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.

Optimizing the test power for a radiation retention model in the human body.

The model that describes the retention in lungs of radioisotope particles is studied in this paper, considering the situation of an accident in facilities that handle radioactive materials. Optimal times to make the bioassays are computed for D- and c-optimality, and efficiencies for the computed designs are provided and compared. Moreover, the test power is checked by means of simulations and replications. After that the inverse of the Fisher information matrix is compared to an estimation of the covariance matrix of the parameters. Finally, a study taking into consideration the randomness of the designs space is performed.

Optimal design and mathematical model applied to establish bioassay programs.

Bioassays can be used to estimate the initial intake I for the case of an acute intake exposure for an individual worker. To evaluate the effective dose, apart from I, we need to know other parameters such as activity median aerodynamic diameter (AMAD) or the fraction absorption ( f(1)) in the blood from the GI tract, but in an accident situation these parameters are often unknown. The bioassay measurement values can be used to estimate by fitting the parameters unknown. In this paper, optimal designs for the estimation of the unknown parameters are developed. The efficiency of the design will depend on the number of samples and the measurement accuracy. The method described applies D-optimality that maximises the determinant of the Fisher information matrix to find the best moments where the bioassay measurements should be taken. It requires obtaining the analytical solution of the biokinetic model as a function of the parameters to be fitted. The method has been implemented in a computer program.