Mathematical Modeling of In Vivo Alpha Particle Generators and Chelator Stability

Background: Targeted α particle therapy using long-lived in vivo α 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 212Pb-labeled pharmaceuticals and its radioactive daughters. Materials and Methods: A bolus of 212Pb-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 212Bi for different chelators, for example, 36% for DOTA. The compartmental model was applied to describe a 212Bi retention study and to assess the stability of the 212Bi-1,4,7,10-tetrakis(carbamoylmethyl)-1,4,7,10-tetraazacyclododecane (212Bi-DOTAM) complex after β- decay of 212Pb. Results: The simulation of the injection showed that α emissions contribute 75% to the total released energy, mostly from 212Po (72%). The simulation of the 212Bi retention study showed that (16 ± 5)% of 212Bi atoms dissociate from the 212Bi-DOTAM complexes. The fractions of energies released by free radionuclides were 21% and 38% for DOTAM and DOTA chelators, respectively. Conclusion: The developed α 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.