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A system approach to pharmacodynamics. I: Theoretical framework.

P Veng-Pedersen1, W R Gillespie

  • 1College of Pharmacy, University of Iowa, Iowa City 52242.

Journal of Pharmaceutical Sciences
|January 1, 1988
PubMed
Summary

This study introduces a general theoretical framework to mathematically describe the relationship between pharmacokinetic responses and pharmacologic effects. It explores mathematical structures for pharmacodynamic systems, aiding drug development.

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Area of Science:

  • Pharmacokinetics and Pharmacodynamics
  • Mathematical Modeling in Pharmacology
  • Systems Biology

Background:

  • Understanding the relationship between drug concentration and effect is crucial for drug development.
  • Existing models often lack a unified theoretical framework to integrate pharmacokinetic and pharmacodynamic components.
  • Pharmacokinetic (PK) response (r) and pharmacologic effect (E) are linked but require a generalized mathematical description.

Purpose of the Study:

  • To construct a general theoretical framework for the PK/PD relationship.
  • To mathematically describe the link between pharmacokinetic response (r) and pharmacologic effect (E).
  • To explore specific mathematical structures applicable to pharmacodynamic systems.

Main Methods:

  • Developed a general operator-based mathematical framework: E = omega(r) = omega p(omega b(omega r(r))).

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  • Analyzed the kinetic basis for applying mathematical properties like linearity.
  • Introduced specific mathematical structures for pharmacodynamic modeling, such as E = phi t(r) and E = phi p(psi p*phi b(psi r*r)).
  • Main Results:

    • A unified theoretical framework was established for PK/PD relationships.
    • The framework allows for the decomposition of the overall relationship into system components (e.g., PK, distribution, effect).
    • Several specific mathematical models were derived, applicable to diverse pharmacodynamic systems.

    Conclusions:

    • The proposed theoretical framework provides a robust mathematical foundation for PK/PD analysis.
    • This generalized approach facilitates a deeper understanding of drug action mechanisms.
    • The introduced mathematical structures can enhance the prediction and optimization of drug therapies.