Section: New Results

Computational Diffusion MRI

Spatio-Temporal dMRI Acquisition Design: Reducing the Number of qt Samples Through a Relaxed Probabilistic Model

Participants : Patryk Filipiak, Rutger Fick, Alexandra Petiet [ICM, CENIR, Paris] , Mathieu Santin [ICM, CENIR, Paris] , Anne-Charlotte Philippe [ICM, CENIR, Paris] , Stephane Lehericy [ICM, CENIR, Paris] , Demian Wassermann, Rachid Deriche.

Acquisition time is a major limitation in recovering brain microstructure with diffusion Magnetic Resonance Imaging. Finding a sampling scheme that maximizes signal quality and satisfies given time constraints is NP-hard. We alleviate that by introducing a relaxed probabilistic model of the problem, for which nearly-optimal solutions can be found effectively. Our model is defined in the qt-space, so that it captures both spacial and temporal phenomena. The experiments on in-vivo diffusion images of the C57Bl6 wild-type mice reveal superiority of our technique over random sampling and even distribution in the qt-space.

This work has been published in [33].

Diffusion MRI microstructure models with in vivo human brain Connectom data: results from a multi-group comparison

Participants : Uran Ferizi [CMIC, Dept. of Computer Science, UCL, UK] , Rutger Fick, Rachid Deriche.

A large number of mathematical models have been proposed to describe the measured signal in diffusion-weighted (DW) magnetic resonance imaging (MRI) and infer properties about the white matter microstructure. However, a head-to-head comparison of DW-MRI models is critically missing in the field. To address this deficiency, we organized the "White Matter Modeling Challenge" during the International Symposium on Biomedical Imaging (ISBI) 2015 conference. This competition aimed at identifying the DW-MRI models that best predict unseen DW data. in vivo DW-MRI data was acquired on the Connectom scanner at the A.A.Martinos Center (Massachusetts General Hospital) using gradients strength of up to 300 mT/m and a broad set of diffusion times. We focused on assessing the DW signal prediction in two regions: the genu in the corpus callosum, where the fibres are relatively straight and parallel, and the fornix, where the configuration of fibres is more complex. The challenge participants had access to three-quarters of the whole dataset, and their models were ranked on their ability to predict the remaining unseen quarter of data. In this work, we provide both an overview and a more in-depth description of each evaluated model, report the challenge results, and infer trends about the model characteristics that were associated with high model ranking. This work provides a much needed benchmark for DW-MRI models. The acquired data and model details for signal prediction evaluation are provided online to encourage a larger scale assessment of diffusion models in the future.

This work has been published in [16].

Advanced dMRI signal modeling for tissue microstructure characterization

Participants : Rutger Fick, Demian Wassermann, Rachid Deriche.

Non-invasive estimation of brain white matter microstructure features using dMRI – otherwise known as Microstructure Imaging – has become an increasingly complex and difficult challenge over the last decade. Within the framework of Fick's PhD thesis [13], we contributed to the challenge to recover microstructure tissue parameters by studying the impact of using well-regularized functional basis together with multi-compartment approaches. We focused on the estimation and interpretation of microstructure-related markers, often referred to as Microstructure Imaging and we reviewed and compared 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. We then presented contributions to 3D q-space imaging and microstructure recovery. We proposed closed-form Laplacian regularization for the recent MAP functional basis, allowing robust estimation of tissue-related q-space indices. We also applied this approach to Human Connectome Project data, where we used it as a preprocessing for other microstructure models. Finally, we compared tissue biomarkers in a ex-vivo study of Alzheimer rats at different ages. Last but not least, we contributed to representing the qt-space- varying over 3D q-space and diffusion time. Overall, we significantly contributed to the challenge of better understanding microstructure-related features of the brain's white matter.

This work has been published in [13].

White matter tractography guided by anatomical and microstructural priors

Participants : Gabriel Girard [SCIL, Sherbrooke University, CA] , Maxime Descoteaux [SCIL, Sherbrooke University, CA] , Demian Wassermann, Rachid Deriche.

