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  • 1.
    Gu, Xuan
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Eklund, Anders
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Özarslan, Evren
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Using the wild bootstrap to quantify uncertainty in mean apparent propagator MRI2019Inngår i: Frontiers in Neuroinformatics, ISSN 1662-5196, E-ISSN 1662-5196, Vol. 13, artikkel-id 43Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Purpose: Estimation of uncertainty of MAP-MRI metricsis an important topic, for several reasons. Bootstrap deriveduncertainty, such as the standard deviation, providesvaluable information, and can be incorporated in MAP-MRIstudies to provide more extensive insight.

    Methods: In this paper, the uncertainty of different MAPMRImetrics was quantified by estimating the empirical distributionsusing the wild bootstrap. We applied the wildbootstrap to both phantom data and human brain data, andobtain empirical distributions for theMAP-MRImetrics returnto-origin probability (RTOP), non-Gaussianity (NG) and propagatoranisotropy (PA).

    Results: We demonstrated the impact of diffusion acquisitionscheme (number of shells and number of measurementsper shell) on the uncertainty of MAP-MRI metrics.We demonstrated how the uncertainty of these metrics canbe used to improve group analyses, and to compare differentpreprocessing pipelines. We demonstrated that withuncertainty considered, the results for a group analysis canbe different.

    Conclusion: Bootstrap derived uncertain measures provideadditional information to the MAP-MRI derived metrics, andshould be incorporated in ongoing and future MAP-MRIstudies to provide more extensive insight.

  • 2.
    Liu, Chunlei
    et al.
    Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, USA; Helen Wills Neuroscience Institute, University of California, Berkeley, CA, USA.
    Özarslan, Evren
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Multimodal integration of diffusion MRI for better characterization of tissue biology2019Inngår i: NMR in Biomedicine, ISSN 0952-3480, E-ISSN 1099-1492, Vol. 32, nr 4Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The contrast in diffusion-weighted MR images is due to variations of diffusion properties within the examined specimen. Certain microstructural information on the underlying tissues can be inferred through quantitative analyses of the diffusion-sensitized MR signals. In the first part of the paper, we review two types of approach for characterizing diffusion MRI signals: Blochs equations with diffusion terms, and statistical descriptions. Specifically, we discuss expansions in terms of cumulants and orthogonal basis functions, the confinement tensor formalism and tensor distribution models. Further insights into the tissue properties may be obtained by integrating diffusion MRI with other techniques, which is the subject of the second part of the paper. We review examples involving magnetic susceptibility, structural tensors, internal field gradients, transverse relaxation and functional MRI. Integrating information provided by other imaging modalities (MR based or otherwise) could be a key to improve our understanding of how diffusion MRI relates to physiology and biology.

  • 3.
    Schultz, Thomas
    et al.
    Institute of Computer Science, University of Bonn, Bonn, Germany.
    Özarslan, EvrenLinköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.Hotz, IngridLinköpings universitet, Institutionen för teknik och naturvetenskap, Medie- och Informationsteknik. Linköpings universitet, Tekniska fakulteten.
    Modeling, Analysis, and Visualization of Anisotropy2017Collection/Antologi (Fagfellevurdert)
    Abstract [en]

    This book focuses on the modeling, processing and visualization of anisotropy, irrespective of the context in which it emerges, using state-of-the-art mathematical tools. As such, it differs substantially from conventional reference works, which are centered on a particular application. It covers the following topics: (i) the geometric structure of tensors, (ii) statistical methods for tensor field processing, (iii) challenges in mapping neural connectivity and structural mechanics, (iv) processing of uncertainty, and (v) visualizing higher-order representations. In addition to original research contributions, it provides insightful reviews.This multidisciplinary book is the sixth in a series that aims to foster scientific exchange between communities employing tensors and other higher-order representations of directionally dependent data. A significant number of the chapters were co-authored by the participants of the workshop titled Multidisciplinary Approaches to Multivalued Data: Modeling, Visualization, Analysis, which was held in Dagstuhl, Germany in April 2016.

    It offers a valuable resource for those working in the field of multi-directional data, vital inspirations for the development of new models, and essential analysis and visualization techniques, thus furthering the state-of-the-art in studies involving anisotropy.

  • 4.
    Shakya, Snehlata
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Batool, Nazre
    School of Technology and Health, KTH Royal Institute of Technology, Stockholm, Sweden.
    Özarslan, Evren
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Multi-Fiber Reconstruction Using Probabilistic Mixture Models for Diffusion MRI Examinations of the Brain2017Inngår i: Modeling, Analysis, and Visualization of Anisotropy / [ed] Thomas Schultz, Evren Özarslan, Ingrid Hotz, Springer, 2017, s. 283-308Kapittel i bok, del av antologi (Annet vitenskapelig)
    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.

  • 5.
    Shakya, Snehlata
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Gu, Xuan
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Batool, Nazre
    KTH, School of Technology and Health, Huddinge, Sweden.
    Özarslan, Evren
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Multi-fiber Estimation and Tractography for Diffusion MRI using mixture of Non-central Wishart Distributions2017Inngår i: VCBM 17: Eurographics Workshop on Visual Computing for Biology and Medicine, The Eurographics Association , 2017, s. 1-5Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Multi-compartmental models are popular to resolve intra-voxel fiber heterogeneity. One such model is the mixture of central Wishart distributions. In this paper, we use our recently proposed model to estimate the orientations of crossing fibers within a voxel based on mixture of non-central Wishart distributions. We present a thorough comparison of the results from other fiber reconstruction methods with this model. The comparative study includes experiments on a range of separation angles between crossing fibers, with different noise levels, and on real human brain diffusion MRI data. Furthermore, we present multi-fiber visualization results using tractography. Results on synthetic and real data as well as tractography visualization highlight the superior performance of the model specifically for small and middle ranges of separation angles among crossing fibers.

