Working Notes on the Time Minimal Saturation of a Pair of Spins and Application in Magnetic Resonance Imaging

Abstract : In this article, we analyse the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control to classify the optimal syntheses in the single spin case to pave the road to analyze the case of two spins. The Bocop software is used to determine local minimizers for physical test cases and Linear Matrix Inequalities approach is applied to estimate the global optimal value and validate the previous computations. This is complemented by numerical computations combining shooting and continuation methods implemented in the HamPath software to analyze the structure of the time minimal solution with respect to the set of parameters species.
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Submitted on : Friday, March 16, 2018 - 9:56:11 AM
Last modification on : Thursday, October 24, 2019 - 2:44:12 PM
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  • HAL Id : hal-01721845, version 2

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Bernard Bonnard, Olivier Cots, Jérémy Rouot, Thibaut Verron. Working Notes on the Time Minimal Saturation of a Pair of Spins and Application in Magnetic Resonance Imaging. 2018. ⟨hal-01721845v2⟩

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