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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: 20] [Impact Index Per Article: 5.0] [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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Anaby D, Morozov D, Seroussi I, Hametner S, Sochen N, Cohen Y. Single- and double-Diffusion encoding MRI for studying ex vivo apparent axon diameter distribution in spinal cord white matter. NMR IN BIOMEDICINE 2019; 32:e4170. [PMID: 31573745 DOI: 10.1002/nbm.4170] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2019] [Revised: 07/28/2019] [Accepted: 07/31/2019] [Indexed: 06/10/2023]
Abstract
Mapping average axon diameter (AAD) and axon diameter distribution (ADD) in neuronal tissues non-invasively is a challenging task that may have a tremendous effect on our understanding of the normal and diseased central nervous system (CNS). Water diffusion is used to probe microstructure in neuronal tissues, however, the different water populations and barriers that are present in these tissues turn this into a complex task. Therefore, it is not surprising that recently we have witnessed a burst in the development of new approaches and models that attempt to obtain, non-invasively, detailed microstructural information in the CNS. In this work, we aim at challenging and comparing the microstructural information obtained from single diffusion encoding (SDE) with double diffusion encoding (DDE) MRI. We first applied SDE and DDE MR spectroscopy (MRS) on microcapillary phantoms and then applied SDE and DDE MRI on an ex vivo porcine spinal cord (SC), using similar experimental conditions. The obtained diffusion MRI data were fitted by the same theoretical model, assuming that the signal in every voxel can be approximated as the superposition of a Gaussian-diffusing component and a series of restricted components having infinite cylindrical geometries. The diffusion MRI results were then compared with histological findings. We found a good agreement between the fittings and the experimental data in white matter (WM) voxels of the SC in both diffusion MRI methods. The microstructural information and apparent AADs extracted from SDE MRI were found to be similar or somewhat larger than those extracted from DDE MRI especially when the diffusion time was set to 40 ms. The apparent ADDs extracted from SDE and DDE MRI show reasonable agreement but somewhat weaker correspondence was observed between the diffusion MRI results and histology. The apparent subtle differences between the microstructural information obtained from SDE and DDE MRI are briefly discussed.
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Affiliation(s)
- Debbie Anaby
- School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
- Department of Diagnostic Imaging, Sheba Medical Center, Tel HaShomer, Israel
| | - Darya Morozov
- School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
| | - Inbar Seroussi
- School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
| | - Simon Hametner
- Neuroimmunology Department, Center of Brain Research, Medical University of Vienna, Vienna, Austria
| | - Nir Sochen
- School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
- The Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel
| | - Yoram Cohen
- School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
- The Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel
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Fieremans E, Lee HH. Physical and numerical phantoms for the validation of brain microstructural MRI: A cookbook. Neuroimage 2018; 182:39-61. [PMID: 29920376 PMCID: PMC6175674 DOI: 10.1016/j.neuroimage.2018.06.046] [Citation(s) in RCA: 59] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2017] [Revised: 06/08/2018] [Accepted: 06/13/2018] [Indexed: 12/24/2022] Open
Abstract
Phantoms, both numerical (software) and physical (hardware), can serve as a gold standard for the validation of MRI methods probing the brain microstructure. This review aims to provide guidelines on how to build, implement, or choose the right phantom for a particular application, along with an overview of the current state-of-the-art of phantoms dedicated to study brain microstructure with MRI. For physical phantoms, we discuss the essential requirements and relevant characteristics of both the (NMR visible) liquid and (NMR invisible) phantom materials that induce relevant microstructural features detectable via MRI, based on diffusion, intra-voxel incoherent motion, magnetization transfer or magnetic susceptibility weighted contrast. In particular, for diffusion MRI, many useful phantoms have been proposed, ranging from simple liquids to advanced biomimetic phantoms consisting of hollow or plain microfibers and capillaries. For numerical phantoms, the focus is on Monte Carlo simulations of random walk, for which the basic principles, along with useful criteria to check and potential pitfalls are reviewed, in addition to a literature overview highlighting recent advances. While many phantoms exist already, the current review aims to stimulate further research in the field and to address remaining needs.
