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Herberthson, Magnus
Publications (10 of 30) Show all publications
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.

Place, publisher, year, edition, pages
Academic Press, 2018
Keywords
Diffusion MRI, Uncertainty quantification, Signal estimation
National Category
Medical Engineering
Identifiers
urn:nbn:se:liu:diva-147245 (URN)10.1016/j.neuroimage.2018.03.059 (DOI)000432949000023 ()29604453 (PubMedID)
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
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
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
Herberthson, M., Johansson, K., Kozlov, V., Ljungkvist, E. & Singull, M. (Eds.). (2017). Proceedings from Workshop: Mathematics in Biology and Medicine, 11-12 May 2017, Linköping University. Paper presented at Workshop: Mathematics in Biology and Medicine, 11-12 May 2017, Linköping University, Sweden. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Proceedings from Workshop: Mathematics in Biology and Medicine, 11-12 May 2017, Linköping University
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2017 (English)Conference proceedings (editor) (Refereed)
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. p. 27
National Category
Mathematics Other Biological Topics Other Medical Sciences
Identifiers
urn:nbn:se:liu:diva-151460 (URN)
Conference
Workshop: Mathematics in Biology and Medicine, 11-12 May 2017, Linköping University, Sweden
Note

Book of Abstracts.

Available from: 2018-09-21 Created: 2018-09-21 Last updated: 2018-09-25Bibliographically 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
Sume, A., Gustafsson, M., Herberthson, M., Jänis, A., Nilsson, S., Rahm, J. & Örbom, A. (2011). Radar Detection of Moving Targets Behind Corners. IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, 49(6), 2259-2267
Open this publication in new window or tab >>Radar Detection of Moving Targets Behind Corners
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2011 (English)In: IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, ISSN 0196-2892, Vol. 49, no 6, p. 2259-2267Article in journal (Refereed) Published
Abstract [en]

Detection of moving objects concealed behind a concrete wall corner has been demonstrated, using Doppler-based techniques with a stepped-frequency radar centered at 10 GHz, in a reduced-scale model of a street scenario. Micro-Doppler signatures have been traced in the return from a human target, both for walking and for breathing. Separate material measurements of the reflection and transmission of the concrete in the wall have showed that wall reflections are the dominating wave propagation mechanism for producing target detections, while wave components transmitted through the walls could be neglected. Weaker detections have been made of target returns via diffraction in the wall corner. A simple and fast algorithm for the detection and generation of detection tracks in down range has been developed, based on moving target indication technique.

Place, publisher, year, edition, pages
IEEE; 1999, 2011
Keywords
Around corner, micro-Doppler, object detection, radar measurements, wall material
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-68912 (URN)10.1109/TGRS.2010.2096471 (DOI)000290997800006 ()
Note
©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Ain Sume, Magnus Gustafsson, Magnus Herberthson, Anna Jänis, Stefan Nilsson, Jonas Rahm and Anders Örbom, Radar Detection of Moving Targets Behind Corners, 2011, IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, (49), 6, 2259-2267. http://dx.doi.org/10.1109/TGRS.2010.2096471 Postprint available at: Linköping University Electronic Press http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-68912 Available from: 2011-06-10 Created: 2011-06-10 Last updated: 2011-08-25
Herberthson, M. (2010). EM Scattering Calculations using Potentials. In: Janne Roos and Luis R.J. Costa (Ed.), Scientific Computing in Electrical Engineering, SCEE 2008. Paper presented at 7th International Conference on Scientific Computing in Electrical Engineering Espoo, Finland, September 28 - October 03, 2008 (pp. 171-172). Springer Berlin/Heidelberg
Open this publication in new window or tab >>EM Scattering Calculations using Potentials
2010 (English)In: Scientific Computing in Electrical Engineering, SCEE 2008 / [ed] Janne Roos and Luis R.J. Costa, Springer Berlin/Heidelberg, 2010, p. 171-172Conference paper, Published paper (Other academic)
Abstract [en]

EM scattering from PEC surfaces are mostly calculated through the induced surface current J. In this paper, we consider PEC surfaces homeomorphic to the sphere, apply Hodge decomposition theorem to a slightly rewritten surface current, and show how this enables us to replace the unknown current with two scalar functions which serve as potentials for the current. Implications of this decomposition are pointed out, and numerical results are demonstrated.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2010
Series
Mathematics in Industry ; 14
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-43880 (URN)10.1007/978-3-642-12294-1_47 (DOI)000290366900047 ()75022 (Local ID)978-3-642-12293-4 (ISBN)75022 (Archive number)75022 (OAI)
Conference
7th International Conference on Scientific Computing in Electrical Engineering Espoo, Finland, September 28 - October 03, 2008
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2012-08-16Bibliographically approved
Herberthson, M. (2010). Static vacuum spacetimes with prescribed multipole moments. Journal of Physics, Conference Series, 229
Open this publication in new window or tab >>Static vacuum spacetimes with prescribed multipole moments
2010 (English)In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, ISSN 1742-6588, Vol. 229Article in journal (Refereed) Published
Abstract [en]

