Diffusion-Controlled Drug Delivery

diffusivity in pill B (10−5 mm2/h): 0.5 4 25

radii of beads within capsule:

pill A (mm) 0.075 pill B (mm) 0.050

This Demonstration models a diffusion-controlled drug delivery system to determine the amount of an active pharmaceutical ingredient (API) released from a polymer sphere as a function of time. The elapsed time is limited to 20 hours to correspond to the digestive cycle of humans. Drugs are often delivered as a capsule that contains many spherical beads, and the API is uniformly distributed throughout each polymer bead. The API is assumed to be immediately swept away once it diffuses to the surface of the bead. Select "varying r, D" to compare two pills. The diffusivity of pill A is fixed at 10−5 mm2/h; click on a button to select the diffusivity of pill B. The radius of each pill can be selected with a slider. Select "CAPI versus r" to plot the normalized concentration of the API as a function of radial position for one diffusivity and one spherical radius. Use the slider to change the time at which the concentration profile is calculated or use the play button to observe the concentration change continuously with time.

The fractional amount of API released from a spherical bead is obtained from the solution of Fick's second law for a sphere with a uniform initial concentration and zero concentration at the surface:

drug released (%) = 100 [1 - \frac{6}{π^{2}} \sum_{n = 1}^{\infty} \frac{1}{n^{2}} \exp (- \frac{D n^{2} π^{2} t}{R^{2}})]

The normalized concentration of API within the bead as a function of radial position is:

\frac{C_{API}}{C_{API}^{o}} (%) = 100 [\frac{2 R}{π r} \sum_{n = 1}^{\infty} \frac{{(- 1)}^{n + 1}}{n} \sin (\frac{n π r}{R}) \exp (- \frac{D n^{2} π^{2} t}{R^{2}})]

where:

CAPI = concentration of API at radial position r

CAPIo = initial (uniform) concentration of API in the bead

D = diffusivity of the API in the polymer (mm2/h)

R = radius of the spherical bead (mm)

r = radial position within the bead (mm)

t = elapsed time (h)

n = summation index

Each series is evaluated with the first 100 terms.

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Rachel Saker and Rachael L. Baumann. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com.