Section: New Results

Tissue Microstructures features recovery & applications

MAPL: Tissue microstructure estimation using Laplacian-regularized MAP-MRI and its application to HCP data

Participants : Rutger Fick, Demian Wassermann, Emanuel Caruyer, Rachid Deriche.

The recovery of microstructure-related features of the brain's white matter is a current challenge in diffusion MRI. To robustly estimate these important features from diffusion MRI data, we propose to analytically regularize MAP-MRI's coefficient estimation using the norm of the Laplacian of the reconstructed signal. We first compare our approach, which we call MAPL, with competing state-of-the-art functional basis approaches. We show that it outperforms the original MAP-MRI implementation and the recently proposed modified Spherical Polar Fourier (mSPF) basis with respect to signal fitting, EAP and ODF reconstruction in noisy, sparsely sampled data of a physical phantom with reference gold standard data. Then, to reduce the variance of parameter estimation using multi-compartment tissue models, we propose to use MAPL's signal fitting and extrapolation as a preprocessing step. We study the effect of MAPL on the estimation of axon diameter using a simplified Axcaliber model and axonal dispersion using the Neurite Orientation Dispersion and Density Imaging (NODDI) model. We show the positive effect of using it as a preprocessing step in estimating and reducing the variances of these parameters in the Corpus Callosum of six different subjects of the MGH Human Connectome Project. Finally we correlate the estimated axon diameter, dispersion and restricted volume fractions with Fractional Anisotropy (FA) and clearly show that changes in FA significantly correlate with changes with all estimated parameters. Overall, we illustrate the potential of using a well-regularized functional basis together with multi-compartment approaches to recover important microstructure tissue parameters with much less variability, thus contributing to the challenge of better understanding microstructure-related features of the brain's white matter.

This work has been published in  [16]

Quantifying White Matter Microstructure with a Unified Spatio-Temporal Diffusion Weighted MRI Continuous Representation

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

A current problem Diffusion MRI (dMRI) based microscopy under the narrow pulse approximation is how to best exploit the 4D (q-space + diffusion time) nature of the signal. Assaf et al. showed that exploring the dMRI attenuation at different diffusion times provides information on the distribution of axonal diameters within a voxel in their seminal work: AxCaliber. However, AxCaliber requires knowing beforehand the predominant orientation of the axons within the analyzed volume to adjust the q-space sampling accordingly. In this work, we show that our novel sparse representation of the 3D+t dMRI signal, enables the recovery of axonal diameter distribution parameters without the need to know the axonal direction at acquisition time.

This work has been published in  [61]

A sensitivity analysis of Q-space Indices with respect to changes in axonal diameter, dispersion and tissue composition

Participants : Rutger Fick, Marco Pizzolato, Demian Wassermann, Mario Zuccheli [Dpt of Computer Science, University of Verona] , Gloria Menegaz [Dpt of Computer Science, University of Verona] , Rachid Deriche.

In Diffusion MRI, q-space indices are scalar quantities that describe properties of the ensemble average propagator (EAP). Their values are often linked to the axonal diameter – assuming that the diffusion signal originates from inside an ensemble of parallel cylinders. However, histological studies show that these assumptions are incorrect, and axonal tissue is often dispersed with various tissue compositions. Direct interpretation of these q-space indices in terms of tissue change is therefore impossible, and we must treat them as as scalars that only give non-specific contrast – just as DTI indices. In this work, we analyze the sensitivity of q-space indices to tissue structure changes by simulating axonal tissue with changing axonal diameter, dispersion and tissue compositions. Using human connectome project data we then predict which indices are most sensitive to tissue changes in the brain. We show that, in both multi-shell and single-shell (DTI) data, q-space indices have higher sensitivity to tissue changes than DTI indices in large parts of the brain. Based on these results, it may be interesting to revisit older DTI studies using q-space indices as a marker for pathology.

This work has been published in  [32]

Assessing the feasibility of estimating axon diameter using diffusion models and machine learning

Participants : Rutger Fick, Neda Sepasian [Eindhoven University of Technology, The Netherlands] , Marco Pizzolato, Andrada Ianus [Centre for Medical Image Computing, Dept. of Computer Science, UCL, London, UK] , Rachid Deriche.

Axon diameter estimation has been a focus of the diffusion MRI community for the past decade. The main argument has been that while diffusion models always overestimate the true axon diameter, their estimation still correlates with changes in true value. Until now, this remains more as a discussion point. The aim of this paper is to clarify this hypothesis using a recently acquired cat spinal cord data set, where the diffusion MRI signal of both a multi-shell and Ax- Caliber acquisition have been registered with the underlying histology values. We find that the axon diameter as estimated by signal models and AxCaliber does not correlate with their true sizes for axon diameters smaller than 3 microns. On the other hand, we also train a random forest machine learning algorithm to map signal-based features to histology values of axon diameter and volume fraction. The results show that, in this dataset, this approach leads to a more reliable estimation of physically relevant axon diameters than using sophisticated diffusion models.

This work has been submitted to ISBI'2017.

Rotational Invariants of Ternary Quartics

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

This work has been developed in the framework of an "Action Transverse" with the Aromath team (see section 9.1.1). It aims at creating building blocks for biomarkers for the case of a representation of the diffusion information (acquired using HARDI sequences) as a ternary quartic. Previous work in the team had some drawbacks such as instabilities in the non-polynomial formulae [99] or missing guarantees of the polynomial results [85] (e.g. unknown completeness or impossibility to establish the redundancy of the obtained expressions). This work proposes an alternative construction based on rational expressions and shares some of the best characteristics of the two previous approaches: the set is complete and generative – and thus also generates polynomial invariants –, the number of generators is close to minimal (13 instead of 12 and the expression relating these 13 formulae is known), and has an improved stability compared to the non-polynomial approach. The obtained formulae are furthermore nested making their computation much more effective than previous approaches. Furthermore, the method is generic and can in theory be expanded to higher polynomial degrees.