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Cai TX, Williamson NH, Ravin R, Basser PJ. The Diffusion Exchange Ratio (DEXR): A minimal sampling of diffusion exchange spectroscopy to probe exchange, restriction, and time-dependence. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2024; 366:107745. [PMID: 39126819 DOI: 10.1016/j.jmr.2024.107745] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2024] [Revised: 07/31/2024] [Accepted: 08/02/2024] [Indexed: 08/12/2024]
Abstract
Water exchange is increasingly recognized as an important biological process that can affect the study of biological tissue using diffusion MR. Methods to measure exchange, however, remain immature as opposed to those used to characterize restriction, with no consensus on the optimal pulse sequence (s) or signal model (s). In general, the trend has been towards data-intensive fitting of highly parameterized models. We take the opposite approach and show that a judicious sub-sample of diffusion exchange spectroscopy (DEXSY) data can be used to robustly quantify exchange, as well as restriction, in a data-efficient manner. This sampling produces a ratio of two points per mixing time: (i) one point with equal diffusion weighting in both encoding periods, which gives maximal exchange contrast, and (ii) one point with the same total diffusion weighting in just the first encoding period, for normalization. We call this quotient the Diffusion EXchange Ratio (DEXR). Furthermore, we show that it can be used to probe time-dependent diffusion by estimating the velocity autocorrelation function (VACF) over intermediate to long times (∼2-500ms). We provide a comprehensive theoretical framework for the design of DEXR experiments in the case of static or constant gradients. Data from Monte Carlo simulations and experiments acquired in fixed and viable ex vivo neonatal mouse spinal cord using a permanent magnet system are presented to test and validate this approach. In viable spinal cord, we report the following apparent parameters from just 6 data points: τk=17±4ms, fNG=0.72±0.01, Reff=1.05±0.01μm, and κeff=0.19±0.04μm/ms, which correspond to the exchange time, restricted or non-Gaussian signal fraction, an effective spherical radius, and permeability, respectively. For the VACF, we report a long-time, power-law scaling with ≈t-2.4, which is approximately consistent with disordered domains in 3-D. Overall, the DEXR method is shown to be highly efficient, capable of providing valuable quantitative diffusion metrics using minimal MR data.
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Affiliation(s)
- Teddy X Cai
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, 20892, MD, USA
| | - Nathan H Williamson
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, 20892, MD, USA
| | - Rea Ravin
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, 20892, MD, USA; Celoptics, Inc., Rockville, 20850, MD, USA
| | - Peter J Basser
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, 20892, MD, USA.
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2
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Ordinola A, Özarslan E, Bai R, Herberthson M. Limitations and generalizations of the first order kinetics reaction expression for modeling diffusion-driven exchange: Implications on NMR exchange measurements. J Chem Phys 2024; 160:084701. [PMID: 38385634 DOI: 10.1063/5.0188865] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2023] [Accepted: 01/28/2024] [Indexed: 02/23/2024] Open
Abstract
The study and modeling of water exchange in complex media using different applications of diffusion and relaxation magnetic resonance (MR) have been of interest in recent years. Most models attempt to describe this process using a first order kinetics expression, which is appropriate to describe chemical exchange; however, it may not be suitable to describe diffusion-driven exchange since it has no direct relationship to diffusion dynamics of water molecules. In this paper, these limitations are addressed through a more general exchange expression that does consider such important properties. This exchange fraction expression features a multi-exponential recovery at short times and a mono-exponential decay at long times, both of which are not captured by the first order kinetics expression. Furthermore, simplified exchange expressions containing partial information of the analyzed system's diffusion and relaxation processes and geometry are proposed, which can potentially be employed in already established estimation protocols. Finally, exchange fractions estimated from simulated MR data and derived here were compared, showing qualitative similarities but quantitative differences, suggesting that the features of the derived exchange fraction in this paper can be partially recovered by employing an existing estimation framework.
