Mathematical Modeling of In Vivo Alpha Particle Generators and Chelator Stability

Background: Targeted alpha particle therapy using long-lived in vivo alpha particle generators is cytotoxic to target tissues. However, the redistribution of released radioactive daughters through the circulation should be considered. A mathematical model was developed to describe the physicochemical kinetics of Pb-212-labeled pharmaceuticals and its radioactive daughters. Materials and Methods: A bolus of Pb-212-labeled pharmaceuticals injected in a developed compartmental model was simulated. The contributions of chelated and free radionuclides to the total released energy were investigated for different dissociation fractions of Bi-212 for different chelators, for example, 36% for DOTA. The compartmental model was applied to describe a Bi-212 retention study and to assess the stability of the Bi-212-1,4,7,10-tetrakis(carbamoylmethyl)-1,4,7,10-tetraazacyclododecane (Bi-212-DOTAM) complex after beta(-) decay of Pb-212. Results: The simulation of the injection showed that alpha emissions contribute 75% to the total released energy, mostly from Po-212 (72%). The simulation of the Bi-212 retention study showed that (16 +/- 5)% of Bi-212 atoms dissociate from the Bi-212-DOTAM complexes. The fractions of energies released by free radionuclides were 21% and 38% for DOTAM and DOTA chelators, respectively. Conclusion: The developed alpha particle generator model allows for simulating the radioactive kinetics of labeled and unlabeled pharmaceuticals being released from the chelating system due to a preceding disintegration.

Automated summary

A mathematical model was developed to describe the kinetics of Pb-212-labeled pharmaceuticals and its radioactive daughters. The simulation revealed that alpha emissions contributed significantly to the total released energy, and the Bi-212-DOTAM complexes had a certain dissociation during retention. The contributions of different chelators to the energy released by free radionuclides were varied.