Modeling of diffusion and crystal dissolution in controlled release systems

• Published in: Journal of controlled release 1997, Vol.45 (3), p.257-264
• Main Authors: Kurnik, Ronald T., Potts, Russell O.
• Format: Article
• Language: English
• Subjects: Biological and medical sciences; Crystals; Diffusion; General pharmacology; Mathematical modeling; Medical sciences; Pharmaceutical technology. Pharmaceutical industry; Pharmacology. Drug treatments; Transdermal
• ISSN: 0168-3659; 1873-4995
• DOI: 10.1016/S0168-3659(96)01575-1

New mathematical models have been derived for the controlled release of pharmaceutical compounds from a transdermal patch with simultaneous dissolution of crystals. The mathematical model used for a one-layer system is for a finite length slab with dissolution. An analytical solution for this system, assuming constant crystal surface area was obtained. A numerical solution for this system, allowing for a variable surface area of the crystal as it dissolves was also obtained. The models have also been extended to two-layer systems, (patch+skin) where the first layer contains crystals of variable area (decreasing as the crystals dissolve). These models were solved by numerical methods using finite difference techniques. The models were applied to release of estradiol from a polymeric matrix into water and through skin. The estradiol consisted of soluble and crystal forms, with the crystals dispersed throughout the polymer. It was found that the crystal size has a significant impact of release of estradiol into water, with roughly a 40% increase in the amount delivered as the crystal size is decreased from 3 to 0.5 μm. When estradiol is delivered transdermally, however, it was found that there is essentially no effect of crystal size on the delivery of estradiol, due to the rate limiting nature of the skin membrane. Consequently, the most likely applications of dispersed phases in the drug delivery industry will be in the area of implanted or mucosal systems, as the stratum corneum will not be a barrier in these cases and the dispersed solid may serve as a drug reservoir for the soluble drug as it is depleted. When the system is used in this manner, a more compact design is possible than if all the drug had to be present initially as a soluble compound.