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Clarke WT, Ligneul C, Cottaar M, Ip IB, Jbabdi S. Universal dynamic fitting of magnetic resonance spectroscopy. Magn Reson Med 2024; 91:2229-2246. [PMID: 38265152 DOI: 10.1002/mrm.30001] [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: 09/29/2023] [Revised: 11/27/2023] [Accepted: 12/17/2023] [Indexed: 01/25/2024]
Abstract
PURPOSE Dynamic (2D) MRS is a collection of techniques where acquisitions of spectra are repeated under varying experimental or physiological conditions. Dynamic MRS comprises a rich set of contrasts, including diffusion-weighted, relaxation-weighted, functional, edited, or hyperpolarized spectroscopy, leading to quantitative insights into multiple physiological or microstructural processes. Conventional approaches to dynamic MRS analysis ignore the shared information between spectra, and instead proceed by independently fitting noisy individual spectra before modeling temporal changes in the parameters. Here, we propose a universal dynamic MRS toolbox which allows simultaneous fitting of dynamic spectra of arbitrary type. METHODS A simple user-interface allows information to be shared and precisely modeled across spectra to make inferences on both spectral and dynamic processes. We demonstrate and thoroughly evaluate our approach in three types of dynamic MRS techniques. Simulations of functional and edited MRS are used to demonstrate the advantages of dynamic fitting. RESULTS Analysis of synthetic functional 1H-MRS data shows a marked decrease in parameter uncertainty as predicted by prior work. Analysis with our tool replicates the results of two previously published studies using the original in vivo functional and diffusion-weighted data. Finally, joint spectral fitting with diffusion orientation models is demonstrated in synthetic data. CONCLUSION A toolbox for generalized and universal fitting of dynamic, interrelated MR spectra has been released and validated. The toolbox is shared as a fully open-source software with comprehensive documentation, example data, and tutorials.
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Affiliation(s)
- William T Clarke
- Wellcome Centre for Integrative Neuroimaging, FMRIB, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, UK
| | - Clémence Ligneul
- Wellcome Centre for Integrative Neuroimaging, FMRIB, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, UK
| | - Michiel Cottaar
- Wellcome Centre for Integrative Neuroimaging, FMRIB, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, UK
| | - I Betina Ip
- Wellcome Centre for Integrative Neuroimaging, FMRIB, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, UK
| | - Saad Jbabdi
- Wellcome Centre for Integrative Neuroimaging, FMRIB, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, UK
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Oeltzschner G, Saleh MG, Rimbault D, Mikkelsen M, Chan KL, Puts NAJ, Edden RAE. Advanced Hadamard-encoded editing of seven low-concentration brain metabolites: Principles of HERCULES. Neuroimage 2019; 185:181-190. [PMID: 30296560 PMCID: PMC6289748 DOI: 10.1016/j.neuroimage.2018.10.002] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2018] [Revised: 09/17/2018] [Accepted: 10/01/2018] [Indexed: 11/25/2022] Open
Abstract
PURPOSE To demonstrate the framework of a novel Hadamard-encoded spectral editing approach for simultaneously detecting multiple low-concentration brain metabolites in vivo at 3T. METHODS HERCULES (Hadamard Editing Resolves Chemicals Using Linear-combination Estimation of Spectra) is a four-step Hadamard-encoded editing scheme. 20-ms editing pulses are applied at: (A) 4.58 and 1.9 ppm; (B) 4.18 and 1.9 ppm; (C) 4.58 ppm; and (D) 4.18 ppm. Edited signals from γ-aminobutyric acid (GABA), glutathione (GSH), ascorbate (Asc), N-acetylaspartate (NAA), N-acetylaspartylglutamate (NAAG), aspartate (Asp), lactate (Lac), and likely 2-hydroxyglutarate (2-HG) are separated with reduced signal overlap into distinct Hadamard combinations: (A+B+C+D); (A+B-C-D); and (A-B+C-D). HERCULES uses a novel multiplexed linear-combination modeling approach, fitting all three Hadamard combinations at the same time, maximizing the amount of information used for model parameter estimation, in order to quantify the levels of these compounds. Fitting also allows estimation of the levels of total choline (tCho), myo-inositol (Ins), glutamate (Glu), and glutamine (Gln). Quantitative HERCULES results were compared between two grey- and white-matter-rich brain regions (11 min acquisition time each) in 10 healthy volunteers. Coefficients of variation (CV) of quantified measurements from the HERCULES fitting approach were compared against those from a single-spectrum fitting approach, and against estimates from short-TE PRESS data. RESULTS HERCULES successfully segregates overlapping resonances into separate Hadamard combinations, allowing for the estimation of levels of seven coupled metabolites that would usually require a single 11-min editing experiment each. Metabolite levels and CVs agree well with published values. CVs of quantified measurements from the multiplexed HERCULES fitting approach outperform single-spectrum fitting and short-TE PRESS for most of the edited metabolites, performing only slightly to moderately worse than the fitting method that gives the lowest CVs for tCho, NAA, NAAG, and Asp. CONCLUSION HERCULES is a new experimental approach with the potential for simultaneous editing and multiplexed fitting of up to seven coupled low-concentration and six high-concentration metabolites within a single 11-min acquisition at 3T.