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Affiliation(s)
- Alfredo Ordinola
- Department of Biomedical Engineering, Linköping University, Linköping, Sweden
| | - Evren Özarslan
- Department of Biomedical Engineering, Linköping University, Linköping, Sweden
- Center for Medical Image Science and Visualization, Linköping University, Linköping, Sweden
| | - Ruiliang Bai
- School of Medicine, Zhejiang University, Hangzhou, China
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3
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Elgersma SV, Sederman AJ, Mantle MD, Gladden LF. Measuring the liquid-solid mass transfer coefficient in packed beds using T2-T2 relaxation exchange NMR. Chem Eng Sci 2022. [DOI: 10.1016/j.ces.2021.117229] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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4
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Cai TX, Williamson NH, Ravin R, Basser PJ. Disentangling the effects of restriction and exchange with diffusion exchange spectroscopy. FRONTIERS IN PHYSICS 2022; 10:805793. [PMID: 37063496 PMCID: PMC10104504 DOI: 10.3389/fphy.2022.805793] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Diffusion exchange spectroscopy (DEXSY) is a multidimensional NMR technique that can reveal how water molecules exchange between compartments within heterogeneous media, such as biological tissue. Data from DEXSY experiments is typically processed using numerical inverse Laplace transforms (ILTs) to produce a diffusion-diffusion spectrum. A tacit assumption of this ILT approach is that the signal behavior is Gaussian - i.e., the spin echo intensity decays exponentially with the degree of diffusion weighting. The assumptions that underlie Gaussian signal behavior may be violated, however, depending on the gradient strength applied and the sample under study. We argue that non-Gaussian signal behavior due to restrictions is to be expected in the study of biological tissue using diffusion NMR. Further, we argue that this signal behavior can produce confounding features in the diffusion-diffusion spectra obtained from numerical ILTs of DEXSY data - entangling the effects of restriction and exchange. Specifically, restricted signal behavior can result in broadening of peaks and in the appearance of illusory exchanging compartments with distributed diffusivities, which pearl into multiple peaks if not highly regularized. We demonstrate these effects on simulated data. That said, we suggest the use of features in the signal acquisition domain that can be used to rapidly probe exchange without employing an ILT. We also propose a means to characterize the non-Gaussian signal behavior due to restrictions within a sample using DEXSY measurements with a near zero mixing time or storage interval. We propose a combined acquisition scheme to independently characterize restriction and exchange with various DEXSY measurements, which we term Restriction and Exchange from Equally-weighted Double and Single Diffusion Encodings (REEDS-DE). We test this method on ex vivo neonatal mouse spinal cord - a sample consisting primarily of gray matter - using a low-field, static gradient NMR system. In sum, we highlight critical shortcomings of prevailing DEXSY analysis methods that conflate the effects of restriction and exchange, and suggest a viable experimental approach to disentangle them.
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Affiliation(s)
- Teddy X. Cai
- 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
- Wellcome Centre for Integrative Neuroimaging, FMRIB, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, UK
| | - Nathan H. Williamson
- 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
- National Institute of General Medical Sciences, National Institutes of Health, Bethesda, Maryland, USA
| | - Rea Ravin
- 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
- Celoptics, Rockville, Maryland, 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
- Correspondence: 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, Building 13, Room 3W16, 13 South Drive, Bethesda, Maryland 20892-5772, USA,
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5
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Williamson NH, Ravin R, Cai TX, Benjamini D, Falgairolle M, O'Donovan MJ, Basser PJ. Real-time measurement of diffusion exchange rate in biological tissue. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2020; 317:106782. [PMID: 32679514 PMCID: PMC7427561 DOI: 10.1016/j.jmr.2020.106782] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Revised: 06/22/2020] [Accepted: 06/26/2020] [Indexed: 05/05/2023]
Abstract
Diffusion exchange spectroscopy (DEXSY) provides a means to isolate the signal attenuation associated with exchange from other sources of signal loss. With the total diffusion weighting b1+b2=bs held constant, DEXSY signals acquired with b1=0 or b2=0 have no exchange weighting, while a DEXSY signal acquired with b1=b2 has maximal exchange weighting. The exchange rate can be estimated by fitting a diffusion exchange model to signals acquired with variable mixing times. Conventionally, acquired signals are normalized by a signal with b1=0 and b2=0 to remove the decay due to spin-lattice relaxation. Instead, division by a signal with equal bs but b1=0 or b2=0 reduces spin-lattice relaxation weighting of the apparent exchange rate (AXR). Furthermore, apparent diffusion-weighted R1 relaxation rates can be estimated from non-exchange-weighted DEXSY signals. Estimated R1 values are utilized to remove signal decay due to spin-lattice relaxation from exchange-weighted signals, permitting a more precise estimate of AXR with less data. Data reduction methods are proposed and tested with regards to statistical accuracy and precision of AXR estimates on simulated and experimental data. Simulations show that the methods are capable of accurately measuring the ground-truth exchange rate. The methods remain accurate even when the assumption that DEXSY signals attenuate with b is violated, as occurs for restricted diffusion. Experimental data was collected from fixed neonatal mouse spinal cord samples at 25 and 7°C using the strong static magnetic field gradient produced by a single-sided permanent magnet (i.e., an NMR MOUSE). The most rapid method for exchange measurements requires only five data points (an 80 s experiment as implemented) and achieves a similar level of accuracy and precision to the baseline method using 44 data points. This represents a significant improvement in acquisition speed, overcoming a barrier which has limited the use of DEXSY on living specimen.
