| Title:
|
Time delay in chemical exchange during an NMR pulse (English) |
| Author:
|
Gamliel, Dan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
139 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
155-162 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Spin exchange with a time delay in NMR (nuclear magnetic resonance) was treated in a previous work. In the present work the idea is applied to a case where all magnetization components are relevant. The resulting DDE (delay differential equations) are formally solved by the Laplace transform. Then the stability of the system is studied using the real and imaginary parts of the determinant in the characteristic equation. Using typical parameter values for the DDE system, stability is shown for all relevant cases. Also non-oscillating terms in the solution were found by studying the same determinant using similar parameter values. (English) |
| Keyword:
|
magnetic resonance |
| Keyword:
|
spin exchange |
| Keyword:
|
delay differential equation |
| Keyword:
|
characteristic equation |
| MSC:
|
11C20 |
| MSC:
|
34C26 |
| MSC:
|
34K06 |
| MSC:
|
82D40 |
| idZBL:
|
Zbl 06362250 |
| idMR:
|
MR3238831 |
| DOI:
|
10.21136/MB.2014.143846 |
| . |
| Date available:
|
2014-07-14T08:08:27Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143846 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
[9] Verheyden, K., Luzyanina, T., Roose, D.: Efficient computation of characteristic roots of delay differential equations using LMS methods.J. Comput. Appl. Math. 214 (2008), 209-226. Zbl 1135.65349, MR 2391684, 10.1016/j.cam.2007.02.025 |
| Reference:
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| Reference:
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[11] Woessner, D. E., Zhang, S., Merritt, M. E., Sherry, A. D.: Numerical solutions of the Bloch equations provides insights into the optimum design of PARACEST agents for MRI.Mag. Reson. Med. 53 (2005), 790-799. 10.1002/mrm.20408 |
| Reference:
|
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| . |
