  We have determined the relation between the in-medium $\omega $ meson mass
and quark condensate in the framework of a Nambu Jona-Lasinio model constrained
by some recent experimental data on the meson properties in nuclei. In addition
to the usual four-quark interactions, we have included eight-quark terms in the
Lagrangian. The parameters of this model have been determined using the meson
properties in the vacuum as well as in the medium. More particularly, we have
constrained both the in-medium pion decay constant to the value measured in
experiments on deeply bound pionic atoms and the in-medium $\omega $ meson mass
to the experimental value obtained either by the TAPS collaboration or by the
E325 experiment at KEK. Our results are compared to several scaling laws and in
particular to that of Brown and Rho.
