Spin dephasing under nonlinear gradients: implications for imaging and field mapping

This work examines the prototypical MR echo that would be expected for a voxel of spins evolving in a strong nonlinear field, specifically focusing on the quadratic z(2) - ½(x(2) + y(2) ) field. Dephasing under nonlinear gradients is increasingly relevant given the growing interest in nonlinear imaging, and here, we report several notable differences from the linear case. Most notably, in addition to signal loss, intravoxel dephasing under gradients creating a wide and asymmetric frequency distribution across the voxel can cause skewed and nonlinear phase evolution. After presenting the qualitative and analytical origins of this difference, we experimentally demonstrate that neglecting these dynamics can lead to significant errors in sequences that assume phase evolution is proportional to voxel frequency, such as those used for field mapping. Finally, simplifying approximations to the signal equations are presented, which not only provide more intuitive forms of the exact expression but also result in simple rules to predict key features of the nonlinear evolution.