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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.

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Correspondence to Gaëtan Rensonnet .

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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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