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Witherspoon VJ, Komlosh ME, Benjamini D, Özarslan E, Lavrik N, Basser PJ. Novel pore size-controlled, susceptibility matched, 3D-printed MRI phantoms. Magn Reson Med 2024; 91:2431-2442. [PMID: 38368618 DOI: 10.1002/mrm.30029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Revised: 12/14/2023] [Accepted: 01/02/2024] [Indexed: 02/20/2024]
Abstract
PURPOSE We report the design concept and fabrication of MRI phantoms, containing blocks of aligned microcapillaires that can be stacked into larger arrays to construct diameter distribution phantoms or fractured, to create a "powder-averaged" emulsion of randomly oriented blocks for vetting or calibrating advanced MRI methods, that is, diffusion tensor imaging, AxCaliber MRI, MAP-MRI, and multiple pulsed field gradient or double diffusion-encoded microstructure imaging methods. The goal was to create a susceptibility-matched microscopically anisotropic but macroscopically isotropic phantom with a ground truth diameter that could be used to vet advanced diffusion methods for diameter determination in fibrous tissues. METHODS Two-photon polymerization, a novel three-dimensional printing method is used to fabricate blocks of capillaries. Double diffusion encoding methods were employed and analyzed to estimate the expected MRI diameter. RESULTS Susceptibility-matched microcapillary blocks or modules that can be assembled into large-scale MRI phantoms have been fabricated and measured using advanced diffusion methods, resulting in microscopic anisotropy and random orientation. CONCLUSION This phantom can vet and calibrate various advanced MRI methods and multiple pulsed field gradient or diffusion-encoded microstructure imaging methods. We demonstrated that two double diffusion encoding methods underestimated the ground truth diameter.
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Affiliation(s)
- Velencia J Witherspoon
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland, USA
| | - Michal E Komlosh
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland, USA
- Center for Neuroscience and Regenerative Medicine, Uniformed Services of Health Sciences, Bethesda, Maryland, USA
| | - Dan Benjamini
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland, USA
- Multiscale Imaging and Integrative Biophysics Unit, National Institute on Aging, National Institutes of Health, Bethesda, Maryland, USA
| | - Evren Özarslan
- Spin Nord AB, Linköping, Sweden
- Department of Biomedical Engineering, Linköping University, Linköping, Sweden
| | - Nickolay Lavrik
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA
| | - Peter J Basser
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland, USA
- Center for Neuroscience and Regenerative Medicine, Uniformed Services of Health Sciences, Bethesda, Maryland, USA
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2
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Afzali M, Knutsson H, Özarslan E, Jones DK. Computing the orientational-average of diffusion-weighted MRI signals: a comparison of different techniques. Sci Rep 2021; 11:14345. [PMID: 34253770 PMCID: PMC8275746 DOI: 10.1038/s41598-021-93558-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2020] [Accepted: 06/28/2021] [Indexed: 02/08/2023] Open
Abstract
Numerous applications in diffusion MRI involve computing the orientationally-averaged diffusion-weighted signal. Most approaches implicitly assume, for a given b-value, that the gradient sampling vectors are uniformly distributed on a sphere (or ‘shell’), computing the orientationally-averaged signal through simple arithmetic averaging. One challenge with this approach is that not all acquisition schemes have gradient sampling vectors distributed over perfect spheres. To ameliorate this challenge, alternative averaging methods include: weighted signal averaging; spherical harmonic representation of the signal in each shell; and using Mean Apparent Propagator MRI (MAP-MRI) to derive a three-dimensional signal representation and estimate its ‘isotropic part’. Here, these different methods are simulated and compared under different signal-to-noise (SNR) realizations. With sufficiently dense sampling points (61 orientations per shell), and isotropically-distributed sampling vectors, all averaging methods give comparable results, (MAP-MRI-based estimates give slightly higher accuracy, albeit with slightly elevated bias as b-value increases). As the SNR and number of data points per shell are reduced, MAP-MRI-based approaches give significantly higher accuracy compared with the other methods. We also apply these approaches to in vivo data where the results are broadly consistent with our simulations. A statistical analysis of the simulated data shows that the orientationally-averaged signals at each b-value are largely Gaussian distributed.