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Affiliation(s)
- Nathan H Williamson
- National Institute of General Medical Sciences, National Institutes of Health, Bethesda, MD, USA; Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, USA.
| | - Rea Ravin
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, USA; Celoptics, Rockville, MD, USA
| | - Teddy X Cai
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, USA
| | - Dan Benjamini
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, USA; The Center for Neuroscience and Regenerative Medicine, Uniformed Service University of the Health Sciences, Bethesda, MD 20814, USA
| | - Melanie Falgairolle
- National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD, USA
| | - Michael J O'Donovan
- National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD, USA
| | - Peter J Basser
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, USA.
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6
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Gao Y, Blümich B. Analysis of three-site T 2-T 2 exchange NMR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2020; 315:106740. [PMID: 32438312 DOI: 10.1016/j.jmr.2020.106740] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2020] [Revised: 04/24/2020] [Accepted: 04/25/2020] [Indexed: 06/11/2023]
Abstract
T2-T2 exchange NMR is a unique method to investigate the pore space and fluid dynamics in porous media. While two-site relaxation exchange is well understood, three-site exchange is not. We analyze the solutions for three-site T2-T2 exchange NMR analytically and by computer simulation. Three main results are obtained. First, the exchange map can be asymmetric in the case of microscale vortex motion in violation of the principle of detailed balance. Second, the apparent longitudinal relaxation times and/or apparent transverse relaxation times can be complex valued. In the case of complex apparent transverse relaxation times, the three-site exchange map coalesces to a two-site exchange map with characteristic oscillations in the time domain. As a result of the oscillations, the shorter relaxation time is less than expected. Third, there can be negative cross-peaks in the exchange map for certain combinations of longitudinal and transverse relaxation times or if the mixing period is shorter than the evolution and detection periods. In view of these results experimental exchange maps may need to be reevaluated.
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Affiliation(s)
- Yang Gao
- College of Science, China University of Petroleum, Beijing 102249, China; Institut für Technische und Makromolekulare Chemie, RWTH Aachen University, Aachen 52056, Germany.
| | - Bernhard Blümich
- Institut für Technische und Makromolekulare Chemie, RWTH Aachen University, Aachen 52056, Germany
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7
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Scher Y, Reuveni S, Cohen Y. Constant gradient FEXSY: A time-efficient method for measuring exchange. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2020; 311:106667. [PMID: 31865183 DOI: 10.1016/j.jmr.2019.106667] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2019] [Revised: 12/01/2019] [Accepted: 12/06/2019] [Indexed: 06/10/2023]
Abstract
Filter-Exchange NMR Spectroscopy (FEXSY) is a method for measurement of apparent transmembranal water exchange rates. The experiment is comprised of two co-linear sequential pulsed-field gradient (PFG) blocks, separated by a mixing period in which exchange takes place. The first block remains constant and serves as a diffusion-based filter that removes signal coming from fast-diffusing water. The mixing time and the gradient area (q-value) of the second block are varied on repeated iterations to produce a 2D data set that is analyzed using a bi-compartmental model which assumes that intra- and extra-cellular water are slow and fast diffusing, respectively. Here we suggest a variant of the FEXSY method in which measurements for different mixing times are taken at a constant gradient. This Constant Gradient FEXSY (CG-FEXSY) allows for the determination of the exchange rate by using a smaller 1D data set, so that the same information can be gathered during a considerably shorter scan time. Furthermore, in the limit of high diffusion weighting, such that the extra-cellular water signal is removed while the intra-cellular signal is retained, CG-FEXSY also allows for determination of the intra-cellular mean residence time (MRT). The theoretical results are validated on a living yeast cells sample and on a fixed porcine optic nerve, where the values obtained from the two methods are shown to be in agreement.
