental paradigm, as it was the case for task-fMRI. Conventional methods, i.e. the general linear model, requires the knowledge of the task paradigm to estimate the contribution of each voxel’s time course to the given task. To overcome this limitation, approaches to deconvolve the blood-oxygen-leveldependent (BOLD) response and recover the underlying neural activations without necessity of prior information has been proposed. Supposing the brain activates in constant blocks, frst we propose a temporal regularized deconvolution technique which uses an exponential operator, whose shape and performance can be adjusted, into a least absolute shrinkage and selection operator (LASSO) model solved via the Least-Angle Regression (LARS) algorithm. We reduced the number of parameters to be set by the user, when compared with the state of the art. Second, we introduce a paradigm-free regularization algorithm that applies on the 4-D fMRI image, acting simultaneously in the 3-D space and the 1-D time dimensions. The approach is based on the idea that large image variations should be preserved as they occur during an activation, whereas small variations should be smoothed to remove noise. It allows to smooth the whole fMRI image with an anisotropic regularization, thus blindly recovering the location of the brain activations in space and their timing and duration.Both approaches were tested on phantom and real data and were demonstrated to improve the results obtained in the state of the art.

Three-dimensional Polarized Light Imaging

Diffusion Magnetic Resonance Imaging (dMRI) is the only non-invasive and invivo imaging modality able to provide human brain structural connectivity information. This is done via an estimation of the fiber orientation distribution (FOD) of white matter and dMRI tractography. In this thesis, three-dimensional Polarized Light Imaging (3D-PLI) is investigated and, thanks to its high spatial resolution, is presented as a complementary and potential technique for validation and guidance of dMRI fiber orientation estimates and tracking. The main goal of this work is, thus, to propose a strategy to close the resolution gap between dMRI and 3D-PLI and to investigate metrics for their quantitative comparison and, henceforth, to pave the way for multiscale and multimodal image analysis.Contributions in this thesis are manifold. First, we study the 3D-PLI fiber orientation and propose a method to disentangle the sign ambiguity of its inclination angle for an accurate determination of the 3D orientation. Second, we introduce an analytical and fast technique to compute the FOD from microscopic 3D-PLI orientation estimates to the meso- or macroscopic dimensions of dMRI. Third, we perform tractography at multiple scales from 3D-PLI human brain data to demonstrate the preservation of the fiber tracts architecture regardless of the decrease in resolution. Finally, we investigate how these obtained tractograms can be inspected using homology theory for a quantitative evaluation between them. Overall, we develop original and efficient dMRI and 3D-PLI methods, validate on both synthetic and human data and lay the foundations for multiscale and multimodal studies between dMRI and 3D-PLI.

Algorithmic Approaches to Forward and Inverse M/EEG problems

Magneto- and Electro-encephalography (M/EEG) are two non-invasive functional imaging modalities which measure the electromagnetic activity of the brain. These tools are used in cognitive studies as well as in clinical applications as, for example, epilepsy. Besides the presentation of some background material about the M/EEG modalities, this thesis describes two main contributions. The first one is a method for a fast approximation of a set of EEG forward problem solutions, parametrized by tissue conductivity values. This forward problem consists in computing how a specific cortical activity would be measured by EEG sensors. The main advantage of our method is that it significantly accelerates the computation time, while controlling the approximation error. Head tissue conductivity values vary across subjects and it might be interesting to estimate them from the EEG data. Our method is an important step towards an efficient solution of such a head tissues conductivity estimation problem. The second contribution is a novel source reconstruction method, which estimates extended cortical sources explaining the M/EEG measurements. The main originality of the method is that instead of providing a unique reconstruction, as the majority of the state-of-the-art methods do, it proposes several equally valid candidates. We validated both our contributions on simulated and real M/EEG data.

