  Background: Treatment verification with PET imaging in charged particle
therapy is conventionally done by comparing measurements of spatial
distributions with Monte Carlo (MC) predictions. However, decay curves can
provide additional independent information about the treatment and the
irradiated tissue. Most studies performed so far focus on long time intervals.
Here we investigate the reliability of MC predictions of space and time (decay
rate) profiles shortly after irradiation, and we show how the decay rates can
give an indication about the elements of which the phantom is made up.
  Methods and Materials: Various phantoms were irradiated in clinical and
near-clinical conditions at the Cyclotron Centre of the Bronowice proton
therapy centre. PET data were acquired with a planar 16x16 cm$^2$ PET system.
MC simulations of particle interactions and photon propagation in the phantoms
were performed using the FLUKA code. The analysis included a comparison between
experimental data and MC simulations of space and time profiles, as well as a
fitting procedure to obtain the various isotope contributions in the phantoms.
  Results and conclusions: There was a good agreement between data and MC
predictions in 1-dimensional space and decay rate distributions. The fractions
of $^{11}$C, $^{15}$O and $^{10}$C that were obtained by fitting the decay
rates with multiple simple exponentials generally agreed well with the MC
expectations. We found a small excess of $^{10}$C in data compared to what was
predicted in MC, which was clear especially in the PE phantom.