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Affiliation(s)
- Yuval Scher
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, The Mark Ratner Institute for Single Molecule Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel.
| | - Shlomi Reuveni
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, The Mark Ratner Institute for Single Molecule Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Yoram Cohen
- School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, The Sagol School of Neuroscience, Tel Aviv University, Tel Aviv 6997801, Israel.
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8
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Williamson NH, Ravin R, Benjamini D, Merkle H, Falgairolle M, O'Donovan MJ, Blivis D, Ide D, Cai TX, Ghorashi NS, Bai R, Basser PJ. Magnetic resonance measurements of cellular and sub-cellular membrane structures in live and fixed neural tissue. eLife 2019; 8:51101. [PMID: 31829935 PMCID: PMC6977971 DOI: 10.7554/elife.51101] [Citation(s) in RCA: 41] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2019] [Accepted: 12/11/2019] [Indexed: 12/21/2022] Open
Abstract
We develop magnetic resonance (MR) methods for real-time measurement of tissue microstructure and membrane permeability of live and fixed excised neonatal mouse spinal cords. Diffusion and exchange MR measurements are performed using the strong static gradient produced by a single-sided permanent magnet. Using tissue delipidation methods, we show that water diffusion is restricted solely by lipid membranes. Most of the diffusion signal can be assigned to water in tissue which is far from membranes. The remaining 25% can be assigned to water restricted on length scales of roughly a micron or less, near or within membrane structures at the cellular, organelle, and vesicle levels. Diffusion exchange spectroscopy measures water exchanging between membrane structures and free environments at 100 s-1.
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Affiliation(s)
- Nathan H Williamson
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, United States
| | - Rea Ravin
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, United States.,Celoptics, Rockville, United States
| | - Dan Benjamini
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, United States.,Center for Neuroscience and Regenerative Medicine, Henry Jackson Foundation, Bethesda, United States
| | - Hellmut Merkle
- National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, United States
| | - Melanie Falgairolle
- National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, United States
| | - Michael James O'Donovan
- National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, United States
| | - Dvir Blivis
- National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, United States
| | - Dave Ide
- National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, United States.,National Institute of Mental Health, National Institutes of Health, Bethesda, United States
| | - Teddy X Cai
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, United States
| | - Nima S Ghorashi
- Cardiovascular Branch, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, United States
| | - Ruiliang Bai
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, United States.,Interdisciplinary Institute of Neuroscience and Technology, School of Medicine, Zhejiang University, Hangzhou, China
| | - Peter J Basser
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, United States
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9
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Maneval JE, Nelson ML, Thrane LW, Codd SL, Seymour JD. A two-region transport model for interpreting T 1-T 2 measurements in complex systems. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2019; 308:106592. [PMID: 31542448 DOI: 10.1016/j.jmr.2019.106592] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2019] [Revised: 09/05/2019] [Accepted: 09/05/2019] [Indexed: 06/10/2023]
Abstract
A 1D two region coupled pore model with discrete pore coupling is developed to elucidate the eigenmode interactions in regions with different surface relaxivity. Numerical solution of the model and simulation of the correlation experiment for varying surface relaxivity, pore connectivity and pore size ratio indicate the role of negative eigenmodes and overlap of T1 and T2 eigenmodes in generating a time domain signal increase with inversion recovery time, t1. The eigenmodes and eigenfunctions are considered in detail providing connection between the mathematical model and the diffusion dynamics and spin physics of the system. Physical systems, i.e. a microporous glass bead pack, a cyclopentane/water hydrate former, and beeswax, showing experimentally measured T1-T2 time domain signal rise are considered within the limitations of the model.
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Affiliation(s)
- James E Maneval
- Department of Chemical Engineering, Bucknell University, Lewisburg, PA, USA
| | | | - Linn W Thrane
- Department of Mechanical and Industrial Engineering, Montana State University, USA
| | - Sarah L Codd
- Department of Mechanical and Industrial Engineering, Montana State University, USA
| | - Joseph D Seymour
- Department of Chemical and Biological Engineering, Montana State University, Bozeman, MT, USA.
