Convex optimisation of gradient and shim coil winding patterns

Area of Science:

• Magnetic Resonance Imaging (MRI) Coil Design
• Computational Electromagnetics
• Optimization Techniques

Background:

• Designing gradient and shim coils is crucial for MRI performance.
• Traditional coil design methods can be complex and computationally intensive.
• Exploring new optimization frameworks can lead to improved coil geometries.

Purpose of the Study:

• To apply convex optimization to the design of gradient and shim coils.
• To investigate the impact of different cost functions, specifically L(p)-norms, on coil design.
• To explore novel regularisation terms for field synthesis in coil design.

Main Methods:

• Utilized boundary element methods (BEM) for coil design.
• Employed convex optimization to define and solve coil design problems.
• Prototyped and simulated various gradient and shim coil designs using different cost functions.

Main Results:

• Demonstrated the feasibility of using convex optimization for coil design.
• Investigated the behavior of L(p)-norms, including L1 and L(infinity), as cost functions.
• A mixture of L1 and L(infinity) norms yielded coils with equally spaced winding bunches, optimizing surface usage.

Conclusions:

• Convex optimization provides a flexible framework for MRI gradient and shim coil design.
• The proposed L1/L(infinity) norm mixture offers a promising approach for designing manufacturable coils with fixed cross-section wires.
• This method facilitates the creation of efficient coil geometries that balance performance and fabrication constraints.