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Sjölund, J., Eklund, A., Özarslan, E., Herberthson, M., Bånkestad, M. & Knutsson, H. (2018). Bayesian uncertainty quantification in linear models for diffusion MRI. NeuroImage, 175, 272-285
Open this publication in new window or tab >>Bayesian uncertainty quantification in linear models for diffusion MRI
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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.

Keyword
Diffusion MRI, Uncertainty quantification, Signal estimation
National Category
Medical Engineering
Identifiers
urn:nbn:se:liu:diva-147245 (URN)
Available from: 2018-04-12 Created: 2018-04-12 Last updated: 2018-04-12
Özarslan, E., Yolcu, C., Herberthson, M., Knutsson, H. & Westin, C.-F. (2018). Influence of the Size and Curvedness of Neural Projections on the Orientationally Averaged Diffusion MR Signal. Frontiers in Physics, 6, 1-10, Article ID 17.
Open this publication in new window or tab >>Influence of the Size and Curvedness of Neural Projections on the Orientationally Averaged Diffusion MR Signal
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2018 (English)In: Frontiers in Physics, E-ISSN 2296-424X, Vol. 6, p. 1-10, article id 17Article in journal (Refereed) Published
Abstract [en]

Neuronal and glial projections can be envisioned to be tubes of infinitesimal diameter as far as diffusion magnetic resonance (MR) measurements via clinical scanners are concerned. Recent experimental studies indicate that the decay of the orientationally-averaged signal in white-matter may be characterized by the power-law, Ē(q) ∝ q−1, where q is the wavenumber determined by the parameters of the pulsed field gradient measurements. One particular study by McKinnon et al. [1] reports a distinctively faster decay in gray-matter. Here, we assess the role of the size and curvature of the neurites and glial arborizations in these experimental findings. To this end, we studied the signal decay for diffusion along general curves at all three temporal regimes of the traditional pulsed field gradient measurements. We show that for curvy projections, employment of longer pulse durations leads to a disappearance of the q−1 decay, while such decay is robust when narrow gradient pulses are used. Thus, in clinical acquisitions, the lack of such a decay for a fibrous specimen can be seen as indicative of fibers that are curved. We note that the above discussion is valid for an intermediate range of q-values as the true asymptotic behavior of the signal decay is Ē(q) ∝ q−4 for narrow pulses (through Debye-Porod law) or steeper for longer pulses. This study is expected to provide insights for interpreting the diffusion-weighted images of the central nervous system and aid in the design of acquisition strategies.

Place, publisher, year, edition, pages
Frontiers Media S.A., 2018
National Category
Biomedical Laboratory Science/Technology Radiology, Nuclear Medicine and Medical Imaging Atom and Molecular Physics and Optics Medical Laboratory and Measurements Technologies
Identifiers
urn:nbn:se:liu:diva-145426 (URN)10.3389/fphy.2018.00017 (DOI)
Available from: 2018-03-02 Created: 2018-03-02 Last updated: 2018-03-27Bibliographically approved
Gu, X., Sidén, P., Wegmann, B., Eklund, A., Villani, M. & Knutsson, H. (2017). Bayesian Diffusion Tensor Estimation with Spatial Priors. In: CAIP 2017: Computer Analysis of Images and Patterns. Paper presented at International Conference on Computer Analysis of Images and Patterns.
Open this publication in new window or tab >>Bayesian Diffusion Tensor Estimation with Spatial Priors
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2017 (English)In: CAIP 2017: Computer Analysis of Images and Patterns, 2017Conference paper, Published paper (Refereed)
Abstract [en]

Spatial regularization is a technique that exploits the dependence between nearby regions to locally pool data, with the effect of reducing noise and implicitly smoothing the data. Most of the currently proposed methods are focused on minimizing a cost function, during which the regularization parameter must be tuned in order to find the optimal solution. We propose a fast Markov chain Monte Carlo (MCMC) method for diffusion tensor estimation, for both 2D and 3D priors data. The regularization parameter is jointly with the tensor using MCMC. We compare FA (fractional anisotropy) maps for various b-values using three diffusion tensor estimation methods: least-squares and MCMC with and without spatial priors. Coefficient of variation (CV) is calculated to measure the uncertainty of the FA maps calculated from the MCMC samples, and our results show that the MCMC algorithm with spatial priors provides a denoising effect and reduces the uncertainty of the MCMC samples.

Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 10424
Keyword
Spatial regularization, Diffusion tensor, Spatial priors Markov chain, Monte Carlo Fractional anisotropy
National Category
Medical Engineering
Identifiers
urn:nbn:se:liu:diva-139844 (URN)10.1007/978-3-319-64689-3_30 (DOI)978-3-319-64689-3 (ISBN)978-3-319-64688-6 (ISBN)
Conference
International Conference on Computer Analysis of Images and Patterns
Available from: 2017-08-17 Created: 2017-08-17 Last updated: 2017-10-12
Özarslan, E., Yolcu, C., Herberthson, M., Westin, C.-F. & Knutsson, H. (2017). Effective Potential for Magnetic Resonance Measurements of Restricted Diffusion. Frontiers in Physics, 5, Article ID 68.
Open this publication in new window or tab >>Effective Potential for Magnetic Resonance Measurements of Restricted Diffusion
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2017 (English)In: Frontiers in Physics, E-ISSN 2296-424X, Vol. 5, article id 68Article in journal (Refereed) Published
Abstract [en]

The signature of diffusive motion on the NMR signal has been exploited to characterize the mesoscopic structure of specimens in numerous applications. For compartmentalized specimens comprising isolated subdomains, a representation of individual pores is necessary for describing restricted diffusion within them. When gradient waveforms with long pulse durations are employed, a quadratic potential profile is identified as an effective energy landscape for restricted diffusion. The dependence of the stochastic effective force on the center-of-mass position is indeed found to be approximately linear (Hookean) for restricted diffusion even when the walls are sticky. We outline the theoretical basis and practical advantages of our picture involving effective potentials.

Place, publisher, year, edition, pages
Frontiers Media S.A., 2017
National Category
Medical Image Processing
Identifiers
urn:nbn:se:liu:diva-143866 (URN)10.3389/fphy.2017.00068 (DOI)
Available from: 2017-12-22 Created: 2017-12-22 Last updated: 2018-03-27Bibliographically approved
Shakya, S., Batool, N., Özarslan, E. & Knutsson, H. (2017). Multi-Fiber Reconstruction Using Probabilistic Mixture Models for Diffusion MRI Examinations of the Brain. In: Thomas Schultz, Evren Özarslan, Ingrid Hotz (Ed.), Modeling, Analysis, and Visualization of Anisotropy: (pp. 283-308). Springer
Open this publication in new window or tab >>Multi-Fiber Reconstruction Using Probabilistic Mixture Models for Diffusion MRI Examinations of the Brain
2017 (English)In: Modeling, Analysis, and Visualization of Anisotropy / [ed] Thomas Schultz, Evren Özarslan, Ingrid Hotz, Springer, 2017, p. 283-308Chapter in book (Other academic)
Abstract [en]

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 ofDTI 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.

Place, publisher, year, edition, pages
Springer, 2017
Series
Mathematics and Visualization (MATHVISUAL), ISSN 1612-3786
Keyword
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
National Category
Medical Engineering
Identifiers
urn:nbn:se:liu:diva-142048 (URN)10.1007/978-3-319-61358-1_12 (DOI)978-3-319-61357-4 (ISBN)978-3-319-61358-1 (ISBN)
Available from: 2017-10-19 Created: 2017-10-19 Last updated: 2017-10-19
Eklund, A., Nichols, T. & Knutsson, H. (2016). Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates. Proceedings of the National Academy of Sciences of the United States of America, 113(28), 7900-7905
Open this publication in new window or tab >>Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates
2016 (English)In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 113, no 28, p. 7900-7905Article in journal (Refereed) Published
Abstract [en]

