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Rotkopf LT, Buschle LR, Schlemmer HP, Ziener CH. Influence of diffusion on transverse relaxation rates and phases of an ensemble of magnetic spheres. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2022; 341:107259. [PMID: 35779309 DOI: 10.1016/j.jmr.2022.107259] [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: 09/14/2021] [Revised: 05/30/2022] [Accepted: 06/19/2022] [Indexed: 06/15/2023]
Abstract
In quantitative susceptibility mapping, the tissue susceptibility is determined from the magnitude and phase of the gradient echo signal, which is influenced by the interplay of complex susceptibility and diffusion effect. Herein, we analytically analyze the influence of diffusion on magnitude and phase images generated by randomly arranged magnetic spheres as a model of intracerebral iron depositions. We demonstrate that both gradient and spin echo relaxation rate constants have a strong and nonlinear dependence on diffusion strength and give empirical formulas for magnitude and phase. This may be used in the future to improve QSM processing methods. In addition, we show that, in theory, combined acquisitions of gradient and spin echo can be used to determine the dimension of the magnetic spheres and the diffusion strength.
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Affiliation(s)
- L T Rotkopf
- Department of Radiology, German Cancer Research Center, Im Neuenheimer Feld 220, 69120 Heidelberg, Germany; Medical Faculty, Ruprecht-Karls-University Heidelberg, Heidelberg, Germany
| | - L R Buschle
- Department of Radiology, German Cancer Research Center, Im Neuenheimer Feld 220, 69120 Heidelberg, Germany
| | - H-P Schlemmer
- Department of Radiology, German Cancer Research Center, Im Neuenheimer Feld 220, 69120 Heidelberg, Germany
| | - C H Ziener
- Department of Radiology, German Cancer Research Center, Im Neuenheimer Feld 220, 69120 Heidelberg, Germany.
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2
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Voxel-size dependent quantitative susceptibility mapping of blood vessel networks: A simulation study. Z Med Phys 2019; 29:282-291. [DOI: 10.1016/j.zemedi.2018.09.002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2018] [Revised: 08/23/2018] [Accepted: 09/18/2018] [Indexed: 11/22/2022]
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3
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Ziener CH, Kampf T, Schlemmer HP, Buschle LR. Spin echoes: full numerical solution and breakdown of approximative solutions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:155101. [PMID: 30641507 DOI: 10.1088/1361-648x/aafe21] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The spin echo signal from vessels in Krogh's capillary model as well in the random distribution vessel model are studied by numerically solving the Bloch-Torrey equation. A comparison is made with the Gaussian local phase approximation, the Gaussian phase approximation and the strong-collision approximation. Differences between the Gaussian local phase approximation and the Gaussian phase approximation are explained. In the intermediate diffusion regime, the full numerical solution shows oscillations which are absent in any of the approximate solutions. In the limit of large diffusion coefficients, where the approximations become exact, the signal shows a linear-exponential decay governed by a single parameter. The features of the exact numerical solution can be explained by an analytically solvable discrete two-level model. There is a one-to-one correspondence between the different diffusion regimes and the three cases of the damped harmonic oscillator.
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Affiliation(s)
- C H Ziener
- German Cancer Research Center DKFZ, E010 Radiology, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany. University Hospital Heidelberg, Neuroradiology, Im Neuenheimer Feld 400, 69120 Heidelberg, Germany
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Ziener CH, Kampf T, Kurz FT, Schlemmer HP, Buschle LR. Pseudo-diffusion effects in lung MRI. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2019; 299:1-11. [PMID: 30529849 DOI: 10.1016/j.jmr.2018.11.015] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2018] [Revised: 11/27/2018] [Accepted: 11/28/2018] [Indexed: 06/09/2023]
Abstract
Magnetic resonance imaging of lung tissue is strongly influenced by susceptibility effects between spin-bearing water molecules and air-filled alveoli. The measured lineshape, however, also depends on the interplay between susceptibility effects and blood-flow around alveoli that can be approximated as pseudo-diffusion. Both effects are quantitatively described by the Bloch-Torrey-equation, which was so far only solved for dephasing on the alveolar surface. In this work, we extend this model to the whole range of physiological relevant air volume fractions. The results agree very well with in vivo measurements in human lung tissue.
