Reconstruction of MRI data encoded with arbitrarily shaped, curvilinear, nonbijective magnetic fields

Abstract

A basic framework for image reconstruction from spatial encoding by curvilinear, nonbijective magnetic encoding fields in combination with multiple receivers is presented. The theory was developed in the context of the recently introduced parallel imaging technique using localized gradients (PatLoc) approach. In this new imaging modality, the linear gradient fields are generalized to arbitrarily shaped, nonbijective spatial encoding magnetic fields, which lead to ambiguous encoding. Ambiguities are resolved by adaptation of concepts developed for parallel imaging. Based on theoretical considerations, a practical algorithm for Cartesian trajectories is derived in the case that the conventional gradient coils are replaced by coils for PatLoc. The reconstruction method extends Cartesian sensitivity encoding (SENSE) reconstruction with an additional voxelwise intensity-correction step. Spatially varying resolution, signal-to-noise ratio, and truncation artifacts are described and analyzed. Theoretical considerations are validated by two-dimensional simulations based on multipolar encoding fields and they are confirmed by applying the reconstruction algorithm to initial experimental data.

Simultaneously driven linear and nonlinear spatial encoding fields in MRI

“…Physiological limitations in the switching rate of such fields have led to the development of alternative geometries for creating linear encoding fields (1), with the aim of reducing the maximal dB/dt by making the gradient fields more local. The general concept of PatLoc (Parallel Imaging Technique using Localized Gradients) (2,3) is to relax the requirement that the spatial encoding magnetic fields (SEMs) must vary linearly across the field-of-view (FoV) by introducing SEMs exhibiting spatial variation of higher order than standard linear gradients. Parallel imaging technology enables MR imaging with spatially ambiguous encoding fields and, once understood, this additional degree of spatial encoding freedom may lead to improved gradient performance or reduced peripheral nerve stimulation.…”

Monoplanar gradient system for imaging with nonlinear gradients

“…To enable both positive and negative maxima the discussed optimization function can be adapted by introducing an absolute value operation inside the sum. This enables optimization of SEMs for enhanced local orthogonality more freely without neglecting oscillating SEMs which could be used for PatLoc imaging [8,10] that is not bound to spherical harmonics. Allowing for this degree of freedom, Eq.…”

“…Previous studies enforced approximate linearity over a reduced volume for monoplanar gradients to accommodate the unavoidable field decay or were specifically designed for small target volumes [4][5][6][7]. In our recent studies [8][9][10] we have shown that reasonable spatial encoding can be achieved as long as the local gradients of the encoding fields are non-collinear and have a non-zero magnitude. With the field geometries proposed it becomes possible to image a large field of view (FOV), comparable with that produced by built-in linear whole-body gradient systems.…”

“…Because of the dependence on the magnitude of each vector this quantity is not only dependent on the orthogonality of the encoding fields, but also depends linearly on the local gradient strength. The resulting scalar corresponds, in fact, to the inverse of the effective image voxel volume [10]. Therefore, maximization of this function is expected to optimize the local imaging properties in each voxel.…”

“…Existing imaging approaches using nonlinear SEMs use gradient systems generated by cylindrical systems. In PatLoc imaging [8][9][10] nonlinear SEMs are designed such that field ambiguities can be resolved by using a SENSE-like reconstruction to enable a novel type of parallel imaging. The current implementations of PatLoc imaging use the locally orthogonal spherical volume harmonics of second-order C2 and S2 and provide a built-in acceleration factor of two.…”