A mathematical analysis of rebound in a target-mediated drug disposition model: I.Without feedback

详细信息    查看全文

• 作者：Philip J. Aston (1)
  Gianne Derks (1)
  Balaji M. Agoram (2)
  Piet H. van der Graaf (3)
  
• 关键词：92C45 ; 92C50 ; 34E10 ; 37L25
• 刊名：Journal of Mathematical Biology
• 出版年：2014
• 出版时间：May 2014
• 年：2014
• 卷：68
• 期：6
• 页码：1453-1478
• 全文大小：857 KB
• 参考文献：1. Agoram B, Martin S, van der Graaf P (2007) The role of mechanism-based pharmacokinetic-pharmacodynamic (pk-pd) modelling in translational research of biologics. Drug Discov Today 12:1018-024 CrossRef
  2. Ait-Oudhia S, Lowe P, Mager D (2012) Bridging clinical outcomes of canakinumab treatment in rheumatoid arthritis patients with a population model of il-1 $\beta $ kinetics. Pharmacomet Syst Pharmacol CPT. doi:10.1038/psp.2012.6
  3. Aston P, Derks G, Raji A, Agoram B, van der Graaf P (2011) Mathematical analysis of the pharmacokinetic-pharmacodynamic (pkpd) behaviour of monoclonal antibodies: predicting in vivo potency. J Theor Biol 281:113-21 CrossRef
  4. Aston P, Derks G, Agoram B, van der Graaf P (2012) A mathematical analysis of rebound in a target-mediated drug disposition model. II. With feedback. Abstract at VPH2012. http://www.vph-noe.eu/vph2012
  5. Bhatia A, Kast R (2007) Tnf can paradoxically increase on etanercept treatment, occasionally contributing to TNF-mediated disease. J Rheum 34:447
  6. Bravo Vergal Y, Hawkins N, Claxton K, Asseburg C, Palmer S, Woolacoot N, Bruce I, Sculpher M (2007) The cost-effectiveness of etanercept and infliximab for the treatment of patients with psoriatic arthritis. Rheumatology 46:1729-735 CrossRef
  7. Cacheux W, Boisserie T, Staudacher L, Vignaux O, Dousset B, Soubrane O, Terris B, Mateus C, Chaussade S, Goldwasser F (2008) Reversible tumor growth acceleration following bevacizumab interruption in metastatic colorectal cancer patients scheduled for surgery. Ann Onc 19:1659-661 CrossRef
  8. Chan J, Piper D, Cao Q, Liu D, King C, Wang W, Tang J, Liu Q, Higbee J, Xia A, Di Y, Shetterly S, Arimura Z, Salomonis H, Romanow W, Thibault S, Zhang R, Cao P, Yang X, Yu T, Lu M, Retter M, Kwon G, Henne K, Pan O, Tsai M, Fuchslocher B, Yang E, Zhou L, Lee K, Daris M, Sheng J, Wang Y, Shen W, Yeh W, Emery M, Walker N, Shan B, Schwarz M, Jackson S (2009) A proprotein convertase subtilisin/kexin type 9 neutralizing antibody reduces serum cholesterol in mice and nonhuman primates. Proc Natl Acad Sci USA 106:9820-825 CrossRef
  9. Fenichel N (1979) Geometric singular perturbation theory for ordinary differential equations. J Differ Equ 31:53-8 CrossRef
  10. Haringman J, Gerlag D, Smeets T, Baeten D, van den Bosch F, Bresnihan B, Breedveld F, Dinant H, Legay F, Gram H, Loetscher P, Schmouder R, Woodworth T, Tak P (2006) A randomized controlled trial with an anti-ccl2 (anti-monocyte chemotactic protein 1) monoclonal antibody in patients with rheumatoid arthritis. Arthritis Rheum 54:2387-392 CrossRef
  11. Jordan D, Smith P (2007) Nonlinear ordinary differential equations, 4th edn. OUP, New York
  12. Klein B, Zhang X, Lu Z, Bataille R (1995) Interleukin-6 in human multiple myeloma. Blood 85:863-72
  13. Krippendorff D, Oyarzun B-F, Huisinga W (2009) Ligand accumulation counteracts therapeutic inhibition of receptor systems. In: Proceedings of foundations of systems biology in engeneering, FOSBE, pp 173-76
  14. Levy G (1994) Pharmacologic target mediated drug disposition. Clin Pharmacol Therap 56:248-52 CrossRef