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Affiliation(s)
- C H Ziener
- German Cancer Research Center - DKFZ, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany; Heidelberg University Hospital, Im Neuenheimer Feld 400, 69120 Heidelberg, Germany
| | - T Kampf
- University of Würzburg, Department of Experimental Physics 5, Am Hubland, 97074 Würzburg, Germany; Würzburg University Hospital, Department of Neuroradiology, Josef-Schneider-Straße 11, 97080 Würzburg, Germany
| | - F T Kurz
- German Cancer Research Center - DKFZ, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany; Heidelberg University Hospital, Im Neuenheimer Feld 400, 69120 Heidelberg, Germany
| | - H P Schlemmer
- German Cancer Research Center - DKFZ, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany
| | - L R Buschle
- German Cancer Research Center - DKFZ, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany; Heidelberg University Hospital, Im Neuenheimer Feld 400, 69120 Heidelberg, Germany; Heidelberg University, Faculty of Physics and Astronomy, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany.
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Auer TA, Breit HC, Marini F, Renovanz M, Ringel F, Sommer CJ, Brockmann MA, Tanyildizi Y. Evaluation of the apparent diffusion coefficient in patients with recurrent glioblastoma under treatment with bevacizumab with radiographic pseudoresponse. J Neuroradiol 2018; 46:36-43. [PMID: 29733920 DOI: 10.1016/j.neurad.2018.04.002] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Revised: 03/16/2018] [Accepted: 04/21/2018] [Indexed: 12/30/2022]
Abstract
BACKGROUND Response Assessment in Neuro-Oncology Criteria (RANO), are used to asses response to first-line treatment of glioblastoma (GBM). Differentiation between response and pseudoresponse under treatment with Bevacizumab (BVZ) remains challenging. This study evaluates ADC changes in patients with radiographic pseudoresponse under treatment with (BVZ). METHODS Patients (n=40) with recurrent GBM under-treatment with BVZ underwent MRI before, two and four months after treatment with BVZ. In patients with radiological pseudoresponse (n=11), ADC analyses were performed. Areas with decreasing T1 contrast enhancement (CE) and FLAIR signal decrease were manually selected and compared to size and position matched healthy contralateral brain parenchyma. RESULTS Histogram based ADC (10-6×mm2/s) of these patients decreased significantly (P<0.005) from baseline MRI (T1-CE, FLAIR: 1124.9±160.3, 1098.4±226.2, respectively) to 2months (781.3±110.7, 783.3±103.3) and remained stable during 4months (777.0±138.5, 784.4±155.4, all mean±1 SD), despite progressive disease. Mean ADC values of the healthy contralateral brain tissue remained stable (P>0.05) (ADC values: baseline: 786.2±110.7, 2months: 781.1±76.2, 4months: 804.1±86.2). CONCLUSION Treatment of GBM with BVZ leads to a decrease of ADC values in areas of pre-treatment T1-CE/FLAIR signal hyperintensity to levels of comparable with normal brain tissue. ADC values remained stable, even when progressive tumor growth was reported.
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Affiliation(s)
- Timo A Auer
- University Medical Center, Department of Neuroradiology, Johannes Gutenberg-University Mainz, Langenbeckstr. 1, 55131 Mainz, Germany; University Medical Center-Charité, Department of Radiology, Berlin, Germany
| | - Hanns-Christian Breit
- University Medical Center, Department of Neuroradiology, Johannes Gutenberg-University Mainz, Langenbeckstr. 1, 55131 Mainz, Germany
| | - Federico Marini
- University Medical Center, Institute of Medical Biostatistics, Epidemiology and Informatics (IMBEI), Mainz, Germany
| | - Mirjam Renovanz
- University Medical Center, Department of Neurosurgery, Mainz, Germany
| | - Florian Ringel
- University Medical Center, Department of Neurosurgery, Mainz, Germany
| | - Clemens J Sommer
- Institute of Neuropathology, University Medical Center Mainz, Germany
| | - Marc A Brockmann
- University Medical Center, Department of Neuroradiology, Johannes Gutenberg-University Mainz, Langenbeckstr. 1, 55131 Mainz, Germany
| | - Yasemin Tanyildizi
- University Medical Center, Department of Neuroradiology, Johannes Gutenberg-University Mainz, Langenbeckstr. 1, 55131 Mainz, Germany.
