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Home arrow Computer Science arrow Computational Diffusion MRI: MICCAI Workshop, Athens, Greece, October 2016

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Introduction

Effective representation of the diffusion signal’s dependence on diffusion time is a sought-after, yet still unsolved challenge in diffusion MRI (dMRI). Recent literature is increasingly emphasizing the need for such a representation, where accounting for the diffusion time dependence of the extra-axonal diffusion signal [1,2] has already resulted in a more accurate estimation of the axon density and diameter [3]. To measure the four-dimensional dMRI signal it is necessary to go beyond a multishell q-space acquisition—which only varies gradient strength and direction—and also vary the diffusion time. This multi-spherical acquisition is hardly feasible in a clinical setting due to a large number of sample points in this four-dimensional space-time framework.

R.H.J. Fick (H) • R. Deriche • D. Wassermann (H)

Universite Cote d’Azur, Inria, France

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A. Petiet • M. Santin • A.-C. Philippe • S. Lehericy

CENIR, Institut du Cerveau et de la Moelle epineere, Paris, France © Springer International Publishing AG 2017

A. Fuster et al. (eds.), Computational Diffusion MRI, Mathematics

and Visualization, DOI 10.1007/978-3-319-54130-3_6

To reduce the number of required samples, we propose to leverage the recently proposed representation of the multi-spherical signal in terms of an orthogonal functional basis inspired by Fick et al. [4]. Particularly, we will show that the multispherical dMRI signal is sparse when represented in terms of this basis. Different sparse signal reconstruction frameworks, e.g. [5, 6], have shown that signal sparsity allows for a significant reduction in the number of acquired samples. Furthermore, sparse signal reconstruction has been successfully used in different dMRI protocols, see e.g. [7-10]. However, to the best of our knowledge, we are the first to facilitate microstructural measurements by leveraging the sparsity of the spatial and temporal dMRI signal using a novel functional basis. We demonstrate that we are able to reduce the number of required samples for a multi-spherical dMRI acquisition and derive time-dependent microstructural features on both simulated data and in-vivo mouse data.

This paper is structured as follows: first, we present the theory behind our estimation method in Sect. 2. We then describe our methods of generating in-silico multi-spherical data and the parameters of our in vivo dMRI acquisition of C57Bl6 wild-type mouse in Sect. 3. In Sect. 4 we then show the results of our method, we discuss our findings and present our conclusions in Sect. 5.

 
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