Author: Lars R Furenlid, Chiao Huang, Matthew A. Kupinski, Brian W. Miller 👨🔬
Affiliation: University of Arizona, Departments of Radiation Oncology and Medical Imaging, University of Arizona 🌍
Purpose: To sample random numbers of decay of radiotracers in a pharmacokinetic compartment model for Monte-Carlo simulation of imaging in targeted alpha therapy.
Methods: Time-activity curves (TACs) solved from a reported two-tissue compartment model of PSMA-11 prostate-cancer tracer and Pb203, an imaging surrogate for targeted alpha therapy, were used as a joint probability density/mass function to describe when and where the isotope will decay randomly. With the administration of 10 million isotopes at time zero, the time and the organ where each isotope decayed were sampled using the chain rule. The number of decays in each organ was counted within a specified 30-minute imaging duration. Multiple realizations were performed and the distribution of the number of decays of each organ in the compartment model was estimated.
Results: We found that with a specified 30-minute imaging time, the number of decays of Pb-203 in each organ sampled from the chain rule follows a Poisson distribution, whose mean aligns with the integration of TAC of that organ within the imaging duration. A mathematical description was also derived to explain the observation based on Multinomial Selection of Poisson.
Conclusion: This study provides a stochastic description of the decay of radiotracers in the tissue compartment model and validated that number of decays of the isotopes in each organ in the model follows a Poisson distribution within a short imaging time. The description is valid for any isotopes, i.e. either therapeutic or imaging isotopes in targeted alpha therapy, and compartment model as long as they follow the first-order decay and transport equation. From the number of decays, emitted photons can be further calculated and used in the future for Monte-Carlo simulation of SPECT imaging in targeted alpha therapy.