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Affiliation(s)
- Els Fieremans
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA.
| | - Hong-Hsi Lee
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA
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Seroussi I, Grebenkov DS, Pasternak O, Sochen N. Microscopic interpretation and generalization of the Bloch-Torrey equation for diffusion magnetic resonance. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 277:95-103. [PMID: 28242566 PMCID: PMC5486415 DOI: 10.1016/j.jmr.2017.01.018] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2016] [Revised: 01/24/2017] [Accepted: 01/25/2017] [Indexed: 05/31/2023]
Abstract
In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal.
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Affiliation(s)
- Inbar Seroussi
- Department of Applied Mathematics, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
| | - Denis S Grebenkov
- Laboratoire de Physique de la Matière Condensée, CNRS - Ecole Polytechnique, University Paris-Saclay, F-91128 Palaiseau, France
| | - Ofer Pasternak
- Departments of Psychiatry and Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA 02215, USA
| | - Nir Sochen
- Department of Applied Mathematics, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
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Xu J, Li H, Harkins KD, Jiang X, Xie J, Kang H, Does MD, Gore JC. Mapping mean axon diameter and axonal volume fraction by MRI using temporal diffusion spectroscopy. Neuroimage 2014; 103:10-19. [PMID: 25225002 PMCID: PMC4312203 DOI: 10.1016/j.neuroimage.2014.09.006] [Citation(s) in RCA: 86] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2014] [Revised: 09/02/2014] [Accepted: 09/04/2014] [Indexed: 02/01/2023] Open
Abstract
Mapping mean axon diameter and intra-axonal volume fraction may have significant clinical potential because nerve conduction velocity is directly dependent on axon diameter, and several neurodegenerative diseases affect axons of specific sizes and alter axon counts. Diffusion-weighted MRI methods based on the pulsed gradient spin echo (PGSE) sequence have been reported to be able to assess axon diameter and volume fraction non-invasively. However, due to the relatively long diffusion times used, e.g. >20ms, the sensitivity to small axons (diameter<2μm) is low, and the derived mean axon diameter has been reported to be overestimated. In the current study, oscillating gradient spin echo (OGSE) diffusion sequences with variable frequency gradients were used to assess rat spinal white matter tracts with relatively short effective diffusion times (1-5ms). In contrast to previous PGSE-based methods, the extra-axonal diffusion cannot be modeled as hindered (Gaussian) diffusion when short diffusion times are used. Appropriate frequency-dependent rates are therefore incorporated into our analysis and validated by histology-based computer simulation of water diffusion. OGSE data were analyzed to derive mean axon diameters and intra-axonal volume fractions of rat spinal white matter tracts (mean axon diameter of ~1.27-5.54μm). The estimated values were in good agreement with histology, including the small axon diameters (<2.5μm). This study establishes a framework for the quantification of nerve morphology using the OGSE method with high sensitivity to small axons.
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Affiliation(s)
- Junzhong Xu
- Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA; Department of Radiology and Radiological Sciences, Vanderbilt University, Nashville, TN 37232, USA; Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37232, USA.
| | - Hua Li
- Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA; Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37232, USA
| | - Kevin D Harkins
- Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA
| | - Xiaoyu Jiang
- Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA; Department of Radiology and Radiological Sciences, Vanderbilt University, Nashville, TN 37232, USA
| | - Jingping Xie
- Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA; Department of Radiology and Radiological Sciences, Vanderbilt University, Nashville, TN 37232, USA
| | - Hakmook Kang
- Department of Biostatistics, Vanderbilt University, Nashville, TN 37203, USA
| | - Mark D Does
- Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA; Department of Radiology and Radiological Sciences, Vanderbilt University, Nashville, TN 37232, USA; Department of Biomedical Engineering, Vanderbilt University, Nashville, TN 37232, USA
| | - John C Gore
- Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA; Department of Radiology and Radiological Sciences, Vanderbilt University, Nashville, TN 37232, USA; Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37232, USA; Department of Biomedical Engineering, Vanderbilt University, Nashville, TN 37232, USA; Department of Molecular Physiology and Biophysics, Vanderbilt University, Nashville, TN 37232, USA
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Morozov D, Bar L, Sochen N, Cohen Y. Microstructural information from angular double-pulsed-field-gradient NMR: From model systems to nerves. Magn Reson Med 2014; 74:25-32. [DOI: 10.1002/mrm.25371] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2013] [Revised: 06/24/2014] [Accepted: 06/24/2014] [Indexed: 11/11/2022]
