Skip to main content
SpringerLink
Log in

Simplification of a pharmacokinetic model for red blood cell methotrexate disposition

  • Pharmacokinetics and Disposition
  • Published:
European Journal of Clinical Pharmacology Aims and scope Submit manuscript

Abstract

Purpose

A pharmacokinetic (PK) model is available for describing the time course of the concentrations of methotrexate (MTX or MTXGlu1) and its active polyglutamated metabolites (MTXGlu2–5) in red blood cells (RBCs). In this study, we aimed to simplify the MTX PK model and to optimise the blood sampling schedules for use in future studies.

Methods

A proper lumping technique was used to simplify the original MTX RBC PK model. The sum of predicted RBC MTXGlu3–5 concentrations in both the simplified and original models was compared. The sampling schedules for MTXGlu3–5 or all MTX polyglutamates in RBCs were optimised using the Population OPTimal design (POPT) software.

Results

The MTX RBC PK model was simplified into a three-state model. The maximum of the absolute value of relative difference in the sum of predicted RBC MTXGlu3–5 concentrations over time was 6.3 %. A five blood sample design was identified for estimating parameters of the simplified model.

Conclusions

This study illustrates the application of model simplification processes to an existing model for MTX RBC PK. The same techniques illustrated in our study may be adopted by other studies with similar interest.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Lambert CM, Sandhu S, Lochhead A, Hurst NP, McRorie E, Dhillon V (2004) Dose escalation of parenteral methotrexate in active rheumatoid arthritis that has been unresponsive to conventional doses of methotrexate: a randomized, controlled trial. Arthritis Rheum 50:364–371

    Article  CAS  PubMed  Google Scholar 

  2. Halilova KI, Brown EE, Morgan SL, Bridges SL Jr, Hwang MH, Arnett DK, Danila MI (2012) Markers of treatment response to methotrexate in rheumatoid arthritis: where do we stand? Int J Rheumatol 2012:978396–978402

    Article  PubMed Central  PubMed  Google Scholar 

  3. Korell J, Stamp LK, Barclay ML, Dalrymple JM, Drake J, Zhang M, Duffull SB (2013) A population pharmacokinetic model for low-dose methotrexate and its polyglutamated metabolites in red blood cells. Clin Pharmacokinet 52:475–485

    Article  CAS  PubMed  Google Scholar 

  4. Okino MS, Mavrovouniotis ML (1998) Simplification of mathematical models of chemical reaction systems. Chem Rev 98:391–408

    Article  CAS  PubMed  Google Scholar 

  5. Matherly LH, Goldman DI (2003) Membrane transport of folates. Vitam Horm 66:403–456

    Article  CAS  PubMed  Google Scholar 

  6. Brooks AJ, Begg EJ, Zhang M, Frampton CM, Barclay ML (2007) Red blood cell methotrexate polyglutamate concentrations in inflammatory bowel disease. Ther Drug Monit 29:619–625

    Article  CAS  PubMed  Google Scholar 

  7. Pan S, Stamp L, Duffull S, Barclay M, Dalrymple J, Drake J, Zhang M, Korell J (2014) Assessment of the relationship between methotrexate polyglutamates in red blood cells and clinical response in patients commencing methotrexate for rheumatoid arthritis. Clin Pharmacokinet 53:1161–1170

    Article  CAS  PubMed  Google Scholar 

  8. Foo LK, McGree J, Duffull S (2012) A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies. Pharm Stat 11:325–333

    Article  PubMed  Google Scholar 

  9. Wei J, Kuo JCW (1969) Lumping analysis in monomolecular reaction systems. Analysis of the exactly lumpable system. Ind Eng Chem Fundam 8:114–123

    Article  CAS  Google Scholar 

  10. Dokoumetzidis A, Aarons L (2009) Proper lumping in systems biology models. IET Syst Biol 3:40–51

    Article  CAS  PubMed  Google Scholar 

  11. Gulati A, Isbister GK, Duffull SB (2014) Scale reduction of a systems coagulation model with an application to modeling pharmacokinetic-pharmacodynamic data. CPT Pharmacometrics Syst Pharmacol 3, e90

