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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
Academic Press, 2018. Vol. 175, p. 272-285
Keywords [en]
Diffusion MRI, Uncertainty quantification, Signal estimation
National Category
Medical Engineering
Identifiers
URN: urn:nbn:se:liu:diva-147245DOI: 10.1016/j.neuroimage.2018.03.059ISI: 000432949000023PubMedID: 29604453OAI: oai:DiVA.org:liu-147245DiVA, id: diva2:1197124
Note

Funding agencies: Swedish Foundation for Strategic Research [AM13-0090]; Swedish Research Council CADICS Linneaus research environment; Swedish Research Council [2012-4281, 2013-5229, 2015-05356, 2016-04482]; Linkoping University Center for Industrial Information Technolog

Available from: 2018-04-12 Created: 2018-04-12 Last updated: 2018-06-28
In thesis
1. Algorithms for magnetic resonance imaging in radiotherapy
Open this publication in new window or tab >>Algorithms for magnetic resonance imaging in radiotherapy
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Radiotherapy plays an increasingly important role in cancer treatment, and medical imaging plays an increasingly important role in radiotherapy. Magnetic resonance imaging (MRI) is poised to be a major component in the development towards more effective radiotherapy treatments with fewer side effects. This thesis attempts to contribute in realizing this potential.

Radiotherapy planning requires simulation of radiation transport. The necessary physical properties are typically derived from CT images, but in some cases only MR images are available. In such a case, a crude but common approach is to approximate all tissue properties as equivalent to those of water. In this thesis we propose two methods to improve upon this approximation. The first uses a machine learning approach to automatically identify bone tissue in MR. The second, which we refer to as atlas-based regression, can be used to generate a realistic, patient-specific, pseudo-CT directly from anatomical MR images. Atlas-based regression uses deformable registration to estimate a pseudo-CT of a new patient based on a database of aligned MR and CT pairs.

Cancerous tissue has a different structure from normal tissue. This affects molecular diffusion, which can be measured using MRI. The prototypical diffusion encoding sequence has recently been challenged with the introduction of more general gradient waveforms. One such example is diffusional variance decomposition (DIVIDE), which allows non-invasive mapping of parameters that reflect variable cell eccentricity and density in brain tumors. To take full advantage of such more general gradient waveforms it is, however, imperative to respect the constraints imposed by the hardware while at the same time maximizing the diffusion encoding strength. In this thesis we formulate this as a constrained optimization problem that is easily adaptable to various hardware constraints. We demonstrate that, by using the optimized gradient waveforms, it is technically feasible to perform whole-brain diffusional variance decomposition at clinical MRI systems with varying performance.

The last part of the thesis is devoted to estimation of diffusion MRI models from measurements. We show that, by using a machine learning framework called Gaussian processes, it is possible to perform diffusion spectrum imaging using far fewer measurements than ordinarily required. This has the potential of making diffusion spectrum imaging feasible even though the acquisition time is limited. A key property of Gaussian processes, which is a probabilistic model, is that it comes with a rigorous way of reasoning about uncertainty. This is pursued further in the last paper, in which we propose a Bayesian reinterpretation of several of the most popular models for diffusion MRI. Thanks to the Bayesian interpretation it possible to quantify the uncertainty in any property derived from these models. We expect this will be broadly useful, in particular in group analyses and in cases when the uncertainty is large.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 63
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1905
National Category
Medical Image Processing
Identifiers
urn:nbn:se:liu:diva-144351 (URN)10.3384/diss.diva-144351 (DOI)9789176853634 (ISBN)
Public defence
2018-03-23, Eken, hus 421, ingång 65, plan 9, Campus US, Linköping, 09:15 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 2012-4281
Available from: 2018-02-20 Created: 2018-01-16 Last updated: 2018-05-09Bibliographically approved

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The full text will be freely available from 2019-03-29 01:00
Available from 2019-03-29 01:00

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Sjölund, JensEklund, AndersÖzarslan, EvrenHerberthson, MagnusKnutsson, Hans

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