  The isospin diffusion of the quasi-projectile formed in the $^{64,58}Ni$ on
$^{64,58}Ni$ reactions in the Fermi energy domain is investigated in the
framework of the Boltzmann-Uehling-Uhlenbeck transport model. The well known
isospin transport ratio observable is revisited, with the aim of insuring an
optimal comparison between experimental data and theoretical calculations and
reducing the present uncertainties in the extraction of empirical equation of
state parameters. We show that isospin transport ratios are sensitive to all
the low order isovector parameters ($E_{sym}$, $L_{sym}$ and $K_{sym}$). We
demonstrate that realistic models of the equation of state, covering the
uncertainty that presently affects the theoretical description of neutron stars
static observables, can be effectively discriminated by isospin diffusion
experiments, provided the neutron to proton ratio of the projectile remnant is
precisely measured as a function of centrality.
