Meena Rajendran^{1} and Shao Ying Huang^{1}

^{1}Singapore University of Technology, Singapore, Singapore

The optimization of an asymmetrical tapered solenoid coil using multi-objective Genetic Algorithm is presented to achieve high sensitivity, high homogeneity, low inductance simultaneously at 2.84MHz within a cylindrical volume(95×95х10mm). The asymmetrical solenoid coil has a lower half that consists of turns with variable pitches and a constant radius and an upper half that consist of turns with variable pitches and profile curvature(variable radius). Two coil winding patterns are included: single winding and multiple windings at each groove. The optimal design shows a sensitivity of 138 μT/√W (29.7%increase), 3.8% homogeneity reduction, comparable inductance compared to a traditional solenoid of similar dimensions.

Multi-objective GA was used for optimization. Fig.2 shows the flow of the algorithm. The optimization objectives are 1) B

The design frequency of the coil is 2.84 MHz. The optimization is considered using two methods with different winding patterns, single turn (Method I: M-I) and multiple turns (Method II: M-II) at each groove. Matlab was used for the implementation.

In Fig. 5., the optimized coil of M-I shows a B

It is a preliminary design and optimization on a high-performance solenoid for low-field MRI. A good balance of coil sensitivity, field homogeneity, and coil inductance is obtained using the proposed coil configuration and the single turn wire winding method. It is a showcase using a relatively small FoV. Moving forward, better designs as well as better optimization approaches for RF coils for a Halbach MRI system need to be sought, especially considering the B

[1] Ren, Zhi Hua, et al. "A low-field portable magnetic resonance imaging system for head imaging." 2017 Progress in Electromagnetics Research Symposium-Fall (PIERS-FALL). IEEE, 2017.

[2] O'Reilly, T., W. M. Teeuwisse, and A. G. Webb. "Three-dimensional MRI in a homogenous 27 cm diameter bore Halbach array magnet." *Journal of Magnetic Resonance* 307 (2019): 106578.

[3] Ren, Zhi Hua, and Shao Ying Huang. "The design of a short solenoid with homogeneous B1 for a low-field portable MRI scanner using genetic algorithm." poster, ISMRM 26th Annual Meeting & Exhibition. 2018.

[4] Shen, Sheng, et al. "Optimization of a Close-Fitting Volume RF Coil for Brain Imaging at 6.5 mT Using Linear Programming." *IEEE Transactions on Biomedical Engineering* 68.4 (2020): 1106-1114.

[5] Dengler, Richard. "Self inductance of a wire loop as a curve integral." arXiv preprint arXiv:1204.1486 (2012).

Figure 1. Illustration of the tapered asymmetrical solenoid coil geometry. A) Side view showing the asymmetrical upper and lower half sections B) 3D view. Design parameters: Total number of turns (N), number of turns in lower half section (Ns), profile curvature of tapering (C) and pitch of each turn (p_{i} [i = 1 to N]).The diameter of the cylindrical portion of the coil and that of the wire is 105 mm and 1mm respectively.

Figure 2. Flow-chart of GA multi-objective optimization algorithm to optimize N_{S }(No. of turns in lower section of the solenoid), p_{i }[i = 1..N] (pitch of each turn i) _{ }and C (curvature/tapering profile) for N = 20, 45 & 90 using two methods with different winding pattern of the coil. In Method I and II, the coils can have single and multiple turns at each pitch level respectively. The number of populations and maximum generation in the optimization is set as 200 & 200 respectively.

Figure. 3. Mean and average fitness value plotted over
generations for A) Fitness function 1 (Objective 1) B) Fitness function 2
(Objective 2) C) Fitness function 3 (Objective 3) obtained for Method-I optimisation when N = 45

Figure. 4. Plot of
Fitness function 1 (Objective 1)
with varying A) Fitness function 2 (Objective 2) B) Fitness function 3 (Objective 3) of the pareto-optimal solutions obtained for Method-I optimisation when N = 45

Figure. 5. Current path of the coil , B_{1} distribution at planes z = 0, z = -5 mm, z = -10 mm (corresponding to 3D FoV: 95 × 95 × 10 mm) from left to right of A) standard solenoid coil with same N = 45, coil diameter = 105 mm, Length = 180 mm, B) Method-I Optimized coil for N =45, C) Method-II Optimized coil for N =45, D) Summary of performance metrics of the above coils. B_{1}^{avg }is the average field and D is the difference between the maximum and the minimum in the respective 2D FoV (95 × 95 ×10) mm.

DOI: https://doi.org/10.58530/2022/1905