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10
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Montrazi ET, Bonagamba TJ. Saturation-recovery as a T 1-filter for T 2-T 2 exchange NMR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2019; 301:67-72. [PMID: 30851667 DOI: 10.1016/j.jmr.2019.03.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2019] [Revised: 02/28/2019] [Accepted: 03/01/2019] [Indexed: 06/09/2023]
Abstract
The Inversion-Recovery (IR) technique has already been proposed to be used as a T1-filter for T2-T2 Exchange experiments. However, when the Exchange experiments are employed for studying samples that show T1 distributions, where the pools are defined by broad relaxation time distributions, e.g. porous media, IR might be difficult to be used as a filter. This paper presents the difficulties found when using IR and proposes the use of Saturation-Recovery (SR) technique as an alternative to T1-filter.
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Affiliation(s)
- E T Montrazi
- São Carlos Institute of Physics, University of São Paulo, PO Box 369, 13560-970 São Carlos, SP, Brazil.
| | - T J Bonagamba
- São Carlos Institute of Physics, University of São Paulo, PO Box 369, 13560-970 São Carlos, SP, Brazil
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11
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Cai TX, Benjamini D, Komlosh ME, Basser PJ, Williamson NH. Rapid detection of the presence of diffusion exchange. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2018; 297:17-22. [PMID: 30340203 PMCID: PMC6289744 DOI: 10.1016/j.jmr.2018.10.004] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2018] [Revised: 10/07/2018] [Accepted: 10/08/2018] [Indexed: 05/08/2023]
Abstract
Diffusion exchange spectroscopy (DEXSY) provides a detailed picture of how fluids in different microenvironments communicate with one another but requires a large amount of data. For DEXSY MRI, a simple measure of apparent exchanging fractions may suffice to characterize and differentiate materials and tissues. Reparameterizing signal intensity from a PGSE-storage-PGSE experiment as a function of the sum, bs=b1+b2, and difference bd=b2-b1 of the diffusion encodings separates diffusion weighting from exchange weighting. Exchange leads to upward curvature along a slice of constant bs. Exchanging fractions can be measured rapidly by a finite difference approximation of the curvature using four data points. The method is generalized for non-steady-state and multi-site exchange. We apply the method to image exchanging fractions and calculate exchange rates of water diffusing across the bulk water interface of a glass capillary array.
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Affiliation(s)
- Teddy X Cai
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA; National Institute of Biomedical Imaging and Bioengineering (BESIP), National Institutes of Health, Bethesda, MD, USA
| | - Dan Benjamini
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, USA
| | - Michal E Komlosh
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, USA; The Henry M. Jackson Foundation for the Advancement of Military Medicine, Inc., Bethesda, MD, USA
| | - Peter J Basser
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, USA
| | - Nathan H Williamson
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, USA.
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12
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Yu Z, Zhang Y, Xiao L, Liao G. Characterization of porous media by T 2-T 2 correlation beyond fast diffusion limit. Magn Reson Imaging 2018; 56:19-23. [PMID: 30343123 DOI: 10.1016/j.mri.2018.10.008] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2018] [Revised: 10/07/2018] [Accepted: 10/18/2018] [Indexed: 10/28/2022]
Abstract
Pore size distribution and surface relaxivity are two important properties of porous media such as rock samples and can be obtained by NMR methods. However, it is difficult to obtain these information beyond the fast diffusion limit. Here we present a new method to directly characterize the averaged pore size of a porous sample with a narrow pore size distribution. This method is based on the parallel plates pore model and the T2-T2 correlation sequence. The pore size (a) - surface relaxivity (ρ) correlation maps were obtained using the non-negative least squares method. Three kinds of glass bead samples were measured and the averaged pore size and surface relaxivity were extracted.
