  We present a Monte Carlo simulation of the perturbative Quantum
Chromodynamics (pQCD) shower developing after a hard process embedded in a
heavy-ion collision. The main assumption is that the cascade of branching
partons traverses a medium which (consistent with standard radiative energy
loss pictures) is characterized by a local transport coefficient qhat which
measures the virtuality per unit length transferred to a parton which
propagates in this medium. This increase in parton virtuality alters the
development of the shower and in essence leads to extra induced radiation and
hence a softening of the momentum distribution in the shower. After
hadronization, this leads to the concept of a medium-modified fragmentation
function. On the level of observables, this is manifest as the suppression of
high transverse momentum (PT) hadron spectra. We simulate the soft medium
created in heavy-ion collisions by a 3-d hydrodynamical evolution and average
the medium-modified fragmentation function over this evolution in order to
compare with data on single inclusive hadron suppression and extract the qhat
which characterizes the medium. Finally, we discuss possible uncertainties of
the model formulation and argue that the data in a soft momentum show evidence
of qualitatively different physics which presumably cannot be described by a
medium-modified parton shower.
