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Modeling the pharmacokinetics of extended release pharmaceutical systems


The pharmacokinetic (PK) models predict the hematic concentration of drugs after the administration. In compartment modeling, the body is described by a set of interconnected “vessels” or “compartments”; the modeling consisting of transient mass balances. Usually the orally administered drugs were considered as immediately available: this cannot describe the administration of extended-release systems. In this work we added to the traditional compartment models the ability to account for a delay in administration, relating this delay to in vitro data. Firstly, the method was validated, applying the model to the dosage of nicotine by chewing-gum; the model was tuned by in vitro/in vivo data of drugs (divalproex-sodium and diltiazem) with medium-rate release kinetics, then it was applied in describing in vivo evolutions due to the assumption of fast- and slow-release systems. The model reveals itself predictive, the same of a Level A in vitro/in vivo correlation, but being physically based, it is preferable to a purely statistical method.

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Area under curve


Biopharmaceutics classification system


Extended release


Gastro-intestinal tract


Immediate release


In vitro/in vivo correlations


Minimum effective concentration


Minimum toxic level


Physiologically based pharmacokinetics




United States pharmacopoeia


  1. Fournier RL (1999) Basic transport phenomena in biomedical engineering. Taylor & Francis, Philadelphia

    Google Scholar 

  2. Saltzman M (2001) Drug delivery. Oxford University Press, Oxford

    Google Scholar 

  3. Grass GM, Sinko PJ (2002) Physiologically based pharmacokinetic simulation modelling. Adv Drug Deliv Rev 54:433–451

    Article  Google Scholar 

  4. Peppas NA, Langer R (2004) Origins and development of biomedical engineering within chemical engineering. AICHE J 50:536–546

    Article  Google Scholar 

  5. Sale M (2001) Modelling and simulation in drug development, promise and reality. Drug Discov World 2:47–50

    Google Scholar 

  6. Rooney KF, Snoeck E, Watson PH (2001) Modelling and simulation in clinical drug development. Drug Discov Today 6:802–806

    Article  Google Scholar 

  7. Holz M, Fahr A (2001) Compartment modeling. Adv Drug Deliv Rev 48:249–264

    Article  Google Scholar 

  8. Veng-Pedersen P (2001) Noncompartmentally based pharmacokinetic modeling. Adv Drug Deliv Rev 48:265–300

    Article  Google Scholar 

  9. FDA (1997) Guidance for industry. Dissolution testing of immediate release solid oral dosage forms. Center for Drug Evaluation and Research (CDER)

  10. USP 23/NF 18 (1995) The United States Pharmacopoeial Convention, Inc., Rockville, MD

  11. FDA (1997) Guidance for industry. Extended release oral dosage forms: development, evaluation, and application of in vitro/in vivo correlations. Center for Drug Evaluation and Research (CDER)

  12. McNabb ME, Ebert RV, McCusher K (1982) Plasma nicotine levels produced by chewing nicotine gum. JAMA 248:865–868

    Article  Google Scholar 

  13. Grassi M, Grassi G, Lapasin R, Colombo I (2007) Understanding drug release and absorption mechanisms. CRC Press, Boca Raton

    Google Scholar 

  14. Dutta S, Yihong Q, Samara E, Cao G, Granneman R (2005) Once-a-day extended-release dosage forms of divalproex sodium III: development and validation of a level A in vitro–in vivo correlation (IVIVC). J Pharm Sci 94(9):1949–1956

    Article  Google Scholar 

  15. FDA (2003) Guidance for industry. Bioavailability and bioequivalence studies for orally administered drug products-general considerations. Center for Drug Evaluation and Research (CDER)

  16. Korhonen O, Kanerva H, Vidgren M, Urtti A, Ketolainen J (2004) Evaluation of novel starch acetate-diltiazem controlled release tablets in healthy human volunteers. J Control Release 95:515–520

    Article  Google Scholar 

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Correspondence to Gaetano Lamberti.

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Di Muria, M., Lamberti, G. & Titomanlio, G. Modeling the pharmacokinetics of extended release pharmaceutical systems. Heat Mass Transfer 45, 579–589 (2009).

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  • Diltiazem
  • Extended Release
  • Immediate Release
  • Divalproex Sodium
  • Drug Release Kinetic