Spin echoes: full numerical solution and breakdown of approximative solutions
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 appro...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
21 February 2019
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| In: |
Journal of physics. Condensed matter
Year: 2019, Volume: 31, Issue: 15 |
| ISSN: | 1361-648X |
| DOI: | 10.1088/1361-648X/aafe21 |
| Online Access: | Verlag, Volltext: https://doi.org/10.1088/1361-648X/aafe21 Verlag, Volltext: https://iopscience.iop.org/article/10.1088/1361-648X/aafe21 
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| Author Notes: | C.H. Ziener, T. Kampf, H.-P. Schlemmer and L.R. Buschle |
| Summary: | 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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| Item Description: | Gesehen am 05.08.2019 |
| Physical Description: | Online Resource |
| ISSN: | 1361-648X |
| DOI: | 10.1088/1361-648X/aafe21 |