Affiliation(s)
- Darya Morozov
- School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Science, Tel Aviv University; Tel Aviv Israel
| | - Leah Bar
- School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact Science, Tel Aviv University; Tel Aviv Israel
| | - Nir Sochen
- School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact Science, Tel Aviv University; Tel Aviv Israel
| | - Yoram Cohen
- School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Science, Tel Aviv University; Tel Aviv Israel
- Sagol School of Neuroscience, Tel Aviv University; Tel Aviv Israel
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Li H, Gore JC, Xu J. Fast and robust measurement of microstructural dimensions using temporal diffusion spectroscopy. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2014; 242:4-9. [PMID: 24583517 PMCID: PMC4008665 DOI: 10.1016/j.jmr.2014.02.007] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2013] [Revised: 01/29/2014] [Accepted: 02/02/2014] [Indexed: 05/22/2023]
Abstract
Mapping axon sizes non-invasively is of interest for neuroscientists and may have significant clinical potential because nerve conduction velocity is directly dependent on axon size. Current approaches to measuring axon sizes using diffusion-weighted MRI, e.g. q-space imaging with pulsed gradient spin echo (PGSE) sequences usually require long scan times and high q-values to detect small axons (diameter <2μm). The oscillating gradient spin echo (OGSE) method has been shown to be able to achieve very short diffusion times and hence may be able to detect smaller axons with high sensitivity. In the current study, OGSE experiments were performed to measure the inner diameters of hollow microcapillaries with a range of sizes (∼1.5-19.3μm) that mimic axons in the human central nervous system. The results suggest that OGSE measurements, even with only moderately high frequencies, are highly sensitive to compartment sizes, and a minimum of two ADC values with different frequencies may be sufficient to extract the microcapillary size accurately. This suggests that the OGSE method may serve as a fast and robust measurement method for mapping axon sizes non-invasively.
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Affiliation(s)
- Hua Li
- Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA; Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37232, USA
| | - John C Gore
- Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA; Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37232, USA; Department of Radiology and Radiological Sciences, Vanderbilt University, Nashville, TN 37232, USA; Department of Biomedical Engineering, Vanderbilt University, Nashville, TN 37232, USA; Department of Molecular Physiology and Biophysics, Vanderbilt University, Nashville, TN 37232, USA
| | - Junzhong Xu
- Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232, USA; Department of Radiology and Radiological Sciences, Vanderbilt University, Nashville, TN 37232, USA.
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Morozov D, Bar L, Sochen N, Cohen Y. Modeling of the diffusion MR signal in calibrated model systems and nerves. NMR IN BIOMEDICINE 2013; 26:1787-1795. [PMID: 24105913 DOI: 10.1002/nbm.3018] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2013] [Revised: 07/23/2013] [Accepted: 08/05/2013] [Indexed: 06/02/2023]
Abstract
Diffusion NMR is a powerful tool for gleaning microstructural information on opaque systems. In this work, the signal decay in single-pulsed-field gradient diffusion NMR experiments performed on a series of phantoms of increasing complexity, where the ground truth is known a priori, was modeled and used to identify microstructural features of these complex phantoms. We were able to demonstrate that, without assuming the number of components or compartments, the modeling can identify the number of restricted components, detect their sizes with an accuracy of a fraction of a micrometer, determine their relative populations, and identify and characterize free diffusion when present in addition to the components exhibiting restricted diffusion. After the accuracy of the modeling had been demonstrated, this same approach was used to study fixed nerves under different experimental conditions. It seems that this approach is able to characterize both the averaged axon diameter and the relative population of the different diffusing components in the neuronal tissues examined.
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Affiliation(s)
- Darya Morozov
- School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Science, Tel Aviv University, Tel Aviv, Israel
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Comment on “Measuring small compartments with relatively weak gradients by angular double-pulsed-field-gradient NMR” by Morozov Bar, Sochen, and Cohen. Magn Reson Imaging 2013; 31:1643-4. [DOI: 10.1016/j.mri.2013.07.006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2013] [Accepted: 07/14/2013] [Indexed: 11/22/2022]
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