  We investigate the relation between the brane-based and the bulk-based
approaches for anisotropic case in brane-world models. In the brane-based
approach, the brane is chosen to be fixed on a coordinate system, whereas in
the bulk-based approach it is no longer static as it moves along the extra
dimension. It was shown that these two approaches are basicly equal for
specific models Mukohyama et al., Bowcock et al. In this paper, it is aimed to
get general formalism of the equivalence obtained in Mukohyama et al. We found
that calculations driven by a general anisotropic bulk-based metric yield a
brane-based metric in Gaussian Normal Coordinates by conserving spatial
anisotropy. We also derive solutions for an anisotropic bulk-based model and
apply to get corresponding brane-based metric of the model.
