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In this work, it is demonstrated how an extended equilibrium magnetization model that allows modeling of uniaxial anisotropy for the nanoparticles can be integrated into the system function component model for magnetic particle imaging with a field-free point moving along a Lissajous trajectory. In previous works, the particle model with anisotropy has been shown to describe the measured system function better than the classical Langevin model of paramagnetism. However, the question arises how this model relates to the observed tensor products of the Chebyshev polynomials in the Fourier series components of the system function. Static uniaxial anisotropy is assumed in this work. It is shown that the structure compared to the isotropic solution can be preserved in this case.