Controlled Release of a Drug from a Hemispherical Matrix

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This Demonstration models the release of a drug from a hemispherical matrix.


Drug transfer occurs only though the hemispherical cavity at the bottom of the matrix. The governing dimensionless equation for this system is:

, with the initial and boundary conditions:




The dimensionless variables are:

, , and ,

where is the drug concentration, is the drug diffusivity, is the radial coordinate, is time, is the initial drug concentration, and and stand for the inner and outer radii of the matrix, respectively.

Siegel [1] solved this problem using separation of variables. The expression for the dimensionless drug concentration is:


and the fractional drug release as a function of dimensionless time is given by


where is the positive root of .

In this system, the drug is released at a near-constant rate. This is a desired goal of all controlled-release drug-delivery mechanisms, because this pattern can guarantee maintenance of plasma drug concentrations within therapeutic levels. Diffusion-controlled monolithic systems such as slabs, cylinders and spheres usually do not yield constant release rates.


Contributed by: Clay Gruesbeck (November 2016)
Open content licensed under CC BY-NC-SA




[1] R. A. Siegel, "Theoretical Analysis of Inward Hemispheric Release above and below Drug Solubility," Journal of Controlled Release, 69(1), 2000 pp. 109–126. doi:10.1016/S0168-3659(00)00292-3.

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