We derive explicit transformation formulae relating the
renormalized quark mass and field as defined in the $\msbar$-scheme
with the corresponding quantities defined in any other scheme. By
analytically computing the three-loop quark propagator in the
high-energy limit (that is keeping only massless terms and terms of
first order in the quark mass) we find the NNNLO conversion factors
transforming the $\msbar$ quark mass and the renormalized quark field
to those defined in a ``Regularization Invariant'' (\RI) scheme which
is more suitable for lattice QCD calculations. The NNNLO contribution
in the mass conversion factor turns out to be large and comparable to
the previous NNLO contribution at a scale of 2 GeV --- the typical
normalization scale employed in lattice simulations. Thus, in order to
get a precise prediction for the $\msbar$ masses of the light quarks
from lattice calculations the latter should use somewhat higher
scale of around, say, 3 GeV where the (apparent) convergence of the
perturbative series for the mass conversion factor is better.
We also compute two more terms in the high-energy expansion of the
$\msbar$ renormalized quark propagator. The result is then used to
discuss the uncertainty caused by the use of the high energy limit in
determining the $\msbar$ mass of the charmed quark. Finally, as a
by-product of our calculations we determine the four-loop anomalous
dimensions of quark mass and field in the Regularization Invariant
scheme.