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Affiliation(s)
- Zhou Yu
- State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China
| | - Yan Zhang
- State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China.
| | - Lizhi Xiao
- State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China; Harvard SEAS-CUPB Joint Laboratory on Petroleum Science, Cambridge, MA 02138, USA
| | - Guangzhi Liao
- State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China
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13
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Mailhiot SE, Zong F, Maneval JE, June RK, Galvosas P, Seymour JD. Quantifying NMR relaxation correlation and exchange in articular cartilage with time domain analysis. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2018; 287:82-90. [PMID: 29306110 DOI: 10.1016/j.jmr.2017.12.014] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2017] [Revised: 12/18/2017] [Accepted: 12/19/2017] [Indexed: 06/07/2023]
Abstract
Measured nuclear magnetic resonance (NMR) transverse relaxation data in articular cartilage has been shown to be multi-exponential and correlated to the health of the tissue. The observed relaxation rates are dependent on experimental parameters such as solvent, data acquisition methods, data analysis methods, and alignment to the magnetic field. In this study, we show that diffusive exchange occurs in porcine articular cartilage and impacts the observed relaxation rates in T1-T2 correlation experiments. By using time domain analysis of T2-T2 exchange spectroscopy, the diffusive exchange time can be quantified by measurements that use a single mixing time. Measured characteristic times for exchange are commensurate with T1 in this material and so impacts the observed T1 behavior. The approach used here allows for reliable quantification of NMR relaxation behavior in cartilage in the presence of diffusive fluid exchange between two environments.
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Affiliation(s)
- Sarah E Mailhiot
- Department of Mechanical Engineering, Montana State University, Bozeman, MT 59715, USA
| | - Fangrong Zong
- School of Chemical and Physical Sciences, Victoria University of Wellington, Wellington, NZ 6140, USA
| | - James E Maneval
- Chemical Engineering, Bucknell University, Lewisburg, PA 17837, USA
| | - Ronald K June
- Department of Mechanical Engineering, Montana State University, Bozeman, MT 59715, USA
| | - Petrik Galvosas
- School of Chemical and Physical Sciences, Victoria University of Wellington, Wellington, NZ 6140, USA
| | - Joseph D Seymour
- Department of Chemical and Biological Engineering, Montana State University, Bozeman, MT 59715, USA.
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Silletta EV, Franzoni MB, Monti GA, Acosta RH. Probing numerical Laplace inversion methods for two and three-site molecular exchange between interconnected pore structures. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2018; 286:82-90. [PMID: 29197695 DOI: 10.1016/j.jmr.2017.11.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2017] [Revised: 11/14/2017] [Accepted: 11/26/2017] [Indexed: 06/07/2023]
Abstract
Two-dimension (2D) Nuclear Magnetic Resonance relaxometry experiments are a powerful tool extensively used to probe the interaction among different pore structures, mostly in inorganic systems. The analysis of the collected experimental data generally consists of a 2D numerical inversion of time-domain data where T2-T2 maps are generated. Through the years, different algorithms for the numerical inversion have been proposed. In this paper, two different algorithms for numerical inversion are tested and compared under different conditions of exchange dynamics; the method based on Butler-Reeds-Dawson (BRD) algorithm and the fast-iterative shrinkage-thresholding algorithm (FISTA) method. By constructing a theoretical model, the algorithms were tested for a two- and three-site porous media, varying the exchange rates parameters, the pore sizes and the signal to noise ratio. In order to test the methods under realistic experimental conditions, a challenging organic system was chosen. The molecular exchange rates of water confined in hierarchical porous polymeric networks were obtained, for a two- and three-site porous media. Data processed with the BRD method was found to be accurate only under certain conditions of the exchange parameters, while data processed with the FISTA method is precise for all the studied parameters, except when SNR conditions are extreme.
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Affiliation(s)
- Emilia V Silletta
- Universidad Nacional de Córdoba, Facultad de Matemática, Física, Astronomía y Computación, Córdoba, Argentina; CONICET, IFEG, Córdoba, Argentina
| | - María B Franzoni
- Universidad Nacional de Córdoba, Facultad de Matemática, Física, Astronomía y Computación, Córdoba, Argentina; CONICET, IFEG, Córdoba, Argentina.
