Tikhonov Regularization Approach for Acoustic Noise Reduction in an Asymmetric, Self-Shielded MRI Gradient Coil

We consider a mathematical method for minimizing the acoustic noise of self-shielded magnetic resonance imaging gradient coils designed to produce an asymmetrically located target field within a cylindrical chamber. During imaging, the gradient coils are being constantly switched on and off, subjecting the coil to large Lorentz forces. These forces cause the chamber to buckle, creating a pressure wave in the bore which manifests as acoustic noise at sound pressure levels up to about 130 dB. In this model, the linearized coil deflection, the pressure wave, and the acoustic noise level inside the chamber are all solved for in closed form. The closed-form nature of the solutions permits simple insights into the behavior of the system. Although reductions of only 0.6 dB were achieved, the method allows some flexibility if other design sacrifices are made. The gradient coil switching frequency plays a major role in the magnitude of the acoustic noise and is studied here. Results are presented for two basic switching functions for shielded gradient coils. Unshielded gradient coils, other switching functions, and other penalty functions can be easily accommodated using the method presented.