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Proceedings Paper

Novel insight into magnetic resonance through a spherical coordinate framework for the Bloch equation
Author(s): Bahman Tahayori; Leigh A. Johnston; Iven M. Y. Mareels; Peter M. Farrell
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Paper Abstract

The behaviour of spins at a classical level in the presence of an external magnetic field is completely described by the Bloch equation. This is the main equation governing the magnetic resonance imaging (MRI) system, and as such the Bloch equation is extensively used for design purposes. Here we have transferred the Bloch equation to the spherical coordinate system that, to the best of our knowledge, has not previously been applied in this field. The mathematical framework and the simulation results show that this fresh view of the Bloch equation provides better insight into the magnetic resonance (MR) phenomenon. In this mathematical framework, without using spinor space, the order of the Bloch equation is reduced in a much simpler way and can therefore provides a novel insight to the slice selection problem. Simulation results are presented for a variety of slice selective pulses, with and without post excitation rephasing gradients. In this paper nonlinear gradient is tried as well which shows an improvement in uniformity of the selected slice. It is feasible to find an analytic approximate solution to the Bloch equation in spherical coordinate system by adopting averaging techniques over spatial variables available available in nonlinear dynamical systems. We anticipate that our new description of the MR phenomenon will allow researchers to revisit the excitation pattern design question to achieve better slice selectivity or to find an optimal excitation pattern from a theoretical basis. This has the potential to result in practical improvements affecting all forms of MR imaging.

Paper Details

Date Published: 11 March 2009
PDF: 12 pages
Proc. SPIE 7258, Medical Imaging 2009: Physics of Medical Imaging, 72580Y (11 March 2009); doi: 10.1117/12.813902
Show Author Affiliations
Bahman Tahayori, The Univ. of Melbourne (Australia)
Leigh A. Johnston, The Univ. of Melbourne (Australia)
Iven M. Y. Mareels, The Univ. of Melbourne (Australia)
Peter M. Farrell, The Univ. of Melbourne (Australia)


Published in SPIE Proceedings Vol. 7258:
Medical Imaging 2009: Physics of Medical Imaging
Ehsan Samei; Jiang Hsieh, Editor(s)

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