Optimal designs for some stochastic processes whose covariance is a function of the mean

Efficient parameter estimation in multiresponse models measuring radioactivity retention

After incorporation of radioactive substances, workers are routinely checked by bioassays (isotopic activity excreted via urine, measurements of radionuclides retained in the whole body or in the lungs, etc.). From the results, the isotopic activity incorporated by the worker is inferred, as well as the values of other parameters related to the metabolism of the incorporated substance, using the 'response function'. This function depends on several factors and it is usually obtained by solving a system of linear differential equations, resulting from the compartmental model which describes the human body (or a part of it). The possibility of using different types of bioassays from the same worker improves estimation of some of the parameters that characterize the solution of the system of equations, specially the unknown incorporated activity to the system. The transfer coefficients are usually considered to be known, using the values that are published in the corresponding International Commission of Radiological Protection (ICRP) publication. In the present study some practical cases will be presented, and optimal design criteria are developed that allow taking the bio-samples at the most informative times. The methodology presented here requires solving the models of element distribution in the human organism as a function of time, for which the recently updated models recommended by the ICRP have been used. Initially thought for workers in facilities dealing with radioactive substances, the study results, procedures and conclusions can be applied to other clinical or laboratory settings, and to the design of action protocols in case of environmental public exposure.