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Drug release from matrix systems: analysis by finite element methods


In this work some problems in drug delivery from solid systems were described in terms of transient mass balances with diffusion and solved by using FEM. Firstly, the solving codes were compared with known analytical solutions, available for simple problems (simple geometries, constant diffusivities). Then, models were written to describe more realistic systems (complex geometries, variable diffusivities). Eventually, the behaviors of some real drug delivery systems were successfully predicted.

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  1. Siepmann J, Siepmann F (2008) Mathematical modeling of drug delivery. Int J Pharm 364:328–343

    Article  Google Scholar 

  2. Higuchi T (1961) Rate of release of medicaments from ointment bases containing drugs in suspensions. J Pharm Sci 50:874–875

    Article  Google Scholar 

  3. Crank J (1975) The mathematic of diffusion, 2nd edn. The Clarendon Press, Oxford

    Google Scholar 

  4. Peppas NA, Sahlin JJ (1989) A simple equation for the description of solute release. III. Coupling of diffusion and relaxation. Int J Pharm 57:169–172

    Article  Google Scholar 

  5. Grassi M, Grassi G (2005) Mathematical modelling and controlled drug delivery: matrix systems. Curr Drug Deliv 2:97–116

    Article  Google Scholar 

  6. Siepmann J, Ainaoui A, Vergnaud JM, Bodmeier R (1998) Calculation of the dimensions of drug-polymer devices based on diffusion parameters. J Pharm Sci 87(7):827–832

    Article  Google Scholar 

  7. Carslaw HS, Jaeger JC (1959) Conduction of heat in solids, 2nd edn. The Clarendon Press, Oxford

    Google Scholar 

  8. Zhou Y, Wu XY (1997) Finite element analysis of diffusional drug release from complex matrix systems. I. Complex geometries and composite structures. J Control Release 49:277–288

    Article  Google Scholar 

  9. Wu XY, Zhou Y (1998) Finite element analysis of diffusional drug release from complex matrix systems. II. Factors influencing release kinetics. J Control Release 51:57–71

    Article  Google Scholar 

  10. Siepmann J, Kranz H, Bodmeier R, Peppas NA (1999) HPMC-matrices for controlled drug delivery: a new model combining diffusion, swelling, and dissolution mechanism and predicting the release kinetics. Pharm Res 16(11):1748–1756

    Article  Google Scholar 

  11. Siepmann J, Peppas NA (2000) Hydrophilic matrices for controlled drug delivery: an improved mathematical model to predict the resulting drug release kinetics (the “sequential layer” model). Pharm Res 17:1290–1298

    Article  Google Scholar 

  12. Grassi M, Colombo I, Lapasin R (2000) Drug release from an ensemble of swellable crosslinked polymer particles. J Control Release 68:97–113

    Article  Google Scholar 

  13. Kiil S, Johansen Dam-K (2003) Controlled drug delivery from swellable hydroxypropylmethylcellulose matrices: model-based analysis of observed radial front movements. J Control Release 90:1–21

    Article  Google Scholar 

  14. Goepferich A, Langer R (1995) Modeling monomer release from bioerodible polymers. J Control Release 33:55–69

    Article  Google Scholar 

  15. Goepferich A, Langer R (1995) Modeling of polymer erosion in three dimensions: rotationally symmetric devices. AIChE J 41:2292–2299

    Article  Google Scholar 

  16. Lapidus L, Pinder GF (1982) Numerical Solution of partial differential equation in science and engineering. Wiley, New York

    Google Scholar 

  17. COMSOL Multiphysics user’s guide (2007) ©COPYRIGHT 1994–2007 (by COMSOL AB)

  18. Barba AA, D’Amore M, Chirico S, Lamberti G, Titomanlio G (2009) A general code to predict the drug release kinetics from different shaped matrices. Eur J Pharm Sci 36:359–368

    Article  Google Scholar 

  19. Horcajada P, Ramila A, Perez-Pariente J, Vallet-Regì M (2004) Influence of pore size of MCM-41 matrices on drug delivery rate. Micropor Mesopor Mat 68:105–109

    Article  Google Scholar 

  20. Grassi M, Lapasin R, Coviello T, Matricardi P, Di Meo C, Alhaique F (2009) Scleroglucan/borax/drug hydrogels: structure characterization by means of rheological and diffusion experiments. Carbohyd Polym 78(3):377–383

    Article  Google Scholar 

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Correspondence to Gaetano Lamberti.

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Galdi, I., Lamberti, G. Drug release from matrix systems: analysis by finite element methods. Heat Mass Transfer 48, 519–528 (2012).

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  • Drug Release
  • Ibuprofen
  • Finite Element Method Result
  • Fractional Release
  • Buflomedil