Multidimensional x-space magnetic particle imaging

Abstract

Magnetic particle imaging (MPI) is a promising new medical imaging tracer modality with potential applications in human angiography, cancer imaging, in vivo cell tracking, and inflammation imaging. Here we demonstrate both theoretically and experimentally that multidimensional MPI is a linear shift-invariant imaging system with an analytic point spread function. We also introduce a fast image reconstruction method that obtains the intrinsic MPI image with high signal-to-noise ratio via a simple gridding operation in x-space. We also demonstrate a method to reconstruct large field-of-view (FOV) images using partial FOV scanning, despite the loss of first harmonic image information due to direct feedthrough contamination. We conclude with the first experimental test of multidimensional x-space MPI.

Fig. 1

Two opposing ring magnets with radial symmetry about the z axis produce a 3-D gradient field with a FFP at the isometric center. This gradient can be remarkably strong. Our current imager produces a gradient of 6 T/m in the z axis, and 3 T/m in the x and y axes across a 8.89 cm free bore through the z axis with excellent linearity.

Fig. 2

The tangential and normal point spread function envelopes, ENV_T and ENV_N shown for ‖kH‖ ≤ 20. ENV_T is the limit to MPI resolution, and defines MPI bandwidth [14]. ENV_N has approximately half the intrinsic resolution with FWHM_T = 4.2 and FWHM_N = 9.5. The value kH is unitless.

Fig. 3

Collinear and transverse components of the matrix point spread function. The received images rotate with vector ${\widehat{\dot{\mathbf{x}}}}_s$ (see Fig. 4). The collinear PSF component peak amplitude is 370% the tangential PSF component peak amplitude. The area of the box drawn in the collinear PSF is experimentally measured in Fig. 7.

Fig. 4

MPI images are acquired on a reference frame formed by vectors collinear and transverse to the velocity vector ${\widehat{\dot{\mathbf{x}}}}_s$.

Fig. 5

X-space MPI imager. (a) Tomographic MPI scanner with 2 cm × 2 cm × 4 cm FOV. The excitation transmit coil generates a 30 mT peak-to-peak oscillating magnetic field at 20 kHz. The NdFeB magnet gradient generates a gradient of 6 T/m down the imaging bore, and 3.25 T/m transverse to the imaging bore. (b) Photograph of x-space MPI scanner. The free bore before addition of the transmit and receive coils is 8.4 cm.

Fig. 6

[Top] Experimental data showing 40 overlapping partial FOV line-scans for a 400 µm point source phantom. The baseline component for each partial FOV is lost in the scanning process due to the contamination of first harmonic imaging data by direct feedthrough. [Bottom] Using standard image processing methods, we can reconstruct a smooth version of the data segments, obtaining the maximally continuous image.

Fig. 7

(a) Measured two-dimensional collinear PSF showing excellent correspondence to Fig. 3. The measured FWHM is 1.6 mm along the imager bore and 7.4 mm transverse to the imager bore. The PSF phantom is a 400 µm tubing oriented perpendicular to the bore. (b) Theoretical PSF assuming SPIO nanoparticle of lognormal size distribution with d = 17 ± 3.4 nm.

Fig. 8

Profiles across the point spread function shown in Fig. 7(a), (b) show good agreement between theoretical and measured values. [TOP] Line scan down the bore. [BOTTOM] Line scan perpendicular to the imager bore.

Fig. 9

(a) “CAL” Phantom built using 400 µm ID tubing filled with undiluted tracer and encapsulated. (b) Intrinsic MPI image of the CAL phantom showing excellent correspondence to the phantom image. FOV: 4 cm × 2 cm, Pixel size: 200 µm × 1 mm. Total imaging time of 28 s not including robot movement.