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Vessel radius mapping in an extended model of transverse relaxation. MAGNETIC RESONANCE MATERIALS IN PHYSICS BIOLOGY AND MEDICINE 2018; 31:531-551. [DOI: 10.1007/s10334-018-0677-9] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2017] [Revised: 01/14/2018] [Accepted: 01/15/2018] [Indexed: 10/18/2022]
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7
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Kurz F, Ziener C, Rückl M, Hahn A, Sturm V, Zhang K, Buschle L, Bendszus M, Heiland S, Schlemmer H, Bauer W, Kampf T. The influence of spatial patterns of capillary networks on transverse relaxation. Magn Reson Imaging 2017; 40:31-47. [DOI: 10.1016/j.mri.2017.03.012] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2017] [Revised: 03/28/2017] [Accepted: 03/30/2017] [Indexed: 11/16/2022]
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Kurz FT, Buschle LR, Kampf T, Zhang K, Schlemmer HP, Heiland S, Bendszus M, Ziener CH. Spin dephasing in a magnetic dipole field around large capillaries: Approximative and exact results. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2016; 273:83-97. [PMID: 27794269 DOI: 10.1016/j.jmr.2016.10.012] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2016] [Revised: 10/17/2016] [Accepted: 10/18/2016] [Indexed: 06/06/2023]
Abstract
We present an analytical solution of the Bloch-Torrey equation for local spin dephasing in the magnetic dipole field around a capillary and for ensembles of capillaries, and adapt this solution for the study of spin dephasing around large capillaries. In addition, we provide a rigorous mathematical derivation of the slow diffusion approximation for the spin-bearing particles that is used in this regime. We further show that, in analogy to the local magnetization, the transverse magnetization of one MR imaging voxel in the regime of static dephasing (where diffusion effects are not considered) is merely the first term of a series expansion that constitutes the signal in the slow diffusion approximation. Theoretical results are in agreement with experimental data for capillaries in rat muscle at 7T.
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Affiliation(s)
- F T Kurz
- Heidelberg University Hospital, INF 400, D-69120 Heidelberg, Germany; German Cancer Research Center, INF 280, D-69120 Heidelberg, Germany.
| | - L R Buschle
- German Cancer Research Center, INF 280, D-69120 Heidelberg, Germany
| | - T Kampf
- University of Würzburg, Am Hubland, D-97074 Würzburg, Germany
| | - K Zhang
- German Cancer Research Center, INF 280, D-69120 Heidelberg, Germany
| | - H P Schlemmer
- German Cancer Research Center, INF 280, D-69120 Heidelberg, Germany
| | - S Heiland
- Heidelberg University Hospital, INF 400, D-69120 Heidelberg, Germany
| | - M Bendszus
- Heidelberg University Hospital, INF 400, D-69120 Heidelberg, Germany
| | - C H Ziener
- Heidelberg University Hospital, INF 400, D-69120 Heidelberg, Germany; German Cancer Research Center, INF 280, D-69120 Heidelberg, Germany
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9
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CPMG relaxation rate dispersion in dipole fields around capillaries. Magn Reson Imaging 2016; 34:875-88. [DOI: 10.1016/j.mri.2016.03.016] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2015] [Revised: 03/23/2016] [Accepted: 03/27/2016] [Indexed: 11/22/2022]
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10
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Kurz FT, Kampf T, Buschle LR, Schlemmer HP, Heiland S, Bendszus M, Ziener CH. Microstructural Analysis of Peripheral Lung Tissue through CPMG Inter-Echo Time R2 Dispersion. PLoS One 2015; 10:e0141894. [PMID: 26544068 PMCID: PMC4636373 DOI: 10.1371/journal.pone.0141894] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2015] [Accepted: 10/14/2015] [Indexed: 11/25/2022] Open
Abstract
Since changes in lung microstructure are important indicators for (early stage) lung pathology, there is a need for quantifiable information of diagnostically challenging cases in a clinical setting, e.g. to evaluate early emphysematous changes in peripheral lung tissue. Considering alveoli as spherical air-spaces surrounded by a thin film of lung tissue allows deriving an expression for Carr-Purcell-Meiboom-Gill transverse relaxation rates R2 with a dependence on inter-echo time, local air-tissue volume fraction, diffusion coefficient and alveolar diameter, within a weak field approximation. The model relaxation rate exhibits the same hyperbolic tangent dependency as seen in the Luz-Meiboom model and limiting cases agree with Brooks et al. and Jensen et al. In addition, the model is tested against experimental data for passively deflated rat lungs: the resulting mean alveolar radius of RA = 31.46 ± 13.15 μm is very close to the literature value (∼34 μm). Also, modeled radii obtained from relaxometer measurements of ageing hydrogel foam (that mimics peripheral lung tissue) are in good agreement with those obtained from μCT images of the same foam (mean relative error: 0.06 ± 0.01). The model’s ability to determine the alveolar radius and/or air volume fraction will be useful in quantifying peripheral lung microstructure.
