The Relationship Between Internal and External Dose: Some General Results Based on a Generic Compartmental Model

Area of Science:

• Pharmacokinetics and toxicokinetics
• Mathematical modeling in toxicology

Background:

• Internal-to-external-dose (IED) relationships are often based on qualitative toxicokinetic arguments.
• The kinetically derived maximum dose (KMD) proposes an inflection point in the IED relationship due to process saturation, lacking quantitative validation.

Purpose of the Study:

• To quantitatively derive expressions for the IED relationship under various saturation scenarios.
• To evaluate the validity of the KMD approach for selecting top doses in toxicological studies.

Main Methods:

• Development of a generic compartmental model incorporating saturation.
• Derivation of explicit and implicit expressions for the IED relationship for single/repeated doses and saturable metabolism/absorption.
• Numerical evaluation for scenarios without explicit expressions.

Main Results:

• Saturable processes result in a nonlinear IED relationship across the entire dose range.
• The IED relationship can be approximated linearly at lower doses, with accuracy decreasing at higher doses.
• Saturation does not produce an inflection point in the IED relationship, contrary to KMD assumptions.

Conclusions:

• The KMD approach is invalid for selecting top doses in toxicological studies due to the absence of an inflection point.
• Derived explicit IED expressions can be fitted to experimental data for dose-response extrapolation.
• This work provides a quantitative foundation for understanding IED relationships under saturation.