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  12. Dalrymple JM, Stamp LK, O'Donnell JL, Chapman PT, Zhang M, Barclay ML (2008) Pharmacokinetics of oral methotrexate in patients with rheumatoid arthritis. Arthritis Rheum 58:3299–3308

    Article  CAS  PubMed  Google Scholar 

  13. Stamp LK, Barclay ML, O'Donnell JL, Zhang M, Drake J, Frampton C, Chapman PT (2011) Effects of changing from oral to subcutaneous methotrexate on red blood cell methotrexate polyglutamate concentrations and disease activity in patients with rheumatoid arthritis. J Rheumatol 38:2540–2547

    Article  CAS  PubMed  Google Scholar 

  14. Shivva V, Korell J, Tucker IG, Duffull SB (2013) An approach for identifiability of population pharmacokinetic-pharmacodynamic models. CPT Pharmacometrics Syst Pharmacol 2, e49

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  15. Duffull SB, Denman N, Kimko H, Eccleston J (2012) Population OPTimal design. In POPT—installation and user guide. Available from: http://www.winpopt.com/

  16. Al-Sallami H, Cheah S, Han S, Liew J, Lim J, Ng M, Solanki H, Soo R, Tan V, Duffull S (2014) Between-subject variability: should high be the new normal? Eur J Clin Pharmacol 70:1403–1404

    Article  PubMed  Google Scholar 

  17. Nyberg J, Bazzoli C, Ogungbenro K, Aliev A, Leonov S, Duffull S, Hooker AC, Mentre F (2015) Methods and software tools for design evaluation in population pharmacokinetics-pharmacodynamics studies. Br J Clin Pharmacol 79:6–17

    Article  CAS  PubMed  Google Scholar 

  18. Bellu G, Saccomani MP, Audoly S, D'Angio L (2007) DAISY: a new software tool to test global identifiability of biological and physiological systems. Comput Methods Prog Biomed 88:52–61

    Article  Google Scholar 

  19. D'Argenio D (1981) Optimal sampling times for pharmacokinetic experiments. J Pharmacokinet Biopharm 9:739–756

    Article  PubMed  Google Scholar 

  20. Foo LK, Duffull SB (2011) Optimal design of pharmacokinetic–pharmacodynamic studies. In: Bonate PL, Howard DR (eds) Pharmacokinetics in drug development. Springer US, pp 175–193

  21. Steven Ernest C 2nd, Nyberg J, Karlsson MO, Hooker AC (2014) Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model. J Pharmacokinet Pharmacodyn 41:639–654

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

The clinical studies were supported by the Health Research Council of New Zealand and New Zealand Pharmacy Education and Research Foundation.

Shan Pan was supported by a University of Otago PhD scholarship.

Author information

Authors and Affiliations

  1. School of Pharmacy, University of Otago, Dunedin, New Zealand

    Shan Pan & Stephen B. Duffull

  2. Model Answers Pty Ltd, Brisbane, Australia

    Julia Korell

  3. Department of Medicine, University of Otago, Christchurch, New Zealand

    Lisa K. Stamp

Authors
  1. Shan Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Julia Korell
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lisa K. Stamp
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Stephen B. Duffull
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shan Pan.

Ethics declarations

Conflict of interest

The authors declare that they have no competing interests.

Author contributions

S.P., J.K., L.K.S., and S.B.D. wrote the manuscript. S.P., J.K., L.K.S., and S.B.D. designed the research. S.P. and S.B.D. performed the research.

Electronic supplementary material

Below is the link to the electronic supplementary material.

ESM 1

(DOCX 250 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pan, S., Korell, J., Stamp, L.K. et al. Simplification of a pharmacokinetic model for red blood cell methotrexate disposition. Eur J Clin Pharmacol 71, 1509–1516 (2015). https://doi.org/10.1007/s00228-015-1951-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00228-015-1951-7

Keywords

Search

Navigation