The NeuroSpin Imaging Center in Saclay, France, houses the strongest full body MRI magnet on the planet, offering unparalleled neuroimaging capabilities. The development of this 11.7 MRI has been a work in progress by Irfu, a CEA Institute in Saclay, since 2003. The MRI started delivering images in 2021, and the first images of a human brain are anticipated to be obtained in 2023.

During Iseult’s design phase, project leader, Thierry Schield faced complex mathematical challenges. MRI magnets require a very homogeneous magnetic field in the field of view to operate. The target is typically set at better than 1 ppm peak-to-peak field discrepancy in most commercial MRI magnets. For Iseult magnet, the initial specification was to have a peak field inhomogeneity better than 0.5 ppm peak-to-peak in the Ø220 cm sphere. This homogeneity level is crucial as it directly links to the final MRI image quality. To reach the target field homogeneity levels of sub-ppm, the team designed an intrinsically homogeneous magnet configuration and, two correction systems for the unavoidable homogeneity defects that results from real-world manufacturing. The magnet’s original design used a stack of double pancakes plunged into a superfluid helium bath. The mathematical challenge in this instance was to find the geometry that minimized the mass of superconductors; a mathematical optimization problem that solved would minimize the quantity of the most expensive magnet component, keeping the project cost-efficient.

Thierry and his team defined their minimization problem to an optimization model with an objective to minimize the superconductor mass by moving or changing the number of double pancakes. The free parameters were in the range of 200. The problem was nonlinear because the field quality, the problem constraint, was nonlinear versus the pancakes displacements.

Having used NAG® Library optimization solvers in previous research, Thierry trusted the NAG® solver to deliver clear-cut model results. The solver provided results in seconds, enabling the team to quickly and easily test different magnet configurations and based on the results, the magnet entered manufacturing, and the project kept crucial material costs to a minimum.

The Iseult team relied on NAG optimization solvers to setup the shimming system as well. Even if a magnet is constructed according to an ideal homogenous design, it will inevitably have geometrical imperfections that lead to field inhomogeneity problems. To address this issue, MRI machines use “shimming” systems, which are flexible correction systems that mitigate any remaining field inhomogeneities. In the case of Iseult, this involved the placement of small iron platelets in the magnet bore to distort the magnetic field. The optimal layout for the iron shims was determined through the use of NAG’s linear programming optimization solvers.


The Iseult development team turned to NAG to provide the optimization solvers needed to solve their mathematical problems quickly, accurately, and efficiently, as and when needed. Leveraging the solvers, they developed optimal magnet configuration and shimming systems, which formed the critical foundation for creating the most potent full body MRI magnet in the world.

This image shows a cross-section of the Iseult magnet ©Irfu, Institut de Recherche sur les lois fondamentales de l’univers (Institute of Research into the Fundamental Laws of the Universe), a CEA Institute.