Momentum‐weighted conjugate gradient descent algorithm for gradient coil optimization

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Abstract
MRI gradient coil design is a type of nonlinear constrained optimization. A practical problem in transverse gradient coil design using the conjugate gradient descent (CGD) method is that wire elements move at different rates along orthogonal directions (r, φ, z), and tend to cross, breaking the constraints. A momentum‐weighted conjugate gradient descent (MW‐CGD) method is presented to overcome this problem. This method takes advantage of the efficiency of the CGD method combined with momentum weighting, which is also an intrinsic property of the Levenberg‐Marquardt algorithm, to adjust step sizes along the three orthogonal directions. A water‐cooled, 12.8 cm inner diameter, three axis torque‐balanced gradient coil for rat imaging was developed based on this method, with an efficiency of 2.13, 2.08, and 4.12 mT · m‐1 · A‐1 along X, Y, and Z, respectively. Experimental data demonstrate that this method can improve efficiency by 40% and field uniformity by 27%. This method has also been applied to the design of a gradient coil for the human brain, employing remote current return paths. The benefits of this design include improved gradient field uniformity and efficiency, with a shorter length than gradient coil designs using coaxial return paths. Magn Reson Med 51:158–164, 2004.

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