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Towards Optimal Sampling in Diffusion MRI

  • Hans KnutssonEmail author
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

The methodology outlined in this chapter is intended to provide a tool for the generation of sets of MRI diffusion encoding waveforms that are optimal for tissue micro-structure estimation. The methodology presented has five distinct components: 1. Defining the class of waveforms allowed, i.e. defining the measurement space. 2. Specifying the expected distribution of microstructure features present in the targeted tissue. 3. Learning the metric in the chosen measurement space. 4. Designing a continuous parametric functional suitable for approximation of the estimated metric. 5. Finding a distribution of a chosen number of waveforms that is optimal given the continuous metric. The tissue is modeled as a collection of simple elliptical compartments with varying size and shape. Two waveform classes are tested: The classical Stejskal-Tanner waveform and an idealized Laun long-short waveform. The estimation of the metric is based on correlations between measurements obtained at given points in the measurement space using an information theoretical approach. Optimal sets of waveforms are found using a simulated annealing inspired energy minimizing approach. The superior performance of the methodology is demonstrated for a number of different cases by means of simulations.

Keywords

Learning Sample space metric Optimal waveform sets 

Notes

Acknowledgements

The author acknowledges the following grants: The Swedish Research Council 2015-05356, the Swedish Foundation for Strategic Research AM13-0090, the Linneaus center ‘CADICS’ and the Wallenberg foundation ’Seeing Organ Function’.

