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Bayesian uncertainty quantification in linear models for diffusion MRI
Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV). Elekta Instrument, Stockholm, Sweden.
Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
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2018 (English)In: NeuroImage, ISSN 1053-8119, E-ISSN 1095-9572, Vol. 175, p. 272-285Article in journal (Refereed) Published
Abstract [en]

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification.

Place, publisher, year, edition, pages
2018. Vol. 175, p. 272-285
Keyword [en]
Diffusion MRI, Uncertainty quantification, Signal estimation
National Category
Medical Engineering
Identifiers
URN: urn:nbn:se:liu:diva-147245OAI: oai:DiVA.org:liu-147245DiVA, id: diva2:1197124
Available from: 2018-04-12 Created: 2018-04-12 Last updated: 2018-04-12

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https://doi.org/10.1016/j.neuroimage.2018.03.059

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Sjölund, JensEklund, AndersÖzarslan, EvrenHerberthson, MagnusKnutsson, Hans

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Sjölund, JensEklund, AndersÖzarslan, EvrenHerberthson, MagnusKnutsson, Hans
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Division of Biomedical EngineeringFaculty of Science & EngineeringCenter for Medical Image Science and Visualization (CMIV)The Division of Statistics and Machine LearningMathematics and Applied Mathematics
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