Equilibrium Model with Anisotropy for Model-Based Reconstruction in Magnetic Particle Imaging
arxiv(2024)
摘要
Magnetic particle imaging is a tracer-based tomographic imaging technique
that allows the concentration of magnetic nanoparticles to be determined with
high spatio-temporal resolution. To reconstruct an image of the tracer
concentration, the magnetization dynamics of the particles must be accurately
modeled. A popular ensemble model is based on solving the Fokker-Plank
equation, taking into account either Brownian or Néel dynamics. The
disadvantage of this model is that it is computationally expensive due to an
underlying stiff differential equation. A simplified model is the equilibrium
model, which can be evaluated directly but in most relevant cases it suffers
from a non-negligible modeling error. In the present work, we investigate an
extended version of the equilibrium model that can account for particle
anisotropy. We show that this model can be expressed as a series of Bessel
functions, which can be truncated based on a predefined accuracy, leading to
very short computation times, which are about three orders of magnitude lower
than equivalent Fokker-Planck computation times. We investigate the accuracy of
the model for 2D Lissajous MPI sequences and show that the difference between
the Fokker-Planck and the equilibrium model with anisotropy is sufficiently
small so that the latter model can be used for image reconstruction on
experimental data with only marginal loss of image quality, even compared to a
system matrix-based reconstruction.
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