The dynamics of shrinking and expanding drug-loaded microspheres: A semi-empirical approach

Laurent Simon, Juan Ospina, Rebecca Kuntz Willits

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)55-62
Number of pages8
JournalEuropean Journal of Pharmaceutical Sciences
Issue number1
StatePublished - Jul 16 2014

All Science Journal Classification (ASJC) codes

  • Pharmaceutical Science


  • Analytical solution
  • Controlled release
  • Effective time constant
  • Hydrogels
  • Polymeric drug delivery systems
  • Swelling/shrinking microspheres


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