| | - Gustavo A Monti
- Universidad Nacional de Córdoba, Facultad de Matemática, Física, Astronomía y Computación, Córdoba, Argentina; CONICET, IFEG, Córdoba, Argentina
| | - Rodolfo H Acosta
- Universidad Nacional de Córdoba, Facultad de Matemática, Física, Astronomía y Computación, Córdoba, Argentina; CONICET, IFEG, Córdoba, Argentina
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15
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Reci A, Sederman AJ, Gladden LF. Retaining both discrete and smooth features in 1D and 2D NMR relaxation and diffusion experiments. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 284:39-47. [PMID: 28957684 DOI: 10.1016/j.jmr.2017.08.017] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2017] [Revised: 08/23/2017] [Accepted: 08/24/2017] [Indexed: 06/07/2023]
Abstract
A new method of regularization of 1D and 2D NMR relaxation and diffusion experiments is proposed and a robust algorithm for its implementation is introduced. The new form of regularization, termed the Modified Total Generalized Variation (MTGV) regularization, offers a compromise between distinguishing discrete and smooth features in the reconstructed distributions. The method is compared to the conventional method of Tikhonov regularization and the recently proposed method of L1 regularization, when applied to simulated data of 1D spin-lattice relaxation, T1, 1D spin-spin relaxation, T2, and 2D T1-T2 NMR experiments. A range of simulated distributions composed of two lognormally distributed peaks were studied. The distributions differed with regard to the variance of the peaks, which were designed to investigate a range of distributions containing only discrete, only smooth or both features in the same distribution. Three different signal-to-noise ratios were studied: 2000, 200 and 20. A new metric is proposed to compare the distributions reconstructed from the different regularization methods with the true distributions. The metric is designed to penalise reconstructed distributions which show artefact peaks. Based on this metric, MTGV regularization performs better than Tikhonov and L1 regularization in all cases except when the distribution is known to only comprise of discrete peaks, in which case L1 regularization is slightly more accurate than MTGV regularization.
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Affiliation(s)
- A Reci
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, United Kingdom
| | - A J Sederman
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, United Kingdom.
| | - L F Gladden
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, United Kingdom
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16
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Determination of exchange ratios in NMR and NQR spectroscopy from the 1D – relaxation dependences for the T2 – relaxation times. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.06.055] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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17
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Reci A, Sederman AJ, Gladden LF. Obtaining sparse distributions in 2D inverse problems. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017. [PMID: 28623744 DOI: 10.1016/j.jmr.2017.05.010] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
The mathematics of inverse problems has relevance across numerous estimation problems in science and engineering. L1 regularization has attracted recent attention in reconstructing the system properties in the case of sparse inverse problems; i.e., when the true property sought is not adequately described by a continuous distribution, in particular in Compressed Sensing image reconstruction. In this work, we focus on the application of L1 regularization to a class of inverse problems; relaxation-relaxation, T1-T2, and diffusion-relaxation, D-T2, correlation experiments in NMR, which have found widespread applications in a number of areas including probing surface interactions in catalysis and characterizing fluid composition and pore structures in rocks. We introduce a robust algorithm for solving the L1 regularization problem and provide a guide to implementing it, including the choice of the amount of regularization used and the assignment of error estimates. We then show experimentally that L1 regularization has significant advantages over both the Non-Negative Least Squares (NNLS) algorithm and Tikhonov regularization. It is shown that the L1 regularization algorithm stably recovers a distribution at a signal to noise ratio<20 and that it resolves relaxation time constants and diffusion coefficients differing by as little as 10%. The enhanced resolving capability is used to measure the inter and intra particle concentrations of a mixture of hexane and dodecane present within porous silica beads immersed within a bulk liquid phase; neither NNLS nor Tikhonov regularization are able to provide this resolution. This experimental study shows that the approach enables discrimination between different chemical species when direct spectroscopic discrimination is impossible, and hence measurement of chemical composition within porous media, such as catalysts or rocks, is possible while still being stable to high levels of noise.
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Affiliation(s)
- A Reci
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United Kingdom
| | - A J Sederman
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United Kingdom.
| | - L F Gladden
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United Kingdom
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18
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Benjamini D, Komlosh ME, Basser PJ. Imaging Local Diffusive Dynamics Using Diffusion Exchange Spectroscopy MRI. PHYSICAL REVIEW LETTERS 2017; 118:158003. [PMID: 28452522 PMCID: PMC11079612 DOI: 10.1103/physrevlett.118.158003] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2016] [Indexed: 06/07/2023]
Abstract
The movement of water between microenvironments presents a central challenge in the physics of soft matter and porous media. Diffusion exchange spectroscopy (DEXSY) is a powerful 2D nuclear magnetic resonance method for measuring such exchange, yet it is rarely used because of its long scan time requirements. Moreover, it has never been combined with magnetic resonance imaging (MRI). Using probability theory, we vastly reduce the required data, making DEXSY MRI feasible for the first time. Experiments are performed on a composite nerve tissue phantom with restricted and free water-exchanging compartments.
