Lock-in-Amplifier Model for Analyzing the Behavior of Signal Harmonics in Magnetic Particle Imaging

The purpose of this study was to present a lock-in-amplifier model for analyzing the behavior of signal harmonics in magnetic particle imaging (MPI) and some simulation results based on this model. In the lock-in-amplifier model, the signal induced by magnetic nanoparticles (MNPs) in a receiving coil was multiplied with a reference signal, and was then fed through a low-pass filter to extract the DC component of the signal (output signal). The MPI signal was defined as the mean of the absolute value of the output signal. The magnetization and particle size distribution of MNPs were assumed to obey the Langevin theory of paramagnetism and a log-normal distribution, respectively, and the strength of the selection magnetic field (SMF) in MPI was assumed to be given by the product of the gradient strength of the SMF and the distance from the field-free region (x). In addition, Gaussian noise was added to the signal induced by MNPs using normally-distributed random numbers. The relationships between the MPI signal and x were calculated for the odd- and even-numbered harmonics and were investigated for various time constants of the low-pass filter used in the lock-in amplifier and particle sizes and their distributions of MNPs. We found that the behavior of the MPI signal largely depended on the time constant of the low-pass filter and the particle size of MNPs. This lock-in-amplifier model will be useful for better understanding, optimizing, and developing MPI, and for designing MNPs appropriate for MPI.

Effect of Signal Filtering on Image Quality of Projection-Based Magnetic Particle Imaging

Purpose: Magnetic particle imaging (MPI) allows for imaging of the spatial distribution of magnetic nanoparticles (MNPs) in positive contrast, with high sensitivity, high spatial resolution, and high imaging speed. It is necessary to increase the signal-to-noise ratio to enhance the reliability of MPI. The purpose of this study was to investigate the effect of signal filtering on the image quality and quantitativity in projection-based MPI using phantoms. Materials and Methods: We fabricated two kinds of phantom (cylindrical tube phantom with a diameter of 6 mm and A-shaped phantom) and evaluated the effect of signal filtering in terms of root-mean-square (RMS) granularity and the correlation coefficient between iron concentrations of MNPs and average MPI values for four filter modes (THRU, BPF, BEF, and LPF). In the THRU mode, the signal input was output without passing through the filter. In the BPF mode, only the third-harmonic signal was passed using a band-pass filter (central frequency: 1200 Hz, band width: 1/3 octave). In the BEF mode, the first-harmonic signal was eliminated using a band-elimination filter (central frequency: 400 Hz, band width: 1/3 octave). In the LPF mode, only the signal with a frequency less than the third-harmonic frequency was passed using a low-pass filter (cut-off frequency: 1200 Hz, -24 ± 2 dB/octave). The RMS granularity was obtained by calculating standard deviations of the pixel values in the MPI image without MNPs, whereas average MPI values were obtained by drawing a circular region of interest with a diameter of 6 mm on the MPI image of the cylindrical tube phantom. Results: When using the filtered back-projection (FBP) method with a ramp filter for image reconstruction, the RMS granularity and correlation coefficient decreased in the order of THRU, BPF, BEF, and LPF. In the BPF mode, however, some artifacts were observed. When using the maximum likelihood-expectation maximization (ML-EM) algorithm with an iteration number of 15, the correlation coefficient decreased in the order of THRU, BPF, BEF, and LPF, whereas the RMS granularity did not largely depend on the filter mode and was significantly (p Conclusion: The BEF mode is adequate for the FBP method in projection-based MPI, whereas THRU is a best option in use of the ML-EM algorithm.