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 188 Re-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. Phar macokinetics of radiopharmaceuticals (e.g., radioimmunotherapy agents) are assumed to follow first-order kinetics and are, therefore, approximated by the sum of discrete rates (1-3). However, the existence of first-order kinetics does not necessarily imply the existence of only a few discrete rates. Instead, complex decay patterns may result from a continuous probability distribution (CPD) of first-order rates (4,5). "Depending on the level of precision, a decay can be fitted with a sum of 2 or 3 exponentials with satisfactory x 2 values and weighted residuals despite the existence of an underlying distribution" (5).We hypothesized that pharmacokinetic processes can be modeled even better by CPDs of rates using only 1-2 parameters than by sums of discrete rates using 3 or more parameters. To test this hypothesis, we used data on biodistribution of 188 Re-labeled antibody to melanin in athymic melanoma xenograft-bearing mice (6,7).We used 7 models to fit the data. Three of them assumed discrete pharmacokinetic rates, and 4 assumed CPDs. We compared the performances of these models, and their predictions for the total time integral of radioactivity (which is needed for radiopharmaceutical dosimetry), using information theoretic methods. Our results provide new insight into modeling of radiopharmaceutical pharmacokinetics.
MATERIALS AND METHODS
DatasetsThe biodistribution studies analyzed here were published (6) and are described in the supplemental data (supplemental materials are available at http://jnm.snmjournals.org). Briefly, athymic mice (maintained in accordance wi...