Lumping of physiologically-based pharmacokinetic models and a mechanistic derivation of classical compartmental models

  • Sabine Pilari
  • Wilhelm Huisinga


In drug discovery and development, classical compartment models and physiologically based pharmacokinetic (PBPK) models are successfully used to analyze and predict the pharmacokinetics of drugs. So far, however, both approaches are used exclusively or in parallel, with little to no cross-fertilization. An approach that directly links classical compartment and PBPK models is highly desirable. We derived a new mechanistic lumping approach for reducing the complexity of PBPK models and establishing a direct link to classical compartment models. The proposed method has several advantages over existing methods: Perfusion and permeability rate limited models can be lumped; the lumped model allows for predicting the original organ concentrations; and the volume of distribution at steady state is preserved by the lumping method. To inform classical compartmental model development, we introduced the concept of a minimal lumped model that allows for prediction of the venous plasma concentration with as few compartments as possible. The minimal lumped parameter values may serve as initial values for any subsequent parameter estimation process. Applying our lumping method to 25 diverse drugs, we identified characteristic features of lumped models for moderate-to-strong bases, weak bases and acids. We observed that for acids with high protein binding, the lumped model comprised only a single compartment. The proposed lumping approach established for the first time a direct derivation of simple compartment models from PBPK models and enables a mechanistic interpretation of classical compartment models.


Classical model Compartment PK model Physiologically based pharmacokinetics PBPK Mechanistic lumping Volume of distribution Minimal lumped model Transfer of knowledge 



The authors kindly acknowledge comments on the manuscript by Charlotte Kloft (Clinical Pharmacy, Martin-Luther-Universität Halle-Wittenberg/ Germany), Steve Kirkland (Hamilton Institute, NUIM/Ireland), Andreas Reichel (Bayer Schering Pharma) and Olaf Lichtenberger (Abbott). S.P. acknowledges financial support from the Graduate Research Training Program PharMetrX: Pharmacometrics and Computational Disease Modeling, Martin-Luther-Universität Halle-Wittenberg and Freie Universität Berlin, Germany (


