Alex C Barksdale^{1,2}, Clarissa Cooley^{1}, and Lawrence Wald^{1}

^{1}MGH, Charlestown, MA, United States, ^{2}MIT, Cambridge, MA, United States

Mid-field (0.5T) MRI is an attractive alternative to higher field strengths for improved cost, accessibility and patient comfort. Magnet length is a major determinant of patient comfort/acceptance but is constrained by escalating wire costs. We present a mid-field magnet design using rare-earth permanent magnets to supplement solenoidal superconducting windings, enabling shorter bore lengths than superconducting windings alone. The optimization problem is formulated and solved using linear programming. For a given superconducting wire length, we demonstrate that adding rare-earth materials can reduce bore lengths by 10% using <250kg of rare-earth material for a 5ppm, 0.5T B0 specification over a 450mm DSV.

The trade-off between magnet length and superconducting wire length (a proxy for cost) has been previously examined in optimal solenoid designs for a given bore diameter, imaging DSV and homogeneity target [8]. In this study, we attempt to further reduce the bore length of a 0.5T B

Fig. 2d also shows the candidate source locations and defines the magnet length neglecting formers and cryostat at the magnet ends. The field is computed over 41 points along a quarter circle arc of a central slice of the DSV, utilizing symmetry and properties of solutions to Laplace’s equation in source-free regions. Fig 2e presents additional optimization parameters used for source material placement. CVXPY is used to compute optimized solutions over currents and remanences [12, 13] by superimposing the fields from candidate source locations.

[1] Marques, J. P., Simonis, F. F. J., & Webb, A. G. (2019). Low-field MRI: An MR physics perspective. In *Journal of Magnetic Resonance Imaging* (Vol. 49, Issue 6, pp. 1528–1542). John Wiley and Sons Inc. https://doi.org/10.1002/jmri.26637

[2] Wald, L.L., McDaniel, P.C., Witzel, T., Stockmann, J.P. and Cooley, C.Z. (2020), Low-cost and portable MRI. In *Journal of Magnetic Resonance Imaging*, (Vol. 52: 686-696. https://doi.org/10.1002/jmri.26942

[3] Stainsby, J. A., Bindseil, G. A., Connell, I. R., Thevathasan, G., Curtis, A. T., Beatty, P. J., Harris, C. T., Wiens, C. N., & Panther, A. (2019). *Imaging at 0.5 T with high-performance system components System Components*. ISMRM 27^{th} Annual Meeting and Exhibition. 1194

[4] Panther, A., Thevathasen, G., Connell, I. R. O., Yao, Y., Wiens, C. N., Curtis, A. T., Bindseil, G. A., Harris, C. T., Beatty, P. J., Stainsby, J. A., Cunningham, C. H., Chronik, B. A., & Piron, C. (2019). *A Dedicated Head-Only MRI Scanner for Point-of-Care Imaging Barriers to MRI being used at the point-of-care*. ISMRM 27^{th} Annual Meeting and Exhibition. 3679

[5] Harris, C. T., Curtis, A. T., Wiens, C. N., Beatty, P. J., & Stainsby, J. A. (2020). *Acoustic Behavior of High Performance Imaging on a Head-only 0.5T Scanner with Asymmetric Gradients*. ISMRM & ASRT Virtual Conference and Exhibition. 4207

[6] Connel, I., Panther, A. (2019). *Increasing MRI Safety for Patients with Implanted Medical Devices: Comparisons of a 0.5T Head-Only MRI to 1.5T and 3T*. 57^{th} Annual ASNR Meeting and Symposium Neuroradiologicum. 3569

[7] Chen, S., Hu, P., Gu, Y., Pang, L., Zhang, Z., Zhang, Y., Meng, X., Cao, T., Liu, X., Fan, Z., & Shi, H. (2019). Impact of patient comfort on diagnostic image quality during PET/MR exam: A quantitative survey study for clinical workflow management. *Journal of Applied Clinical Medical Physics*, *20*(7), 184–192. https://doi.org/10.1002/acm2.12664

[8] Xu, H., Conolly, S. M., Scott, G. C., & Macovski, A. (1999). *Fundamental Scaling Relations for Homogeneous Magnets*. ISMRM

[9] Aubert, G., Centre National de la Recherche Scientifique CNRS, 1991. Cylindrical permanent magnet with longitudinal induced field. U.S. Patent 5,014,032.

[10] Ortner, M., & Coliado Bandeira, L. G. (2020). Magpylib: A free Python package for magnetic field computation. *SoftwareX*, *11*. https://doi.org/10.1016/j.softx.2020.100466

[11] Xu, H., Conolly, S. M., Scott, G. C., & Macovski, A. (2000). Homogeneous Magnet Design Using Linear Programming. In *IEEE TRANSACTIONS ON MAGNETICS* (Vol. 36, Issue 2).

[12] Agrawal, A., Verschueren, R., Diamond, S., & Boyd, S. (2017). *A Rewriting System for Convex Optimization Problems*. http://arxiv.org/abs/1709.04494

[13] Diamond, S., & Boyd, S. (2016). *CVXPY: A Python-Embedded Modeling Language for Convex Optimization*. http://arxiv.org/abs/1603.00943

**Figure 1** (a) Aubert ring configuration of rare earth permanent magnets. (b) Illustrated field profile of configuration in (a). (c) Rare earth magnets aligned parallel with B_{0} field (reminiscent of ferroshims). Note that unlike ferroshims, rare earth magnets can be oriented to flip magnetization, so that they are aligned anti-parallel with B_{0}. (d) Illustration of the field lines from the magnet configuration in (c).

**Figure 2** (a) Table of dimension parameters detailing the magnet designs (b), (c). (b) Rare-Earth magnet design with space for rare earth magnets (orange region) to supplement the superconducting windings (gray region) for short magnet design. (c) Design without rare-earth materials space for comparison. (d) Schematic of optimization for magnet design and optimization objective and constraints, closely following methodology from [8, 11]. (e) Relevant parameters used in optimization for magnet design.

**Figure 3 **Homogeneity contours from joint design using superconducting windings and Aubert rings. This considers a 1000mm bore length, 0.5T design at 5ppm homogeneity, using 250kg of rare earth material. It requires approximately 2.94 * 10^{6} ampere turns (a) Superconducting homogeneity lines (b) Aubert ring homogeneity lines (c) Total design homogeneity lines. Note that the rare-earth Aubert rings reduce the superconducting only homogeneity, reducing the total current required for the design.

**Figure 4 **(a) L-curves illustrating the tradeoffs between constrained length max rare-earth mass for Aubert rings only in the rare-earth space (b) tradeoffs between constrained length, and rare-earth configurations. For all designs the field target is 0.5T at 5ppm. Note that for a given current, designs with rare-earth material enable shorter magnet designs (Circled in red: design at a 1.27*10^{6} amp-turn current can be reduced by 12cm with inclusion of rare earth materials)

DOI: https://doi.org/10.58530/2022/1373