Bart de Vos^{1}, Rob F. Remis^{2}, and Andrew G. Webb^{1,2}

^{1}Leiden University Medical Center, C.J. Gorter Center for High Field MRI, Leiden, Netherlands,, Leiden, Netherlands, ^{2}Delft University of Technology, Circuits and Systems, Delft, Netherlands, Delft, Netherlands

In this work a low field point-of-care system design framework is created using target field methods for all of the hardware components. A new target field method for Halbach-based magnet optimization with variable ring diameter and spacing is derived. Magnet, gradient and RF are combined into a single framework which includes a feedback loop for dealing with the component interdependencies. The result is a pipeline which with a few user inputs can create an optimal magnet, gradient and RF design in minutes.

Starting from the quasi-static Maxwell’s equations an integral representation for the magnetic field in terms of a continuous cylindrical Halbach magnetization is derived. The continuous magnetization is discretized to represent individual magnets. The magnets are located within rings of variable radii and spacing. The goal is to obtain a set of ring radii

The initial guess for the field strength and number of rings is found by taking the most compact design given the minimum radius and a length/diameter ratio of 1.7 (based on previous literature). Next, power optimized gradient coils (with dimensions determined by the magnet) are designed. Using the efficiency [Tm

For a 300 mm clear bore, the inner magnet layer diameter is set to 320 mm. The initial uniform ring spacing of 25 mm combined with a length/diameter ratio of 1.7, dictates that 23 rings constitute the initial setup. The output of the first pipeline iteration is shown in the first column of Figure 3. The B

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Flowchart
of the system design methodology including the feedback loop.

Table
containing the input parameters of the design framework for the adult size
neuroimaging example.

Table showing the key output parameters
for three events during the design framework: (A) the initial compact design
from which the pipeline starts the iterations. (B) the magnet design after iterating
to the user specified minimum target field strength of 50 mT. (C) The improved
design after the number of rings is increased. Right) The magnets displayed correspond to the columns (A),(B) and (C). Only the inner radial layer of magnets is shown for
clarity.

The
homogeneity in PPM per Newton iteration step for the final magnet design
discussed in the results section. The ring radii optimization is shown in red and
ring spacing in black. The Newton update scheme is shown below the figure:
Delta r/d can be calculated by taking the Moore-Penrose inverse of the Jacobian
matrix which holds the derivatives with respect to each radius/spacing for every
target point in space. This is multiplied with the target field vector minus
the system vector. The minimum and maximum ring spacing and diameter
constraints are included in this scheme.

Visualization of the framework output. The gradient
coils, Magnet and RF-coil are shown separately as well as together in a
telescopic view. RF coil (green), x-gradient (black), z-gradient (red),
y-gradient (yellow), magnet (blue&red)

DOI: https://doi.org/10.58530/2022/0314