First-Order Spatial Encoding Simulations for Improved Accuracy in the Presence of Strong B₀ and Gradient Field...

Low-cost and application-specific scanners with unconventional designs can entail substantial inhomogeneities of the main magnetic field $B_0$ and non-linearities of the gradient fields, which challenge assumptions made in MRI simulators. This work aims to develop a simulation framework that captures the encoding effects of strong field variations, accurately and efficiently, to enable the assessment of effects such as geometrical distortions, signal dropout, and foldover artifacts.

Like many other MRI simulators, ours discretizes magnetic fields in space. However, we extend the MR signal simulation at each grid point from the 0th-order approximation, which assumes piecewise constant fields, to a 1st-order approximation, which assumes piecewise linear fields. We solve the signal equation by analytically integrating over each grid cube, assuming linear field variations, and then summing over all cubes. We provide analytical integrals for several pulse sequences.

The 1st-order approximation captures strongly varying fields and associated intravoxel dephasing more accurately, avoiding severe "ringing" artifacts present in the usual 0th-order simulations. This enables simulations on a much coarser grid, facilitating computational feasibility.

The first-order simulator enables the evaluation of unconventional scanner designs with strongly varying magnetic fields.