Advanced dMRI signal modeling for tissue microstructure characterization

This thesis is dedicated to furthering neuroscientific understanding of the human brain using diffusion-sensitized Magnetic Resonance Imaging (dMRI). Within dMRI, we focus on the estimation and interpretation of microstructure-related markers, often referred to as “Microstructure Imaging”. This thesis is organized in three parts. Part I focuses on understanding the state-of-the-art in Microstructure Imaging. We start with the basic of diffusion MRI and a brief overview of diffusion anisotropy. We then review and compare most state-of-the-art microstructure models in PGSE-based Microstructure Imaging, emphasizing model assumptions and limitations, as well as validating them using spinal cord data with registered ground truth histology. In Part II we present our contributions to 3D q-space imaging and microstructure recovery. We propose closed-form Laplacian regularization for the recent MAP functional basis, allowing robust estimation of tissue-related q-space indices. We also apply this approach to Human Connectome Project data, where we use it as a preprocessing for other microstructure models. Finally, we compare tissue biomarkers in a ex-vivo study of Alzheimer rats at different ages. In Part III, we present our contributions to representing the qt-space – varying over 3D q-space and diffusion time. We present an initial approach that focuses on 3D axon diameter estimation from the qt-space. We end with our final approach, where we propose a novel, regularized functional basis to represent the qt-signal, which we call qt-dMRI. Our approach allows for the estimation of time-dependent q-space indices, which quantify the time-dependence of the diffusion signal.

White matter information flow mapping from diffusion MRI and EEG

The human brain can be described as a network of specialized and spatially distributed regions. The activity of individual regions can be estimated using electroencephalography and the structure of the network can be measured using diffusion magnetic resonance imaging. However, the communication between the different cortical regions occurring through the white matter, coined information flow, cannot be observed by either modalities independently. Here, we present a new method to infer information flow in the white matter of the brain from joint diffusion MRI and EEG measurements. This is made possible by the millisecond resolution of EEG which makes the transfer of information from one region to another observable. A subject specific Bayesian network is built which captures the possible interactions between brain regions at different times. This network encodes the connections between brain regions detected using diffusion MRI tractography derived white matter bundles and their associated delays. By injecting the EEG measurements as evidence into this model, we are able to estimate the directed dynamical functional connectivity whose delays are supported by the diffusion MRI derived structural connectivity. We present our results in the form of information flow diagrams that trace transient communication between cortical regions over a functional data window. The performance of our algorithm under different noise levels is assessed using receiver operating characteristic curves on simulated data. In addition, using the well-characterized visual motor network as grounds to test our model, we present the information flow obtained during a reaching task following left or right visual stimuli. These promising results present the transfer of information from the eyes to the primary motor cortex. The information flow obtained using our technique can also be projected back to the anatomy and animated to produce videos of the information path through the white matter, opening a new window into multi-modal dynamic brain connectivity.

Interpretable Deep Learning for Decrypting Disease Signature in Multiple Sclerosis

The mechanisms driving multiple sclerosis (MS) are still largely unknown, calling for new methods allowing to detect and characterize tissue degeneration since the early stages of the disease. Our aim is to decrypt the microstructural signatures of the Primary Progressive versus the Relapsing-Remitting state of disease based on diffusion and structural magnetic resonance imaging data.Approach.A selection of microstructural descriptors, based on the 3D-Simple Harmonics Oscillator Based Reconstruction and Estimation and the set of new algebraically independent Rotation Invariant spherical harmonics Features, was considered and used to feed convolutional neural networks (CNNs) models. Classical measures derived from diffusion tensor imaging, that are fractional anisotropy and mean diffusivity, were used as benchmark for diffusion MRI (dMRI). Finally, T1-weighted images were also considered for the sake of comparison with the state-of-the-art. A CNN model was fit to each feature map and layerwise relevance propagation (LRP) heatmaps were generated for each model, target class and subject in the test set. Average heatmaps were calculated across correctly classified patients and size-corrected metrics were derived on a set of regions of interest to assess the LRP contrast between the two classes.Main results.Our results demonstrated that dMRI features extracted in grey matter tissues can help in disambiguating primary progressive multiple sclerosis from relapsing-remitting multiple sclerosis patients and, moreover, that LRP heatmaps highlight areas of high relevance which relate well with what is known from literature for MS disease.Significance.Within a patient stratification task, LRP allows detecting the input voxels that mostly contribute to the classification of the patients in either of the two classes for each feature, potentially bringing to light hidden data properties which might reveal peculiar disease-state factors.

