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Karaman MM, Zhou XJ. A fractional motion diffusion model for a twice-refocused spin-echo pulse sequence. NMR IN BIOMEDICINE 2018; 31:e3960. [PMID: 30133769 DOI: 10.1002/nbm.3960] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2017] [Revised: 05/14/2018] [Accepted: 05/20/2018] [Indexed: 06/08/2023]
Abstract
The purpose of this study was to develop an analytical expression for a fractional motion (FM) diffusion model to characterize diffusion-induced signal attenuation in a twice-refocused spin-echo (TRSE) sequence that is resilient to eddy currents, and to demonstrate its applicability to human brain imaging in vivo. Based on the FM theory, which provides a unified statistical description for Langevin motions, the diffusion-weighted (DW) MR signal was measured with a TRSE sequence that balances the concomitant gradients. The analytical expression was fitted to a set of DW images acquired with 14 b-values (0-4000 s/mm2 ) from a total of 10 healthy human subjects at 3 T, yielding three FM parameter maps based on anomalous diffusion coefficient Dφ, ψ , diffusion increment variance φ, and diffusion correlation ψ, respectively. These parameters were used to characterize different brain regions in gray matter (GM), white matter (WM), and cerebrospinal fluid. The analytical expression for the TRSE-based FM model accurately described diffusion signal attenuation in healthy brain tissues at high b-values. TRSE's robustness against eddy currents was illustrated by comparing results from an expression for a conventional Stejskal-Tanner sequence. The TRSE-based FM model also produced consistent GM-WM contrast (p < 0.01) across all brain regions studied, whereas the consistency was not observed with the Stejskal-Tanner-based FM model. This new analytical expression is expected to enable further investigations to probe tissue structures by exploiting anomalous diffusion properties without being hindered by eddy-current perturbations at high b-values.
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Affiliation(s)
- M Muge Karaman
- Center for MR Research, University of Illinois at Chicago, Chicago, IL, USA
| | - Xiaohong Joe Zhou
- Center for MR Research, University of Illinois at Chicago, Chicago, IL, USA
- Department of Radiology, University of Illinois at Chicago, Chicago, IL, USA
- Department of Neurosurgery, University of Illinois at Chicago, Chicago, IL, USA
- Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, USA
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Ingo C, Magin RL, Colon-Perez L, Triplett W, Mareci TH. On random walks and entropy in diffusion-weighted magnetic resonance imaging studies of neural tissue. Magn Reson Med 2016; 71:617-27. [PMID: 23508765 DOI: 10.1002/mrm.24706] [Citation(s) in RCA: 63] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
PURPOSE In diffusion-weighted MRI studies of neural tissue, the classical model assumes the statistical mechanics of Brownian motion and predicts a monoexponential signal decay. However, there have been numerous reports of signal decays that are not monoexponential, particularly in the white matter. THEORY We modeled diffusion in neural tissue from the perspective of the continuous time random walk. The characteristic diffusion decay is represented by the Mittag-Leffler function, which relaxes a priori assumptions about the governing statistics. We then used entropy as a measure of the anomalous features for the characteristic function. METHODS Diffusion-weighted MRI experiments were performed on a fixed rat brain using an imaging spectrometer at 17.6 T with b-values arrayed up to 25,000 s/mm(2). Additionally, we examined the impact of varying either the gradient strength, q, or mixing time, Δ, on the observed diffusion dynamics. RESULTS In white and gray matter regions, the Mittag-Leffler and entropy parameters demonstrated new information regarding subdiffusion and produced different image contrast from that of the classical diffusion coefficient. The choice of weighting on q and Δ produced different image contrast within the regions of interest. CONCLUSION We propose these parameters have the potential as biomarkers for morphology in neural tissue.
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Affiliation(s)
- Carson Ingo
- Department of Bioengineering, University of Illinois at Chicago, Chicago, Illinois, USA
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Ingo C, Sui Y, Chen Y, Parrish TB, Webb AG, Ronen I. Parsimonious continuous time random walk models and kurtosis for diffusion in magnetic resonance of biological tissue. FRONTIERS IN PHYSICS 2015; 3:11. [PMID: 28344972 PMCID: PMC5365033 DOI: 10.3389/fphy.2015.00011] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifications of the Mittag-Leffler function. For the case of time-fractional subdiffusion, we compute the kurtosis for the Mittag-Leffler function, which provides both a connection and physical context to the much-used approach of diffusional kurtosis imaging. We provide Monte Carlo simulations to illustrate the concepts of anomalous diffusion as stochastic processes of the random walk. Finally, we demonstrate the clinical utility of the Mittag-Leffler function as a model to describe tissue microstructure through estimations of subdiffusion and kurtosis with diffusion MRI measurements in the brain of a chronic ischemic stroke patient.
