  The use of dual-energy CT (DECT) potentially decreases range uncertainties in
proton and ion therapy treatment planning via determination of the involved
physical target quantities. For eventual clinical application, the correct
treatment of tissue mixtures and heterogeneities is an essential feature, as
they naturally occur within a patient's CT. Here, we present how existing
methods for DECT-based ion-range prediction can be modified in order to
incorporate proper mixing behavior on several structural levels. Our approach
is based on the factorization of the stopping-power ratio into the relative
electron density and the relative stopping number. The latter is confined for
tissue between about 0.95 and 1.02 at a therapeutic beam energy of 200 MeV/u
and depends on the I-value. We show that convenient mixing and averaging
properties arise by relating the relative stopping number to the relative cross
section obtained by DECT. From this, a maximum uncertainty of the
stopping-power ratio prediction below 1% is suggested for arbitrary mixtures of
human body tissues.
