Single Echo MRI

Purpose: Previous nonlinear gradient research has focused on trajectories that reconstruct images with a minimum number of echoes. Here we describe sequences where the nonlinear gradients vary in time to acquire the image in a single readout. The readout is designed to be very smooth so that it can be compressed to minimal time without violating peripheral nerve stimulation limits, yielding an image from a single 4 ms echo. Theory and Methods: This sequence was inspired by considering the code of each voxel, i.e. the phase accumulation that a voxel follows through the readout, an approach connected to traditional encoding theory. We present simulations for the initial sequence, a low slew rate analog, and higher resolution reconstructions. Results: Extremely fast acquisitions are achievable, though as one would expect, SNR is reduced relative to the slower Cartesian sampling schemes because of the high gradient strengths. Conclusions: The prospect that nonlinear gradients can acquire images in a single