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Affiliation(s)
- Felix T. Kurz
- Department of Neuroradiology, Heidelberg University, Heidelberg, Germany
- Department of Radiology, German Cancer Research Center, Heidelberg, Germany
- * E-mail:
| | - Thomas Kampf
- Department of Experimental Physics 5, Würzburg University, Würzburg, Germany
| | - Lukas R. Buschle
- Department of Radiology, German Cancer Research Center, Heidelberg, Germany
| | | | - Sabine Heiland
- Department of Neuroradiology, Heidelberg University, Heidelberg, Germany
| | - Martin Bendszus
- Department of Neuroradiology, Heidelberg University, Heidelberg, Germany
| | - Christian H. Ziener
- Department of Neuroradiology, Heidelberg University, Heidelberg, Germany
- Department of Radiology, German Cancer Research Center, Heidelberg, Germany
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11
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Buschle LR, Kurz FT, Kampf T, Triphan SM, Schlemmer HP, Ziener CH. Diffusion-mediated dephasing in the dipole field around a single spherical magnetic object. Magn Reson Imaging 2015; 33:1126-1145. [DOI: 10.1016/j.mri.2015.06.001] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2014] [Revised: 05/21/2015] [Accepted: 06/20/2015] [Indexed: 10/23/2022]
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12
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Ziener CH, Kurz FT, Kampf T. Free induction decay caused by a dipole field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032707. [PMID: 25871144 DOI: 10.1103/physreve.91.032707] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2014] [Indexed: 06/04/2023]
Abstract
We analyze the free induction decay of nuclear spins under the influence of restricted diffusion in a magnetic dipole field around cylindrical objects. In contrast to previous publications no restrictions or simplifications concerning the diffusion process are made. By directly solving the Bloch-Torrey equation, analytical expressions for the magnetization are given in terms of an eigenfunction expansion. The field strength-dependent complex nature of the eigenvalue spectrum significantly influences the shape of the free induction decay. As the dipole field is the lowest order of the multipole expansion, the obtained results are important for understanding fundamental mechanisms of spin dephasing in many other applied fields of nuclear magnetic resonance such as biophysics or material science. The analytical methods are applied to interpret the spin dephasing in the free induction decay in cardiac muscle and skeletal muscle. A simple expression for the relevant transverse relaxation time is found in terms of the underlying microscopic parameters of the muscle tissue. The analytical results are in agreement with experimental data. These findings are important for the correct interpretation of magnetic resonance images for clinical diagnosis at all magnetic field strengths and therapy of cardiovascular diseases.
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Affiliation(s)
- C H Ziener
- German Cancer Research Center-DKFZ, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany
- Heidelberg University, Department of Neuroradiology, Im Neuenheimer Feld 400, 69120 Heidelberg, Germany
| | - F T Kurz
- German Cancer Research Center-DKFZ, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany
- Heidelberg University, Department of Neuroradiology, Im Neuenheimer Feld 400, 69120 Heidelberg, Germany
| | - T Kampf
- University of Würzburg, Department of Experimental Physics 5, Am Hubland, 97074 Würzburg, Germany
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13
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Kurz FT, Kampf T, Heiland S, Bendszus M, Schlemmer HP, Ziener CH. Theoretical model of the single spin-echo relaxation time for spherical magnetic perturbers. Magn Reson Med 2014; 71:1888-95. [DOI: 10.1002/mrm.25196] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2013] [Revised: 02/07/2014] [Accepted: 02/07/2014] [Indexed: 02/01/2023]
Affiliation(s)
- Felix T. Kurz
- Division of Neuroradiology, Department of Neurology; University of Heidelberg; INF 400 69120 Heidelberg Germany
| | - Thomas Kampf
- Department of Experimental Physics 5; University of Würzburg; Am Hubland 97074 Würzburg Germany
| | - Sabine Heiland
- Division of Neuroradiology, Department of Neurology; University of Heidelberg; INF 400 69120 Heidelberg Germany
| | - Martin Bendszus
- Division of Neuroradiology, Department of Neurology; University of Heidelberg; INF 400 69120 Heidelberg Germany
| | - Heinz-Peter Schlemmer
- Department of Radiology (E010); German Cancer Research Center; INF 280 69120 Heidelberg Germany
| | - Christian H. Ziener
