Small-bore gradient coil design with plate-rolling error correction for use in micro-MRI

For high-field MRI, ensuring high fidelity between the as-built gradient field and the optimized design is critical for accurate gradient-field generation and spatial encoding. Conventional manufacturing approaches for gradient coils typically employ a copper-plate cutting and bending method, where a 2D unwrapped conductor pattern is reshaped into a cylindrical geometry. However, the bending process inevitably introduces geometric distortions, resulting in additional magnetic-field deviations. This study aims to develop a high-precision engineering approach that minimizes discrepancies between the magnetic fields produced by the designed patterns and the as-built coils. To this end, a mid-surface-based approach is proposed (i.e., the geometric mid-surface of the conductor thickness), in which the three-dimensional current paths are defined directly on the cylindrical mid-surface, thereby eliminating planar unfolding and subsequent bending assumptions. The methodology is demonstrated on an X-gradient coil designed for a 7 T superconducting MRI magnet with a 54 mm bore and a 25 mm DSV. Finite-element simulations show that the proposed approach substantially improves magnetic-field fidelity, reducing the maximum field deviation from 10.92% with the conventional copper-plate cutting and bending method to 3.71% with the mid-surface extrusion approach. Prototype gradient coils for the X, Y, and Z axes were fabricated and tested independently, yielding coefficients of determination of R² > 0.997 for all three axes. These results confirm that the mid-surface-based approach provides a higher-fidelity conversion from stream-function contour patterns to manufacturable gradient coils, yielding improved as-built field accuracy and enhanced design-to-fabrication consistency in compact high-field MRI gradient systems.