References

  1. 1.
    Jones, D.K., Horsfield, M.A., Simmons, A.: Optimal strategies for measuring diffusion in anisotropic systems by magnetic resonance imaging. Magn. Reson. Med. 42, 515525 (1999)Google Scholar
  2. 2.
    Caruyer, E., Cheng, J., Lenglet, C., Sapiro, G., Jiang, T., Deriche, R.: Optimal Design of Multiple Q-shells experiments for Diffusion MRI. In: MICCAI Workshop CDMRI’11Google Scholar
  3. 3.
    Wu, Y.C., Alexander, A.L.: Hybrid diffusion imaging. Neuroimage 36(3), 617–629 (2007)CrossRefGoogle Scholar
  4. 4.
    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), 439–48 (2008)CrossRefGoogle Scholar
  5. 5.
    Ozarslan, E., Shemesh, N., Basser, P.J.: A general framework to quantify the effect of restricted diffusion on the NMR signal with applications to double pulsed field gradient NMR experiments. J. Chem. Phys. 130, 104702 (2009)CrossRefGoogle Scholar
  6. 6.
    Merlet, S., Caruyer, E., Deriche, R.: Impact of radial and angular sampling on multiple shells acquisition in diffusion MRI. Med. Image Comput. Comput. Assist Interv. 14(Pt 2), 116–23 (2011)Google Scholar
  7. 7.
    Ye, W., Portnoy, S., Entezari, A., Blackband, S.J., Vemuri, B.C.: An Efficient Interlaced Multi-shell Sampling Scheme for Reconstruction of Diffusion Propagators IEEE Trans. Med. Imaging 31(5), 1043–1050 (2012)CrossRefGoogle Scholar
  8. 8.
    Assaf, Y., Freidlin, R.Z., Rohde, G.K., Basser, P.J.: New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter. Magn. Reson. Med. 52(5), 965–978 (2004)CrossRefGoogle Scholar
  9. 9.
    Westin, C.F., Pasternak, O., Knutsson, H.: Rotationally invariant gradient schemes for diffusion MRI. In: Proceedings of the ISMRM Annual Meeting (ISMRM’12), vol. 3537 (2012)Google Scholar
  10. 10.
    Koaya, C.G., zarslan, E., Johnson, K.M., Meyerand, M.E.: Sparse and optimal acquisition design for diffusion MRI and beyond. Med. Phys. 39(5) (2012)CrossRefGoogle Scholar
  11. 11.
    Siow, B., Ianus, A., Drobnjak, I., Lythgoe, M.F., Alexander, D.C.: Optimised oscillating gradient diffusion MRI for the estimation of axon radius in an ex-vivo rat brain. In: Proceedings of International Society for Magnetic Resonance in Medicine (2012)Google Scholar
  12. 12.
    Knutsson, H., Westin, C.-F.: Charged containers for optimal 3D Q-space sampling. In: MICCAI (2013)Google Scholar
  13. 13.
    Knutsson, H., Westin, C.-F.: From expected propagator distribution to optimal Q-space sample metric. In: MICCAI (2014)Google Scholar
  14. 14.
    Avram, A.V., Ozarslan, E., Sarlls, J.E., Basser, P.J.: In vivo detection of microscopic anisotropy using quadruple pulsed-field gradient (qPFG) diffusion MRI on a clinical scanner. Neuroimage 1(64), 229–239 (2013)CrossRefGoogle Scholar
  15. 15.
    Nilsson, M., Lätt, J., van Westen, D., Brockstedt, S., Lasi, S., Ståhlberg, F., Topgaard, D.: Noninvasive mapping of water diffusional exchange in the human brain using filter-exchange imaging. Mag. Reson. Med. 69(6), 1573–1581 (2013)CrossRefGoogle Scholar
  16. 16.
    Topgaard, D.: Isotropic diffusion weighting in PGSE NMR: numerical optimization of the q-MAS PGSE sequence. Microporous Mesoporous Mater. 178, 60–63 (2013)CrossRefGoogle Scholar
  17. 17.
    Tobish, A., Varela, G., Stirnberg, R., Knutsson, H., Schultz, T., Irarrazaval, P., Stöcker, T.: Sparse isotropic q-space sampling distribution for Compressed Sensing in DSI. Magn. Reson. Med. (ISMRM) (2014)Google Scholar
  18. 18.
    Ozarslan, E., Avram, A., Basser, P.J., Westin, C.F.: Rotating field gradient (RFG) MR for direct measurement of the diffusion orientation distribution function (dODF). In: ISMRM 2014 (2014)Google Scholar
  19. 19.
    Westin, C.-F., Nilsson, M., Szczepankiewicz, F., Pasternak, O., Ozarslan, E., Topgaard, D., Knutsson, H.: In-vivo diffusion q-space trajectory imaging. In: ISMRM (2014)Google Scholar
  20. 20.
    Westin, C.-F., Knutsson, H., Pasternak, O., Szczepankiewicz, F., Ozarslan, E., van Westen, D., Mattisson, C., Bogren, M., O’Donnell, L.J., Kubicki, M., Topgaard, D., Nilsson, M.: Q-space trajectory imaging for multidimensional diffusion MRI of the human brain. NeuroImage 135, 345–362 (2016)CrossRefGoogle Scholar
  21. 21.
    Knutsson, H., Szczepankiewicz, F., Yolcu, C., Herberthson, H., Zarslan E, Nilsson, M., Westin, C.-F.: A quadrature filter approach to diffusion weighted imaging with application in pore size estimation. In: ISMRM (2018)Google Scholar
  22. 22.
    Callaghan. Translational Dynamics & Magnetic Resonance. Oxford University Press, Oxford (2011)Google Scholar
  23. 23.
    Laun, F.B., Kuder, T.A., Semmler, W., Stieltjes, B.: Determination of the defining boundary in nuclear magnetic resonance diffusion experiments. Phys. Rev. Lett. 107, 048102 (2011)CrossRefGoogle Scholar
  24. 24.
    Knutsson, H., Herberthson, M., Westin, C.F.: An iterated complex matrix approach for simulation and analysis of diffusion MRI processes. In: Navab, N., Hornegger, J., Wells, W., Frangi, A. (eds.) Medical Image Computing and Computer-Assisted Intervention–MICCAI 2015. Lecture Notes in Computer Science, vol. 9349. Springer (2015)Google Scholar
  25. 25.
    Rao, C.R.: Bull. Calcutta Math. Soc. 37 (1945)Google Scholar
  26. 26.
    Shannon, C.: Communication in the presence of noise. Proc. IRE 37(1), 1021 (1949)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Pires, C.A.L., Perdigo, R.A.P.: Minimum mutual information and non-gaussianity through the maximum entropy method: theory and properties. Entropy 14, 1103–1126 (2012)CrossRefGoogle Scholar
  28. 28.
    Knutsson, H.: Representing local structure using tensors, SCIA’89, pp. 244–251. Finland, Oulu (1989)Google Scholar
  29. 29.
    Scherrer, B., Warfield, S.K.: Parametric representation of multiple white matter fascicles from cube and sphere diffusion MRI. PLoS ONE 7(11), 1–20 (2012)Google Scholar
  30. 30.
    Hummer, G.: Electrostatic potential of a homogeneously charged square and cube in two and three dimensions. 36(3), 285–291 (1996)Google Scholar
  31. 31.
    Knutsson, H., Herbertsson, M., Westin, C.-F.: Analysis of local spatial magnetization frequency sheds new light on diffusion MRI. In: ISMRM (2015)Google Scholar
  32. 32.
    Assaf, Y., Pasternak, O.: Diffusion tensor imaging (DTI)-based white matter mapping in brain research: a review. J. Mol. Neurosci. 34, 5161 (2008)CrossRefGoogle Scholar
  33. 33.
    Rathi, Y., Gagoski, B., Setsompop, K., Michailovich, O., Grant, P.E., Westin, C.F.: Diffusion propagator estimation from sparse measurements in a tractography framework. In: Medical Image Computing and Computer-Assisted Intervention, MICCAI 2013, pp. 510–517. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  34. 34.
    Paquette, M., Merlet, S., Gilbert, G., Deriche, R., Descoteaux, M.: Comparison of sampling strategies and sparsifying transforms to improve compressed sensing diffusion spectrum imaging. Magn. Reson. Med. (2014)Google Scholar
  35. 35.
    Mitra, P., Halperin, B.: Effects of finite gradient-pulse widths in pulsed-field-gradient diffusion measurements. JMR, Series A 113(1), 94–101 (1995)Google Scholar
  36. 36.
    Stepisnik, J., Duh, A., Mohoric, A., Sersa, I.: MRI edge enhancement as a diffusive discord of spin phase structure. JMR (San Diego, Calif : 1997) 137(1), 154–160 (1999)CrossRefGoogle Scholar
  37. 37.
    Aslund, I., Topgaard, D.: Determination of the self-diffusion coefficient of intracellular water using PGSE NMR with variable gradient pulse length. JMR (San Diego, Calif : 1997) 201(2), 250–254 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Linköping UniversityLinköpingSweden

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