The most widely used task functional magnetic resonance imaging (fMRI) analyses use parametric statistical methods that depend on a variety of assumptions. In this work, we use real resting-state data and a total of 3 million random task group analyses to compute empirical familywise error rates for the fMRI software packages SPM, FSL, and AFNI, as well as a nonparametric permutation method. For a nominal familywise error rate of 5%, the parametric statistical methods are shown to be conservative for voxelwise inference and invalid for clusterwise inference. Our results suggest that the principal cause of the invalid cluster inferences is spatial autocorrelation functions that do not follow the assumed Gaussian shape. By comparison, the nonparametric permutation test is found to produce nominal results for voxelwise as well as clusterwise inference. These findings speak to the need of validating the statistical methods being used in the field of neuroimaging.

Place, publisher, year, edition, pages
National Academy of Sciences, 2016
Keyword
fMRI, statistics, false positives, familywise error rate, permutation test, cluster inference
National Category
Medical Image Processing Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-129884 (URN)10.1073/pnas.1602413113 (DOI)000379694100060 ()27357684 (PubMedID)
Funder
Swedish Research Council, 2013-5229Wellcome trust
Note

Funding agencies:We thank Robert Cox, Stephen Smith, Mark Woolrich, Karl Friston, and Guillaume Flandin, who gave us valuable feedback on this work. This study would not be possible without the recent data-sharing initiatives in the neuroimaging field. We therefore thank the Neuroimaging Informatics Tools and Resources Clearinghouse and all of the researchers who have contributed with resting-state data to the 1,000 Functional Connectomes Project. Data were also provided by the Human Connectome Project, WU-Minn Consortium (principal investigators: David Van Essen and Kamil Ugurbil; Grant 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. We also thank Russ Poldrack and his colleagues for starting the OpenfMRI Project (supported by National Science Foundation Grant OCI-1131441) and all of the researchers who have shared their task-based data. The Nvidia Corporation, which donated the Tesla K40 graphics card used to run all the permutation tests, is also acknowledged. This research was supported by the Neuroeconomic Research Initiative at Linkoping University, by Swedish Research Council Grant 2013-5229 ("Statistical Analysis of fMRI Data"), the Information Technology for European Advancement 3 Project BENEFIT (better effectiveness and efficiency by measuring and modelling of interventional therapy), and the Wellcome Trust.

Available from: 2016-06-30 Created: 2016-06-30 Last updated: 2017-11-28
Cros, O., Knutsson, H., Andersson, M., Pawels, E., Borga, M. & Gaihede, M. (2016). Determination of the mastoid surface area and volume based on micro-CT scanning of human temporal bone: Geometrical parameters dependence on scanning resolutions. Hearing Research, 340, 127-134
Open this publication in new window or tab >>Determination of the mastoid surface area and volume based on micro-CT scanning of human temporal bone: Geometrical parameters dependence on scanning resolutions
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2016 (English)In: Hearing Research, ISSN 0378-5955, E-ISSN 1878-5891, Vol. 340, p. 127-134Article in journal (Other academic) Published
Abstract [en]

The mastoid air cell system (MACS) with its large complex of interconnected air cells reflects an enhanced surface area (SA) relative to its volume (V), which may indicate that the MACS is adapted to gas exchange and has a potential role in middle ear pressure regulation. Thus, these geometric parameters of the MACS have been studied by high resolution clinical CT scanning. However, the resolution of these scans is limited to a voxel size of around 0.6 mm in all dimensions, and so, the geometrical parameters are also limited. Small air cells may appear below the resolution and cannot be detected. Such air cells may contribute to a much higher SA than the V, and thus, also the SA/V ratio. More accurate parameters are important for analysis of the function of the MACS including physiological modeling.

Our aim was to determine the SA, V, and SA/V ratio in MACS in human temporal bones at highest resolution by using micro-CT-scanning. Further, the influence of the resolution on these parameters was investigated by downsampling the data. Eight normally aerated temporal bones were scanned at the highest possible resolution (30-60 μm). The SA was determined using a triangular mesh fitted onto the segmented MACS. The V was determined by summing all the voxels containing air. Downsampling of the original data was applied four times by a factor of 2.