In this work, performed within the framework of G. Girard's PhD thesis  [81], we mainly focused in developing beyond the state-of-the-art and well grounded tractography solutions to recover the brain structural connectivity: We started reporting biases from tractography reconstruction and suggested to use anatomical priors, derived from a high resolution T1-weighted image to reduce these biases and to embed additional spatial information of the brain tissues in the tractography to guide tractography. We showed that optimizing tractography parameters, stopping and seeding strategies can reduce the biases in position, shape, size and length of the streamline distribution. Overall, we very nicely succeeded to show that this idea was able to significantly improve the tractography by reducing the rate of false positives produced and provides a more quantitative characterization of the WM structure. Going further, we then proposed to embed more intrinsic microstructural information in the reconstruction process and remarkably succeeded to show the great added value brought to tractography by the addition of intrinsic microstructural information such as the mean axonal diameter information estimated from the orientation of maximal diffusion probability. This is an original and important step forward in microstructure informed tractography, paving the way to a new generation of algorithms able to deal with intricate configurations of white matter fibres and providing quantitative brain connectivity analysis.

This work has been published in [13] and its part related to AxTract, the micro-informed tractography algorithm, in [19].

Rational invariants of ternary forms under the orthogonal group

Participants : Paul Görlach, Evelyne Hubert, Théodore Papadopoulo, Rachid Deriche.

In  [79], [80], [95] we started to explore the theory of tensor invariants as a mathematical framework for computing new biomarkers for HARDI. We pursued this work and, in collaboration with the project-team GALAAD/AROMATH , we succeeded to develop a complete set of rational invariants for ternary quartics [44]. Being rational, they are very close to the polynomial invariants developed in  [80] but they constitute a complete set of invariants. They are also good tools to understand better the algebraic invariants of  [95] and some others based on spherical harmonics decomposition  [61]. We determined a generating set of rational invariants of minimal cardinality for the action of the orthogonal group O3 on the space $R{[x,y,z]}_{2d}$ of ternary forms of even degree 2d. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup B3 of signed permutations. On the other hand, our construction relies in a fundamental way on specific bases of harmonic polynomials. These bases provide maps with prescribed B3-equivariance properties. Our explicit construction of these bases should be relevant well beyond the scope of this work. The expression of the B3-invariants can then be given in a compact form as the composition of two equivariant maps. Instead of providing (cumbersome) explicit expressions for the O3-invariants, we provide efficient algorithms for their evaluation and rewriting. We also use the constructed B3-invariants to determine the O3-orbit locus and provide an algorithm for the inverse problem of finding an element in $R{[x,y,z]}_{2d}$ with prescribed values for its invariants. These are the computational issues relevant in brain imaging.

This work has been sumitted and is currently under review. A preprint is available in [44].

Non-parametric graphnet-regularized representation of dMRI in space and time

Participants : Rutger Fick, Alexandra Petiet [ICM, CENIR, Paris] , Mathieu Santin [ICM, CENIR, Paris] , Anne-Charlotte Philippe [ICM, CENIR, Paris] , Stéphane Lehericy [ICM, CENIR, Paris] , Demian Wassermann, Rachid Deriche.

Effective representation of the four-dimensional diffusion MRI signal – varying over three-dimensional q-space and diffusion time τ – is a sought-after and still unsolved challenge in diffusion MRI (dMRI). We propose a functional basis approach that is specifically designed to represent the dMRI signal in this qτ-space. Following recent terminology, we refer to our qτ-functional basis as “qτ-dMRI”. qτ-dMRI can be seen as a time-dependent realization of q-space imaging by Paul Callaghan and colleagues. We use GraphNet regularization – imposing both signal smoothness and sparsity – to drastically reduce the number of diffusion-weighted images (DWIs) that is needed to represent the dMRI signal in the qτ-space. As the main contribution, qτ-dMRI provides the framework to – without making biophysical assumptions – represent the qτ-space signal and estimate time-dependent q-space indices (qτ-indices), providing a new means for studying diffusion in nervous tissue. We validate our method on both in-silico generated data using Monte–Carlo simulations and an in-vivo test-retest study of two C57Bl6 wild-type mice, where we found good reproducibility of estimated qτ-index values and trends. In the hopes of opening up new τ-dependent venues of studying nervous tissues, qτ-dMRI is the first of its kind in being specifically designed to provide open interpretation of the qτ-diffusion signal.