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Affiliation(s)
- Georg Oeltzschner
- Russell H. Morgan Department of Radiology and Radiological Science, The Johns Hopkins University School of Medicine, Baltimore, MD, United States; F. M. Kirby Research Center for Functional Brain Imaging, Kennedy Krieger Institute, Baltimore, MD, United States.
| | - Muhammad G Saleh
- Russell H. Morgan Department of Radiology and Radiological Science, The Johns Hopkins University School of Medicine, Baltimore, MD, United States; F. M. Kirby Research Center for Functional Brain Imaging, Kennedy Krieger Institute, Baltimore, MD, United States
| | - Daniel Rimbault
- Medical Imaging Research Unit, Division of Biomedical Engineering, Department of Human Biology, University of Cape Town, Cape Town, South Africa
| | - Mark Mikkelsen
- Russell H. Morgan Department of Radiology and Radiological Science, The Johns Hopkins University School of Medicine, Baltimore, MD, United States; F. M. Kirby Research Center for Functional Brain Imaging, Kennedy Krieger Institute, Baltimore, MD, United States
| | - Kimberly L Chan
- Russell H. Morgan Department of Radiology and Radiological Science, The Johns Hopkins University School of Medicine, Baltimore, MD, United States; F. M. Kirby Research Center for Functional Brain Imaging, Kennedy Krieger Institute, Baltimore, MD, United States; Department of Bioengineering, The Johns Hopkins University School of Medicine, Baltimore, MD, United States
| | - Nicolaas A J Puts
- Russell H. Morgan Department of Radiology and Radiological Science, The Johns Hopkins University School of Medicine, Baltimore, MD, United States; F. M. Kirby Research Center for Functional Brain Imaging, Kennedy Krieger Institute, Baltimore, MD, United States
| | - Richard A E Edden
- Russell H. Morgan Department of Radiology and Radiological Science, The Johns Hopkins University School of Medicine, Baltimore, MD, United States; F. M. Kirby Research Center for Functional Brain Imaging, Kennedy Krieger Institute, Baltimore, MD, United States
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Jensen JE, Auerbach RP, Pisoni A, Pizzagalli DA. Localized MRS reliability of in vivo glutamate at 3 T in shortened scan times: a feasibility study. NMR IN BIOMEDICINE 2017; 30:10.1002/nbm.3771. [PMID: 28731544 PMCID: PMC5774335 DOI: 10.1002/nbm.3771] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/01/2017] [Revised: 06/05/2017] [Accepted: 06/06/2017] [Indexed: 05/22/2023]
Abstract
Glutamate is the prime excitatory neurotransmitter in the mammalian brain and has been implicated in a wide range of psychiatric conditions. To improve the applicability and clinical reach of magnetic resonance spectroscopy (MRS), research is needed to develop shortened, yet reliable, MRS scanning procedures for standard 1.5-3-T clinical magnetic resonance imaging (MRI) systems, particularly with young or vulnerable populations unable to tolerate longer protocols. To this end, we evaluated the test-retest reliability of a shortened J-resolved MRS sequence in healthy adolescents (n = 22) aged 12-14 years. Participants underwent a series of sequential 6-min MRS scans, with the participants remaining in situ between successive scans. Glutamate and other metabolites were acquired from the rostral anterior cingulate cortex, as glutamatergic function in this region has been implicated in a number of psychiatric illnesses. Thirteen neurochemicals were quantified as ratios to total creatine, and reliability scores were expressed as the percentage difference between the two scans for each metabolite. Test-retest assessment of glutamate was reliable, as scores were less than 10% different (7.1 ± 4.2%), and glutamate values across scans were significantly correlated (Pearson r = 0.680, p < 10-4 ). Several other neurochemicals demonstrated satisfactory reliability, including choline (Cho) (7.4 ± 5.6%), glutathione (GSH) (8.6 ± 4.1%), myo-inositol (mI) (6.5 ± 7.1%) and N-acetylaspartate (NAA) (3.5 ± 3.6%), with test-retest correlations ranging from 0.747 to 0.953. A number of metabolites, however, did not demonstrate acceptable test-retest reliability using the current J-resolved MRS sequence, ranging from 13.8 ± 13.7% (aspartate, Asp) to 45.9 ± 38.3% (glycine, Gly). Collectively, test-retest analyses suggest that clinically viable quantitative data can be obtained on standard MRI systems for glutamate, as well as the other metabolites, during short scan times in a traditionally challenging brain region.
