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Weingärtner S. Magnetic resonance imaging-based ID of the vasculature across the heart-brain axis. Eur Heart J 2023:ehad265. [PMID: 37317653 DOI: 10.1093/eurheartj/ehad265] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 06/16/2023] Open
Affiliation(s)
- Sebastian Weingärtner
- Department of Imaging Physics, Delft University of Technology, Lorentzweg 1, 2628CJ Delft, The Netherlands
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Rotkopf LT, Wehrse E, Kampf T, Vogel P, Schlemmer HP, Ziener CH. Spin echo formation in muscle tissue. Phys Rev E 2021; 104:034419. [PMID: 34654209 DOI: 10.1103/physreve.104.034419] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Accepted: 09/13/2021] [Indexed: 11/07/2022]
Abstract
Determination of the spin echo signal evolution and of transverse relaxation rates is of high importance for microstructural modeling of muscle tissue in magnetic resonance imaging. So far, numerically exact solutions for the NMR signal dynamics in muscle tissue models have been reported only for the gradient echo free induction decay, with spin echo problems usually solved by approximate methods. In this work, we modeled the spin echo signal numerically exact by discretizing the radial dimension of the Bloch-Torrey equation and expanding the angular dependency in terms of even Chebyshev polynomials. This allows us to express the time dependence of the local magnetization as a closed-form matrix expression. Using this method, we were able to accurately capture the spin echo local and total magnetization dynamics. The obtained transverse relaxation rates showed a high concordance with random walker and finite-element simulations. We could demonstrate that in cases of smaller diffusion coefficients, the commonly used strong collision approximation significantly underestimates the true value considerably. Instead, the limiting behavior in this regime is correctly described either by the full solution or by the slow diffusion approximation. Experimentally measured transverse relaxation rates of a mouse limb muscle showed an angular dependence in accordance with the theoretical prediction.
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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, Im Neuenheimer Feld 672, 69120 Heidelberg, Germany
| | - E Wehrse
- Department of Radiology, German Cancer Research Center, Im Neuenheimer Feld 220, 69120 Heidelberg, Germany.,Medical Faculty, Ruprecht-Karls-University Heidelberg, Im Neuenheimer Feld 672, 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
| | - P Vogel
- University of Würzburg, Department of Experimental Physics 5, Am Hubland, 97074 Würzburg, 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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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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