Grid search: an innovative method for the estimation of the rates of lead exchange between body compartments

Abstract

This paper describes a new metabolic model for lead in humans and a numerical method to solve the differential equations governing the transfer of lead between body compartments. The model includes 3 compartments—cortical bone, trabecular bone and blood—and accounts for absorption from external sources and release through excreta. Estimation of the lead kinetics parameters was performed using the grid search method. Grid search is a simple procedure that allows the fit of an arbitrary function to data. When applied to data from occupationally exposed populations, the method demonstrated the exposure dependence of the rate of lead uptake and release by the compartments in the model. The results confirm and refine previous observations of the significant decrease of the transfer rate of lead from cortical bone to blood with increasing exposure, as expressed by half-lives of (in years): 6.5 ± 0.7, 13.6 ± 1.0 and 47.5 ± 2.3, in subgroups of low, intermediate and high long-term lead exposure. A similar trend was observed for the transfer rate from trabecular bone, which could be statistically supported for the first time. Reduction by a factor of 7 to 10 in the default values assigned to the fractional removal of lead from cortical bone to plasma in existing metabolic models was also predicted. These results can be used in the review of current metabolic models for lead, which are still based on the assumption of a constant rate of lead removal from bone, independently of the level of exposure.