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Analytical solution of linear multi-compartment models with non-zero initial condition and its implementation with R.

David Z D'Argenio1, Kyun-Seop Bae2

  • 1University of Southern California School of Engineering, USA.

Translational and Clinical Pharmacology
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Solving complex multi-compartment models with initial conditions is now easier. The new analytical solution, implemented in the R package

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Area of Science:

  • Pharmacokinetics and Computational Biology

Background:

  • Analytical solutions for multi-compartment models are complex due to inter-compartmental transfer, especially with non-zero initial conditions.
  • Existing methods often require numerical approximations, limiting their direct application in certain contexts.

Purpose of the Study:

  • To develop an elegant analytical solution for multi-compartment models with non-zero initial conditions.
  • To implement this solution within the 'wnl' R package for practical application.

Main Methods:

  • Utilized Laplace transformation and convolution techniques.
  • Employed matrix inversion and the principle of summing homogeneous and particular solutions for inhomogeneous ordinary differential equations.

Main Results:

  • An elegant analytical solution for multi-compartment models with non-zero initial conditions was derived.
  • The solution was successfully implemented in the 'wnl' R package, demonstrating its utility.

Conclusions:

  • The developed analytical solution simplifies the analysis of complex pharmacokinetic models.
  • The 'wnl' R package provides a valuable tool for textbook examples, therapeutic drug monitoring, pharmacokinetic simulation, and parameter estimation.