Mathematical solutions to problems in radiological protection involving air sampling and biokinetic modelling

Birchall, Alan (1998) Mathematical solutions to problems in radiological protection involving air sampling and biokinetic modelling. Doctoral thesis, University of Bristol.

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Intakes of radionuclides are estimated with the personal air sampler (PAS) and by biological monitoring techniques: in the case of plutonium, there are problems with both methods. The statistical variation in activity collected when sampling
radioactive aerosols with low number concentrations was investigated. By treating man as an ideal sampler, an analytical expression was developed for the probability distribution of intake following a single measurement on a PAS. The dependence on aerosol size, specific activity and density was investigated. The methods were extended to apply to routine monitoring procedures for plutonium. Simple algebraic approximations were developed to give the probability of exceeding estimated intakes and doses by given factors. The conditions were defined under which PAS monitoring meets the ICRP
definition of adequacy. It was shown that the PAS is barely adequate for monitoring plutonium at ALl levels in typical workplaceconditions.
Two algorithms were developed, enabling non-recycling and recycling compartmental models to be solved. Their accuracy and speed were investigated, and methods of dealing with partitioning, continuous intake, and radioactive progeny were discussed. Analytical, rather than numerical, methods were used. These are faster, and thus ideally suited for implementation on microcomputers. The algorithms enable non-specialists to solve quickly and easily any first order
compartmental model, including all the ICRP metabolic models. Nonrecycling models with up to 50 compartments can be solved in seconds: recycling models take a little longer.
A biokinetic model for plutonium in man following systemic uptake was developed. The proposed ICRP lung model (1989) was represented by a first order compartmental model. These two models were combined, and the recycling algorithm was used to calculate urinary and faecal excretion of plutonium following acute or chronic intake by inhalation. The results indicate much lower urinary excretion than predicted by ICRP Publication 54.

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