Passive Shimming for Magic-Angle-Spinning NMR

Noguchi, So; Hahn, Seungyong; Iwasa, Y.

doi:10.1109/tasc.2013.2284548

Cited by 8 publications

(3 citation statements)

References 9 publications

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“…13,[16][17][18]21,22 The spherical harmonic coefficients presented in this paper facilitate active shimming for various kinds of coils by eliminating the higher terms of the entirecomponent coefficients than the 0th one. On the other hand, in the case of passive shimming, it is difficult to eliminate the higher terms of the coefficients.…”

Section: Discussionmentioning

confidence: 99%

“…The passive shimming is done by combining the magnetic moment method with an optimization method. 22 Recently, a few magnets are designed to generate a magnetic field tilted from the z-axis. The forms of the spherical harmonic coefficients presented in this paper and the previous ones 4-17 cannot be easily used for shimming design computation.…”

Section: Discussionmentioning

confidence: 99%

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Formulation of the spherical harmonic coefficients of the entire magnetic field components generated by magnetic moment and current for shimming

Noguchi

2014

Journal of Applied Physics

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For MRI and NMR magnet design, a highly homogeneous and high magnetic field has to be achieved by active and/or passive shimming. The active and passive shimming commonly homogenize the magnetic field around the magnet center by cancellation of the higher terms of a spherical harmonic series than the 0th term. So far, the spherical harmonic expression in the cylindrical coordinate system is well known for a circular coil, a solenoid coil, and magnetization of ferromagnetic material with/without its volume. In a shimming design, only the z-component of an inhomogeneous magnetic field is compensated because it is dominant to the performance of MRI/NMR. However, various kinds of MRI and NMR systems have recently been developed, and these magnets sometimes have an axially asymmetric configuration or generate a tilted magnetic field. Therefore, the entire x-, y-, and z-components have to be homogenized for such magnets. I derive the spherical harmonic expression of the entire components of magnetic field generated by a circular coil, a dipole coil, and a straight line current. In addition, since the entire magnetization components of the ferromagnetic material having the volume contribute the entire components of the magnetic field around the magnet center, I also derive the equations of the spherical harmonic coefficients of the magnetic field generated by ferromagnetic material. Since these equations need a numerical integration, such as the Gauss quadrature integration, the computation accuracy of the spherical harmonic coefficients is investigated against the number of the evaluation points. We can calculate the highly accurate spherical harmonic coefficients with the small number of the evaluation points. (C) 2014 AIP Publishing LLC

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Formulation of the spherical harmonic coefficients of the entire magnetic field components generated by magnetic moment and current for shimming

Noguchi

2014

Journal of Applied Physics

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“…Much research has been conducted in ferromagnetic and active shimming of a solenoidal (z-axis) NMR magnet [7]-[11]. Additionally, previous research has shown ferromagnetic shimming algorithms for the magic-angle magnet [12]-[14]. …”

Section: Introductionmentioning

confidence: 99%

A Theoretical Design Approach for Passive Shimming of a Magic-Angle-Spinning NMR Magnet

Voccio²,

Sammartino

et al. 2016

IEEE Trans. Appl. Supercond.

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This paper presents a passive shimming design approach for a magic-angle-spinning (MAS) NMR magnet. In order to achieve a 1.5-T magic-angle field in NMR samples, we created two independent orthogonal magnetic vector fields by two separate coils: the dipole and solenoid. These two coils create a combined 1.5-T magnetic field vector directed at the magic angle (54.74° from the spinning axis). Additionally, the stringent magnetic field homogeneity requirement of the MAS magnet is the same as that of a solenoidal NMR magnet. The challenge for the magic-angle passive shimming design is to correct both the dipole and solenoid magnetic field spherical harmonics with one set of iron pieces, the so-called ferromagnetic shimming. Furthermore, the magnetization of the iron pieces is produced by both the dipole and solenoid coils. In our design approach, a matrix of 2 mm by 5 mm iron pieces with different thicknesses was attached to a thin-walled tube, 90-mm diameter and 40-mm high. Two sets of spherical harmonic coefficients were calculated for both the dipole and solenoid coil windings. By using the multiple-objective linear programming optimization technique and coordinate transformations, we have designed a passive shimming set that can theoretically reduce 22 lower-order spherical harmonics and improve the homogeneity of our MAS NMR magnet.

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A hybrid, nonlinear programming approach for optimizing passive shimming in MRI

Zhao,

Zhu,

Xia

et al. 2024

Medical Physics

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BackgroundIn magnetic resonance imaging (MRI), maintaining a highly uniform main magnetic field (B0) is essential for producing detailed images of human anatomy. Passive shimming (PS) is a technique used to enhance B0 uniformity by strategically arranging shimming iron pieces inside the magnet bore. Traditionally, PS optimization has been implemented using linear programming (LP), posing challenges in balancing field quality with the quantity of iron used for shimming.PurposeIn this work, we aimed to improve the efficacy of passive shimming that has the advantages of balancing field quality, iron usage, and harmonics in an optimal manner and leads to a smoother field profile.MethodsThis study introduces a hybrid algorithm that combines particle swarm optimization with sequential quadratic programming (PSO‐SQP) to enhance shimming performance. Additionally, a regularization method is employed to reduce the iron pieces' weight effectively.ResultsThe simulation study demonstrated that the magnetic field was improved from 462 to 3.6 ppm, utilizing merely 1.2 kg of iron in a 40 cm diameter spherical volume (DSV) of a 7T MRI magnet. Compared to traditional optimization techniques, this method notably enhanced magnetic field uniformity by 96.7% and reduced the iron weight requirement by 81.8%.ConclusionThe results indicated that the proposed method is expected to be effective for passive shimming.

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Passive Shimming for Magic-Angle-Spinning NMR

Cited by 8 publications

References 9 publications

Formulation of the spherical harmonic coefficients of the entire magnetic field components generated by magnetic moment and current for shimming

Formulation of the spherical harmonic coefficients of the entire magnetic field components generated by magnetic moment and current for shimming

A Theoretical Design Approach for Passive Shimming of a Magic-Angle-Spinning NMR Magnet

A hybrid, nonlinear programming approach for optimizing passive shimming in MRI

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