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Simple relations between administered and internal doses in compartmental flow models

L A Cox1

  • 1Cox Associates, Denver, Colorado 80218, USA.

Risk Analysis : an Official Publication of the Society for Risk Analysis
|April 1, 1995
PubMed
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Complex biologically-based risk assessment (BBRA) models can be simplified. A single aggregate constant can predict model behavior, reducing the need for extensive pharmacokinetic and pharmacodynamic data.

Area of Science:

  • Toxicology
  • Pharmacokinetics
  • Mathematical Modeling

Background:

  • Biologically-based risk assessment (BBRA) models aim to improve mechanistic understanding of toxicological processes.
  • Increasing model complexity necessitates large amounts of pharmacokinetic and pharmacodynamic data, posing a practical barrier.

Purpose of the Study:

  • To demonstrate that complex dynamical models used in BBRA do not require estimation of individual parameters.
  • To show that input-output behavior can be determined by a single aggregate constant.

Main Methods:

  • Analysis of linear, constant-coefficient, globally stable compartmental flow systems.
  • Derivation of a "reduced" constant representing aggregate system behavior.
  • Application to a cyclophosphamide (CP) pharmacokinetics and metabolism model.

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Main Results:

  • Input-output properties (e.g., dose-response) are determined by a single aggregate "reduced" constant.
  • This constant can be estimated from measured input and output quantities.
  • Uncertainties in individual parameters and model structure are irrelevant for quantifying input-output behavior.

Conclusions:

  • Complex BBRA models can be simplified by focusing on aggregate parameters.
  • This approach reduces data requirements and overcomes practical barriers in risk assessment.
  • The method is applicable to pharmacokinetic and low-dose physiologically based pharmacokinetic (PBPK) models.