Mathematical Modeling of Alpha Particle Generators and Chelator Stability.

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