  Diffusion-weighted imaging (DWI) in the female breast is a magnetic resonance
imaging (MRI) technique, which may potentially replace or effectively
complement both x-ray mammography and contrast-enhanced MR mammography. To
further improve specificity of DWI in the breast, stronger and faster diffusion
weighting is advantageous. With the target application in mind, the gradient
coil is designed on an irregularly shaped semi-open current-carrying surface.
Due to the coil former closely fitting the non-spherical target region,
non-linear encoding fields become particularly advantageous for achieving
locally exceptionally high gradient strengths. As the breast tissue has a
predominantly isotropic cellular microstructure, the direction of the
diffusion-weighting gradient may be allowed to vary within the target volume.
However, due to the quadratic dependency of the b-factor on the gradient
strength, variation of the gradient magnitude needs to be carefully controlled.
  To achieve the above design goals the corresponding multi-objective
optimization problem is reformulated as a constrained optimization, allowing
for flexible and precise control of the coil properties. A novel constraint is
proposed limiting the gradient magnitude variation within every slice while
allowing for variations both the direction of the gradient within the slice and
the magnitude across the slices. The above innovations enable the design of a
unilateral coil for diffusion weighting in the female breast with the local
gradient strengths exceeding 1~T/m with highly homogeneous diffusion weighting
for imaging in the coronal slice orientation.
