Chapter 14: External Diffusion Effects on Heteregeneous Reactions

Side Note: Transdermal Drug Delivery

The principles of steady state diffusion have been used in a number of drug delivery systems. Specifically medicated patches are commonly used to attach to the skin to deliver drugs for nicotine withdrawal, birth control, and motion sickness to name a few. The U.S. transdermal drug delivery market was $1.2 billion in 2001. Equations similar to Equation 11-26 have been used the model the release, diffusion and absorption of the drug from the patch into the body. Figure SN11.1 shows a drug delivery vehicle (patch) along with the concentration gradient in the epidermis and dermis skin layers.

Image showing a nicotine transdermal patch on a person's upper arm, labeled 'Nicotine Transdermal System, 7 mg delivered over 24 hours, NCH 0830.' To the right, a diagram of skin layers shows diffusion through the delivery patch, epidermis, and dermis. Concentration profiles are shown with sharp drops from CAp to CA1 to CA = 0. The epidermis spans from z=0 to z=0.002 mm and the dermis from z=0.002 mm to z=0.039 mm. Diffusion coefficients D_AB1 and D_AB2 are labeled in each layer.

Figure SN 11.1 Transdermal Drug Delivery Schematic

As a first approximations, the delivery rate can be written as

\( F_A = A_p W_A = \frac{A_p \left[ C_{Ap} - 0 \right]}{R} \)

Where

\( R = R_p + \frac{\delta_1}{D_{AB_1}} + \frac{\delta_2}{D_{AB_2}} \)

Where Ap is the area of the patch, CAp the concentration of drug in the patch, R the overall resistance and Rp the resistance to release form the patch.  There are a number of situations one can consider, such as the patch resistance limits the delivery or diffusion through the epidermis limits delivery or the concentration of the  drug is kept constant in the patch by using solid hydrogels. When diffusion through the epidermis layer limits, the rate of drug delivery rate is

\( F_A = A_p \left[ \frac{D_{AB_1}}{\delta_1} \right] C_{Ap} \)

Other models include the use a quasi-steady analysis to couple the diffusion equation with a balance on the drug in the patch or the zero order dissolution of the hydrogel in the patch.† Problem 11-2(f) explores these situations.

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†For further information see

  1. Kalia, Y.H. and R. Guy Advanced Drug Delivery Reviews 48,(2001) p159
  2. Muller,B,M.Kasper,C. Surber, and G. Imanidis  European Journal of Pharmaceutical Science 20(2003) p181