- Department of Radiology (E010); German Cancer Research Center; INF 280 69120 Heidelberg Germany
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14
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Lutz K, Wiestler B, Graf M, Bäumer P, Floca R, Schlemmer HP, Heiland S, Wick W, Bendszus M, Radbruch A. Infiltrative patterns of glioblastoma: Identification of tumor progress using apparent diffusion coefficient histograms. J Magn Reson Imaging 2013; 39:1096-103. [DOI: 10.1002/jmri.24258] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2013] [Accepted: 05/15/2013] [Indexed: 11/05/2022] Open
Affiliation(s)
- Kira Lutz
- Department of Neuroradiology; University of Heidelberg, Medical Center; Heidelberg Germany
| | - Benedikt Wiestler
- Department of Neurooncology; University of Heidelberg, Medical Center; Heidelberg Germany
| | - Markus Graf
- German Cancer Research Center Heidelberg; Department for Radiology; Heidelberg Germany
| | - Philipp Bäumer
- Department of Neuroradiology; University of Heidelberg, Medical Center; Heidelberg Germany
| | - Ralf Floca
- German Cancer Research Center Heidelberg; Department for Radiology; Heidelberg Germany
| | - Heinz-Peter Schlemmer
- German Cancer Research Center Heidelberg; Department for Radiology; Heidelberg Germany
| | - Sabine Heiland
- Department of Neuroradiology; University of Heidelberg, Medical Center; Heidelberg Germany
| | - Wolfgang Wick
- Department of Neurooncology; University of Heidelberg, Medical Center; Heidelberg Germany
| | - Martin Bendszus
- Department of Neuroradiology; University of Heidelberg, Medical Center; Heidelberg Germany
| | - Alexander Radbruch
- Department of Neuroradiology; University of Heidelberg, Medical Center; Heidelberg Germany
- German Cancer Research Center Heidelberg; Neuro-oncologic Imaging (E012) Heidelberg Germany
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15
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Zuo Z, Wang R, Zhuo Y, Xue R, St Lawrence KS, Wang DJJ. Turbo-FLASH based arterial spin labeled perfusion MRI at 7 T. PLoS One 2013; 8:e66612. [PMID: 23818950 PMCID: PMC3688599 DOI: 10.1371/journal.pone.0066612] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2013] [Accepted: 05/08/2013] [Indexed: 12/04/2022] Open
Abstract
Motivations of arterial spin labeling (ASL) at ultrahigh magnetic fields include prolonged blood T1 and greater signal-to-noise ratio (SNR). However, increased B0 and B1 inhomogeneities and increased specific absorption ratio (SAR) challenge practical ASL implementations. In this study, Turbo-FLASH (Fast Low Angle Shot) based pulsed and pseudo-continuous ASL sequences were performed at 7T, by taking advantage of the relatively low SAR and short TE of Turbo-FLASH that minimizes susceptibility artifacts. Consistent with theoretical predictions, the experimental data showed that Turbo-FLASH based ASL yielded approximately 4 times SNR gain at 7T compared to 3T. High quality perfusion images were obtained with an in-plane spatial resolution of 0.85×1.7 mm2. A further functional MRI study of motor cortex activation precisely located the primary motor cortex to the precentral gyrus, with the same high spatial resolution. Finally, functional connectivity between left and right motor cortices as well as supplemental motor area were demonstrated using resting state perfusion images. Turbo-FLASH based ASL is a promising approach for perfusion imaging at 7T, which could provide novel approaches to high spatiotemporal resolution fMRI and to investigate the functional connectivity of brain networks at ultrahigh field.
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Affiliation(s)
- Zhentao Zuo
- State Key Laboratory of Brain and Cognitive Science, Institute of Biophysics, Chinese Academy of Sciences, Beijing, China.
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16
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Ziener CH, Kampf T, Jakob PM, Bauer WR. Diffusion effects on the CPMG relaxation rate in a dipolar field. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2010; 202:38-42. [PMID: 19853483 DOI: 10.1016/j.jmr.2009.09.016] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2009] [Revised: 09/15/2009] [Accepted: 09/26/2009] [Indexed: 05/28/2023]
Abstract
The diffusion in the magnetic dipolar field around a sphere is considered. The diffusion is restricted to the space between two concentric spheres, where the inner sphere is the source of the magnetic dipolar field. Analytical expressions for the CPMG transverse relaxation rate as well as the free induction decay and the spin echo time evolution are given in the Gaussian approximation. The influence of the inter-echo time is analyzed. The limiting cases of small and large inter-echo times as well as the short and long time behavior are evaluated.
