Mathematical Modeling of In Vivo Alpha Particle Generators and Chelator Stability

Abstract

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.