The relationship between internal and external dose: Some general results based on a generic compartmental model.

Statements on how the IED (internal-to-external-dose) relationship looks like are often based on qualitative toxicokinetic arguments. For example, the recently proposed KMD (Kinetically-derived Maximum Dose) states that the IED relationship must have an inflection point, due to saturation of underlying processes like metabolism or absorption. However, such statements lack a solid quantitative foundation. Therefore, we derived expressions for the IED relationship for a number of scenarios based on a generic compartmental model involving saturation. The scenarios included repeated or single dose, and saturable metabolism or saturable absorption. For some of these scenarios an explicit expression for the IED relationship can be derived, for others only implicit expressions can be established, which need to be evaluated numerically. The results show that saturable processes will lead to an IED relationship that is nonlinear over the whole dose range, i.e., it can be approximated by a linear relationship at the lower end, while the approximation will become gradually poorer with increasing doses. The finding that saturation does not lead to an inflection point in the IED relationship, as assumed in the KMD (Kinetically-derived Maximum Dose), implies that the KMD is not a valid approach for selecting the top dose in toxicological studies. An additional use of our results is that the derived explicit expressions of the IED relationship can be fitted to internal-to-external-dose data, and, possibly, for extrapolation outside the observed dose range.