Two-Dimensional Solution and Analysis of a Cylindrical Matrix Device With a Circular Release Area

Abstract

A cylindrical device was analyzed using a Laplace transform-based method. The two-dimensional model represented a pharmaceutical agent uniformly distributed in a polymeric matrix surrounded by an impermeable layer. Molecules could be transferred only through a small hole centered at the top surface of the cylinder. A closed-form solution was obtained to help study the effects of design parameters and geometries on the cumulative amount of drug released. The latter variable increased with the mass transfer and diffusion coefficients and decreased with any increment in the device's length. The delivery rate was described by an effective time constant calculated from Laplace transforms. Reducing the orifice diameter or fabricating a longer system would delay transport of the medication. Simplified expressions for the release profile and the time constant were derived for special design cases.

Analytical solution using computer algebra of a biosensor for detecting toxic substances in water

“…The explicit form of the concentration profile of the electrolyte in the Laplace domain is given by (12) The explicit form of the output current from the biosensor in the Laplace domain is given by (13) From (13) the explicit form of the output current from the biosensor in the temporal domain is given by (14) From (14) From (17) we obtain the following limit cases:…”

“…The explicit form of the output current for the biosensor is computed analytically both in the Laplace domain as in the temporal domain. Also, the effective time constant [8,11,12] for the biosensor is analytically computed and its algebraic form will be an important tool for designing a biosensor. All the computations will be performed using computer algebra software [9], specifically Maple [10].…”

Three-dimensional analyses of a perforated cylindrical drug delivery device

“…This model could predict the delivery of benzoic acid from a cylindrical agar gel. A closed-form solution was derived using a Laplace transform-based technique (Simon and Ospina, 2012). This analytical approach provided further insight into the influences of geometries and polymer properties on the performance of the device.…”

“…The method does not extend to implantable cylindrical matrices with release holes located on the surface of the design (Ertan et al, 1997;Hsu et al, 1992). Even with the assumption of angular symmetry, the concentration distribution is not easily obtained through the above-mentioned technique (Simon and Ospina, 2012). Analytical tools are lacking in the literature to study drug mechanisms in 3-D coordinates.…”

Analytical solution of a model for shrinking drug-loaded microspheres

“…An increasingly important topic of investigation is concerned with controlled drug delivery [1,2,3,4,5,6]. An important example is the controlled drug delivery from micro-spheres [7,8,9].…”