Transdermal Drug Delivery by Diffusion

A transdermal patch is a popular, noninvasive method of drug administration. When the patch is applied to the skin, the drug embedded in the patch passively diffuses through the skin into the bloodstream. In some commercial patches, the drug must first move from a reservoir through a gel matrix or multiple layers of synthetic membranes before reaching the skin.
This Demonstration is based on a simple patch model in which the drug is incorporated directly in the adhesive, allowing us to focus on the diffusion rate at the patch-skin interface. The diffusion rate depends largely on the thickness of the skin, the diffusion coefficient (a value unique to each drug) and the difference between drug concentrations in the patch and the skin. Fick's law can be manipulated to give the diffusion rate and amount of drug in the body as functions of time. This Demonstration describes, both quantitatively and qualitatively, the diffusion of various common drugs embedded in transdermal patches.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The controls can vary the skin thickness as well as the initial mass of drug in the patch, thereby determining the concentration gradient. These changes are reflected in two plots: the amount of drug in the body over time and the diffusion rate over time. An animation shows the relative motion of drug molecules from the patch through the skin. The drug options are progesterone, nicotine, fentanyl, lidocaine and metoprolol.
See the references for the sources of diffusion coefficient data: progesterone [1], nicotine [2], fentanyl [3], lidocaine [4], metoprolol [5].
[1] K. Tojo, C. C. Chiang and Y. W. Chien, "Drug Permeation across the Skin: Effect of Penetrant Hydrophilicity," Journal of Pharmaceutical Sciences, 76(2), 1987 pp. 123–126. doi:10.1002/jps.2600760208.
[2] J. Wu, K. S. Paudel, C. Strasinger, D. Hammell, A. L. Stinchcomb and B. J. Hinds, "Programmable Transdermal Drug Delivery of Nicotine Using Carbon Nanotube Membranes," Proceedings of the National Academy of Sciences of the United States of America, 107(26), 2010 pp. 11698–11702. doi:10.1073/pnas.1004714107.
[3] D. Mori and K. Tojo, "SKIN-CAD®: Pharmacokinetic Model for Transdermal Drug Delivery," 2006 AIChE Annual Meeting, San Francisco.
[4] Y. Miwa, H. Hamamoto and T. Ishida, "Lidocaine Self-Sacrificially Improves the Skin Permeation of the Acidic and Poorly Water-Soluble Drug Etodolac via Its Transformation into an Ionic Liquid," European Journal of Pharmaceutics and Biopharmaceutics, 102, 2016 pp. 92–100. doi:10.1016/j.ejpb.2016.03.003.
[5] L. Simon, "A Computational Procedure for Assessing the Dynamic Performance of Diffusion-Controlled Transdermal Delivery Devices," Pharmaceutics, 3(3), 2011 pp. 485–496. doi:10.3390/pharmaceutics3030485.
Submission from the Compute-to-Learn course at the University of Michigan.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.