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 language | English (US) |
|---|---|
| Pages (from-to) | 593-607 |
| Number of pages | 15 |
| Journal | Mathematical Biosciences |
| Volume | 209 |
| Issue number | 2 |
| DOIs | |
| State | Published - Oct 2007 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modeling and Simulation
- General Biochemistry, Genetics and Molecular Biology
- General Immunology and Microbiology
- General Agricultural and Biological Sciences
- Applied Mathematics
Keywords
- Integral transform technique
- Optimal control
- Partial differential equations
- Percutaneous absorption