  We present evidence of strain-induced modulation of electron correlation
effects and increased orbital anisotropy in the rutile phase of epitaxial
VO$_2$/TiO$_2$ films from hard x-ray photoelectron spectroscopy and soft V
L-edge x-ray absorption spectroscopy, respectively. By using the U(1) slave
spin formalism, we further argue that the observed anisotropic correlation
effects can be understood by a model of orbital selective Mott transition at a
filling that is non-integer, but close to the half-filling. Because the
overlaps of wave functions between $d$ orbitals are modified by the strain,
orbitally-dependent renormalizations of the bandwidths and the crystal fields
occur with the application of strain. These renormalizations generally result
in different occupation numbers in different orbitals. We find that if the
system has a non-integer filling number near the half-filling such as for
VO$_2$, certain orbitals could reach an occupation number closer to
half-filling under the strain, resulting in a strong reduction in the
quasiparticle weight $Z_{\alpha}$ of that orbital. Moreover, an orbital
selective Mott transition, defined as the case with $Z_{\alpha} = 0$ in some,
but not all orbitals, could be accessed by epitaxial strain-engineering of
correlated electron systems.