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Affiliation(s)
- Carson Ingo
- Department of Radiology, C.J. Gorter Center for High Field MRI, Leiden University Medical Center, Leiden, Netherlands
| | - Yi Sui
- Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, USA
| | - Yufen Chen
- Department of Radiology, Northwestern University, Chicago, IL, USA
| | - Todd B. Parrish
- Department of Radiology, Northwestern University, Chicago, IL, USA
| | - Andrew G. Webb
- Department of Radiology, C.J. Gorter Center for High Field MRI, Leiden University Medical Center, Leiden, Netherlands
| | - Itamar Ronen
- Department of Radiology, C.J. Gorter Center for High Field MRI, Leiden University Medical Center, Leiden, Netherlands
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Park M, O'Malley D, Cushman JH. Generalized similarity, renormalization groups, and nonlinear clocks for multiscaling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042104. [PMID: 24827190 DOI: 10.1103/physreve.89.042104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2013] [Indexed: 06/03/2023]
Abstract
Fixed points of the renormalization group operator Rp,rX(t)≡X(rt)/rp are said to be p-self-similar. Here X(t) is an arbitrary stochastic process. The concept of a p-self-similar process is generalized via the renormalization group operator RF,GX(t)=F[X(G(t))], where F and G are bijections on (-∞,∞) and [0,∞), respectively. If X(t) is a fixed point of RF,G, then X(t) is said to be (F,G)-self-similar. We say Y(t) is (F,G)-X(t)-similar if RF,GX(t)=Y(t) in distribution. Exit time distributions and finite-size Lyapunov exponents were obtained for these latter processes. A power law multiscaling process is defined with a multipower-law clock. This process is employed to statistically represent diffusion in a nanopore, a monolayer fluid confined between atomically structured surfaces. The tools presented provide a straightforward method to statistically represent any multiscaling process in time.
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Affiliation(s)
- M Park
- Department of Mathematics and Department of Earth, Atmospheric, and Planetary Sciences (EAPS), Purdue University, West Lafayette Indiana, 47907, USA
| | - D O'Malley
- Computational Earth Science Group, Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA
| | - J H Cushman
- Department of Mathematics and Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, West Lafayette Indiana, 47907, USA
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Lamar M, Zhou XJ, Charlton RA, Dean D, Little D, Deoni SC. In vivo quantification of white matter microstructure for use in aging: a focus on two emerging techniques. Am J Geriatr Psychiatry 2014; 22:111-21. [PMID: 24080382 PMCID: PMC3947219 DOI: 10.1016/j.jagp.2013.08.001] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 01/17/2013] [Revised: 05/31/2013] [Accepted: 08/12/2013] [Indexed: 12/30/2022]
Abstract
Human brain imaging has seen many advances in the quantification of white matter in vivo. For example, these advances have revealed the association between white matter damage and vascular disease as well as their impact on risk for and development of dementia and depression in an aging population. Current neuroimaging methods to quantify white matter damage provide a foundation for understanding such age-related neuropathology; however, these methods are not as adept at determining the underlying microstructural abnormalities signaling at risk tissue or driving white matter damage in the aging brain. This review will begin with a brief overview of the use of diffusion tensor imaging (DTI) in understanding white matter alterations in aging before focusing in more detail on select advances in both diffusion-based methods and multi-component relaxometry techniques for imaging white matter microstructural integrity within myelin sheaths and the axons they encase. Although DTI greatly extended the field of white matter interrogation, these more recent technological advances will add clarity to the underlying microstructural mechanisms that contribute to white matter damage. More specifically, the methods highlighted in this review may prove more sensitive (and specific) for determining the contribution of myelin versus axonal integrity to the aging of white matter in brain.
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Affiliation(s)
- Melissa Lamar
- Department of Psychiatry, University of Illinois at Chicago, Chicago, IL; Graduate Program in Neuroscience, University of Illinois at Chicago, Chicago, IL.
