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A Signal Peak Separation Index for Axisymmetric B-Tensor Encoding

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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References

  1. Aganj, I., Lenglet, C., Sapiro, G., Yacoub, E., Ugurbil, K., Harel, N.: Reconstruction of the orientation distribution function in single-and multiple-shell q-ball imaging within constant solid angle. Magn. Reson. Med. 64(2), 554–566 (2010)

    CrossRef  Google Scholar 

  2. Avram, A.V., Sarlls, J.E., Basser, P.J.: Measuring non-parametric distributions of intravoxel mean diffusivities using a clinical MRI scanner. Neuroimage 185, 255–262 (2019)

    CrossRef  Google Scholar 

  3. Basser, P.J., Jones, D.K.: Diffusion-tensor MRI: theory, experimental design and data analysis-a technical review. NMR in Biomed.: Int. J. Devoted Dev. Appl. Magn. Reson. In Vivo 15(7–8), 456–467 (2002)

    CrossRef  Google Scholar 

  4. Canales-Rodríguez, E.J., Legarreta, J.H., Pizzolato, M., Rensonnet, G., Girard, G., Rafael-Patino, J., Barakovic, M., Romascano, D., Alemán-Gómez, Y., Radua, J., et al.: Sparse wars: a survey and comparative study of spherical deconvolution algorithms for diffusion MRI. Neuroimage 184, 140–160 (2019)

    CrossRef  Google Scholar 

  5. Coelho, S., Pozo, J.M., Jespersen, S.N., Jones, D.K., Frangi, A.F.: Resolving degeneracy in diffusion MRI biophysical model parameter estimation using double diffusion encoding. Magn. Reson. Med. 82(1), 395–410 (2019)

    CrossRef  Google Scholar 

  6. Cottaar, M., Szczepankiewicz, F., Bastiani, M., Hernandez-Fernandez, M., Sotiropoulos, S.N., Nilsson, M., Jbabdi, S.: Improved fibre dispersion estimation using b-tensor encoding. NeuroImage 116832 (2020)

    Google Scholar 

  7. Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast, and robust analytical Q-ball imaging. Magn. Reson. Med. 58(3), 497–510 (2007)

    CrossRef  Google Scholar 

  8. Drobnjak, I., Alexander, D.C.: Optimising time-varying gradient orientation for microstructure sensitivity in diffusion-weighted MR. J. Magn. Reson. 212(2), 344–354 (2011)

    CrossRef  Google Scholar 

  9. Eriksson, S., Lasič, S., Nilsson, M., Westin, C.F., Topgaard, D.: NMR diffusion-encoding with axial symmetry and variable anisotropy: distinguishing between prolate and oblate microscopic diffusion tensors with unknown orientation distribution. J. Chem. Phys. 142(10), 104201 (2015)

    CrossRef  Google Scholar 

  10. Garyfallidis, E., Brett, M., Amirbekian, B., Rokem, A., Van Der Walt, S., Descoteaux, M., Nimmo-Smith, I.: Dipy, a library for the analysis of diffusion MRI data. Front. Neuroinformatics 8, 8 (2014)

    CrossRef  Google Scholar 

  11. Jensen, J.H., Helpern, J.A.: Characterizing intra-axonal water diffusion with direction-averaged triple diffusion encoding MRI. NMR Biomed. 31(7), e3930 (2018)

    CrossRef  Google Scholar 

  12. Jespersen, S.N., Lundell, H., Sønderby, C.K., Dyrby, T.B.: Orientationally invariant metrics of apparent compartment eccentricity from double pulsed field gradient diffusion experiments. NMR Biomed. 26(12), 1647–1662 (2013)

    CrossRef  Google Scholar 

  13. Kunz, N., da Silva, A.R., Jelescu, I.O.: Intra-and extra-axonal axial diffusivities in the white matter: which one is faster? Neuroimage 181, 314–322 (2018)

    CrossRef  Google Scholar 

  14. Lasič, S., Szczepankiewicz, F., Eriksson, S., Nilsson, M., Topgaard, D.: Microanisotropy imaging: quantification of microscopic diffusion anisotropy and orientational order parameter by diffusion MRI with magic-angle spinning of the q-vector. Front. Phys. 2, 11 (2014)

