  Careful determination of the heating performance of magnetic nanoparticles
under AC fields is critical for magnetic hyperthermia applications. However,
most interpretations of experimental data are based on the uniaxial anisotropy
approximation, which in first instance can be correlated with particle aspect
ratio. This is to say, the intrinsic magnetocrystalline anisotropy is
discarded, under the assumption that the shape contribution dominates. We show
in this work that such premise, generally valid for large field amplitudes,
does not hold for describing hyperthermia experiments carried out under small
field values. Specifically, given its relevance for \textit{in vivo}
applications, we focus our analysis on the so-called "Brezovich criterion",
$H\cdot{f}=4.85\times{10^8}A/m\cdot{s}$. By means of a computational model, we
show that the intrinsic magnetocrystalline anisotropy plays a critical role in
defining the heat output, determining also the role of shape and aspect ratio
of the particles on the SLP. Our results indicate that even small deviations
from spherical shape have an important impact in optimizing the heating
performance. The influence of interparticle interactions on the dissipated heat
is also evaluated. Our results call therefore for an improvement in the
theoretical models used to interpret magnetic hyperthermia performance.
