New Approaches for Modeling Radiopharmaceutical Pharmacokinetics Using Continuous Distributions of Rates

Abstract

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...

Usefulness of continuous probability distributions of rates for modelling radionuclide biokinetics in humans and animals

“…In other words, instead of using a sum of several discrete rates, one can use an integral over an infinite number of rates described by a certain probability distribution. This approach, which is known in pharmacokinetics, chemistry and physics 3,6,21,27–29 , allows multiple incompletely understood processes to be combined into a “mixture” represented by only a few adjustable parameters. Specifically, solutions for kinetic equations that characterize relaxation in disordered systems often lead to simple functions such as the stretched exponential or stretched hyperbola, which are known since the 19 th century 5,6,21,29 .…”

Effect of dose and dose rate on temporal γ-H2AX kinetics in mouse blood and spleen mononuclear cells in vivo following Cesium-137 administration

“…The term Q 2 , which contains the parameters r and p , represents time-dependent decrease in γ-H2AX levels due to radionuclide excretion, DNA repair, and death of heavily damaged cells. The mathematical structure of term Q 2 is based on a modified stretched exponential function, which is useful for describing complex decay patterns using small numbers of parameters [28].…”

Enhancing low-dose risk assessment using mechanistic mathematical models of radiation effects

“…A simple alternative involves using CPDs of decay rates [45,46]. This concept in the field of radionuclide biokinetics goes back at least 40 years [47], but has not been used extensively.…”

“…We applied the CPD approach to a variety of human and animal data with different radionuclides (including plutonium, strontium, cesium) measured in the laboratory and in regions contaminated by the Fukushima and Chernobyl nuclear accidents [45,46]. Performances of CPD models with those of sums of discrete rates were compared.…”