| | - Xiaohong Joe Zhou
- Center for Magnetic Resonance Research and Departments of Radiology and Neurosurgery, University of Illinois at Chicago, Chicago, IL
| | - Rebecca A Charlton
- Department of Psychiatry, University of Illinois at Chicago, Chicago, IL
| | - Douglas Dean
- School of Engineering, Brown University, Providence, RI
| | - Deborah Little
- Scott & White Healthcare and Texas A&M Health Sciences, Temple, TX
| | - Sean C Deoni
- School of Engineering, Brown University, Providence, RI
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Özarslan E, Shepherd TM, Koay CG, Blackband SJ, Basser PJ. Temporal scaling characteristics of diffusion as a new MRI contrast: findings in rat hippocampus. Neuroimage 2012; 60:1380-93. [PMID: 22306798 PMCID: PMC3303993 DOI: 10.1016/j.neuroimage.2012.01.105] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2011] [Revised: 01/18/2012] [Accepted: 01/20/2012] [Indexed: 11/21/2022] Open
Abstract
Features of the diffusion-time dependence of the diffusion-weighted magnetic resonance imaging (MRI) signal provide a new contrast that could be altered by numerous biological processes and pathologies in tissue at microscopic length scales. An anomalous diffusion model, based on the theory of Brownian motion in fractal and disordered media, is used to characterize the temporal scaling (TS) characteristics of diffusion-related quantities, such as moments of the displacement and zero-displacement probabilities, in excised rat hippocampus specimens. To reduce the effect of noise in magnitude-valued MRI data, a novel numerical procedure was employed to yield accurate estimation of these quantities even when the signal falls below the noise floor. The power-law dependencies characterize the TS behavior in all regions of the rat hippocampus, providing unique information about its microscopic architecture. The relationship between the TS characteristics and diffusion anisotropy is investigated by examining the anisotropy of TS, and conversely, the TS of anisotropy. The findings suggest the robustness of the technique as well as the reproducibility of estimates. TS characteristics of the diffusion-weighted signals could be used as a new and useful marker of tissue microstructure.
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Affiliation(s)
- Evren Özarslan
- Section on Tissue Biophysics and Biomimetics, PPITS, NICHD, National Institutes of Health, Bethesda, MD 20892, USA.
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Nevo U, Özarslan E, Komlosh ME, Koay CG, Sarlls JE, Basser PJ. A system and mathematical framework to model shear flow effects in biomedical DW-imaging and spectroscopy. NMR IN BIOMEDICINE 2010; 23:734-44. [PMID: 20886564 PMCID: PMC4164167 DOI: 10.1002/nbm.1591] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
The pulsed-field gradient (PFG) MR experiment enables one to measure particle displacements, velocities, and even higher moments of complex fluid motions. In diffusion-weighted MRI (DWI) in living tissue, where the PFG MRI experiment is used to measure diffusion, Brownian motion is assumed to dominate the displacements causing the observed signal loss. However, motions of water molecules caused by various active biological processes occurring at different length and time scales may also cause additional dephasing of magnetization and signal loss. To help understand their relative effects on the DWI signal attenuation, we used an integrated experimental and theoretical framework: a Rheo-NMR, which served as an experimental model system to precisely prescribe a microscopic velocity distribution; and a mathematical model that relates the DW signal intensity in the Rheo-NMR to experimental parameters that characterize the impressed velocity field. A technical innovation reported here is our use of 'natural' (in this case, polar) coordinates both to simplify the description the fluid motion within the Couette cell of the Rheo-NMR, as well as to acquire and reconstruct magnitude and phase MR images obtained within it. We use this integrated model system to demonstrate how shear flows appears as pseudo-diffusion in magnitude DW MR signals obtained using PFG spin-echo (PGSE) NMR and MRI sequences. Our results lead us to reinterpret the possible causes of signal loss in DWI in vivo, in particular to revise and generalize the previous notion of intra-voxel incoherent motion (IVIM) in order to describe activity driven flows that appear as pseudo-diffusion over multiple length and time scales in living tissues.
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Affiliation(s)
- Uri Nevo
- Department of Biomedical Engineering, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
- Section on Tissue Biophysics and Biomimetics (STBB), Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), NIH, Bethesda, MD, USA
| | - Evren Özarslan
- Section on Tissue Biophysics and Biomimetics (STBB), Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), NIH, Bethesda, MD, USA
| | - Michal E. Komlosh
- Section on Tissue Biophysics and Biomimetics (STBB), Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), NIH, Bethesda, MD, USA
| | - Cheng Guan Koay
- Section on Tissue Biophysics and Biomimetics (STBB), Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), NIH, Bethesda, MD, USA
| | - Joelle E. Sarlls
- Section on Tissue Biophysics and Biomimetics (STBB), Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), NIH, Bethesda, MD, USA
| | - Peter J. Basser
- Section on Tissue Biophysics and Biomimetics (STBB), Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), NIH, Bethesda, MD, USA
- Correspondence to: P. J. Basser, NIH, 13 South Drive, MSC 5772, Building 13, Room 3W16, Bethesda, MD 20892 USA.
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