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Affiliation(s)
- Maryam Afzali
- Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, Cardiff University, Cardiff, CF24 4HQ, UK. .,Leeds Institute of Cardiovascular and Metabolic Medicine, University of Leeds, Leeds, LS2 9JT, UK.
| | - Hans Knutsson
- Department of Biomedical Engineering, Linköping University, 581 83, Linköping, Sweden.,Center for Medical Image Science and Visualization, Linköping University, 581 83, Linköping, Sweden
| | - Evren Özarslan
- Department of Biomedical Engineering, Linköping University, 581 83, Linköping, Sweden.,Center for Medical Image Science and Visualization, Linköping University, 581 83, Linköping, Sweden
| | - Derek K Jones
- Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, Cardiff University, Cardiff, CF24 4HQ, UK
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3
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Herberthson M, Boito D, Haije TD, Feragen A, Westin CF, Özarslan E. Q-space trajectory imaging with positivity constraints (QTI+). Neuroimage 2021; 238:118198. [PMID: 34029738 PMCID: PMC9596133 DOI: 10.1016/j.neuroimage.2021.118198] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2021] [Revised: 05/02/2021] [Accepted: 05/20/2021] [Indexed: 01/18/2023] Open
Abstract
Q-space trajectory imaging (QTI) enables the estimation of useful scalar measures indicative of the local tissue structure. This is accomplished by employing generalized gradient waveforms for diffusion sensitization alongside a diffusion tensor distribution (DTD) model. The first two moments of the underlying DTD are made available by acquisitions at low diffusion sensitivity (b-values). Here, we show that three independent conditions have to be fulfilled by the mean and covariance tensors associated with distributions of symmetric positive semidefinite tensors. We introduce an estimation framework utilizing semi-definite programming (SDP) to guarantee that these conditions are met. Applying the framework on simulated signal profiles for diffusion tensors distributed according to non-central Wishart distributions demonstrates the improved noise resilience of QTI+ over the commonly employed estimation methods. Our findings on a human brain data set also reveal pronounced improvements, especially so for acquisition protocols featuring few number of volumes. Our method’s robustness to noise is expected to not only improve the accuracy of the estimates, but also enable a meaningful interpretation of contrast in the derived scalar maps. The technique’s performance on shorter acquisitions could make it feasible in routine clinical practice.
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Affiliation(s)
| | - Deneb Boito
- Department of Biomedical Engineering, Linköping University, Linköping, Sweden; Center for Medical Image Science and Visualization, Linköping University, Linköping, Sweden.
| | - Tom Dela Haije
- Department of Computer Science, University of Copenhagen, Copenhagen, Denmark.
| | - Aasa Feragen
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark.
| | - Carl-Fredrik Westin
- Laboratory for Mathematics in Imaging, Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
| | - Evren Özarslan
- Department of Biomedical Engineering, Linköping University, Linköping, Sweden; Center for Medical Image Science and Visualization, Linköping University, Linköping, Sweden.
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4
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Reymbaut A, Caron AV, Gilbert G, Szczepankiewicz F, Nilsson M, Warfield SK, Descoteaux M, Scherrer B. Magic DIAMOND: Multi-fascicle diffusion compartment imaging with tensor distribution modeling and tensor-valued diffusion encoding. Med Image Anal 2021; 70:101988. [PMID: 33611054 DOI: 10.1016/j.media.2021.101988] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Revised: 01/25/2021] [Accepted: 01/29/2021] [Indexed: 01/05/2023]
Abstract
Diffusion tensor imaging provides increased sensitivity to microstructural tissue changes compared to conventional anatomical imaging but also presents limited specificity. To tackle this problem, the DIAMOND model subdivides the voxel content into diffusion compartments and draws from diffusion-weighted data to estimate compartmental non-central matrix-variate Gamma distributions of diffusion tensors. It models each sub-voxel fascicle separately, resolving crossing white-matter pathways and allowing for a fascicle-element (fixel) based analysis of microstructural features. Alternatively, specific features of the intra-voxel diffusion tensor distribution can be selectively measured using tensor-valued diffusion-weighted acquisition schemes. However, the impact of such schemes on estimating brain microstructural features has only been studied in a handful of parametric single-fascicle models. In this work, we derive a general Laplace transform for the non-central matrix-variate Gamma distribution, which enables the extension of DIAMOND to tensor-valued encoded data. We then evaluate this "Magic DIAMOND" model in silico and in vivo on various combinations of tensor-valued encoded data. Assessing uncertainty on parameter estimation via stratified bootstrap, we investigate both voxel-based and fixel-based metrics by carrying out multi-peak tractography. We demonstrate using in silico evaluations that tensor-valued diffusion encoding significantly improves Magic DIAMOND's accuracy. Most importantly, we show in vivo that our estimated metrics can be robustly mapped along tracks across regions of fiber crossing, which opens new perspectives for tractometry and microstructure mapping along specific white-matter tracts.
