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We previously presented a lock-in-amplifier model for analyzing the behaviorof signal harmonics in magnetic particle imaging (MPI). In that study, themagnetization and particle size distribution of magnetic nanoparticles (MNPs)were assumed to obey the Langevin theory of paramagnetism and a log-normaldistribution, respectively, and a drive magnetic field was assumed to beapplied parallel to a selection magnetic field. The purpose of the currentstudy was to investigate the behavior of signal harmonics in MPI with the drivemagnetic field being applied to the selection magnetic field in an arbitrarydirection using the lock-in-amplifier model. In the lock-in-amplifier model,the signal induced by MNPs in a receiving coil was multiplied with a referencesignal, and was then fed through a low-pass filter to extract the DC componentof the filtered signal (MPI signal). The strength of the selection magneticfield in MPI was assumed to be given by the product of the gradient strength ofthe selection magnetic field and the distance from the field-free region (x).The relationships between the MPI signal and x were calculated for odd- andeven-numbered harmonics and were investigated for various angles between theaxis of a receiving coil and the selection magnetic field. The behavior ofsignal harmonics in MPI largely depended on the angle between them. This studywill be useful for improved understanding, optimization, and development ofMPI.

Behavior of Signal Harmonics in Magnetic Particle Imaging Based on a Lock-in-Amplifier Model