Multi-Fiber Reconstruction Using Probabilistic Mixture Models for Diffusion MRI Examinations of the Brain

  • Snehlata ShakyaEmail author
  • Nazre Batool
  • Evren Özarslan
  • Hans Knutsson
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


In the field of MRI brain image analysis, Diffusion tensor imaging ( DTI) provides a description of the diffusion of water through tissue and makes it possible to trace fiber connectivity in the brain, yielding a map of how the brain is wired. DTI employs a second order diffusion tensor model based on the assumption of Gaussian diffusion. The Gaussian assumption, however, limits the use of DTI in solving intra-voxel fiber heterogeneity as the diffusion can be non-Gaussian in several biological tissues including human brain. Several approaches to modeling the non-Gaussian diffusion and intra-voxel fiber heterogeneity reconstruction have been proposed in the last decades. Among such approaches are the multi-compartmental probabilistic mixture models. These models include the discrete or continuous mixtures of probability distributions such as Gaussian, Wishart or von Mises-Fisher distributions. Given the diffusion weighted MRI data, the problem of resolving multiple fibers within a single voxel boils down to estimating the parameters of such models.

In this chapter, we focus on such multi-compartmental probabilistic mixture models. First we present a review including mathematical formulations of the most commonly applied mixture models. Then, we present a novel method based on the mixture of non-central Wishart distributions. A mixture model of central Wishart distributions has already been proposed earlier to resolve intra-voxel heterogeneity. However, we show with detailed experiments that our proposed model outperforms the previously proposed probabilistic models specifically for the challenging scenario when the separation angles between crossing fibers (two or three) are small. We compare our results with the recently proposed probabilistic models of mixture of central Wishart distributions and mixture of hyper-spherical von Mises-Fisher distributions. We validate our approach with several simulations including fiber orientations in two and three directions and with real data. Resistivity to noise is also demonstrated by increasing levels of Rician noise in simulated data. The experiments demonstrate the superior performance of our proposed model over the prior probabilistic mixture models.


Crossing fibers Diffusion MRI DTI review Intra-voxel fiber orientation Mixture models Mixture of hyper-spherical von Mises-Fisher distributions Mixture of Wishart distributions Wishart non-centrality parameter Rician noise 



This research is a part of the project “Seeing Organ Function” funded by “The Knut and Alice Wallenberg Foundation”. EÖ acknowledges support by Linköping University Center for Industrial Information Technology (CENIIT). We would also like to thank Russell Poldrack and his colleagues for sharing diffusion MRI data from the project MyConnectome. The HCP Data were provided (in part) by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH institutes and centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University. The MGH data were provided (in part) by the Human Connectome Project, MGH-USC Consortium (Principal Investigators: Bruce R. Rosen, Arthur W. Toga and Van Wedeen; U01MH093765), funded by the NIH Blueprint Initiative for Neuroscience Research grant; the National Institutes of Health grant P41EB015896; and the Instrumentation Grants S10RR023043, 1S10RR023401, 1S10RR019307.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Snehlata Shakya
    • 1
    Email author
  • Nazre Batool
    • 2
  • Evren Özarslan
    • 1
  • Hans Knutsson
    • 1
  1. 1.Department of Biomedical EngineeringLinköping UniversityLinköpingSweden
  2. 2.School of Technology and HealthKTH Royal Institute of TechnologyStockholmSweden

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