Elsevier

IFAC Proceedings Volumes

Volume 44, Issue 1, January 2011, Pages 9650-9655
IFAC Proceedings Volumes

The Bloch Equation Revisited through Averaging under Adiabatic Passages

https://doi.org/10.3182/20110828-6-IT-1002.00884Get rights and content

Abstract

In order to derive a simplified solution to a bilinear system originating from the Bloch equation under adiabatic excitation, we have employed a nonlinear averaging technique for the first time in magnetic resonance context. We achieve an averaged solution with an acceptable level of error by transferring the dynamics of the Bloch equation to a novel rotating frame of reference through a rotation and a proper time-scaling. In this frame, the states of the system which represent the components of magnetic resonance signal are slowly varying and thus can be averaged to achieve an approximate solution. Error analysis of the averaged solution as well as the simulation results clearly show that the error of the averaged solution is negligible. Therefore, the simplified solution presented in this paper in conjunction with adaptive control techniques, particularly extremum seeking, can be used to find optimal adiabatic modulation functions in a computationally efficient manner.

Keywords

Nonlinear averaging
Biomedical imaging systems
Magnetic resonance imaging
Bloch equation
Adiabatic passages

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This work is supported by NICTA Victorian Research Laboratory Life Sciences Program.

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