This work has been published in [17]

Computational diffusion & perfusion MRI in brain imaging

Participants : Marco Pizzolato, Rachid Deriche.

Diffusion and Perfusion Magnetic Resonance Imaging (dMRI & pMRI) represent two modalities that allow sensing important and different but complementary aspects of brain imaging. This work performed within the framework of M. Pizzolato's PhD thesis presents a theoretical and methodological investigation on the MRI modalities based on diffusion-weighted (DW) and dynamic susceptibility contrast (DSC) images. For both modalities, the contributions of the thesis are related to the development of new methods to improve quality, processing, and exploitation of the obtained signals. With respect to contributions in diffusion MRI, the nature of the complex DW signal is investigated to explore a new potential contrast related to tissue microstructure. In addition, the complex signal is exploited to correct a bias induced by acquisition noise of DW images, thus improving the estimation of structural scalar metrics. With respect to contributions in perfusion MRI, the DSC signal processing is revisited in order to account for the bias due to bolus dispersion. This phenomenon prevents the correct estimation of perfusion metrics but, at the same time, can give important insights about the pathological condition of the brain tissue. The contributions of the thesis are presented within a theoretical and methodological framework, validated on both synthetic and real images.

This work has been published in [15].

Solving the Inclination Sign Ambiguity in Three Dimensional Polarized Light Imaging with a PDE-Based Method

Participants : Abib Alimi, Marco Pizzolato, Rutger Fick, Rachid Deriche.

Three dimensional Polarized Light Imaging (3D-PLI) is a contrast-enhancing technique that measures the spatial fiber architecture in the human postmortem brain or heart at a submillimeter resolution. In a voxel, the 3D fiber orientation is defined by the direction angle and the inclination angle whose sign is unknown. To have an accurate explanation of fiber orientation, it is compulsory to clear up this sign ambiguity. A tilting process provides information about the true inclination sign, however the technique is highly sensitive to noise. In this work, a partial differential equations based method is proposed to reduce the noise: the total variation model of Rudin-Osher-Fatemi is extended to 3D orientation vector images to restore the sign. The proposed algorithm is evaluated on synthetic and human heart data and results show that the true sign of the inclination angle can be successfully extracted.

This work has been published in [27]

Brain correlates of apathy in Kleine Levin syndrome: a mean apparent propagator study

Participants : Anne-Charlotte Philippe [ICM, CENIR, Paris] , Sophie Lavault [ICM, CENIR, Paris] , Romain Valabregue [ICM, CENIR, Paris] , Richard Levy [ICM, CENIR, Paris] , Isabelle Arnulf [ICM, CENIR, Paris] , Stéphane Lehericy [ICM, CENIR, Paris] , Rutger Fick, Demian Wassermann, Rachid Deriche.

Kleine-Levin syndrome (KLS) is a rare neurological disorder characterized by episodes of severe hypersomnia, apathy, cognitive impairment, derealization and behavioral disturbances. Between episodes, patients have normal sleep, mood and behavior. Apathy is a prominent clinical feature of KLS but its pathophysiology is not known. Using new techniques to boost signal-to-noise ration and biomarker extraction in multi-shell dMRI [13], we have studied, in collaboration with the Brain and Spine Institute (ICM, Paris) the Klein-Levin syndrome (KLS) [45]. Our results highlight the presence of structural changes correlated to the apathy score i n the anterior portion of the CC during episodes, a region where fibers project onto the medial orbitofrontal cortex. As, these prefrontal regions are involved in motivation processes, this suggests that apathy in KLS could result from difficul ties to provide the affective/motivational value of a given behavioral context.

This work has been published in [45].