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Affiliation(s)
| | | | - Guillaume Gilbert
- MR Clinical Science, Philips Healthcare Canada, Markham, ON L6C 2S3, Canada
| | - Filip Szczepankiewicz
- Department of Clinical Sciences, Lund University, 22184, Lund, Sweden; Random Walk Imaging AB, 22224, Lund, Sweden
| | - Markus Nilsson
- Department of Clinical Sciences, Lund University, 22184, Lund, Sweden
| | - Simon K Warfield
- Department of Radiology, Boston Children's Hospital, Boston, MA 02115, United States
| | | | - Benoit Scherrer
- Department of Radiology, Boston Children's Hospital, Boston, MA 02115, United States
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5
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Afzali M, Pieciak T, Newman S, Garyfallidis E, Özarslan E, Cheng H, Jones DK. The sensitivity of diffusion MRI to microstructural properties and experimental factors. J Neurosci Methods 2021; 347:108951. [PMID: 33017644 PMCID: PMC7762827 DOI: 10.1016/j.jneumeth.2020.108951] [Citation(s) in RCA: 47] [Impact Index Per Article: 15.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2020] [Revised: 08/27/2020] [Accepted: 09/15/2020] [Indexed: 12/13/2022]
Abstract
Diffusion MRI is a non-invasive technique to study brain microstructure. Differences in the microstructural properties of tissue, including size and anisotropy, can be represented in the signal if the appropriate method of acquisition is used. However, to depict the underlying properties, special care must be taken when designing the acquisition protocol as any changes in the procedure might impact on quantitative measurements. This work reviews state-of-the-art methods for studying brain microstructure using diffusion MRI and their sensitivity to microstructural differences and various experimental factors. Microstructural properties of the tissue at a micrometer scale can be linked to the diffusion signal at a millimeter-scale using modeling. In this paper, we first give an introduction to diffusion MRI and different encoding schemes. Then, signal representation-based methods and multi-compartment models are explained briefly. The sensitivity of the diffusion MRI signal to the microstructural components and the effects of curvedness of axonal trajectories on the diffusion signal are reviewed. Factors that impact on the quality (accuracy and precision) of derived metrics are then reviewed, including the impact of random noise, and variations in the acquisition parameters (i.e., number of sampled signals, b-value and number of acquisition shells). Finally, yet importantly, typical approaches to deal with experimental factors are depicted, including unbiased measures and harmonization. We conclude the review with some future directions and recommendations on this topic.
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Affiliation(s)
- Maryam Afzali
- Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, Cardiff University, Cardiff, United Kingdom.
| | - Tomasz Pieciak
- AGH University of Science and Technology, Kraków, Poland; LPI, ETSI Telecomunicación, Universidad de Valladolid, Valladolid, Spain.
| | - Sharlene Newman
- Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405, USA; Program of Neuroscience, Indiana University, Bloomington, IN 47405, USA.
| | - Eleftherios Garyfallidis
- Program of Neuroscience, Indiana University, Bloomington, IN 47405, USA; Department of Intelligent Systems Engineering, Indiana University, Bloomington, IN 47408, USA.
| | - Evren Özarslan
- Department of Biomedical Engineering, Linköping University, Linköping, Sweden; Center for Medical Image Science and Visualization, Linköping University, Linköping, Sweden.
| | - Hu Cheng
- Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405, USA; Program of Neuroscience, Indiana University, Bloomington, IN 47405, USA.
| | - Derek K Jones
- Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, Cardiff University, Cardiff, United Kingdom.
