Coil optimization for MRI by conjugate gradient descent.

A flexible iterative algorithm is presented for optimizing gradient and radio frequency coils for MRI. It is based on a model using discrete current elements and direct Biot-Savart calculation of the fields. An error function is defined over a region of interest (ROI) and is minimized by conjugate gradient descent. The choice of error function allows optimization of the field uniformity, the inductance, and the efficiency of the coil in any combination. Neither the coil nor the ROI is restricted to any particular geometry. A 40-turn cylindrical z-gradient coil of radius a and length 4a, designed for ROI of radius 0.7a and length 2a has an average error in the gradient fields generated of 0.85%, an inductance of 0.014a mH/cm, and an efficiency of 6.65a-2 Gcm/A. A 16-turn birdcage-like RF coil of radius 5 cm, designed for a ROI of radius 4 cm has an average error of 0.79%.