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Related Experiment Video

Updated: Jun 13, 2026

Quantitative [18F]-Naf-PET-MRI Analysis for the Evaluation of Dynamic Bone Turnover in a Patient with Facetogenic Low Back Pain

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Fractional dynamics pharmacokinetics-pharmacodynamic models.

Davide Verotta¹

¹Department of Bioengineering and Therapeutic Sciences, University of California, Box 0912, San Francisco, CA, USA. davide.verotta@ucsf.edu

Journal of Pharmacokinetics and Pharmacodynamics

|May 11, 2010

Summary

This study introduces novel fractional calculus models for pharmacokinetics-pharmacodynamics (PKPD) to address computational challenges. These new models extend existing PKPD frameworks, offering a more detailed understanding of drug behavior.

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Area of Science:

Pharmacology and Computational Biology
Application of Fractional Calculus

Background:

Fractional calculus applications are prevalent in science and engineering but underutilized in pharmacokinetics-pharmacodynamics (PKPD).
Existing PKPD models often lack analytical solutions, posing computational challenges for complex dynamics.
Fractional differential equations offer a powerful framework for modeling complex biological systems.

Purpose of the Study:

To introduce novel PKPD models incorporating fractional order integrals and differential equations.
To investigate the qualitative behavior of these new fractional PKPD models.
To extend existing PK link and PD direct/indirect action models using fractional calculus.

Main Methods:

Development of new families of PKPD models using fractional calculus.
Implementation of numerical algorithms for fractional integration.
Numerical solution of systems of fractional differential equations for model analysis.
Focus on the pharmacodynamic (PD) aspects, assuming standard (integer order) pharmacokinetics.

Main Results:

The proposed fractional PKPD models extend established PK and PD models.
A fractional integral transformation allows modeling drug concentration transitions (concentration, exposure, hyper-exposure).
Numerical methods were successfully applied to solve and analyze the behavior of the fractional models.

Conclusions:

Fractional calculus provides a viable and powerful approach for developing advanced PKPD models.
The proposed models offer a flexible framework for capturing complex drug disposition and effect dynamics.
Numerical investigation demonstrates the feasibility of analyzing these complex fractional PKPD models.