Incorporation of Temporal Factors Into Physiologically Based Kinetic Models for Risk Assessment

Abstract

The dependence of physiologically based models on measurable anatomic characteristics and physiologic functions renders them especially suited for consideration of the effects of temporal factors. Incorporation of temporal factors into a physiologically based model requires an understanding of their time dependence and the translation of that time dependence into a mathematically tractable curve description. The age dependencies of many physiologic functions are known. Glomerular filtration rate and respiration rate, for example, are well-characterized from birth to maturity. Certain conditions, such as pregnancy, are associated with rapid and definable anatomic and physiologic changes. Generally, these time dependencies are describable in terms of simple mathematical expressions such as exponentials, polynomials, and sine and logistic functions. An example of the combined use of a hyperbola and a logistic function to fit the growth curve for Standard Man is given. Practical applications of two physiologically based models with temporal features are illustrated. One of the models, for the rapidly growing rat, is used to estimate the fractional bioavailability of lead added to the diet in experimental studies in the juvenile rat. The other, for human pregnancy, is used to estimate the rate of return of lead from bone in late pregnancy when bone resorption tends to increase in order to contribute to the supply of calcium to the developing fetus.