Simultaneous correction of sensitivity and spatial resolution in projection‐based magnetic particle imaging

Abstract

Purpose: The purpose of this study was to develop a method to simultaneously correct the spatial resolution and inhomogeneous sensitivity of a receiving coil in projection-based magnetic particle imagingand to investigate its efficacy through simulation and experimental studies. Methods: Magnetic particle imaging (MPI) images were reconstructed using the simultaneous algebraic reconstruction technique (SART), and simultaneous corrections to sensitivity and spatial resolution were performed by incorporating the sensitivity map of the receiving coil and the system function into the SART algorithm. After each SART update, the regularization methodwith total variation (TV) minimizationwas used to suppress noise amplification and artifact generation. For comparison, MPI images were also reconstructed using the filtered backprojection (FBP) method and the FBP-truncated singular value decomposition (TSVD) method, in which the system function was deconvolved from the projection data using TSVD. In simulation studies, the sensitivity map of a second-order, gradiometer-type receiving coil was generated using the Biot-Savart law, while the system function was obtained by calculating the MPI signals induced by magnetic nanoparticles at various distances from a field-free line (FFL), using a lock-in-amplifier model. The effects of a regularization parameter for TV minimization (a), number of iterations (N), and signal-to-noise ratio (SNR) of the MPI signals on the reconstructed MPI images of a numerical phantom were evaluated, using the image profiles and percent root mean square error (PRMSE). Experimental studies involved the calculation of the system function using a tube phantom. Projection data for an A-shaped phantom were acquired using our MPI scanner, and their MPI images were reconstructed from the projection data, as described above. Results: When both the sensitivity and spatial resolution were corrected (SART-SR), the quality of the reconstructed images was seen to have improved, compared to when the spatial resolution was not correctedor when the FBP and FBP-TSVD methods were used. When SNR was low (20), a larger a value yielded a better image. The minimum PRMSE occurred at N % 200-400 and increased with increasing N thereafter. When SNR was high (100), the image quality was generally not dependent on the a value within its studied range. The PRMSE decreased slowly with increasing N, and tended to converge to a constant value. The full width at half maximum (FWHM) of the profile was obtained from the A-shaped phantom, reconstructed using the SART-SR algorithm with a = 0.05 and N = 1000. The FWHM value of the tube (2 mm diameter) in the A-shaped phantom image was found to be 2.2 mm on average, whereas those calculated from the images obtained by the FBP and FBP-TSVD methods were 4.4 and 3.0 mm on average, respectively. Spatial resolution improved when using the FBP-TSVD method as compared to the FBP method but image distortion and artifacts were observed. Conclusions: Although further studies are necessary to opti...

Three-dimensional image reconstruction in projection-based magnetic particle imaging

“…12,13) Recently, we developed a method for the simultaneous correction of sensitivity and spatial resolution in projectionbased MPI. 14) In this method, we incorporated the system function (SF) into a simultaneous algebraic reconstruction technique (SART). 15) An SF is a function that describes the blur derived from the magnetization characteristics of MNPs.…”

“…In this method, the relationship between the elements of the SM and SF is derived and used. 14) However, our previous study was limited to two-dimensional (2D) image reconstruction. To extend our method to a 3D case, it is necessary to acquire multislice projection data and use the 2D SF map instead of the SF.…”

“…( 5), a regularization method with total variation (TV) minimization was used to suppress noise amplification. For TV minimization, 3D isotropic TV 17) was used, and the gradient descent method 14) was applied on f , n with f n,1 set as…”

“…To perform simulation studies, we constructed a numerical phantom (helix; length: 42 mm, outer diameter: 24 mm, inner diameter: 16 mm, pitch: 19 mm, inside pixel value: 1, and outside pixel value: 0) and generated the projection data for each slice via the Radon transform, 14) with the assumption that S j ( ) in Eq. ( 4) was unity, and the FFL rotated around the receiving coil axis through 180°in intervals of 6°and translated in the direction perpendicular to the receiving coil axis, from −16 to +16 mm in intervals of 1 mm.…”

“…In projection-based MPI, the SF map can be measured using a point source at a single location. 14) Meanwhile, the standard system-matrix-based MPI requires an intensive calibration procedure to generate A, in which the MPI signal spectra are measured individually for a point source positioned at all pixel locations within the FOV. 1,2,11) When rotating and translating the FFL mechanically, 20) the temporal resolution of projectionbased MPI is inferior to that of system-matrix-based MPI.…”