Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance

TL;DR

This paper introduces a geometric optimal control framework for analyzing and selecting optimal trajectories in Nuclear Magnetic Resonance contrast imaging, focusing on extremal solutions and transfer time optimization.

Contribution

It develops a geometric control approach based on Hamiltonian dynamics to analyze extremals in NMR contrast imaging, providing a new method for trajectory optimization.

Findings

Application to cerebrospinal fluid and water contrast

Analysis of singular extremals and their optimality

Reduction of the problem to Hamiltonian dynamics

Abstract

The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid / water and grey / white matter of cerebrum.