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Affiliation(s)
- J. Eric Jensen
- McLean Imaging Center, McLean Hospital
- Harvard Medical School
| | - Randy P. Auerbach
- Center for Anxiety and Stress Research, McLean Hospital
- Harvard Medical School
| | - Angela Pisoni
- Center for Anxiety and Stress Research, McLean Hospital
- Harvard Medical School
| | - Diego A. Pizzagalli
- McLean Imaging Center, McLean Hospital
- Center for Anxiety and Stress Research, McLean Hospital
- Harvard Medical School
- Address correspondence to: Diego A. Pizzagalli, Ph.D., McLean Hospital/Harvard Medical School, Mailstop 331, 115 Mill Street, Belmont, MA 02478-9106;
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Harris AD, Saleh MG, Edden RAE. Edited 1 H magnetic resonance spectroscopy in vivo: Methods and metabolites. Magn Reson Med 2017; 77:1377-1389. [PMID: 28150876 PMCID: PMC5352552 DOI: 10.1002/mrm.26619] [Citation(s) in RCA: 118] [Impact Index Per Article: 16.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2016] [Revised: 12/30/2016] [Accepted: 12/30/2016] [Indexed: 12/13/2022]
Abstract
The Proton magnetic resonance (1 H-MRS) spectrum contains information about the concentration of tissue metabolites within a predefined region of interest (a voxel). The conventional spectrum in some cases obscures information about less abundant metabolites due to limited separation and complex splitting of the metabolite peaks. One method to detect these metabolites is to reduce the complexity of the spectrum using editing. This review provides an overview of the one-dimensional editing methods available to interrogate these obscured metabolite peaks. These methods include sequence optimizations, echo-time averaging, J-difference editing methods (single BASING, dual BASING, and MEGA-PRESS), constant-time PRESS, and multiple quantum filtering. It then provides an overview of the brain metabolites whose detection can benefit from one or more of these editing approaches, including ascorbic acid, γ-aminobutyric acid, lactate, aspartate, N-acetyl aspartyl glutamate, 2-hydroxyglutarate, glutathione, glutamate, glycine, and serine. Magn Reson Med 77:1377-1389, 2017. © 2017 International Society for Magnetic Resonance in Medicine.
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Affiliation(s)
- Ashley D Harris
- Department of Radiology, University of Calgary, Calgary, AB T2N 1N4, Canada
- Child and Adolescent Imaging Research (CAIR) Program, Alberta Children's Hospital Research Institute, University of Calgary, Calgary, AB T3B 6A9, Canada
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB T2N 1N4, Canada
| | - Muhammad G Saleh
- Russell H. Morgan Department of Radiology and Radiological Science, The Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- F.M. Kirby Center for Functional Brain Imaging, Kennedy Krieger Institute, Baltimore, MD 21205, USA
| | - Richard A E Edden
- Russell H. Morgan Department of Radiology and Radiological Science, The Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- F.M. Kirby Center for Functional Brain Imaging, Kennedy Krieger Institute, Baltimore, MD 21205, USA
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Goryawala MZ, Sheriff S, Maudsley AA. Regional distributions of brain glutamate and glutamine in normal subjects. NMR IN BIOMEDICINE 2016; 29:1108-16. [PMID: 27351339 PMCID: PMC4962701 DOI: 10.1002/nbm.3575] [Citation(s) in RCA: 49] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2016] [Revised: 05/19/2016] [Accepted: 05/20/2016] [Indexed: 05/06/2023]
Abstract
Glutamate (Glu) and glutamine (Gln) play an important role in neuronal regulation and are of value as MRS-observable diagnostic biomarkers. In this study the relative concentrations of these metabolites have been measured in multiple regions in the normal brain using a short-TE whole-brain MRSI measurement at 3 T combined with a modified data analysis approach that used spatial averaging to obtain high-SNR spectra from atlas-registered anatomic regions or interest. By spectral fitting of high-SNR spectra this approach yielded reliable measurements across a wide volume of the brain. Spectral averaging also demonstrated increased SNR and improved fitting accuracy for the sum of Glu and Gln (Glx) compared with individual voxel fitting. Results in 26 healthy controls showed relatively constant Glu/Cr and Gln/Cr throughout the cerebrum, although with increased values in the anterior cingulum and paracentral lobule, and increased Gln/Cr in the superior motor area. The deep gray-matter regions of thalamus, putamen, and pallidum show lower Glu/Cr compared with cortical white-matter regions. Lobar measurements demonstrated reduced Glu/Cr and Gln/Cr in the cerebellum as compared with the cerebrum, where white-matter regions show significantly lower Glu/Cr and Gln/Cr as compared with gray-matter regions across multiple brain lobes. Regression analysis showed no significant effect of gender on Glu/Cr or Gln/Cr measurement; however, Glx/Cr ratio was found to be significantly negatively correlated with age in some lobar brain regions. In summary, this methodology provides the spectral quality necessary for reliable separation of Glu and Gln at 3 T from a single MRSI acquisition enabling generation of regional distributions of metabolites over a large volume of the brain, including cortical regions. Copyright © 2016 John Wiley & Sons, Ltd.
