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

DOI: 10.4236/ojapps.2018.85014, PP. 170-183

Keywords: Magnetic Particle Imaging (MPI), Lock-in-Amplifier Model, Signal Harmonics, Magnetic Nanoparticles (MNPs)

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Abstract:

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.

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