Optimal designs for compartmental models with correlated observations

The flow of internally deposited radioisotope particles inside the body of people exposed to inhalation, ingestion, injection or other ways is usually evaluated using compartmental models (see Sanchez & Lopez-Fidalgo, (2003, and Lopez-Fidalgo & Sanchez, 2005). The International Commission on Radiological Protection (ICRP, 1994) describes the model of the human respiratory tract, represented by two main regions. One of these, the thoracic region (lungs) is divided into different compartments. The retention in the lungs is given by a large combination of ratios of exponential sums depending on time. The aim of this work is to provide optimal times for making bioassays when there has been an accidental radioactivity intake and there is interest in estimating it. In this paper, a large two-parameter model is studied and a simplified model is proposed in order to obtain optimal designs in a more suitable way. Local c-optimal designs for the main parameters are obtained using the results of Lopez-Fidalgo & Rodriguez-Diaz, 2004). Efficiencies for all the computed designs are provided and compared.