The mean SA was 194 cm2, the mean V was 9 cm3, and the mean SA/V amounted to 22 cm-1. Decreasing the resolution resulted in a non-linear decrement of SA and SA/V, whereas V was mainly independent of the resolution.

The current study found significantly higher SA and SA/V compared with previous studies using clinical CT scanning at lower resolutions. These findings indicate a separate role of the MACS compared with the tympanum, and the results are important for a more accurate modeling of the middle ear physiology.

Keyword
Mastoid air cells; medical imaging; micro-CT; surface area; volume
National Category
Radiology, Nuclear Medicine and Medical Imaging
Identifiers
urn:nbn:se:liu:diva-122176 (URN)10.1016/j.heares.2015.12.005 (DOI)000386417900016 ()
Available from: 2015-10-23 Created: 2015-10-23 Last updated: 2017-12-01Bibliographically approved
Westin, C.-F., Knutsson, H., Pasternak, O., Szczepankiewicz, F., Özarslan, E., van Westen, D., . . . Nilsson, M. (2016). Q-space trajectory imaging for multidimensional diffusion MRI of the human brain. NeuroImage, 135, 345-362
Open this publication in new window or tab >>Q-space trajectory imaging for multidimensional diffusion MRI of the human brain
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2016 (English)In: NeuroImage, ISSN 1053-8119, E-ISSN 1095-9572, Vol. 135, p. 345-362Article in journal (Refereed) Published
Abstract [en]

This work describes a new diffusion MR framework for imaging and modeling of microstructure that we call q-space trajectory imaging (QTI). The QTI framework consists of two parts: encoding and modeling. First we propose q-space trajectory encoding, which uses time-varying gradients to probe a trajectory in q-space, in contrast to traditional pulsed field gradient sequences that attempt to probe a point in q-space. Then we propose a microstructure model, the diffusion tensor distribution (DTD) model, which takes advantage of additional information provided by QTI to estimate a distributional model over diffusion tensors. We show that the QTI framework enables microstructure modeling that is not possible with the traditional pulsed gradient encoding as introduced by Stejskal and Tanner. In our analysis of QTI, we find that the well-known scalar b-value naturally extends to a tensor-valued entity, i.e., a diffusion measurement tensor, which we call the b-tensor. We show that b-tensors of rank 2 or 3 enable estimation of the mean and covariance of the DTD model in terms of a second order tensor (the diffusion tensor) and a fourth order tensor. The QTI framework has been designed to improve discrimination of the sizes, shapes, and orientations of diffusion microenvironments within tissue. We derive rotationally invariant scalar quantities describing intuitive microstructural features including size, shape, and orientation coherence measures. To demonstrate the feasibility of QTI on a clinical scanner, we performed a small pilot study comparing a group of five healthy controls with five patients with schizophrenia. The parameter maps derived from QTI were compared between the groups, and 9 out of the 14 parameters investigated showed differences between groups. The ability to measure and model the distribution of diffusion tensors, rather than a quantity that has already been averaged within a voxel, has the potential to provide a powerful paradigm for the study of complex tissue architecture.

Place, publisher, year, edition, pages
Elsevier, 2016
Keyword
DDE, DTI, Diffusion MRI, Diffusion tensor distribution, Microscopic anisotropy, Microscopic fractional anisotropy μFA, QTI, SDE, TDE, q-space, q-space trajectory
National Category
Medical Engineering
Identifiers
urn:nbn:se:liu:diva-129986 (URN)10.1016/j.neuroimage.2016.02.039 (DOI)000378047600031 ()26923372 (PubMedID)
Note

Funding agencies:The authors acknowledge the NIH grants R01MH074794, R01MH092862, R01MH102377, R01AG042512, P41EB015902, P41EB015898, U01CA199459, and the Swedish Research Council (VR) grants 2012-3682, 2011-5176, 2014-3910, TUBITAK-EU COFUND project no. 114C015, ITEA/Vinnova/13031 BENEFIT, and Swedish Foundation for Strategic Research (SSF) grant AM13-0090.

