We recently reported a new absorbed dose conversion method, RAP (RAtio of Pharmacokinetics), for 211At-meta-astatobenzylguanidine (211At-MABG) using a single biodistribution measurement (%ID/g). However, there were some mathematical ambiguities in determing the optimal timing of a single measurement of %ID/g. Thus, we aimed to mathematically reconstruct the RAP method and to examine the optimal timing of a single measurement.
We derived a new formalism of the RAP dose conversion method at time t and investigated the new formalism’s performance using a representative RAP coefficient with radioactive-decay weighting. Dose conversions by representative RAP coefficients predicted the true [211At]MABG absorbed doses with an error of 10% or less. The inverses of the representative RAP coefficients plotted at 4 h post-injection, which was the optimal timing reported in the previous work, were very close to the new inverses of the RAP coefficients 4 h post-injection. Next, we acquired a formula to determine the optimal timing of a single measurement of %ID/g, assuming the one-compartment model for biological clearance. The behavior of the optimal timing was analyzed by radiolabeled compounds with physical half-lives of 7.2 h and 10 d on various biological clearance half-lives. Behavior maps of optimal timing showed a tendency to converge to a constant value as the biological clearance half-life of a target increased. The areas of optimal timing for both compounds within a 5% or 10% prediction error were distributed around the optimal timing when the biological clearance half-life of a target was equal to that of the reference. Finally, an example of RAP dose conversion was demonstrated for [211At]MABG.
The RAP dose conversion method renovated by the new formalism was able to estimate the [211At]MABG absorbed dose using a similar pharmacokinetics, such as [131I]MIBG. The present formalism revealed optimizing imaging time points on absorbed dose conversion between two radiopharmaceuticals. Further analysis and clinical data will be needed to elucidate the validity of a behavior map of the optimal timing of a single measurement for targeted alpha-nuclide therapy.