Harmonic‐mapping‐based design of gradient coils on irregular MRI surfaces
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2026
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| author | Zhengrong Liu Qing Zhang Huiyu Du Qingyun Liu Lin Chen Xiaoyan Huang Bensheng Qiu Yufu Zhou |
| author_facet | Zhengrong Liu Qing Zhang Huiyu Du Qingyun Liu Lin Chen Xiaoyan Huang Bensheng Qiu Yufu Zhou Zhengrong Liu Qing Zhang Huiyu Du Qingyun Liu Lin Chen Xiaoyan Huang Bensheng Qiu Yufu Zhou |
| collection | Wiley Open Access |
| contents | Harmonic‐mapping‐based design of gradient coils on irregular MRI surfaces Zhengrong Liu Qing Zhang Huiyu Du Qingyun Liu Lin Chen Xiaoyan Huang Bensheng Qiu Yufu Zhou Medical Physics Abstract Background Head‐mounted gradient coils for brain imaging need to be designed on irregular surfaces. However, current gradient coil design methodologies often struggle to produce optimal magnetic field solutions for these specialized geometries. The stream function method is typically not applicable to irregular two‐dimensional surfaces, while the boundary element method involves excessive variables that are difficult to optimize. Purpose To develop a new gradient coil design method with fewer variables suitable for irregular surfaces, and to complete the design of gradient coils for brain imaging on a semi‐ellipsoidal surface. Methods Triangular meshes are constructed on the target surface, which is then harmonically mapped to a rectangle. After obtaining the mapping relationship, the connection between the stream function on the rectangle and the coil shape on the original surface is established via the inverse of the harmonic map. Finally, the particle swarm algorithm is used to optimize the basis function coefficients and complete the coil design. Results The method was used to design and coils on a semi‐ellipsoid surface. The resulting coils were manufactured and measured to verify the effectiveness of the method. Both simulation and measurement results show that the and coils designed with this method can generate more linear magnetic fields with roughly the same inductance. The maximum deviation of the magnetic field generated by the Gy coil is 4.02% (simulated) and 15.78% (measured), while that by the compared method is 33.3%. The maximum deviation of the magnetic field generated by the Gz coil is 2.57% (simulated) and 7.20% (measured), while that by the compared method is 27.8%. Conclusions This paper provides a new method for coil design on irregular two‐dimensional single connected bounded surface, to design gradient coil with better magnetic field with only a few basis functions. The linearity and uniformity of the obtained magnetic field have significant advantages over the boundary element method. Even with manufacturing and measurement errors amplifying the deviation, the measured deviation remains far lower than that of the reference design. 10.1002/mp.70365 http://onlinelibrary.wiley.com/termsAndConditions#vor |
| doi_str_mv | 10.1002/mp.70365 |
| format | Artículo Open Access |
| id | wiley_oa_10_1002_mp_70365 |
| institution | Wiley Open Access |
| license_str_mv | http://onlinelibrary.wiley.com/termsAndConditions#vor |
| publishDate | 2026 |
| publisher | Wiley |
| record_format | wiley_oa |
| spellingShingle | Harmonic‐mapping‐based design of gradient coils on irregular MRI surfaces Zhengrong Liu Qing Zhang Huiyu Du Qingyun Liu Lin Chen Xiaoyan Huang Bensheng Qiu Yufu Zhou Medical Physics Harmonic‐mapping‐based design of gradient coils on irregular MRI surfaces Zhengrong Liu Qing Zhang Huiyu Du Qingyun Liu Lin Chen Xiaoyan Huang Bensheng Qiu Yufu Zhou Medical Physics Abstract Background Head‐mounted gradient coils for brain imaging need to be designed on irregular surfaces. However, current gradient coil design methodologies often struggle to produce optimal magnetic field solutions for these specialized geometries. The stream function method is typically not applicable to irregular two‐dimensional surfaces, while the boundary element method involves excessive variables that are difficult to optimize. Purpose To develop a new gradient coil design method with fewer variables suitable for irregular surfaces, and to complete the design of gradient coils for brain imaging on a semi‐ellipsoidal surface. Methods Triangular meshes are constructed on the target surface, which is then harmonically mapped to a rectangle. After obtaining the mapping relationship, the connection between the stream function on the rectangle and the coil shape on the original surface is established via the inverse of the harmonic map. Finally, the particle swarm algorithm is used to optimize the basis function coefficients and complete the coil design. Results The method was used to design and coils on a semi‐ellipsoid surface. The resulting coils were manufactured and measured to verify the effectiveness of the method. Both simulation and measurement results show that the and coils designed with this method can generate more linear magnetic fields with roughly the same inductance. The maximum deviation of the magnetic field generated by the Gy coil is 4.02% (simulated) and 15.78% (measured), while that by the compared method is 33.3%. The maximum deviation of the magnetic field generated by the Gz coil is 2.57% (simulated) and 7.20% (measured), while that by the compared method is 27.8%. Conclusions This paper provides a new method for coil design on irregular two‐dimensional single connected bounded surface, to design gradient coil with better magnetic field with only a few basis functions. The linearity and uniformity of the obtained magnetic field have significant advantages over the boundary element method. Even with manufacturing and measurement errors amplifying the deviation, the measured deviation remains far lower than that of the reference design. 10.1002/mp.70365 http://onlinelibrary.wiley.com/termsAndConditions#vor |
| title | Harmonic‐mapping‐based design of gradient coils on irregular MRI surfaces |
| topic | Medical Physics |
| url | https://aapm.onlinelibrary.wiley.com/doi/10.1002/mp.70365 |