  15. Lowe P, Tannenbaum S, Gautier A, Jimenez P (2009) Relationship between omalizumab pharmacokinetics, IgE pharmacodynamics and symptoms in patients with severe persistent allergic (IgE-mediated) asthma. Br J Clin Pharmacol 68:61-6 CrossRef
  16. Mager D, Jusko W (2001) General pharmacokinetic model for drugs exhibiting target-mediated drug disposition. J Pharmacokinet Pharmacodyn 28:507-32 CrossRef
  17. Meno-Tetang G, Lowe P (2005) On the prediction of the human response: a recycled mechanistic pharmacokinetic/pharmacodynamic approach. Bas Clin Pharm Tox 96:182-92 CrossRef
  18. Munafo A, Priestley A, Nestorov I, Visich J, Rogge M (2007) Safety, pharmacokinetics and pharmacodynamics of atacicept in healthy volunteers. Eur J Clin Pharmacol 63:647-56 CrossRef
  19. Ng C, Stefanich E, Anand B, Fielder P, Vaickus L (2006) Pharmacokinetics/pharmacodynamics of nondepleting anti-CD4 monoclonal antibody (TRX1) in healthy human volunteers. Pharm Res 23:95-03 CrossRef
  20. Peletier L, Gabrielsson J (2009) Dynamics of target-mediated drug disposition. Eur J Pharm Sci 38:445-64 CrossRef
  21. Peletier L, Gabrielsson J (2012a) Dynamics of target-mediated drug disposition: characteristic profiles and parameter identification. J Pharmacokinet Pharmacodyn 39:429-51 CrossRef
  22. Peletier L, Gabrielsson J (2012b) Dynamics of target-mediated drug disposition: how a drug reaches its target. Comput Geosc. doi:10.1007/s10596-012-9312-4
  23. Smith H (1995) Monotone dynamical systems. In: An introduction to the theory of competitive and cooperative systems, Mathematical surveys and monographs, vol 41. AMS, Providence
  24. Stefanini M, Wu F, Gabhann F, Popel A (2010) Increase of plasma vegf after intravenous administration of bevacizumab is predicted by a pharmacokinetic model. Cancer Res 70:9886-894 CrossRef
  25. Vugmeister Y, Tian X, Szlut P, Kasaian M, Xu X (2009) Pharmacokinetic and pharmacodynamics modeling of a humanized anti-IL-13 antibody in naive and ascaris-challenged cynomolgus monkeys. Pharmaceut Res 26:306-15 CrossRef
  26. Wang B, Lau YY, Liang M, Vainshtein I, Zusmanovich M, Lu H, Magrini F, Sleeman M, Roskos L (2012) Mechanistic modeling of antigen sink effect for mavrilimumab following intravenous administration in patients with rheumatoid arthritis. J Clin Pharmacol 52:1150-161 CrossRef
  
• 作者单位：Philip J. Aston (1)
  Gianne Derks (1)
  Balaji M. Agoram (2)
  Piet H. van der Graaf (3)
  
  1. Department of Mathematics, University of Surrey, Guildford, UK
  2. MedImmune, Pharmacokinetics/Dynamics and Bioanalysis, Cambridge, UK
  3. Leiden Academic Centre for Drug Research (LACDR), 2300 RA, Leiden, The Netherlands
  
• ISSN：1432-1416

文摘

We consider the possibility of free receptor (antigen/cytokine) levels rebounding to higher than the baseline level after one or more applications of an antibody drug using a target-mediated drug disposition model. Using geometry and dynamical systems analysis, we show that rebound will occur if and only if the elimination rate of the drug–receptor product is slower than the elimination rates of the drug and of the receptor. We also analyse the magnitude of rebound through approximations and simulations and demonstrate that it increases if the drug dose increases or if the difference between the elimination rate of the drug–receptor product and the minimum of the elimination rates of the drug and of the receptor increases.