Parallel imaging in non-bijective, curvilinear magnetic field gradients: a concept study

Abstract

Objectives The paper presents a novel and more generalized concept for spatial encoding by non-unidirectional, nonbijective spatial encoding magnetic fields (SEMs). In combination with parallel local receiver coils these fields allow one to overcome the current limitations of neuronal nerve stimulation. Additionally the geometry of such fields can be adapted to anatomy. Materials and methods As an example of such a parallel imaging technique using localized gradients (PatLoc)-system, we present a polar gradient system consisting of 2×8 rectangular current loops in octagonal arrangement, which generates a radial magnetic field gradient. By inverting the direction of current in alternating loops, a near sinusoidal field variation in the circumferential direction is produced. Ambiguities in spatial assignment are resolved by use of multiple receiver coils and parallel reconstruction. Simulations demonstrate the potential advantages and limitations of this approach. Results and conclusionsThe exact behaviour of PatLoc fields with respect to peripheral nerve stimulation needs to be tested in practice. Based on geometrical considerations SEMs of radial geometry allow for about three times faster gradient switching compared to conventional head gradient inserts and even more compared to whole body gradients. The strong nonlinear geometry of the fields needs to be considered for practical applications.

Higher order reconstruction for MRI in the presence of spatiotemporal field perturbations

“…Time integration according to Eq. 1 then yields the phase model (37) [3] where B ref (r) denotes the net field at some reference point in time and the sum represents phase accumulation due to any field dynamics relative to B ref (r). h l denotes the l-th out of N l solid harmonics (36) and k l the corresponding expansion coefficient.…”

“…To use the model [3] for image reconstruction, the time courses of the phase coefficients k l (t) need to be determined in some reliable way. As detailed in a later section, in this work, they are measured with an array of NMR field probes mounted around the imaging volume (28,32).…”

“…To fully determine the model [3], B ref (r) equally needs to be measured, e.g., by conventional B 0 mapping based on …”

“…In this case, the coils generate curvilinear yet time-invariant field patterns and standard Fourier imaging still applies in the resulting curved coordinate system. The corresponding image distortions can be removed by unwarping (1) and, in the extreme case of non-bijective gradient fields, by unfolding based on array detection (2,3). Magnetic fields of higher than first order in space also arise from imperfection of the main magnet and susceptibility effects.…”

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.…”