  We previously presented a lock-in-amplifier model for analyzing the behavior
of signal harmonics in magnetic particle imaging (MPI). In that study, the
magnetization and particle size distribution of magnetic nanoparticles (MNPs)
were assumed to obey the Langevin theory of paramagnetism and a log-normal
distribution, respectively, and a drive magnetic field was assumed to be
applied parallel to a selection magnetic field. The purpose of the current
study was to investigate the behavior of signal harmonics in MPI with the drive
magnetic field being applied to the selection magnetic field in an arbitrary
direction 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 reference
signal, and was then fed through a low-pass filter to extract the DC component
of the filtered signal (MPI signal). The strength of the selection magnetic
field in MPI was assumed to be given by the product of the gradient strength of
the selection magnetic field and the distance from the field-free region (x).
The relationships between the MPI signal and x were calculated for odd- and
even-numbered harmonics and were investigated for various angles between the
axis of a receiving coil and the selection magnetic field. The behavior of
signal harmonics in MPI largely depended on the angle between them. This study
will be useful for improved understanding, optimization, and development of
MPI.
