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.
Murase, K., Konishi, T., Takeuchi, Y. and Takata, H. (2013) Experimental and Simulation Studies on the Behavior of Signal Harmonics in Magnetic Particle Imaging. Radiological Physics and Technology, 6, 399-414.
Murase, K., Hiratsuka, S., Song, R. and Takeuchi, Y. (2014) Development of a System for Magnetic Particle Imaging Using Neodymium Magnets and Gradiometer. Japanese Journal of Applied Physics, 53, Article ID: 067001.
Rahmer, J., Weizenecker, J., Gleich, B. and Borgert, J. (2009) Signal Encoding in Magnetic Particle Imaging: Properties of the System Function. BMC Medical Imaging, 4, 1-21. https://doi.org/10.1186/1471-2342-9-4
Kiss, L.B., Soderlund, J., Niklasson, G.A. and Granqvist, C.G. (1999) New Approach to the Origin of Lognormal Size Distributions of Nanoparticles. Nanotechnology, 10, 25-28. https://doi.org/10.1088/0957-4484/10/1/006
Murase, K., Oonoki, J., Takata, H., Song, R., Angraini, A., Ausanai, P. and Matsushita, T. (2011) Simulation and Experimental Studies on Magnetic Hyperthermia with Use of Superparamagnetic Iron Oxide Nanoparticles. Radiological Physics and Technology, 4, 194-202. https://doi.org/10.1007/s12194-011-0123-4
Reeves, D.B. and Weaver, J.B. (2015) Combined Néel and Brown Rotational Langevin Dynamics in Magnetic Particle Imaging, Sensing, and Therapy. Applied Physics Letters, 107, Article ID: 223106. https://doi.org/10.1063/1.4936930
Murase, K., Shimada, K. and Banura, N. (2016) Correction of Blurring Due to a Difference in Scanning Direction of Field-Free Line in Projection-Based Magnetic Particle Imaging. 6th International Workshop on Magnetic Particle Imaging, 16-18 March 2016, Lübeck.
Macias-Bobadilla, G., Rodríguez-Reséndiz, J., Mota-Valtierra, G., Soto-Zarazúa, G., Méndez-Loyola, M. and Garduño-Aparicio, M. (2016) Dual-Phase Lock-in Amplifier Based on FPGA for Low-Frequencies Experiments. Sensors, 16, Article ID: 379. https://doi.org/10.3390/s16030379