Parameterization of the harmonic content of the complex MPI signal of magnetic tracers using a set of polynomial coefficients

• Ways to parameterize the MPI signal using polynomials were investigated.
• The Taylor series diverges at ξ=±π when applied to the Langevin function.
• The parameterization using a numerical model was successful.
• The Langevin function and simulated time shifted signals could be parameterized.

In our work, we investigate the possibility of a polynomial interpolation of the Magnetic Particle Imaging (MPI) signal to parameterize the harmonic content of the signal to analyze the imaging quality at a limited number of harmonics. The traditional Taylor expansion of the magnetization curve is limited by a radius of convergence which is exceeded by the physical properties of real nanoparticle ensembles and MPI setups. This led us to the derivation of an alternative method using polynomial interpolation. Our method enabled us to express MPI signals based on the analytical Langevin function as well as numerical simulated data using other magnetization functions and a phase shift in relation to the excitation signal. The argument range of the interpolation function is wide enough to cover real cases. We conclude that the polynomial interpolation method represents a versatile tool to describe the relation between the magnetization curve and the MPI signals.