Advertisement

Comprehensive Maximum Likelihood Estimation of Diffusion Compartment Models Towards Reliable Mapping of Brain Microstructure

  • Aymeric Stamm
  • Olivier Commowick
  • Simon K. Warfield
  • S. Vantini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9902)

Abstract

Diffusion MRI is a key in-vivo non invasive imaging capability that can probe the microstructure of the brain. However, its limited resolution requires complex voxelwise generative models of the diffusion. Diffusion Compartment (DC) models divide the voxel into smaller compartments in which diffusion is homogeneous. We present a comprehensive framework for maximum likelihood estimation (MLE) of such models that jointly features ML estimators of (i) the baseline MR signal, (ii) the noise variance, (iii) compartment proportions, and (iv) diffusion-related parameters. ML estimators are key to providing reliable mapping of brain microstructure as they are asymptotically unbiased and of minimal variance. We compare our algorithm (which efficiently exploits analytical properties of MLE) to alternative implementations and a state-of-the-art strategy. Simulation results show that our approach offers the best reduction in computational burden while guaranteeing convergence of numerical estimators to the MLE. In-vivo results also reveal remarkably reliable microstructure mapping in areas as complex as the centrum semi-ovale. Our ML framework accommodates any DC model and is available freely for multi-tensor models as part of the ANIMA software (https://github.com/Inria-Visages/Anima-Public/wiki).

Keywords

Maximum Likelihood Estimation Microstructure Mapping Human Connectome Project Brain Microstructure Constrain Maximization Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Farooq, H., et al.: Brain microstructure mapping from diffusion MRI using least squares variable separation. In: CDMRI (MICCAI Workshop), pp. 1–9 (2015)Google Scholar
  2. 2.
    Johnson, S.: The NLOpt package. http://ab-initio.mit.edu/nlopt
  3. 3.
    Marquardt, D.: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Panagiotaki, et al.: Compartment models of the diffusion MR signal in brain white matter: a taxonomy and comparison. Neuroimage 59(3), 2241–2254 (2012)CrossRefGoogle Scholar
  5. 5.
    Powell, M.: The BOBYQA algorithm for bound constrained optimization without derivatives. Technical report, University of Cambridge (2009)Google Scholar
  6. 6.
    Scherrer, B., Warfield, S.: Parametric representation of multiple white matter fascicles from cube and sphere diffusion MRI. PLoS One 7(11), e48232 (2012)CrossRefGoogle Scholar
  7. 7.
    Scherrer, B., et al.: Characterizing brain tissue by assessment of the distribution of anisotropic microstructural environments in DCI (DIAMOND). MRM 76(3), 963–977 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Stamm, et al.: Fast identification of optimal fascicle configurations from standard clinical diffusion MRI using Akaike information criterion. In: ISBI, pp. 238–41 (2014)Google Scholar
  9. 9.
    Stamm, A., Pérez, P., Barillot, C.: A new multi-fiber model for low angular resolution diffusion MRI. In: ISBI, pp. 936–939 (2012)Google Scholar
  10. 10.
    Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J.Optim. 12(2), 555–573 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Essen, V., et al.: The WU-minn human connectome project: an overview. Neuroimage 80, 62–79 (2013)CrossRefGoogle Scholar
  12. 12.
    Zhang, et al.: NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain. Neuroimage 61(4), 1000–1016 (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Aymeric Stamm
    • 1
    • 2
  • Olivier Commowick
    • 3
  • Simon K. Warfield
    • 2
  • S. Vantini
    • 1
  1. 1.MOX, Department of MathematicsPolitecnico di MilanoMilanItaly
  2. 2.CRL, Harvard Medical SchoolBoston Children’s HospitalBostonUSA
  3. 3.VISAGES, INSERM U746, CNRS UMR6074, INRIA, University of Rennes IRennesFrance

Personalised recommendations