Repeated applications of a transdermal patch: Analytical solution and optimal control of the delivery rate

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Abstract

The integral transform technique was implemented to solve a mathematical model developed for percutaneous drug absorption. The model included repeated application and removal of a patch from the skin. Fick's second law of diffusion was used to study the transport of a medicinal agent through the vehicle and subsequent penetration into the stratum corneum. Eigenmodes and eigenvalues were computed and introduced into an inversion formula to estimate the delivery rate and the amount of drug in the vehicle and the skin. A dynamic programming algorithm calculated the optimal doses necessary to achieve a desired transdermal flux. The analytical method predicted profiles that were in close agreement with published numerical solutions and provided an automated strategy to perform therapeutic drug monitoring and control.

Original languageEnglish (US)
Pages (from-to)593-607
Number of pages15
JournalMathematical Biosciences
Volume209
Issue number2
DOIs
StatePublished - Oct 1 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Keywords

  • Integral transform technique
  • Optimal control
  • Partial differential equations
  • Percutaneous absorption

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