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Affiliation(s)
- Dan Benjamini
- Section on Quantitative Imaging and Tissue Sciences, NICHD, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Michal E. Komlosh
- Section on Quantitative Imaging and Tissue Sciences, NICHD, National Institutes of Health, Bethesda, Maryland 20892, USA
- Center for Neuroscience and Regenerative Medicine, Henry M. Jackson Foundation for the Advancement of Military Medicine, Bethesda, Maryland 20892, USA
| | - Peter J. Basser
- Section on Quantitative Imaging and Tissue Sciences, NICHD, National Institutes of Health, Bethesda, Maryland 20892, USA
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Bai R, Benjamini D, Cheng J, Basser PJ. Fast, accurate 2D-MR relaxation exchange spectroscopy (REXSY): Beyond compressed sensing. J Chem Phys 2016; 145:154202. [PMID: 27782473 PMCID: PMC5074998 DOI: 10.1063/1.4964144] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2016] [Accepted: 09/19/2016] [Indexed: 11/14/2022] Open
Abstract
Previously, we showed that compressive or compressed sensing (CS) can be used to reduce significantly the data required to obtain 2D-NMR relaxation and diffusion spectra when they are sparse or well localized. In some cases, an order of magnitude fewer uniformly sampled data were required to reconstruct 2D-MR spectra of comparable quality. Nonetheless, this acceleration may still not be sufficient to make 2D-MR spectroscopy practicable for many important applications, such as studying time-varying exchange processes in swelling gels or drying paints, in living tissue in response to various biological or biochemical challenges, and particularly for in vivo MRI applications. A recently introduced framework, marginal distributions constrained optimization (MADCO), tremendously accelerates such 2D acquisitions by using a priori obtained 1D marginal distribution as powerful constraints when 2D spectra are reconstructed. Here we exploit one important intrinsic property of the 2D-MR relaxation exchange spectra: the fact that the 1D marginal distributions of each 2D-MR relaxation exchange spectrum in both dimensions are equal and can be rapidly estimated from a single Carr-Purcell-Meiboom-Gill (CPMG) or inversion recovery prepared CPMG measurement. We extend the MADCO framework by further proposing to use the 1D marginal distributions to inform the subsequent 2D data-sampling scheme, concentrating measurements where spectral peaks are present and reducing them where they are not. In this way we achieve compression or acceleration that is an order of magnitude greater than that in our previous CS method while providing data in reconstructed 2D-MR spectral maps of comparable quality, demonstrated using several simulated and real 2D T2 - T2 experimental data. This method, which can be called "informed compressed sensing," is extendable to other 2D- and even ND-MR exchange spectroscopy.
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Affiliation(s)
- Ruiliang Bai
- Section on Quantitative Imaging and Tissue Sciences, DIBGI, NICHD, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Dan Benjamini
- Section on Quantitative Imaging and Tissue Sciences, DIBGI, NICHD, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Jian Cheng
- Section on Quantitative Imaging and Tissue Sciences, DIBGI, NICHD, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Peter J Basser
- Section on Quantitative Imaging and Tissue Sciences, DIBGI, NICHD, National Institutes of Health, Bethesda, Maryland 20892, USA
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d’Eurydice MN, Montrazi ET, Fortulan CA, Bonagamba TJ. T2-Filtered T2 − T2 Exchange NMR. J Chem Phys 2016; 144:204201. [DOI: 10.1063/1.4951712] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Marcel Nogueira d’Eurydice
- Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, 13560-970 São Carlos, São Paulo, Brazil
| | - Elton Tadeu Montrazi
- Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, 13560-970 São Carlos, São Paulo, Brazil
| | - Carlos Alberto Fortulan
- Escola de Engenharia de São Carlos, Universidade de São Paulo, CP 359, 13560-970 São Carlos, São Paulo, Brazil
| | - Tito José Bonagamba
- Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, 13560-970 São Carlos, São Paulo, Brazil
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