  A novel strategy for extracting axial (AV) and toroidal (TV) vortices in the
magnetically-induced current density (MICD) in molecular systems is introduced,
and its pilot application to LiH molecule is demonstrated. It exploits
differences in the topologies of AV and TV cores and involves two key steps:
selecting a scalar function that can describe vortex cores in MICD and its
subsequent topological analysis. The scalar function of choice is
$\Omega^{B_\alpha}$ based on the velocity-gradient $\Omega$ method known in
research on classical flows. The Topological Data Analysis (TDA) is then used
to analyze the $\Omega^{B_\alpha}$ scalar field. In particular, TDA robustly
assigns distinct topological features of this field to different vortex types
in LiH: AV to saddle-maximum separatrices which connect maxima to 2-saddles
located on the domain's boundary, TV to a 1-cycle of the super-level sets of
the input data. Both are extracted as the most \emph{persistent} features of
the topologically-simplified $\Omega^{B_\alpha}$ scalar field.