  • 6.
    Sjölund, Jens
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Elekta Instrument AB, Kungstensgatan 18, Box 7593, SE-103 93 Stockholm, Sweden.
    Eklund, Anders
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Özarslan, Evren
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Gaussian process regression can turn non-uniform and undersampled diffusion MRI data into diffusion spectrum imaging2017Inngår i: IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017), 2017, Institute of Electrical and Electronics Engineers (IEEE), 2017, s. 778-782Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We propose to use Gaussian process regression to accurately estimate the diffusion MRI signal at arbitrary locations in qspace. By estimating the signal on a grid, we can do synthetic diffusion spectrum imaging: reconstructing the ensemble averaged propagator (EAP) by an inverse Fourier transform. We also propose an alternative reconstruction method guaranteeing a nonnegative EAP that integrates to unity. The reconstruction is validated on data simulated from two Gaussians at various crossing angles. Moreover, we demonstrate on nonuniformly sampled in vivo data that the method is far superior to linear interpolation, and allows a drastic undersampling of the data with only a minor loss of accuracy. We envision the method as a potential replacement for standard diffusion spectrum imaging, in particular when acquistion time is limited.

  • 7.
    Sjölund, Jens
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Elekta Instrument, Stockholm, Sweden.
    Eklund, Anders
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Özarslan, Evren
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Herberthson, Magnus
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Bånkestad, Maria
    RISE SICS, Kista, Sweden.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Bayesian uncertainty quantification in linear models for diffusion MRI2018Inngår i: NeuroImage, ISSN 1053-8119, E-ISSN 1095-9572, Vol. 175, s. 272-285Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 8.
    Tampu, Iulian Emil
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik.
    Yolcu, Cem
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Koay, Cheng Guan
    Özarslan, Evren
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Estimation of the orientationally-averaged magnetic resonance (MR) signal for characterizing neurite morphology2019Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    The orientationally-averaged diffusion magnetic resonance (MR) signal acquired at high diffusion weighting shows great potential for answering fundamental questions about neural tissue microstructure[1]. The noise-induced bias in the magnitude-valued signal and angular resolution limitations in diffusion encoding are among the challenges in obtaining an accurate estimate. Here, we present a data processing framework for computing the orientationally-averaged diffusion signal that corrects the noise induced bias and accounts for the low angular resolution of the acquisition. Noise correction is performed using a statistical transformation framework [2] that converts the noisy MR signal from a noncentralChi distribution to a noisy Gaussian one. Weights for each of the probing directions are computed to improve the rotationally invariant representation of the sample. Synthetic data, generated to mimic diffusion acquisitions with different noise levels and number of acquisition directions, were used to test the data processing framework. The performance of the framework was evaluated by comparing the processed data with the analytical solution of the orientationally-averaged signal. Results show that the computation of the orientationally-averaged signal benefits from both the noise correction and the weighted averaging, especially in the low signal regime. This work provides a tool for processing high diffusion-weighted MR signals whose interpretation could improve our knowledge about neural tissue microstructure.

    [1] Özarslan E, Yolcu C, Herberthson M, Knutsson H, Westin CF. Influence of the size and curvedness ofneural projections on the orientationally averaged diffusion MR signal. Front Phys, 2018; 6:17.

    [2] Koay CG, Özarslan E, Basser PJ. A signal transformational framework for breaking the noise floorand its applications in MRI. J Magn Reson 2009; 197(2):108–119.

  • 9.
    Westin, Carl-Fredrik
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska fakulteten. Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Linköpings universitet, Tekniska fakulteten.
    Pasternak, Ofer
    Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
    Szczepankiewicz, Filip
    Department of Medical Radiation Physics, Lund University, Lund, Sweden.
    Özarslan, Evren
    Linköpings universitet, Institutionen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA; Department of Physics, Bogazici University, Istanbul, Turkey.
    van Westen, Danielle
    Department of Diagnostic Radiology, Lund University, Lund, Sweden.
    Mattisson, Cecilia
    Clinical Sciences, Psychiatry, Lund University, Lund, Sweden.
    Bogren, Mats
    Clinical Sciences, Psychiatry, Lund University, Lund, Sweden.
    O'Donnell, Lauren J
    Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
    Kubicki, Marek
    Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
    Topgaard, Daniel
    Division of Physical Chemistry, Department of Chemistry, Lund University, Lund, Sweden.
    Nilsson, Markus
    Lund University Bioimaging Center, Lund University, Lund, Sweden.
    Q-space trajectory imaging for multidimensional diffusion MRI of the human brain2016Inngår i: NeuroImage, ISSN 1053-8119, E-ISSN 1095-9572, Vol. 135, s. 345-362Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 10.
    Özarslan, Evren
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Yolcu, Cem
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Herberthson, Magnus
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Westin, Carl-Fredrik
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Laboratory for Mathematics in Imaging, Department of Radiology, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA.
    Influence of the Size and Curvedness of Neural Projections on the Orientationally Averaged Diffusion MR Signal2018Inngår i: Frontiers in Physics, E-ISSN 2296-424X, Vol. 6, s. 1-10, artikkel-id 17Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 11.
    Özarslan, Evren
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Yolcu, Cem
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Herberthson, Magnus
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Westin, Carl-Fredrik
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Laboratory for Mathematics in Imaging, Department of Radiology, Harvard Medical School, Brigham and Women's Hospital, Boston, MA, United States.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten.
    Effective Potential for Magnetic Resonance Measurements of Restricted Diffusion2017Inngår i: Frontiers in Physics, E-ISSN 2296-424X, Vol. 5, artikkel-id 68Artikkel i tidsskrift (Fagfellevurdert)
    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.

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