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6
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Reymbaut A, Mezzani P, de Almeida Martins JP, Topgaard D. Accuracy and precision of statistical descriptors obtained from multidimensional diffusion signal inversion algorithms. NMR IN BIOMEDICINE 2020; 33:e4267. [PMID: 32067322 DOI: 10.1002/nbm.4267] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Revised: 01/15/2020] [Accepted: 01/16/2020] [Indexed: 05/22/2023]
Abstract
In biological tissues, typical MRI voxels comprise multiple microscopic environments, the local organization of which can be captured by microscopic diffusion tensors. The measured diffusion MRI signal can, therefore, be written as the multidimensional Laplace transform of an intravoxel diffusion tensor distribution (DTD). Tensor-valued diffusion encoding schemes have been designed to probe specific features of the DTD, and several algorithms have been introduced to invert such data and estimate statistical descriptors of the DTD, such as the mean diffusivity, the variance of isotropic diffusivities, and the mean squared diffusion anisotropy. However, the accuracy and precision of these estimations have not been assessed systematically and compared across methods. In this article, we perform and compare such estimations in silico for a one-dimensional Gamma fit, a generalized two-term cumulant approach, and two-dimensional and four-dimensional Monte-Carlo-based inversion techniques, using a clinically feasible tensor-valued acquisition scheme. In particular, we compare their performance at different signal-to-noise ratios (SNRs) for voxel contents varying in terms of the aforementioned statistical descriptors, orientational order, and fractions of isotropic and anisotropic components. We find that all inversion techniques share similar precision (except for a lower precision of the two-dimensional Monte Carlo inversion) but differ in terms of accuracy. While the Gamma fit exhibits infinite-SNR biases when the signal deviates strongly from monoexponentiality and is unaffected by orientational order, the generalized cumulant approach shows infinite-SNR biases when this deviation originates from the variance in isotropic diffusivities or from the low orientational order of anisotropic diffusion components. The two-dimensional Monte Carlo inversion shows remarkable accuracy in all systems studied, given that the acquisition scheme possesses enough directions to yield a rotationally invariant powder average. The four-dimensional Monte Carlo inversion presents no infinite-SNR bias, but suffers significantly from noise in the data, while preserving good contrast in most systems investigated.
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Affiliation(s)
- Alexis Reymbaut
- Physical Chemistry Department, Lund University, Lund, Sweden
- Random Walk Imaging AB, Lund, Sweden
| | - Paolo Mezzani
- Physical Chemistry Department, Lund University, Lund, Sweden
- Physics Department, Università degli Studi di Milano, Milan, Italy
| | | | - Daniel Topgaard
- Physical Chemistry Department, Lund University, Lund, Sweden
- Random Walk Imaging AB, Lund, Sweden
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7
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Henriques RN, Palombo M, Jespersen SN, Shemesh N, Lundell H, Ianuş A. Double diffusion encoding and applications for biomedical imaging. J Neurosci Methods 2020; 348:108989. [PMID: 33144100 DOI: 10.1016/j.jneumeth.2020.108989] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2020] [Revised: 09/25/2020] [Accepted: 10/20/2020] [Indexed: 12/11/2022]
Abstract
Diffusion Magnetic Resonance Imaging (dMRI) is one of the most important contemporary non-invasive modalities for probing tissue structure at the microscopic scale. The majority of dMRI techniques employ standard single diffusion encoding (SDE) measurements, covering different sequence parameter ranges depending on the complexity of the method. Although many signal representations and biophysical models have been proposed for SDE data, they are intrinsically limited by a lack of specificity. Advanced dMRI methods have been proposed to provide additional microstructural information beyond what can be inferred from SDE. These enhanced contrasts can play important roles in characterizing biological tissues, for instance upon diseases (e.g. neurodegenerative, cancer, stroke), aging, learning, and development. In this review we focus on double diffusion encoding (DDE), which stands out among other advanced acquisitions for its versatility, ability to probe more specific diffusion correlations, and feasibility for preclinical and clinical applications. Various DDE methodologies have been employed to probe compartment sizes (Section 3), decouple the effects of microscopic diffusion anisotropy from orientation dispersion (Section 4), probe displacement correlations, study exchange, or suppress fast diffusing compartments (Section 6). DDE measurements can also be used to improve the robustness of biophysical models (Section 5) and study intra-cellular diffusion via magnetic resonance spectroscopy of metabolites (Section 7). This review discusses all these topics as well as important practical aspects related to the implementation and contrast in preclinical and clinical settings (Section 9) and aims to provide the readers a guide for deciding on the right DDE acquisition for their specific application.
