  The magnetohydrodynamic-kinetic (MHD-kinetic) hybrid model [Park et. al.,
1992] has been widely applied in studying energetic particles (EPs) problems in
fusion plasmas for past decades. The pressure-coupling scheme or the
current-coupling scheme is adopted in this model. However, two noteworthy
issues arise in the model application: firstly, the coupled term introduced in
the pressure-coupling scheme, $\left( \nabla \cdot \mathbf{P}_{\mathrm{h}}
\right)_{\bot}$, is often simplified by $\nabla \cdot \mathbf{P}_{\mathrm{h}}$,
which is equivalent to neglecting the parallel inertial term of EPs; secondly,
besides the $\delta f $ contribution caused by changing in the EP distribution
function, the magnetic field perturbation (the $\delta \mathbf{B} $
contribution) generated during development of the instabilities should also be
considered, but it is often ignored in existing hybrid simulations. In this
paper, we derive the analytical formulations under these two coupling schemes
and then numerically study the representative case of the linear stability of
the m/n=1/1 internal kink mode (IKM) [Fu et. al., 2006] by using the CLT-K
code. It is found that the approximated models can still yield reasonable
results when EPs are isotopically distributed. But it fails completely in cases
with anisotropic EP distributions. In addition, we further investigate the
influence of EP's orbit width on the stability of IKM and verify the
equivalence between pressure-coupling scheme and the current-coupling scheme.
