title: The dynamics of shrinking and expanding drug-loaded microspheres: A semi-empirical approach.
abstract: The dynamics of shrinking and expanding drug-loaded microspheres were studied using a diffusion equation in spherical coordinates. A movable boundary condition was incorporated as a convection term in the original model. The resulting convective-diffusive problem was solved using Laplace transform techniques with the Bromwich integral and the residue theorem. Analytical solutions were derived for the general case of shrinking or expanding microspheres and three particular kinetics expressions: linear growth, exponential swelling and exponential shrinking. Simulations show that microspheres with fast-swelling kinetics released their therapeutic cargo at a relatively slow rate in the first two cases. Ninety-nine percent of the medication was delivered at four times the effective time constant. In line with laboratory studies using bovine serum albumin, an increase in the shrinking rate led to a fast release of the medication from its carrier. The method was applied to analyze insulin transport through spherical Ca-alginate beads. A good agreement was noted between predicted and experimental data. The theoretical effective time constant was 114.0 min.
authors.affiliation: Otto H. York Department of Chemical, Biological and Pharmaceutical Engineering, New Jersey Institute of Technology, Newark, NJ 0702, USA. Electronic address: laurent.simon@njit.edu.
authors.forename: Laurent
authors.initials: L
authors.lastname: Simon
authors.affiliation: Logic and Computation Group, Physics Engineering Program, School of Sciences and Humanities, EAFIT University, Medellin, Colombia.
authors.forename: Juan
authors.initials: J
authors.lastname: Ospina
authors.affiliation: Department of Biomedical Engineering, The University of Akron, 260 S. Forge St, OLRC 301, Akron, OH 44325-0302, USA.
authors.forename: Rebecca Kuntz
authors.initials: RK
authors.lastname: Willits
mesh_terms: D000464:Alginates / Q000737:chemistry*; D020723:Glucuronic Acid / Q000737:chemistry; D006603:Hexuronic Acids / Q000737:chemistry; D007328:Insulin / Q000737:chemistry*; D008863:Microspheres; D008962:Models, Theoretical
chemical_list: D000464:Alginates; D006603:Hexuronic Acids; D007328:Insulin; D020723:Glucuronic Acid
keywords: Analytical solution; Controlled release; Effective time constant; Hydrogels; Polymeric drug delivery systems; Swelling/shrinking microspheres