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, non- bijective 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 x 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 conclusions: The 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.

Fig. 1

Octagonal coil arrangement used in the simulations. 2 × 8 planar coils are arranged in an octagonal arrangement around the direction of the main field (z). r and ϕ denote the radial resp. azimuthal directions in polar coordinates. Arrows next to the rungs indicate the current direction

Fig. 2

A color-coded field plot of magnetic field B_z produced by the coil array in (Fig. 1) with a current of 10 A through each of the six rungs at the center of the planar coils at a radius r = 6 cm. The maximum field is 0.68 mT at a radius r = 5.56cm from the center

Fig. 3

a Field Bz along r. The dotted line represents a constant gradient with identical maximum and minimum. b Gradient G corresponding to the derivative of Bz alongr. The dotted line represents the mean gradient between the field maximum and minimum

Fig. 4

a Spectrum F_ω of a periodically modulated spin distribution with a peak-to-peak distance of 4 pixels and ∼1 pixel halfwidth measured with a constant mean gradient G_const at a bandwidth ω = 40,960 Hz. The observed halfwidth of the spectrum is ∼2 pixels. b Spectrum F_ω of same spin distribution observed in the radial SEM_R shown in Fig. 3b at identical bandwidth. c Spectra from a and b mapped to spatial coordinates

Fig. 5

a Magnetic field profile of SEM_C generated from an octopole arrangement of coils with a current of 10 A flowing in alternating directions through the coil configuration shown in Fig. 1. Arrows indicate the primary direction of the field gradient. The wedge shaped outline shows one of the eight subregions for unambiguous (but curved) spatial encoding. b Gradient of the SEM_C at equidistant positions in the dotted ring shown in (Fig. 5a) as a function of the azimuth angle ϕ. Only two of the four gradient lobes (0 < ϕ < 180°) are shown for clarity

Fig. 6

Basic workflow for PatLoc reconstruction of a spin distribution I_ρ(x, y) into its PatLoc image I_xy(x, y). For explanation see text

Fig. 7

Results of simulations of circular (a, b), spokewheel (c, d) and random (e, f) spin distribution patterns imaged by constant Cartesian gradients (left column) versus PatLoc gradients SEM_C and SEM_R (right column). Linewidth of the modulated geometrical patterns was roughly 1 pixel at 256 × 256 matrix size

Fig. 8

Spin distribution taken from a 512 × 512 volunteer image imaged simulated to be imaged with conventional gradients (a) and with PatLoc gradients SEM_R and SEM_C acquired at 384 × 384 (b) and 256 × 256 (c) matrix size

Fig. 9

a Colour encoded display of the angle α between the gradients produced by the multipolar SEM_C and the interleaved multipolar SEM_CI generated from SEM_C by rotation by 22.5°. b Superposition of isocontour lines of SEM_CI and SEM_C

Fig. 10

Simulation of a phantom image produced by combining the circular and spoke wheel patterns in (Fig. 7a, c) when imaged with conventional gradients and with SEM_C and SEM_CI. Linewidth of the geometrical patterns was ∼1 pixel at 256 × 256 matrix size