Harmonic-mapping-based design of gradient coils on irregular MRI surfaces

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.

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.

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.

The method was used to design $G_y$ and $G_z$ 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 $G_y$ and $G_z$ 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%.

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.