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Bayesian uncertainty quantification in linear models for diffusion MRI
Elekta Instrument AB, Sweden ; Linköping University, Sweden.
Linköping University, Sweden.
Linköping University, Sweden.
Linköping University, Sweden.
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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. © 2018 Elsevier Inc.

Place, publisher, year, edition, pages
2018. Vol. 175, p. 272-285
Keywords [en]
Diffusion MRI, Signal estimation, Uncertainty quantification, Article, Bayesian learning, bootstrapping, diffusion weighted imaging, fractional anisotropy, human, least square analysis, linear regression analysis, mathematical analysis, mathematical model, priority journal, signal processing, statistical model, uncertainty
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:ri:diva-34290DOI: 10.1016/j.neuroimage.2018.03.059Scopus ID: 2-s2.0-85045413205OAI: oai:DiVA.org:ri-34290DiVA, id: diva2:1236826
Note

 Funding details: 2013-5229;

Funding details: 2015-05356;

Funding details: 2012-4281;

Funding details: 2016-04482;

Funding details: R01MH074794, NIH, National Institutes of Health;

Funding details: P41EB015902, NIH, National Institutes of Health;

Funding details: P41EB015898, NIH, National Institutes of Health;

Funding details: USC, University of Southern California;

Funding details: AM13-0090, SSF, Stiftelsen för Strategisk Forskning;

Funding details: NIMH, National Institute of Mental Health;

Funding details: U01-MH93765, Knut och Alice Wallenbergs Stiftelse;

Funding details: NINDS, National Institute of Neurological Disorders and Stroke;

Funding details: 2014-00593; Funding details: NIDCR, NIDCR, National Institute of Dental and Craniofacial Research; Funding text: This study was supported by the Swedish Foundation for Strategic Research (grant AM13-0090 ), the Swedish Research Council CADICS Linneaus research environment, the Swedish Research Council (grants 2012-4281 , 2013-5229 , 2015-05356 and 2016-04482 ), Linköping University Center for Industrial Information Technology (CENIIT) , VINNOVA/ITEA3 BENEFIT (grant 2014-00593 ), and National Institutes of Health (grants P41EB015902 , R01MH074794 , P41EB015898 ), and the Knut and Alice Wallenberg Foundation project “Seeing Organ Function”.

Data collection and sharing for this project was provided by the Human Connectome Project ( U01-MH93765 ) (HCP; Principal Investigators: Bruce Rosen, M.D., Ph.D., Arthur W. Toga, Ph.D., Van J. Weeden, MD). HCP funding was provided by the National Institute of Dental and Craniofacial Research (NIDCR), the National Institute of Mental Health (NIMH), and the National Institute of Neurological Disorders and Stroke (NINDS). HCP data are disseminated by the Laboratory of Neuro Imaging at the University of Southern California.

Available from: 2018-08-06 Created: 2018-08-06 Last updated: 2018-08-06Bibliographically approved

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