General solution of the ICRP 66 model and its application to given radionuclides

To implement the Human Respiratory Tract Model (ICRP Publication 66), iterative codes were developed. This paper presents an analytic method to generate the general solution of this model, developed by using a symbolic mathematical software (Maple). Once having formulated the set of the differential equations describing the model, it is solved for a unit acute inhalation. The solution ('impulse response' of the model) is expressed as a set of analytical functions of parameters and time for each compartment contributing to the thoracic retention. In the case of chronic intake, the solution of the model is derived by convoluting the impulse response. These functions can be programmed using any language and readily implemented on a PC. The use of analytical functions considerably shortens the computing time. The results are presented for unit acute or chronic inhalation, and for industrial compounds taking into account the uncertainty of experimental parameters. (author)