A Bayesian approach to biokinetic models of internally deposited radionuclides

Author

Mamun F. Amer

Date of Award

5-1997

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Nuclear Engineering

Major Professor

Peter G. Groer

Committee Members

Laurence Miller, Belle Upadhyaya, Yueh-er Kuo

Abstract

Bayesian methods were developed and applied to estimate parameters of biokinetic models of internally deposited radionuclides for the first time. Marginal posterior densities for the parameters, given the available data, were obtained and graphed. These densities contain all the information available about the parameters and fully describe their uncertainties. Two different numerical integration methods were employed to approximate the multi-dimensional integrals needed to obtain these densities and to verify our results. One numerical method was based on Gaussian quadrature. The other method was a lattice rule that was developed by Conroy. The lattice rule method is applied here for the first time in conjunction with Bayesian analysis. Computer codes were developed in Mathematicals own programming language to perform the integrals. Several biokinetic models were studied. The first model was a single power function, a t^-b, that was used to describe ²²⁶Ra whole body retention data for long periods of time in many patients. The posterior odds criterion for model identification was applied to select, from among some competing models, the best model to represent ²²⁶Ra retention in man. The highest model posterior was attained by the single power function. Posterior densities for the model parameters were obtained for each patient. Also, predictive densities for retention, given the available retention values and some selected times, were obtained. These predictive densities characterize the uncertainties in the unobservable retention values taking into consideration the uncertainties of other parameters in the model. The second model was a single exponential function, α e^-βt , that was used to represent one patient's whole body retention as well as total excretion of ¹³⁷Cs. Missing observations (censored data) in the two responses were replaced by unknown parameters and were handled in the same way other model parameters are treated. By applying the Bayesian method of Box and Draper, a better inference in addition to an increased precision of parameter estimates was achieved. The last model we considered was a two-compartment model used to describe the metabolism of radioactive sulfate in humans. Measurements of activity in serum and urine were available. The solutions of the two differential equations that describe the metabolic process were used to produce posterior densities for the rate constants. The linkage between the compartments made it possible to combine activity measurements in each to increase the precision of parameter estimates.

Recommended Citation

Amer, Mamun F., "A Bayesian approach to biokinetic models of internally deposited radionuclides. " PhD diss., University of Tennessee, 1997.
https://trace.tennessee.edu/utk_graddiss/9426