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Computational Diffusion MRI pp 29–42Cite as

A Signal Peak Separation Index for Axisymmetric B-Tensor Encoding

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Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

Diffusion-weighted MRI (DW-MRI) has recently seen a rising interest in planar, spherical and general B-tensor encodings. Some of these sequences have aided traditional linear encoding in the estimation of white matter microstructural features, generally by making DW-MRI less sensitive to the orientation of axon fascicles in a voxel. However, less is known about their potential to make the signal more sensitive to fascicle orientation, especially in crossing-fascicle voxels. Although planar encoding has been commended for the resemblance of its signal with the voxel’s orientation distribution function (ODF), linear encoding remains the near undisputed method of choice for orientation estimation. This paper presents a theoretical framework to gauge the sensitivity of axisymmetric B-tensors to fascicle orientations. A signal peak separation index (SPSI) is proposed, motivated by theoretical considerations on a simple multi-tensor model of fascicle crossing. Theory and simulations confirm the intuition that linear encoding, because it maximizes B-tensor anisotropy, possesses an intrinsic advantage over all other axisymmetric B-tensors. At identical SPSI however, oblate B-tensors yield higher signal and may be more robust to acquisition noise than their prolate counterparts. The proposed index relates the properties of the B-tensor to those of the tissue microstructure in a straightforward way and can thus guide the design of diffusion sequences for improved orientation estimation and tractography.

Keywords

  • Diffusion-weighted MRI
  • B-tensor encoding
  • Linear encoding
  • Planar encoding
  • Signal peak separation
  • Sequence design

Gabriel Girard and Marco Pizzolato—These senior authors contributed equally.

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Acknowledgements

This work was supported by the Swiss National Science Foundation Spark grant number 190297 and has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 754462.

Author information

Authors and Affiliations

  1. Signal Processing Lab (LTS5), École polytechnique fédérale de Lausanne, Lausanne, Switzerland

    Gaëtan Rensonnet, Jonathan Rafael-Patiño, Jean-Philippe Thiran, Gabriel Girard & Marco Pizzolato

  2. ICTEAM Institute, Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Gaëtan Rensonnet & Benoît Macq

  3. Center for BioMedical Imaging (CIBM), Lausanne, Switzerland

    Jean-Philippe Thiran & Gabriel Girard

  4. Radiology Department, Centre hospitalier universitaire vaudois and University of Lausanne, Lausanne, Switzerland

    Jean-Philippe Thiran & Gabriel Girard

  5. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs. Lyngby, Denmark

    Marco Pizzolato

Authors
  1. Gaëtan Rensonnet
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  2. Jonathan Rafael-Patiño
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  3. Benoît Macq
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  4. Jean-Philippe Thiran
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  5. Gabriel Girard
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  6. Marco Pizzolato
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Corresponding author

Correspondence to Gaëtan Rensonnet .

Editor information

Editors and Affiliations

  1. University College London, London, UK

    Dr. Noemi Gyori

  2. Centre for Medical Engineering, King's College London, London, UK

    Dr. Jana Hutter

  3. Nvidia, Nashville, TN, USA

    Dr. Vishwesh Nath

  4. University College London, London, UK

    Dr. Marco Palombo

  5. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs. Lyngby, Denmark

    Dr. Marco Pizzolato

  6. Laboratory of Mathematics in Imaging, Harvard Medical School, Boston, MA, USA

    Dr. Fan Zhang

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Cite this paper

Rensonnet, G., Rafael-Patiño, J., Macq, B., Thiran, JP., Girard, G., Pizzolato, M. (2021). A Signal Peak Separation Index for Axisymmetric B-Tensor Encoding. In: Gyori, N., Hutter, J., Nath, V., Palombo, M., Pizzolato, M., Zhang, F. (eds) Computational Diffusion MRI. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-030-73018-5_3

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