    CrossRef  Google Scholar 

  15. Lawrenz, M., Finsterbusch, J.: Double-wave-vector diffusion-weighted imaging reveals microscopic diffusion anisotropy in the living human brain. Magn. Reson. Med. 69(4), 1072–1082 (2013)

    CrossRef  Google Scholar 

  16. Lundell, H., Sønderby, C.K., Dyrby, T.B.: Diffusion weighted imaging with circularly polarized oscillating gradients. Magn. Reson. Med. 73(3), 1171–1176 (2015)

    CrossRef  Google Scholar 

  17. Mori, S., Van Zijl, P.C.: Diffusion weighting by the trace of the diffusion tensor within a single scan. Magn. Reson. Med. 33(1), 41–52 (1995)

    CrossRef  Google Scholar 

  18. Neeman, M., Freyer, J.P., Sillerud, L.O.: Pulsed-gradient spin-echo diffusion studies in NMR imaging. Effects of the imaging gradients on the determination of diffusion coefficients. J. Magn. Reson. 90(2), 303–312 (1969, 1990)

    Google Scholar 

  19. Özarslan, E., Memiç, M., Avram, A.V., Afzali, M., Basser, P.J., Westin, C.F.: Rotating field gradient (RFG) MR offers improved orientational sensitivity. In: 2015 IEEE 12th International Symposium on Biomedical Imaging (ISBI), pp. 955–958 (2015)

    Google Scholar 

  20. Rensonnet, G., Scherrer, B., Warfield, S.K., Macq, B., Taquet, M.: Assessing the validity of the approximation of diffusion-weighted-MRI signals from crossing fascicles by sums of signals from single fascicles. Magn. Reson. Med. 79(4), 2332–2345 (2018)

    CrossRef  Google Scholar 

  21. Stejskal, E.O., Tanner, J.E.: Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J. Chem. Phys. 42(1), 288–292 (1965)

    CrossRef  Google Scholar 

  22. Szczepankiewicz, F., Lasič, S., van Westen, D., Sundgren, P.C., Englund, E., Westin, C.F., Ståhlberg, F., Lätt, J., Topgaard, D., Nilsson, M.: Quantification of microscopic diffusion anisotropy disentangles effects of orientation dispersion from microstructure: applications in healthy volunteers and in brain tumors. Neuroimage 104, 241–252 (2015)

    CrossRef  Google Scholar 

  23. Tax, C.M., Jeurissen, B., Vos, S.B., Viergever, M.A., Leemans, A.: Recursive calibration of the fiber response function for spherical deconvolution of diffusion MRI data. Neuroimage 86, 67–80 (2014)

    CrossRef  Google Scholar 

  24. Topgaard, D.: Diffusion tensor distribution imaging. NMR Biomed. 32(5), e4066 (2019)

    CrossRef  Google Scholar 

  25. Tournier, J.D., Calamante, F., Connelly, A.: Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution. Neuroimage 35(4), 1459–1472 (2007)

    CrossRef  Google Scholar 

  26. Wedeen, V.J., Rosene, D.L., Wang, R., Dai, G., Mortazavi, F., Hagmann, P., Kaas, J.H., Tseng, W.Y.I.: The geometric structure of the brain fiber pathways. Science 335(6076), 1628–1634 (2012)

    CrossRef  Google Scholar 

  27. Westin, C.F., Szczepankiewicz, F., Pasternak, O., Özarslan, E., Topgaard, D., Knutsson, H., Nilsson, M.: Measurement tensors in diffusion MRI: generalizing the concept of diffusion encoding. In: International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 209–216. Springer (2014)

    Google Scholar 

  28. Westin, C.F., Knutsson, H., Pasternak, O., Szczepankiewicz, F., Özarslan, E., van Westen, D., Mattisson, C., Bogren, M., O’Donnell, L.J., Kubicki, M., et al.: Q-space trajectory imaging for multidimensional diffusion MRI of the human brain. Neuroimage 135, 345–362 (2016)

    CrossRef  Google Scholar 

Download references

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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