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Analytical Solutions for Nuclear Magnetic Resonance Signal Bloch Equations with Varied Magnetic Excitation and Frequency Phase Shift |
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PP: 1219-1227 |
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doi:10.18576/amis/200507
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Author(s) |
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Nadia Boutabba,
Sofiane Grira,
Hichem Eleuch,
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Abstract |
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| Modern Nuclear Magnetic Resonance NMR research is highly interested in Bloch equation solutions and their dynamical evolution using pulse sequences under static or variable radio-frequency ”RF” fields. Sophisticated combinations of these pulses enable the manipulation and extraction of information about the behavior of spin systems. Nonetheless, few analytical exact solutions to Bloch equations exist to the best of our knowledge. In this context, our research investigates exact analytical solutions of Bloch equations governing nuclear magnetic resonance NMR signals in response to an external magnetic field. We address the case where external radio-frequency magnetic field strength is time-dependent, the magnetization of the medium ( which is experimentally equivalent to a spectrometer magnetic field) is also a time-variable, and, the frequency shift caused by spatial variations in the magnetic field is chirped. Hence, the temporal dynamics of spin magnetization components are fully determined. These solutions are in terms of the RF magnetic field, the relaxation times T1 and T2 (representing the rates at which the longitudinal and transverse magnetization recover or decay, respectively), and the frequency shift. Finally, we numerically derive these signals for two RF excitations: Eburp and Sine, which we compare to our exact solutions (denoted by the EX pulse). Interestingly, we observe that the magnetization signal is almost identical for Eburp and EX pulses while the absorption and dispersion are similar for a short excitation time. |
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