This paper gives sufficient conditions on a sequence of multipole moments for a static spacetime to exist with precisely these moments. We outline the proof, which is constructive in the sense that a metric having prescribed multipole moments up to a given order can be calculated. These sufficient conditions agree with already known necessary conditions, and hence this completes the proof of a long standing conjecture due to Geroch

Place, publisher, year, edition, pages
IOP Publishing, 2010
Keywords
multipole moments
National Category
Other Physics Topics
Identifiers
urn:nbn:se:liu:diva-66093 (URN)10.1088/1742-6596/229/1/012009 (DOI)
Available from: 2011-03-03 Created: 2011-03-03 Last updated: 2017-12-11
Brun, A., Martin-Fernandez, M., Acar, B., Munoz-Moreno, E., Cammoun, L., Sigfridsson, A., . . . Knutsson, H. (2009). Similar Tensor Arrays - A Framework for Storage of Tensor Array Data (1ed.). In: Santiago Aja-Fern´andez, Rodrigo de Luis Garc´ıa, Dacheng Tao, Xuelong Li (Ed.), Santiago Aja-Fern´andez, Rodrigo de Luis Garc´ıa, Dacheng Tao, Xuelong Li (Ed.), Tensors in Image Processing and Computer Vision: . Paper presented at Tensor in Image Processing and Computer Vision (pp. 407-428). Paper presented at Tensor in Image Processing and Computer Vision. Springer Science+Business Media B.V.
Open this publication in new window or tab >>Similar Tensor Arrays - A Framework for Storage of Tensor Array Data
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2009 (English)In: Tensors in Image Processing and Computer Vision / [ed] Santiago Aja-Fern´andez, Rodrigo de Luis Garc´ıa, Dacheng Tao, Xuelong Li, Springer Science+Business Media B.V., 2009, 1, p. 407-428Chapter in book (Refereed)
Abstract [en]

This chapter describes a framework for storage of tensor array data, useful to describe regularly sampled tensor fields. The main component of the framework, called Similar Tensor Array Core (STAC), is the result of a collaboration between research groups within the SIMILAR network of excellence. It aims to capture the essence of regularly sampled tensor fields using a minimal set of attributes and can therefore be used as a “greatest common divisor” and interface between tensor array processing algorithms. This is potentially useful in applied fields like medical image analysis, in particular in Diffusion Tensor MRI, where misinterpretation of tensor array data is a common source of errors. By promoting a strictly geometric perspective on tensor arrays, with a close resemblance to the terminology used in differential geometry, (STAC) removes ambiguities and guides the user to define all necessary information. In contrast to existing tensor array file formats, it is minimalistic and based on an intrinsic and geometric interpretation of the array itself, without references to other coordinate systems.

Place, publisher, year, edition, pages
Springer Science+Business Media B.V., 2009 Edition: 1
Series
Advances in Pattern Recognition, ISSN 1617-7916
National Category
Computer Vision and Robotics (Autonomous Systems)
Identifiers
urn:nbn:se:liu:diva-58091 (URN)10.1007/978-1-84882-299-3_19 (DOI)978-1-84882-298-6 (ISBN)978-1-84882-299-3 (ISBN)
Conference
Tensor in Image Processing and Computer Vision
Available from: 2010-07-29 Created: 2010-07-29 Last updated: 2018-01-12Bibliographically approved
Herberthson, M. (2009). Static spacetimes with prescribed multipole moments: a proof of a conjecture by Geroch. Classical and quantum gravity, 26(21), 1-26
Open this publication in new window or tab >>Static spacetimes with prescribed multipole moments: a proof of a conjecture by Geroch
2009 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 26, no 21, p. 1-26Article in journal (Refereed) Published
Abstract [en]

In this paper we give sufficient conditions on a sequence of multipole moments for a static spacetime to exist with precisely these moments. The proof is constructive in the sense that a metric having prescribed multipole moments up to a given order can be calculated. Since these sufficient conditions agree with already known necessary conditions, this completes the proof of a long standing conjecture due to Geroch.

Place, publisher, year, edition, pages
Bristol, UK: IOP Publishing, 2009
Keywords
static spacetimes, multipole moments
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-52726 (URN)10.1088/0264-9381/26/21/215009 (DOI)
Available from: 2010-01-11 Created: 2010-01-11 Last updated: 2017-12-12
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