Spatio-Temporal dMRI Acquisition Design: Reducing the Number of Samples Through a Relaxed Probabilistic Model

  • Patryk Filipiak
  • Rutger Fick
  • Alexandra Petiet
  • Mathieu Santin
  • Anne-Charlotte Philippe
  • Stephane Lehericy
  • Rachid Deriche
  • Demian Wassermann
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


Acquisition time is a major limitation in recovering brain white matter microstructure with diffusion Magnetic Resonance Imaging. Finding a sampling scheme that maximizes signal quality and satisfies given time constraints is NP-hard. We alleviate that by introducing a relaxed probabilistic model of the problem, for which sub-optimal solutions can be found effectively. Our model is defined in the space, so that it captures both spacial and temporal phenomena. The experiments on synthetic data and in-vivo diffusion images of the C57Bl6 wild-type mice reveal superiority of our technique over random sampling and even distribution in the space.



This work has received funding from the ANR/NSF award NeuroRef; the European Research Council (ERC) under the Horizon 2020 research and innovation program (ERC Advanced Grant agreement No 694665 : CoBCoM); the MAXIMS grant funded by ICM’s The Big Brain Theory Program and ANR-10-IAIHU-06.


  1. 1.
    Callaghan, P.T.: Pulsed-gradient spin-echo nmr for planar, cylindrical, and spherical pores under conditions of wall relaxation. J. Magn. Reson. Ser. A 113(1), 53–59 (1995)CrossRefGoogle Scholar
  2. 2.
    Tuch, D.S.: Q-ball imaging. MR Med. 52(6), 1358–1372 (2004)Google Scholar
  3. 3.
    Wedeen, V.J., Hagmann, P., Tseng, W.Y.I., Reese, T.G., Weisskoff, R.M.: Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magn. Reson. Med. 54(6), 1377–1386 (2005)CrossRefGoogle Scholar
  4. 4.
    Wu, Y.C., Field, A.S., Alexander, A.L.: Computation of diffusion function measures in q-space using magnetic resonance hybrid diffusion imaging. IEEE Trans. Med. Imag. 27(6) (2008) 858–865CrossRefGoogle Scholar
  5. 5.
    Khachaturian, M.H., Wisco, J.J., Tuch, D.S.: Boosting the sampling efficiency of q-ball imaging using multiple wavevector fusion. MR Med. 57(2), 289–296 (2007)Google Scholar
  6. 6.
    Koay, C.G., Özarslan, E., Johnson, K.M., Meyerand, M.E.: Sparse and optimal acquisition design for diffusion MRI and beyond. Med. Ph. 39(5), 2499–2511 (2012)CrossRefGoogle Scholar
  7. 7.
    Alexander, D.C.: A general framework for experiment design in diffusion MRI and its application in measuring direct tissue-microstructure features. Magn. Reson. Med. 60(2), 439–448 (2008)CrossRefGoogle Scholar
  8. 8.
    Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Lustig, M., Donoho, D., Pauly, J.M.: Sparse MRI: the application of compressed sensing for rapid MR imaging. MR Med. 58(6), 1182–1195 (2007)Google Scholar
  10. 10.
    Merlet, S., Deriche, R.: Compressed sensing for accelerated EAP recovery in diffusion MRI. In: MICCAI, pp. 1–14 (2010)Google Scholar
  11. 11.
    Saint-Amant, E., Descoteaux, M.: Sparsity characterisation of the diffusion propagator. In: Proceedings of the International Society for Magnetic Resonance in Medicine, 2011, vol. 19 (1915)Google Scholar
  12. 12.
    Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast, and robust analytical q-ball imaging. MR Med. 58(3), 497–510 (2007)Google Scholar
  13. 13.
    Assemlal, H.E., Tschumperlé, D., Brun, L.: Efficient and robust computation of PDF features from diffusion MR signal. Med. Image Anal. 13(5), 715–729 (2009)CrossRefGoogle Scholar
  14. 14.
    Özarslan, E., Koay, C.G., Shepherd, T.M., Komlosh, M.E., İrfanoğlu, M.O., Pierpaoli, C., Basser, P.J.: Mean apparent propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure. NeuroImage 78, 16–32 (2013)CrossRefGoogle Scholar
  15. 15.
    Fick, R., Petiet, A., Santin, M., Philippe, A.C., Lehericy, S., Deriche, R., Wassermann, D.: Multi-spherical diffusion MRI: exploring diffusion time using signal sparsity. In: MICCAI 2016 Workshop on Computational dMRI (CDMRI’16) (2016)Google Scholar
  16. 16.
    Fick, R., Wassermann, D., Pizzolato, M., Deriche, R.: A unifying framework for spatial and temporal diffusion in diffusion MRI. In: International Conference on Information Processing in Medical Imaging, pp. 167–178. Springer, New York (2015)Google Scholar
  17. 17.
    Hochbaum, D.S.: Approximation Algorithms for NP-Hard Problems. PWS, Boston (1996)zbMATHGoogle Scholar
  18. 18.
    Gilks, W.R., Richardson, S., Spiegelhalter, D.: Markov Chain Monte Carlo in Practice. CRC Press, Boca Raton (1995)zbMATHGoogle Scholar
  19. 19.
    Grosenick, L., Klingenberg, B., Katovich, K., Knutson, B., Taylor, J.E.: Interpretable whole-brain prediction analysis with GraphNet. NeuroImage 72, 304–321 (2013)CrossRefGoogle Scholar
  20. 20.
    Stejskal, E.: Use of spin echoes in a pulsed magnetic-field gradient to study anisotropic, restricted diffusion and flow. J. Chem. Phys. 43(10), 3597–3603 (1965)CrossRefGoogle Scholar
  21. 21.
    Caruyer, E., Lenglet, C., Sapiro, G., Deriche, R.: Design of multishell sampling schemes with uniform coverage in diffusion MRI. Magn. Reson. Med. 69(6), 1534–1540 (2013)CrossRefGoogle Scholar
  22. 22.
    Fick, R.H., Wassermann, D., Caruyer, E., Deriche, R.: MAPL: tissue microstructure estimation using Laplacian-regularized MAP-MRI and its application to HCP data. NeuroImage 134, 365–385 (2016)CrossRefGoogle Scholar
  23. 23.
    Kaden, E., Knösche, T., Anwander, A.: Parametric spherical deconvolution: inferring anatomical connectivity using diffusion MR imaging. Neuroimage 37, 474–488 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Patryk Filipiak
    • 1
  • Rutger Fick
    • 1
  • Alexandra Petiet
    • 2
  • Mathieu Santin
    • 2
  • Anne-Charlotte Philippe
    • 2
  • Stephane Lehericy
    • 2
  • Rachid Deriche
    • 1
  • Demian Wassermann
    • 1
  1. 1.Université Côte d’Azur - Inria Sophia Antipolis-MéditerranéeValbonneFrance
  2. 2.CENIR - Center for NeuroImaging ResearchICM - Brain and Spine InstituteParisFrance

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