• UNCERTAINTY MODELING OF RETENTION FUNCTION IN BIOKINETIC MODEL USING POLYNOMIAL CHAOS THEORY - DEVELOPMENT OF COMPUTATIONAL ALGORITHM

Abstract

Uncertainty analysis of the retention function of any radionuclide either ingested or inhaled plays a central role in the dosimetry of internally deposited radionuclide. The modeling approach presented in International Commission of Radiological Protection publication used exponential retention curves to calculate dose to the possible target or critical organs. Presence of large scatter or imprecision measurement of biokinetic model parameters demands uncertainty analysis of model for its better refinement. Uncertainty analysis of the retention function of a typical radionuclide say strontium is the focal theme of the paper. Uncertainties present in strontium retention function in biokinetic models arise from the assumptions of the biokinetic model, values of the model parameters, radiation weighting factor and tissue weighting coefficients. Mathematically, strontium retention function is expressed as the product of the parameters representing the fraction of strontium absorbed from the gastrointestinal tract, fraction initially retained in the skeleton, proportional to uptake rate, power function slope and strontium elimination rate. Uncertainty associated with a biokinetic model is expressed in terms of lower and upper bounds, A and B, such that there is judged to be roughly a 90% probability that the true central value is no less than A and no more than B. Uncertainty is expressed in terms of these bounds termed as uncertainty factor defined details in the paper. Polynomial chaos expansion method has been adopted to estimate the propagation of uncertainties in the parameters of the strontium retention function. The   paper describes the details of polynomial chaos expansion technique to address the uncertainty propagation. Polynomial chaos expansion is an efficient simulation compared to traditional Monte Carlo.