MagTetris: A simulator for fast magnetic field and force calculation for permanent magnet array designs.

In this paper, a simulator named "MagTetris" is proposed for fast magnetic field (B-field) and force calculation for permanent magnet arrays (PMAs) designs consisting of cuboid and arc-shaped magnets (approximated by cuboids) with arbitrary configurations. The proposed simulator can compute the B-field of a PMA on arbitrary observation planes and the magnetic force acting on any magnet/group of magnets. An accelerated calculation method for B-fields of PMAs is developed based on the current model of permanent magnet, which is further extended to magnetic force calculation. The proposed method and the associated codes were validated with numerical simulation and experimental results. The calculation speed of "MagTetris" is at least 500 times higher than that using finite-element method (FEM)-based software with uncompromised accuracy. Compared with a freeware in Python, Magpylib, "MagTetris" has a calculation acceleration of greater than 50% using the same language. "MagTetris" has a simple data structure, which can be easily migrated to other programming languages maintaining similar performances. This proposed simulator can accelerate a PMA design and/or allow designs with high flexibility considering the B-field and force simultaneously. It can facilitate and accelerate innovations of magnet designs to advance dedicated portable MRI in terms of compactness, weight, and performance.

High-performance permanent magnet array design by a fast genetic algorithm (GA)-based optimization for low-field portable MRI.

Lightweight and compact permanent magnet arrays (PMAs) are suitable for portable dedicated magnetic resonance imaging (MRI). It is worth exploring different PMA design possibilities and optimization methods with an adequate balance between weight, size, and performance, in addition to Halbach arrays and C-shaped/H-shaped magnets which are widely used. In this paper, the design and optimization of a sparse high-performance inward-outward ring-pair PMA consisting of magnet cuboids is presented for portable imaging of the brain. The design is lightweight (151kg) and compact (inner bore diameter: 270mm, outer diameter: 616mm, length: 480mm, 5-Gauss range: 1840×1840×2340mm3). The optimization framework is based on the genetic algorithm with a consideration of both field properties and simulated image quality. The resulting PMA design has an average field strength of 101.5 mT and a field pattern with a built-in linear readout gradient. Subtracting the best fit to the linear gradient target resulted in a residual deviation from the target field of 0.76mT and an average linear regression coefficient of 0.85 to the linear gradient. The required radiofrequency bandwidth is 6.9% within a field of view (FoV) with a diameter of 200mm and a length of 125mm. It has a magnetic field generation efficiency of 0.67mT/kg, which is high among the sparse PMAs that were designed for an FoV with a diameter of 200mm. The field can be used to supply gradients in one direction working with gradient coils in the other two directions, or can be rotated to encode signals for imaging with axial slice selection. The encoding capability of the designed PMA was examined through the simulated reconstructed images. The force experienced by each magnet in the design was calculated, and the feasibility of a physical implementation was confirmed. The design can offer an increased field strength, and thus, an increased signal-to-noise ratio. It has a longitudinal field direction that allows the application of technologies developed for solenoidal magnets. This proposed design can be a promising alternative to supplying the main and gradient fields in combination for dedicated portable MRI. Lastly, the design is resulted from a fast genetic algorithm-based optimization in which fast magnetic field calculation was applied and high design flexibility was feasible. Within optimization iterations, image quality metrics were used for the encoding field of a magnet configuration to guide the design of the magnet array.