Exceptional Trajectories in the Contrast Problem in Nuclear Magnetic Resonance

In this paper we focus on the contrast problem in medical imaging. It consists of using a single magnetic field to control a pair of non-interacting spins, each representing a specific substance, with the goal of maximizing the difference of the moduli of the magnetization vectors of the two substances. Prior work analyzed the saturation contrast problem which brings one of the spins to magnetization zero while maximizing the modulus of the other. Here we relax the saturation constraint that one of the spins must reach magnetization zero, providing more flexibility to obtain a higher contrast. We focus on the study of exceptional arcs and construct bang-exceptional extremals based on a methodology that searches for the highest possible contrast. Numerical calculations are provided, and we graphically illustrate the results.