Three-dimensional analyses of a perforated cylindrical drug delivery device.

A closed-formed solution of a perforated drug-delivery model was developed. Laplace transforms were applied to the governing equation, which included diffusion through the tubular device and mass transfer across a rectangular cut. A first-order estimate for the fraction of drug released, in terms of the Laplace variable, was derived after employing suitable boundary and initial conditions. The effective time constant for the process was calculated. The residue theorem and the Zakian method were proposed as two reliable approaches to recover the solution in the time domain. Simulations show that the drug was released faster at higher Sherwood numbers. Ninety-eight percent (98%) of the loading dose was delivered after a period corresponding to four time constants. This analytical platform can aid in the design of implants for long-term delivery applications.