New approaches for modeling radiopharmaceutical pharmacokinetics using continuous distributions of rates

Radiopharmaceutical pharmacokinetics are usually approximated by sums of discrete first-order rates, using 3 or more parameters. We hypothesized that pharmacokinetic processes can be modeled even better by continuous probability distributions (CPD) of rates, using only 1-2 parameters. Methods: To test this hypothesis, we used biodistribution data for 188Re-labeled melanin-specific antibody in blood, kidneys, liver, bone marrow, and lungs of melanoma xenograft-bearing mice. We used 3 discrete-rate models (monoexponential, monoexponential with constant, and biexponential) and 4 CPD models (stretched-exponential, modified stretched-exponential, simplified versions of stretched-exponential, and modified stretched-exponential). They were compared by sample-size-corrected Akaike information criterion. Total time integrals of radioactivity were computed for each model and averaged across all models. Results: The ratio of weights of evidence for CPD versus discrete-rate models was high for blood (12.2) and lungs (2.7), almost unity (0.99) for bone marrow, and slightly lower for kidneys (0.81) and liver (0.73). In all organs or tissues except lungs, model-averaged time integrals were 12.7%-54.0% higher than biexponential model estimates. Conclusion: Simple CPD models often outperform more complex discrete-rate models on pharmacokinetic data. Radioactivity time integrals are more robustly estimated by multimodel inference than using any single model.