Author: Lars R Furenlid, Chiao Huang, Matthew A. Kupinski, Brian W. Miller 👨🔬
Affiliation: University of Arizona, Departments of Radiation Oncology and Medical Imaging, University of Arizona 🌍
Purpose: To sample correlated k-constants in tissue-compartment model for pharmacokinetic study in targeted alpha therapy.
Methods: This work simulated the biodistribution of PSMA-11 tracers labeled with Pb-212 α-emitting isotopes in a two-tissue compartment model. With reported mean and variance of k = {K1, k2, k3, k4} in the model, Approximate-Bayesian Computation (ABC) was used to sample random k to represent stochastic patient trials. The ABC method is a rejection method which samples posterior distribution from an assumed prior and provides information of correlations between k’s inter- and intra-organs. We assumed independent k’s as prior and calculated the posterior (1) correlation between k’s within an organ, (2) correlation of total volume distribution VT = K1/k2(1 + k3/k4) among the organs, and (3) organ dose, and compared them to the prior assumption.
Results: While sampling independent k’s in prior, in the posterior we found both intra-organ correlation (positive correlations between K1 and k2 and k2 and k3, and negative correlation between K1 and k2 in kidneys, for example) and inter-organ correlations with an increased correlation among VT of some of the organs. The distribution of organ dose calculated from correlated k’s also showed lower relative mean square error to the mean dose calculated from mean k’s with lower acceptance rate of ABC method, showing the stabilization of dose distribution in the sampling.
Conclusion: Most reported k’s in compartment models only provide mean and variance of individual k, but not the correlation among them. Sampling k’s independently is a rough approximation; correlations are expected among the k values. By using the ABC method, our results showed the correlation of k’s intra- and inter-organs. The work provides a way to generate stochastic trials of tracer-distribution and organ doses from a correlated compartment model and has potential benefits to pharmacokinetic studies in targeted alpha therapy.