Analytical analysis of multi-pulse NMR

Journal of Magnetic Resonance
Irina Nazarova, Marcus A Hemminga

Abstract

It is well known that in multi-pulse applications in high-resolution NMR and MRI a steady state is reached for the magnetisation vector by the effect of relaxation in combination with the pulse repetition time. In this paper, a mathematical model is developed to understand how the parameters of the pulse sequence and relaxation times T(1) and T(2) affect the behaviour of the magnetisation vector. It will be shown that even under strong simplifying conditions an analytical analysis becomes very complex and only an analytical solution can be found for 90 degrees pulses and T(1)=T(2). For other cases a numerical approach is needed. Nevertheless, the basic approach of the mathematical analysis provides a general tool for analytical multi-operator applications. Our results provide a quantitative insight in the process by which the magnetisation relaxes towards the steady-state situation in a multi-pulse sequence.

References

Nov 1, 1996·Journal of Magnetic Resonance. Series a·A D Bain, E W Randall
Oct 10, 2002·Journal of the American Chemical Society·Nikolai R SkrynnikovLewis E Kay
Mar 26, 2003·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Wolfgang Hänicke, Horst U Vogel
Jun 20, 2003·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Brian A HargreavesDwight G Nishimura
Jul 11, 2003·Journal of Magnetic Resonance·Patrick Le Roux

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Citations

Aug 29, 2013·Computational and Mathematical Methods in Medicine·D F Gochberg, Z Ding
Mar 7, 2014·IEEE Transactions on Medical Imaging·Christos G XanthisAnthony H Aletras
Jan 30, 2008·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Anthony H AletrasAndrew E Arai

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