  1. 1.
    Kwon Y (2001) Handbook of essential pharmacokinetics, pharmacodynamics, and drug metabolism for industrial scientists. Springer-Verlag, New York, IncGoogle Scholar
  2. 2.
    Derendorf H, Lesko LJ, Chaikin P, Colburn WA, Lee P, Miller R, Powell R, Rhodes G, Stanski D, Venitz J (2000) Pharmacokinetic/pharmacodynamic modeling in drug research and development. J Clin Pharmacol 40:1399–1418PubMedGoogle Scholar
  3. 3.
    Schoenwald RD (2002) Pharmacokinetics in drug discovery and development. CRC Press, Boca RatonGoogle Scholar
  4. 4.
    Tozer TN, Rowland M (2006) Introduction to pharmacokinetics and pharmacodynamics. Lippincott Williams & Wilkins, PhiladelphiaGoogle Scholar
  5. 5.
    Lüpfert C, Reichel A (2005) Development and application of physiologically based pharmacokinetic modeling toos to support drug discovery. Chem Biodivers 2:1462–1486CrossRefPubMedGoogle Scholar
  6. 6.
    Jones HM, Parrott N, Jorga K, Lavé T (2006) A novel strategy for physiologically based predictions of human pharmacokinetics. Clin Pharmacokinet 45:511–542CrossRefPubMedGoogle Scholar
  7. 7.
    Theil FP, Guentert TW, Haddad S, Poulin P (2003) Utility of physiologically based pharmacokinetic models to drug development and rational drug discovery candidate selection. Toxicol Lett 138:29–49CrossRefPubMedGoogle Scholar
  8. 8.
    Schmitt W, Willmann S (2005) Physiology-based pharmacokinetic modeling: ready to be used. Drug Discov Today 2:125–132CrossRefGoogle Scholar
  9. 9.
    Jones HM, Gardner IB, Watson KJ (2009) Modelling and PBPK simulation in drug discovery. AAPS J 11:155–166CrossRefPubMedGoogle Scholar
  10. 10.
    Bourne DWA (1995) Mathematical modeling of pharmacokinetic data. Technomic Publishing Company, Inc., LancasterGoogle Scholar
  11. 11.
    Nestorov IA, Aarons LJ, Arundel PA, Rowland M (1998) Lumping of whole-body physiologcally based pharmacokinetic models. J Pharmacokinet Pharmacodyn 26:21–46CrossRefGoogle Scholar
  12. 12.
    Brochot C, Toth J, Bois FY (2005) Lumping in pharmacokinetics. J Pharmacokinet Pharmacodyn 32:719–736CrossRefPubMedGoogle Scholar
  13. 13.
    Gueorguieva I, Nestorov IA, Rowland M (2006) Reducing whole body physiologically based pharmacokinetic models using global sensitivity analysis: diazepam case study. J Pharmacokinet Pharmacodyn 33:1–27CrossRefPubMedGoogle Scholar
  14. 14.
    Björkman S (2003) Reduction and lumping of physiologically based pharmacokinetic models: prediction of the disposition of fentanyl and pethidine in human by successively simplified models. J Pharmacokinet Pharmacodyn 30:285–307CrossRefPubMedGoogle Scholar
  15. 15.
    Rodgers T, Leahy D, Rowland M (2005) Physiologically based pharmacokinetic modeling 1: predicting the tissue distribution of moderate-to-strong bases. J Pharm Sci 94:1259–1276CrossRefPubMedGoogle Scholar
  16. 16.
    Rodgers T, Leahy D, Rowland M (2007) Errata: Physiologically based pharmacokinetic modeling 1: predicting the tissue distribution of moderate-to-strong bases. J Pharm Sci 96:3151–3152CrossRefGoogle Scholar
  17. 17.
    Rodgers T, Rowland M (2005) Physiologically based pharmacokinetic modelling 2: predicting the tissue distribution of acids, very weak bases, neutrals and zwitterions. J Pharm Sci 95:1238–1257CrossRefGoogle Scholar
  18. 18.
    Rodgers T, Rowland M (2007) Errata: physiologically based pharmacokinetic modelling 2: predicting the tissue distribution of acids, very weak bases, neutrals and zwitterions. J Pharm Sci 96:3153–3154CrossRefGoogle Scholar
  19. 19.
    Gerlowski LE, Jain RK (1983) Physiologically based pharmacokinetic modeling: principles and application. J Pharm Sci 72:1103–1127CrossRefPubMedGoogle Scholar
  20. 20.
    Nestorov IA (2003) Whole body pharmacokinetic models. Clin Pharmacokinet 42:883–908CrossRefPubMedGoogle Scholar
  21. 21.
    Luttringer O, Theil FP, Poulin P, Schmitt-Hoffmann AH, Guentert TW, Lavé T (2003) Physiologically based pharmacokinetic modelling of disposition of epiroprim in humans. J Pharm Sci 92:1990–2007CrossRefPubMedGoogle Scholar
  22. 22.
    Willmann S, Höhn K, Edginton A, Sevestre M, Solodenko J, Weiss W, Lippert J, Schmitt W (2007) Development of a physiologically-based whole-body population model for assessing the influence of individual variability on the pharmacokinetics of drugs. J Pharmacokinet Pharmacodyn 34:401–431CrossRefPubMedGoogle Scholar
  23. 23.
    International Commission on Radiological Protection (ICRP) (2002) Basic anatomical and physiological data for use in radiological protection: reference values. ICRP Publication 89Google Scholar
  24. 24.
    Poulin P, Theil FP (2009) Development of a novel method for predicting human volume of distribution at steady-state of basic drugs and comparative assessment with existing methods. J Pharm Sci 9999:1–29Google Scholar
  25. 25.
    Obach RS (1999) Prediction of human clearance of twenty-nine drugs from hepatic microsomal intrinsic clearance data: an examination of in vitro half-life approach and nonspecific binding to microsomes. Drug Metab Dispos 27:1350–1359PubMedGoogle Scholar
  26. 26.