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Iqbal Z, Wilson NE, Thomas MA. 3D spatially encoded and accelerated TE-averaged echo planar spectroscopic imaging in healthy human brain. NMR IN BIOMEDICINE 2016; 29:329-339. [PMID: 26748673 DOI: 10.1002/nbm.3469] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2015] [Revised: 11/17/2015] [Accepted: 11/23/2015] [Indexed: 06/05/2023]
Abstract
Several different pathologies, including many neurodegenerative disorders, affect the energy metabolism of the brain. Glutamate, a neurotransmitter in the brain, can be used as a biomarker to monitor these metabolic processes. One method that is capable of quantifying glutamate concentration reliably in several regions of the brain is TE-averaged (1) H spectroscopic imaging. However, this type of method requires the acquisition of multiple TE lines, resulting in long scan durations. The goal of this experiment was to use non-uniform sampling, compressed sensing reconstruction and an echo planar readout gradient to reduce the scan time by a factor of eight to acquire TE-averaged spectra in three spatial dimensions. Simulation of glutamate and glutamine showed that the 2.2-2.4 ppm spectral region contained 95% glutamate signal using the TE-averaged method. Peak integration of this spectral range and home-developed, prior-knowledge-based fitting were used for quantitation. Gray matter brain phantom measurements were acquired on a Siemens 3 T Trio scanner. Non-uniform sampling was applied retrospectively to these phantom measurements and quantitative results of glutamate with respect to creatine 3.0 (Glu/Cr) ratios showed a coefficient of variance of 16% for peak integration and 9% for peak fitting using eight-fold acceleration. In vivo scans of the human brain were acquired as well and five different brain regions were quantified using the prior-knowledge-based algorithm. Glu/Cr ratios from these regions agreed with previously reported results in the literature. The method described here, called accelerated TE-averaged echo planar spectroscopic imaging (TEA-EPSI), is a significant methodological advancement and may be a useful tool for categorizing glutamate changes in pathologies where affected brain regions are not known a priori. Copyright © 2016 John Wiley & Sons, Ltd.
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Affiliation(s)
- Zohaib Iqbal
- Department of Radiological Sciences, University of California Los Angeles, USA
| | - Neil E Wilson
- Department of Radiological Sciences, University of California Los Angeles, USA
| | - M Albert Thomas
- Department of Radiological Sciences, University of California Los Angeles, USA
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On the use of Cramér–Rao minimum variance bounds for the design of magnetic resonance spectroscopy experiments. Neuroimage 2013; 83:1031-40. [DOI: 10.1016/j.neuroimage.2013.07.062] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2013] [Revised: 07/03/2013] [Accepted: 07/23/2013] [Indexed: 11/21/2022] Open
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Ramadan S, Lin A, Stanwell P. Glutamate and glutamine: a review of in vivo MRS in the human brain. NMR IN BIOMEDICINE 2013; 26:1630-46. [PMID: 24123328 PMCID: PMC3849600 DOI: 10.1002/nbm.3045] [Citation(s) in RCA: 182] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2012] [Revised: 08/08/2013] [Accepted: 09/08/2013] [Indexed: 05/21/2023]
Abstract
Our understanding of the roles that the amino acids glutamate (Glu) and glutamine (Gln) play in the mammalian central nervous system has increased rapidly in recent times. Many conditions are known to exhibit a disturbance in Glu-Gln equilibrium, and the exact relationships between these changed conditions and these amino acids are not fully understood. This has led to increased interest in Glu/Gln quantitation in the human brain in an array of conditions (e.g. mental illness, tumor, neuro-degeneration) as well as in normal brain function. Accordingly, this review has been undertaken to describe the increasing number of in vivo techniques available to study Glu and Gln separately, or pooled as 'Glx'. The present MRS methods used to assess Glu and Gln vary in approach, complexity, and outcome, thus the focus of this review is on a description of MRS acquisition approaches, and an indication of relative utility of each technique rather than brain pathologies associated with Glu and/or Gln perturbation. Consequently, this review focuses particularly on (1) one-dimensional (1)H MRS, (2) two-dimensional (1)H MRS, and (3) one-dimensional (13)C MRS techniques.