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Affiliation(s)
- C H Ziener
- Julius-Maximilians-Universität Würzburg, Lehrstuhl für Experimentelle Physik 5, Würzburg, Germany.
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17
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Ziener CH, Glutsch S, Jakob PM, Bauer WR. Spin dephasing in the dipole field around capillaries and cells: numerical solution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:046701. [PMID: 19905476 DOI: 10.1103/physreve.80.046701] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2009] [Indexed: 05/28/2023]
Abstract
We numerically solve the Bloch-Torrey equation by discretizing the differential operators in real space using finite differences. The differential equation is either solved directly in time domain as initial-value problem or in frequency domain as boundary-value problem. Especially the solution in time domain is highly efficient and suitable for arbitrary domains and dimensions. As examples, we calculate the average magnetization and the frequency distribution for capillaries and cells which are idealized as cylinders and spheres, respectively. The solution is compared with the commonly used Gaussian approximation and the strong-collision approximation. While these approximations become exact in limiting cases (small or large diffusion coefficient), they strongly deviate from the numerical solution for intermediate values of the diffusion coefficient.
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Affiliation(s)
- C H Ziener
- Julius-Maximilians-Universität Würzburg, Lehrstuhl für Experimentelle Physik 5, Würzburg, Germany
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18
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Ziener CH, Kampf T, Herold V, Jakob PM, Bauer WR, Nadler W. Frequency autocorrelation function of stochastically fluctuating fields caused by specific magnetic field inhomogeneities. J Chem Phys 2008; 129:014507. [DOI: 10.1063/1.2949097] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Marques JP, Bowtell RW. Using forward calculations of the magnetic field perturbation due to a realistic vascular model to explore the BOLD effect. NMR IN BIOMEDICINE 2008; 21:553-565. [PMID: 18078307 DOI: 10.1002/nbm.1224] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
This paper assesses the reliability of the infinite cylinder model used previously in the literature to simulate blood oxygenation level dependent (BOLD) signal changes. A three-dimensional finite element method was applied to a realistic model of the cortical vasculature, and the results compared with those generated from a simple model of the vasculature as a set of independent, randomly oriented, infinite cylinders. The realistic model is based on scanning electron microscopy measurements of the terminal vascular bed in the superficial cortex of the rat. Good agreement is found between the two models with regard to the extravascular R(2)* and R(2) dependence on the cerebral blood volume and blood oxygenation fraction. Using the realistic model, it is also possible to gain further understanding of the relative importance of intravascular and extravascular BOLD contrast. A simple parameterisation of the dependence of the relaxation rates on relative cerebral blood volume and blood-tissue susceptibility difference was carried out, allowing discussion of the variation in the form of the haemodynamic response with field strength.
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Affiliation(s)
- José P Marques
- Visual Neuroscience Laboratory, IBILI, University of Coimbra, Portugal.
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Ziener CH, Kampf T, Melkus G, Herold V, Weber T, Reents G, Jakob PM, Bauer WR. Local frequency density of states around field inhomogeneities in magnetic resonance imaging: effects of diffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:031915. [PMID: 17930279 DOI: 10.1103/physreve.76.031915] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2006] [Revised: 04/27/2007] [Indexed: 05/25/2023]
Abstract
A method describing NMR-signal formation in inhomogeneous tissue is presented which covers all diffusion regimes. For this purpose, the frequency distribution inside the voxel is described. Generalizing the results of the well-known static dephasing regime, we derive a formalism to describe the frequency distribution that is valid over the whole dynamic range. The expressions obtained are in agreement with the results obtained from Kubos line-shape theory. To examine the diffusion effects, we utilize a strong collision approximation, which replaces the original diffusion process by a simpler stochastic dynamics. We provide a generally valid relation between the frequency distribution and the local Larmor frequency inside the voxel. To demonstrate the formalism we give analytical expressions for the frequency distribution and the free induction decay in the case of cylindrical and spherical magnetic inhomogeneities. For experimental verification, we performed measurements using a single-voxel spectroscopy method. The data obtained for the frequency distribution, as well as the magnetization decay, are in good agreement with the analytic results, although experiments were limited by magnetic field gradients caused by an imperfect shim and low signal-to-noise ratio.
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Affiliation(s)
- C H Ziener
- Julius-Maximilians-Universität Würzburg, Lehrstuhl für Experimentelle Physik 5, Am Hubland, 97074 Würzburg, Germany
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