Mathematical algorithms in the field of optimization often require the simultaneous computation of a function and its derivative.The derivative of many functions can be found automatically, a process referred to as automatic differentiation.Dual numbers, close relatives of the complex numbers, are of particular use in automatic differentiation.This library provides an extremely fast implementation of dual numbers for C++, duals::dual<>, which, when replacing scalar types, can be used to automatically calculate a derivative.

This article presents a new motion encoding strategy to perform magnetic resonance elastography (MRE). Instead of using standard motion encoding gradients, a tailored RF pulse is designed to simultaneously perform selective excitation and motion encoding in presence of a constant gradient. The RF pulse is designed with a numerical optimal control algorithm, in order to obtain a magnetization phase distribution that depends on the displacement characteristics inside each voxel. As a consequence, no post-excitation encoding gradients are required. This offers numerous advantages, such as reducing eddy current artifacts, and relaxing the constraint on the gradients maximum switch rate. It also allows to perform MRE with ultra-short TE acquisition schemes, which limits T2 decay and optimizes signal-to-noise ratio. The pulse design strategy is developed and analytically analyzed to clarify the encoding mechanism. Finally, simulations, phantom and ex vivo experiments show that phase-to-noise ratios are improved when compared to standard MRE encoding strategies.

Purpose: This article proposes a rigorous optimal control framework for the design of preparation schemes that optimize MRI contrast based on relaxation time differences. Methods: Compared to previous optimal contrast preparation schemes, a drastic reduction of the optimization parameter number is performed. The preparation scheme is defined as a combination of several block pulses whose flip angles, phase terms and inter-pulse delays are optimized to control the magnetization evolution. Results: The proposed approach reduces the computation time of B-0-robust preparation schemes to around a minute (whereas several hours were required with previous schemes), with negligible performance loss. The chosen parameterization allows to formulate the total preparation duration as a constraint, which improves the overall compromise between contrast performance and preparation time. Simulation, in vitro and in vivo results validate this improvement, illustrate the straightforward applicability of the proposed approach, and point out its flexibility in terms of achievable contrasts. Major improvement is especially achieved for short-T-2 enhancement, as shown by the acquisition of a non-trivial contrast on a rat brain, where a short-T-2 white matter structure (corpus callosum) is enhanced compared to surrounding gray matter tissues (hippocampus and neocortex). Conclusions: This approach proposes key advances for the design of optimal contrast preparation sequences, that emphasize their ability to generate non-standard contrasts, their potential benefit in a clinical context, and their straightforward applicability on any MR system.

This work investigates the use of MRI radio-frequency (RF) pulses designed within the framework of optimal control theory for image contrast optimization. The magnetization evolution is modeled with Bloch equations, which defines a dynamic system that can be controlled via the application of the Pontryagin Maximum Principle (PMP). This framework allows the computation of optimal RF pulses that bring the magnetization to a given state to obtain the desired contrast after acquisition. Creating contrast through the optimal manipulation of Bloch equations is a new way of handling contrast in MRI, which can explore the theoretical limits of the system. Simulation experiments carried out on-resonance quantify the contrast improvement when compared to standard T1 or T2 weighting strategies. The use of optimal pulses is also validated for the first time in both in vitro and in vivo experiments on a small-animal 4.7 T MR system. Results demonstrate their robustness to static field inhomogeneities as well as the fact that they can be embedded in standard imaging sequences without affecting standard parameters such as slice selection or echo type. In vivo results on rat and mouse brains illustrate the ability of optimal contrast pulses to create non-trivial contrasts on well-studied structures (white matter versus gray matter).

We introduce the optimal fingerprinting process which is aimed at accurately identifying the parameters which characterize the dynamics of a physical system. A database is first built from the time evolution of an ensemble of dynamical systems driven by a specific field, which is designed by optimal control theory to maximize the efficiency of the recognition process. Curve fitting is then applied to enhance the precision of the identification. As an illustrative example, we consider the estimation of the relaxation parameters of a spin-1/2 particle. The experimental results are in good accord with the theoretical computations. We show on this example a physical limit of the estimation process.

The variety of achievable contrasts by MRI makes it a highly flexible and valuable diagnostic tool. Contrast results from relaxation time differences, which are intrinsic properties of each tissue. Using optimal control theory, one can control the obtained contrast by applying excitation pulses that bring the magnetization in a user-defined target state. Simulation results are presented to illustrate the feasibility and the flexibility of using optimal contrast pulses. The robustness to experimental variable parameters such as field inhomogeneities is also studied. Finally, an in-vitro contrast experiment is performed on a small-animal MRI showing a reasonable match with the simulation results.

Magnetic Resonance Imaging (MRI) uses the difference in tissue relaxation times to create contrast. Various image weightings can be obtained by tuning acquisition parameters which are usually empirically defined. In this article, optimal control theory is used to design excitation pulses that produce the optimal contrast between given tissues. The designed pulses are tested on numerical phantoms with and without magnetic field inhomogeneities and for the first time in vitro on a small-animal MRI. The reasonable match between simulation and real experiments is promising for the development of such pulses in further in vivo applications.