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Affiliation(s)
- Saadallah Ramadan
- School of Health Sciences, Faculty of Health, Hunter Building, University of Newcastle, Callaghan NSW 2308, Australia
| | - Alexander Lin
- Alexander Lin: Center for Clinical Spectroscopy, Department of Radiology, Brigham and Women’s Hospital, Harvard Medical School, 4 Blackfan Street, HIM-820, Boston MA 02115
| | - Peter Stanwell
- School of Health Sciences, Faculty of Health, Hunter Building, University of Newcastle, Callaghan NSW 2308, Australia
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Joshi G, Biederman J, Wozniak J, Goldin RL, Crowley D, Furtak S, Lukas SE, Gönenç A. Magnetic resonance spectroscopy study of the glutamatergic system in adolescent males with high-functioning autistic disorder: a pilot study at 4T. Eur Arch Psychiatry Clin Neurosci 2013; 263:379-84. [PMID: 22986449 DOI: 10.1007/s00406-012-0369-9] [Citation(s) in RCA: 55] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/05/2012] [Accepted: 09/06/2012] [Indexed: 10/27/2022]
Abstract
The pilot study aimed at examining the neural glutamatergic activity in autism. Seven adolescent males (mean age: 14 ± 1.8; age range: 12-17 years) with intact intellectual capacity (mean IQ: 108 ± 14.26; IQ range: 85-127) suffering from autistic disorder and an equal number of age- and sex-matched healthy controls underwent a two-dimensional magnetic resonance spectroscopy scan at 4T. Results indicated significantly high glutamate (Glu) levels in the anterior cingulate cortex of autistic disorder versus control subjects (paired t test p = 0.01) and a trend for lower Glu in the right medial temporal lobe, which was not statistically different between the groups (paired t test p = 0.06). These preliminary findings support the glutamatergic dysregulation hypothesis in autism and need to be replicated in a larger sample.
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Affiliation(s)
- Gagan Joshi
- Pediatric Psychopharmacology Clinical and Research Program, Massachusetts General Hospital, 55 Fruit Street, YAW 6900, Boston, MA, 02114, USA.
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Hancu I, Port J. The case of the missing glutamine. NMR IN BIOMEDICINE 2011; 24:529-35. [PMID: 21264975 DOI: 10.1002/nbm.1620] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2010] [Revised: 08/13/2010] [Accepted: 08/19/2010] [Indexed: 05/13/2023]
Abstract
A theoretical study was performed to determine the accuracy and repeatability of multiple one-dimensional pulse sequences in the quantification of glutamine concentration at 3 T. Variable repeatability (12% to > 50%) and significant absolute error (-50% to +70%) were noted for the eight pulse sequences considered. Data acquired in vivo using three of the pulse sequences used for simulation matched the predicted repeatability well; among the pulse sequences considered, point-resolved spectroscopy (TE = 80 ms) offered minimal error and acceptable repeatability (12%) for brain glutamine measurements. Following correction for the expected bias of each pulse sequence, consistent glutamine measurements, in the 1-mM range, were reported with the three sequences. An explanation for the mismatch between in vivo (1)H MRS and in vitro (13)C/(1)H MRS at high field was attempted.
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Affiliation(s)
- Ileana Hancu
- GE Global Research Center, Niskayuna, NY 12309, USA.
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Chong DGQ, Kreis R, Bolliger CS, Boesch C, Slotboom J. Two-dimensional linear-combination model fitting of magnetic resonance spectra to define the macromolecule baseline using FiTAID, a Fitting Tool for Arrays of Interrelated Datasets. MAGNETIC RESONANCE MATERIALS IN PHYSICS BIOLOGY AND MEDICINE 2011; 24:147-64. [DOI: 10.1007/s10334-011-0246-y] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2010] [Revised: 02/03/2011] [Accepted: 02/28/2011] [Indexed: 10/18/2022]
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