Heavy-ion radiotherapy is an efficient method for the treatment of deep-seated tumors, because the stopping of ions in a tissue delivers the maximal absorbed dose to the tumor-affected areas with minimal damage to the healthy tissues. However, heavy ions can undergo nuclear reactions, giving products with lower Z-values and hence a longer range in the tissue. This causes a dose increase beyond the mean range of the primary beam. The contribution of such reaction products was examined in an experiment where a stack of tissue-like targets interleaved with CR-39 etched track detectors (ETD) was irradiated with heavy ions. The analysis was performed using a recently developed technique of trajectory tracing, which enables the spectroscopy of fragments with different Z-values.