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Affiliation(s)
- Rafael N Henriques
- Champalimaud Research, Champalimaud Centre for the Unknown, Lisbon, Portugal
| | - Marco Palombo
- Centre for Medical Image Computing and Dept. of Computer Science, University College London, London, UK
| | - Sune N Jespersen
- Center of Functionally Integrative Neuroscience (CFIN) and MINDLab, Department of Clinical Medicine, Aarhus University, Aarhus, Denmark; Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark
| | - Noam Shemesh
- Champalimaud Research, Champalimaud Centre for the Unknown, Lisbon, Portugal
| | - Henrik Lundell
- Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre, Denmark
| | - Andrada Ianuş
- Champalimaud Research, Champalimaud Centre for the Unknown, Lisbon, Portugal.
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8
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Afzali M, Aja-Fernández S, Jones DK. Direction-averaged diffusion-weighted MRI signal using different axisymmetric B-tensor encoding schemes. Magn Reson Med 2020; 84:1579-1591. [PMID: 32080890 PMCID: PMC7318161 DOI: 10.1002/mrm.28191] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2019] [Revised: 01/08/2020] [Accepted: 01/09/2020] [Indexed: 12/21/2022]
Abstract
Purpose It has been shown, theoretically and in vivo, that using the Stejskal‐Tanner pulsed‐gradient, or linear tensor encoding (LTE), and in tissue exhibiting a “stick‐like” diffusion geometry, the direction‐averaged diffusion‐weighted MRI signal at high b‐values (
7000<b<10000s/mm2) follows a power‐law, decaying as
1/b. It has also been shown, theoretically, that for planar tensor encoding (PTE), the direction‐averaged diffusion‐weighted MRI signal decays as 1/b. We aimed to confirm this theoretical prediction in vivo. We then considered the direction‐averaged signal for arbitrary b‐tensor shapes and different tissue substrates to look for other conditions under which a power‐law exists. Methods We considered the signal decay for high b‐values for encoding geometries ranging from 2‐dimensional PTE, through isotropic or spherical tensor encoding to LTE. When a power‐law behavior was suggested, this was tested using in silico simulations and, when appropriate, in vivo using ultra‐strong (300 mT/m) gradients. Results Our in vivo results confirmed the predicted 1/b power law for PTE. Moreover, our analysis showed that using an axisymmetric b‐tensor a power‐law only exists under very specific conditions: (a) “stick‐like” tissue geometry and purely LTE or purely PTE waveforms; and (b) "pancake‐like" tissue geometry and a purely LTE waveform. Conclusions A complete analysis of the power‐law dependencies of the diffusion‐weighted signal at high b‐values has been performed. Only three specific forms of encoding result in a power‐law dependency, pure linear and pure PTE when the tissue geometry is “stick‐like” and pure LTE when the tissue geometry is "pancake‐like". The different exponents of these encodings could be used to provide independent validation of the presence of different tissue geometries in vivo.
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Affiliation(s)
- Maryam Afzali
- Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, Cardiff University, Cardiff, United Kingdom
| | - Santiago Aja-Fernández
- Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, Cardiff University, Cardiff, United Kingdom.,Laboratorio de Procesado de Imagen, ETSI Telecomunicación Edificio de las Nuevas Tecnologías, Universidad de Valladolid, Valladolid, Spain
| | - Derek K Jones
- Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, Cardiff University, Cardiff, United Kingdom.,Mary MacKillop Institute for Health Research, Faculty of Health Sciences, Australian Catholic University, Melbourne, VIC, Australia
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