Available from: 2016-07-04 Created: 2016-07-04 Last updated: 2017-11-28Bibliographically approved
Knutsson, H., Herberthson, M. & Westin, C.-F. (2015). An Iterated Complex Matrix Approach for Simulation and Analysis of Diffusion MRI Processes. In: MEDICAL IMAGE COMPUTING AND COMPUTER-ASSISTED INTERVENTION - MICCAI 2015, PT I: . Paper presented at 18th International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI) (pp. 61-68). SPRINGER INT PUBLISHING AG, 9349
Open this publication in new window or tab >>An Iterated Complex Matrix Approach for Simulation and Analysis of Diffusion MRI Processes
2015 (English)In: MEDICAL IMAGE COMPUTING AND COMPUTER-ASSISTED INTERVENTION - MICCAI 2015, PT I, SPRINGER INT PUBLISHING AG , 2015, Vol. 9349, p. 61-68Conference paper, Published paper (Refereed)
Abstract [en]

We present a novel approach to investigate the properties of diffusion weighted magnetic resonance imaging (dMRI). The process of restricted diffusion of spin particles in the presence of a magnetic field is simulated by an iterated complex matrix multiplication approach. The approach is based on first principles and provides a flexible, transparent and fast simulation tool. The experiments carried out reveals fundamental features of the dMRI process. A particularly interesting observation is that the induced speed of the local spatial spin angle rate of change is highly shift variant. Hence, the encoding basis functions are not the complex exponentials associated with the Fourier transform as commonly assumed. Thus, reconstructing the signal using the inverse Fourier transform leads to large compartment estimation errors, which is demonstrated in a number of 1D and 2D examples. In accordance with previous investigations the compartment size is under-estimated. More interestingly, however, we show that the estimated shape is likely to be far from the true shape using state of the art clinical MRI scanners.

Place, publisher, year, edition, pages
SPRINGER INT PUBLISHING AG, 2015
Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 9349
National Category
Medical Biotechnology Mathematics
Identifiers
urn:nbn:se:liu:diva-124149 (URN)10.1007/978-3-319-24553-9_8 (DOI)000366205700008 ()978-3-319-24553-9 (ISBN)978-3-319-24552-2 (ISBN)
Conference
18th International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI)
Available from: 2016-01-22 Created: 2016-01-19 Last updated: 2018-01-25
Sjölund, J., Nilsson, M., Topgaard, D., Westin, C.-F. & Knutsson, H. (2015). Constrained optimization of gradient waveforms for generalized diffusion encoding. Journal of magnetic resonance, 261, 157-168
Open this publication in new window or tab >>Constrained optimization of gradient waveforms for generalized diffusion encoding
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2015 (English)In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 261, p. 157-168Article in journal (Refereed) Published
Abstract [en]

Diffusion MRI is a useful probe of tissue structure. The prototypical diffusion encoding sequence, the single pulsed field gradient, has recently been challenged with the introduction of more general gradient waveforms. Out of these, we focus on q-space trajecory imaging, which generalizes the scalar b-value to a tensor valued property. To take full advantage of its capabilities, it is imperative to respect the constraints imposed by the hardware, while at the same time maximizing the diffusion encoding strength. We formulate this as a constrained optimization problem that accomodates constraints on maximum gradient amplitude, slew rate, coil heating and positioning of radiofrequency pulses. The power of this approach is demonstrated by a comparison with previous work on optimization of isotropic diffusion sequences, showing possible gains in diffusion weighting or in heat dissipation, which in turn means increased signal or reduced scan-times.

Place, publisher, year, edition, pages
Elsevier, 2015
Keyword
Diffusion MR; Generalized gradient waveforms; Q-space trajectory imaging; Optimization; Hardware constraints
National Category
Medical Image Processing
Identifiers
urn:nbn:se:liu:diva-115795 (URN)10.1016/j.jmr.2015.10.012 (DOI)000367212100021 ()
Note

On the day of the defence date the status of this article was Manuscript.

Available from: 2015-03-20 Created: 2015-03-20 Last updated: 2018-01-16Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9091-4724

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