    Riley RJ, McGinnity DF, Austin RP (2005) A unified model for predicting human hepatic, metabolic clearance from in vitro intrinsic clearance data in hepatocytes and microsomes. Drug Metab Dispos 33:1304–1311CrossRefPubMedGoogle Scholar
  27. 27.
    Rodgers T, Rowland M (2007) Mechanistic approaches to volume of distribution predictions: understanding the process. Pharm Res 24:918–933CrossRefPubMedGoogle Scholar
  28. 28.
    Jones HM, Houston JB (2004) Substrate depletion approach for determining in vitro metabolic clearance: time dependencies in hepatocyte and microsomal incubations. Drug Metab Dispos 32:973–982CrossRefPubMedGoogle Scholar
  29. 29.
    DrugBank (2010) Diclofenac.
  30. 30.
    DrugBank (2010) Warfarin.
  31. 31.
    Jung D, Mayersohn M, Perrier D, Calkins J, Saunders R (1982) Thiopental disposition in lean and obese patients undergoing surgery. Anesthesiology 56:269–274CrossRefPubMedGoogle Scholar
  32. 32.
    Russo H, Simon N, Duboin MP, Urien S (1997) Population pharmacokinetics of high-dose thiopental in patients with cerebral injuries. Clin Pharmacol Ther 62:15–20CrossRefPubMedGoogle Scholar
  33. 33.
    Löscher W (1978) Serum protein binding and pharmacokinetics of valproate in man, dog, rat and mouse. J Pharmacol Exp Ther 204:255–261PubMedGoogle Scholar
  34. 34.
    Food and Drug Administration (2004) Approval letter: LidocaineGoogle Scholar
  35. 35.
    Blakey GE, Nestorov IA, Arundel PA, Aarons LJ, Rowland M (1997) Quantitative structure pharmacokinetics relationship I: development of a whole-body physiologically based pharmacokinetic model to characterize changes in pharmacokinetics across a homologous series of barbiturates in the rat. J Pharmacokinet Biopharm 25:277–312CrossRefPubMedGoogle Scholar
  36. 36.
    von Kleist M, Huisinga W (2007) Physiologically based pharmacokinetic modelling: a sub-compartmentalized model of tissue distribution. J Pharmacokinet Pharmacodyn 34:789–806CrossRefGoogle Scholar
  37. 37.
    Boyes RN, Adams HJ, Duce BR (1970) Oral absorption and disposition kinetics of lidocaine hydrochloride in dogs. J Pharmacol Exp Ther 174:1–8PubMedGoogle Scholar
  38. 38.
    Adjepon-Yamoah KK, Scott DB, Prescott LF (1974) The effect of atropine on the oral absorption of lidocaine in man. Eur J Clin Pharmacol 7:397–400CrossRefPubMedGoogle Scholar
  39. 39.
    Berezhkovskiy LM (2004) Volume of distribution at steady state for a linear pharmacokinetic system with peripheral elimination. J Pharm Sci 93:1628–1640CrossRefPubMedGoogle Scholar
  40. 40.
    Yates JWT, Arundel PA (2008) On the volume of distribution at steady state and its relationship with two-compartmental models. J Pharm Sci 97:111–122CrossRefPubMedGoogle Scholar
  41. 41.
    Heizmann P, Eckert M, Ziegler WH (1983) Pharmacokinetics and bioavailability of midazolam in man. Br J Clin Pharmacol 16:43–49Google Scholar
  42. 42.
    Zomorodi K, Donner A, Somma J, Barr J, Sladen R, Ramsay J, Geller E, Shafer SL (1998) Population pharmacodynamics of midazolam administered by target controlled infusion for sedation following coronary artery bypass grafting. Anesthesiology 89:1418–1429CrossRefPubMedGoogle Scholar
  43. 43.
    Swart EL, Zuideveld KP, de Jongh J, Danhof M, Thijs LG, van Schijndel RMJS (2003) Comparative population pharmacokinetics of lorazepam and midazolam during long-term continuous infusion in critically ill patients. Br J Clin Pharmacol 57:135–145CrossRefGoogle Scholar
  44. 44.
    Stanski DR, Maitre PO (1990) Population pharmacokinetics and pharmacodynamics of thiopental: the effect of age revisited. Anesthesiology 72:399–402CrossRefGoogle Scholar
  45. 45.
    Gugler R, Schell A, Eichelbaum M, Fröscher W, Schulz HU (1977) Disposition of valproic acid in man. Eur J Clin Pharmacol 12:125–132CrossRefPubMedGoogle Scholar
  46. 46.
    Blanco-Serrano B, Otero MJ, Santos-Buelga D, Garcia-Sanchez MJ, Serrano J, Dominguez-Gil A (1999) Population estimation of valproic acid clearance in adult patients using routine clinical pharmacokinetic data. Biopharm Drug Dispos 20:233–240CrossRefPubMedGoogle Scholar
  47. 47.
    Rostami-Hodjegan A, Peacey SR, George E, Heller SR, Tucker GT (1998) Population-based modeling to demonstrate extrapancreatic effects of tolbutamide. Am J Physiol Endocrinol Metab 274:758–771Google Scholar
  48. 48.
    Kwa A, Sprung J, Van Guilder M, Jelliffe RW (2008) A population pharmacokinetic model of epidural lidocaine in geriatric patients: effects of low-dose dopamine. Ther Drug Monit 30:379–389CrossRefPubMedGoogle Scholar
  49. 49.
    Price PS, Conolly RB, Chaisson CF, Gross EA, Young JS, Mathis ET, Tedder DR (2003) Modeling interindividual variation in physiological factors used in PBPK models of humans. Crit Rev Toxicol 33:469–503PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceFreie UniversitätBerlinGermany
  2. 2.Graduate Research Training Program PharMetrX: Pharmacometrics and Computational Disease ModelingMartin- Luther- Universität Halle-Wittenberg and Freie UniversitätBerlinGermany
  3. 3.Hamilton Institute, National University of Ireland Maynooth (NUIM)MaynoothIreland

Personalised recommendations