Novel insight into magnetic resonance through a spherical coordinate framework for the Bloch equation

Bahman Tahayori; Leigh A. Johnston; Iven M. Y. Mareels; Peter M. Farrell

doi:10.1117/12.813902

10 March 2009 Novel insight into magnetic resonance through a spherical coordinate framework for the Bloch equation

Bahman Tahayori, Leigh A. Johnston, Iven M. Y. Mareels, Peter M. Farrell

Proceedings Volume 7258, Medical Imaging 2009: Physics of Medical Imaging; 72580Y (2009) https://doi.org/10.1117/12.813902
Event: SPIE Medical Imaging, 2009, Lake Buena Vista (Orlando Area), Florida, United States

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.

Citation Download Citation

Bahman Tahayori, Leigh A. Johnston, Iven M. Y. Mareels, and Peter M. Farrell "Novel insight into magnetic resonance through a spherical coordinate framework for the Bloch equation", Proc. SPIE 7258, Medical Imaging 2009: Physics of Medical Imaging, 72580Y (10 March 2009); https://doi.org/10.1117/12.813902

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available