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Bayesian uncertaint...
Bayesian uncertainty quantification in linear models for diffusion MRI
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- Sjölund, Jens, 1987- (author)
- Linköpings universitet,Avdelningen för medicinsk teknik,Tekniska fakulteten,Centrum för medicinsk bildvetenskap och visualisering, CMIV,Elekta Instrument, Stockholm, Sweden
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- Eklund, Anders, 1981- (author)
- Linköpings universitet,Avdelningen för medicinsk teknik,Statistik och maskininlärning,Tekniska fakulteten,Centrum för medicinsk bildvetenskap och visualisering, CMIV
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- Özarslan, Evren, 1976- (author)
- Linköpings universitet,Avdelningen för medicinsk teknik,Tekniska fakulteten,Centrum för medicinsk bildvetenskap och visualisering, CMIV
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- Herberthson, Magnus, 1963- (author)
- Linköpings universitet,Matematik och tillämpad matematik,Tekniska fakulteten
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- Bånkestad, Maria (author)
- RISE,SICS,RISE SICS, Kista, Sweden
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- Knutsson, Hans, 1950- (author)
- Linköpings universitet,Avdelningen för medicinsk teknik,Tekniska fakulteten,Centrum för medicinsk bildvetenskap och visualisering, CMIV
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- Elsevier BV, 2018
- 2018
- English.
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In: NeuroImage. - : Elsevier BV. - 1053-8119 .- 1095-9572. ; 175, s. 272-285
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Abstract
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- 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.
Subject headings
- TEKNIK OCH TEKNOLOGIER -- Medicinteknik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Medical Engineering (hsv//eng)
Keyword
- 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
Publication and Content Type
- ref (subject category)
- art (subject category)
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NeuroImage
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Sjölund, Jens, 1 ...
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Eklund, Anders, ...
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Özarslan, Evren, ...
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Herberthson, Mag ...
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Bånkestad, Maria
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Knutsson, Hans, ...
- About the subject
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- ENGINEERING AND TECHNOLOGY
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ENGINEERING AND ...
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and Medical Engineer ...
- Articles in the publication
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NeuroImage
- By the university
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RISE
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Linköping University