Probability Based Positron Range Modeling in Inhomogeneous Medium for PET

This paper introduces a novel probability based positron range model accounting for the typical case of inhomogeneous medium in experimental or clinical implementations. A survival probability for given energy, medium type and thickness, is used to describe the propagation of monoenergetic positrons with increasing distance in homogeneous medium. This follows from the fact that annihilation distribution of monoenergetic positrons in homogeneous medium can be approximately expressed as an exponential distribution. Similarly, we consider the transport and annihilation of monoenergetic positrons in each layer of inhomogeneous medium as probability events, which can be easily computed using a set of survival probabilities. The ultimate annihilation distribution is a weighted summation over the energy spectrum. Monte Carlo simulation is used to validate the availability and performance of this model. Simulated and estimated annihilation distributions are presented with close agreement. The new model can be used to improve the image resolution without introducing serious artifacts due to the mismatching between models and fact.