Flux tracking in drug delivery

José A. Ferreira, Paula de Oliveira, Pascoal da Silva, Laurent Simon

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


The dynamics of diffusive and stress-induced transport in polymeric delivery systems was investigated. Partial and ordinary differential equations were first written to describe drug release behaviors in Maxwell and Maxwell-Voigt materials. The time constants governing the flux and concentration responses of a permeating species were determined from a Laplace transform solution of the original model. A " tracking strategy" , based on the estimated characteristic times, was proposed to estimate the delivery rate and the concentration near the exit side of the membrane. The methodology was more efficient at times greater than the time constant and the prediction error decreased further as the process approached steady state. Numerical illustrations and comparisons made with published data show the effectiveness of the proposed approach in describing the influence of the Young modulus, viscosity and relaxation time on the transient regime.

Original languageEnglish (US)
Pages (from-to)4684-4696
Number of pages13
JournalApplied Mathematical Modelling
Issue number10
StatePublished - Oct 2011

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics


  • Controlled drug delivery
  • Effective time
  • Integro-differential equations
  • Laplace transforms
  • Visco-elasticity


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