Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




Dr. N. Balakrishnan


Dr. D. R. Chettle

Committee Member

Dr. P. D. M. Macdonald


In the major part of this thesis, two-compartment and four-compartment models in this form of linear differential equations, associated with human in vivo cadmium data, have been constructed to describe a particular biological phenomenon of cadmium metabolism in the human body. The two-compartment model constitutes the preliminary work, and the complete analysis and discussions are finally achieved through the four-compartment model. Since it was expensive to technically perform the in vivo measurements and also difficult to collect the data over a period of a decade, the data set analyzed in this thesis are quite precious and one of very few existing data sets in the area of cadmium research. Cadmium researchers are very much interested in drawing as much information as possible from these data. A method is developed for deriving the expectation functions and analyzing this special data set. The parameter estimation for the compartment models developed is based on two parameter estimation methods based on classical and Bayesian approaches. It is the first time a whole system of the human body has been analyzed simultaneously without any additional assumptions on the derivation of the compartment models. This contrasts with the approach of discussing each compartment separately with a large number of assumptions from different sources as in Kjellström's model. The results obtained from these statistical approaches based on simpler and more direct mathematical models are not only interpreted very reasonably in terms of the biological phenomenon, but they also show great consistency with previous studies, even though the data are sparse and noisy which poses a special difficulty in this study. This thesis also considers the application of segmented models to examine the relationship between renal dysfunction and blood or urine cadmium, and to locate abrupt change points as kidneys become abnormal.

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Mathematics Commons