Inferring and comparing structural parcellations of the human brain using diffusion MRI

Understanding how brain connectivity is organized, and how this constrains brain functionality is a key question of neuroscience. The advent of Diffusion Magnetic Resonance Imaging (dMRI) permitted the in vivo estimation of brain axonal connectivity. In this talk, we leverage these advances in order to: study how the brain connectivity is organized; study the relationship between brain connectivity, anatomy, and function, and find correspondences between structurally-defined regions of different subjects. Our first contribution is a model for the long-range axonal connectivity, and an efficient technique to divide the brain in regions with homogeneous connectivity. Our parceling technique can create both single-subject and groupwise structural parcellations of the brain. The resulting parcels are in agreement with anatomical, structural and functional parcellations extant in the literature. Our second contribution is a method to find correspondence between structural parcellations of different subjects. Based on Optimal Transport, it performs significantly better than the state-of-the-art ones.

Incorporating Transmission Delays in MEG source reconstruction

Information between brain regions is transferred through white matter fibers with delays that are measurable with magnetoencephalography and electroencephalography (M/EEG) due to its millisecond temporal resolution. Therefore, a useful representation of the brain is that of a graph where its nodes are the cortical areas and edges are the physical connections between them: either local (between adjacent vertices on the cortical mesh) or non-local (long-range white matter fibers). These long-range anatomical connections can be obtained by diffusion MRI (dMRI) tractography, thus giving us an insight on interaction delays of the macroscopic brain network. A fundamental role in shaping the rich temporal structure of functional connectivity is played by the structural connectivity that places constraints on which functional interactions occur in the network. In the context of regularizing the dynamics of M/EEG and recovering electrical activity of the brain from M/EEG measurements, traditional linear inverse methods deploy different constraints such as minimum norm, maximum-smoothness in space and/or time along the cortical surface. However, they usually do not take into account the structural connectivity and very few include delays supported by dMRI as a prior information. The goal of this work is to include these delays into the MEG source reconstruction process by imposing temporal smoothness in structurally connected sources, with the corresponding delays. We propose to encapsulate delays provided by dMRI in a graph representation and show their potential in improving the MEG source reconstruction when compared to a state-of-the-art approach.

Consequences of Tractography Filtering on Structural Brain Network Topology

The use of non-invasive techniques for the estimation of structural brain networks (i.e. connectomes) opened the door to large-scale investigations on the functioning and the architecture of the brain, unveiling the link between neurological disorders and topological changes of the brain network. This study aims at assessing if and how the topology of structural connectomes estimated non-invasively with diffusion MRI is affected by the employment of tractography filtering techniques in structural connectomic pipelines. Additionally, this work investigates the robustness of topological descriptors of filtered connectomes to the common practice of density-based thresholding. We investigate the changes in global efficiency, characteristic path length, modularity and clustering coefficient on filtered connectomes obtained with the spherical deconvolution informed filtering of tractograms and using the convex optimization modelling for microstructure informed tractography. The analysis is performed on both healthy subjects and patients affected by traumatic brain injury and with an assessment of the robustness of the computed graph-theoretical measures with respect to density-based thresholding of the connectome. Our results demonstrate that tractography filtering techniques change the topology of brain networks, and thus alter network metrics both in the pathological and the healthy cases. Moreover, the measures are shown to be robust to density-based thresholding. The present work highlights how the inclusion of tractography filtering techniques in connectomic pipelines requires extra caution as they systematically change the network topology both in healthy subjects and patients affected by traumatic brain injury. Finally, the practice of low-to-moderate density-based thresholding of the connectomes is confirmed to have negligible effects on the topological analysis.

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