Pharmaceutical Research

, 36:38 | Cite as

A Population Dynamic Energy Budget-Based Tumor Growth Inhibition Model for Etoposide Effects on Wistar Rats

  • E. M. Tosca
  • M. C. Pigatto
  • T. Dalla Costa
  • P. Magni
Research Paper



This work aimed to develop a population PK/PD tumor-in-host model able to describe etoposide effects on both tumor cells and host in Walker-256 tumor-bearing rats.


Etoposide was investigated on thirty-eight Wistar rats randomized in five arms: two groups of tumor-free animals receiving either placebo or etoposide (10 mg/kg bolus for 4 days) and three groups of tumor-bearing animals receiving either placebo or etoposide (5 or 10 mg/kg bolus for 8 or 4 days, respectively). To analyze experimental data, a tumor-in-host growth inhibition (TGI) model, based on the Dynamic Energy Budget (DEB) theory, was developed. Total plasma and free-interstitial tumor etoposide concentrations were assessed as driver of tumor kinetics.


The model simultaneously describes tumor and host growths, etoposide antitumor effect as well as cachexia phenomena related to both the tumor and the drug treatment. The schedule-dependent inhibitory effect of etoposide is also well captured when the intratumoral drug concentration is considered as the driver of the tumor kinetics.


The DEB-based TGI model capabilities, up to now assessed only in mice, are fully confirmed in this study involving rats. Results suggest that well designed experiments combined with a mechanistic modeling approach could be extremely useful to understand drug effects and to describe all the dynamics characterizing in vivo tumor growth studies.


tumor-bearing rats etoposide intratumoral concentration PK/PD model tumor-in-host interactions DEB-theory 



Akaike’s information criterion


Area under the curve


Bayesian information criterion


Below limit of quantification


Body weight loss


Coefficient of variation


Dynamic energy budget


Goodness of fit




Normalized prediction distribution errors






Residual standard error




Tumor Growth Inhibition


Visual predictive check




Supplementary material

11095_2019_2568_MOESM1_ESM.pdf (1.5 mb)
ESM 1 (PDF 1575 kb)
11095_2019_2568_MOESM2_ESM.pdf (99 kb)
ESM 2 (PDF 99 kb)


  1. 1.
    Carrara L, Lavezzi SM, Borella E, De Nicolao G, Magni P, Poggesi I. Current mathematical models for cancer drug discovery. Expert Opin Drug Discovery. 2017;12(8):785–99.Google Scholar
  2. 2.
    Bonate PL. Modeling tumor growth in oncology. In: Pharmacokinetics in drug development: Springer; 2011. p. 1–19.Google Scholar
  3. 3.
    Ribba B, Holford NH, Magni P, Trocóniz I, Gueorguieva I, Girard P, et al. A review of mixed-effects models of tumor growth and effects of anticancer drug treatment used in population analysis. CPT: Pharmacometrics & Systems Pharmacology. 2014;3(5):1–10.Google Scholar
  4. 4.
    Benzekry S, Lamont C, Beheshti A, Tracz A, Ebos JM, Hlatky L, et al. Classical mathematical models for description and prediction of experimental tumor growth. PLoS Comput Biol. 2014;10(8):e1003800.CrossRefPubMedGoogle Scholar
  5. 5.
    Rajman I. PK/PD modelling and simulations: utility in drug development. Drug Discov Today. 2008;13(7):341–6.CrossRefGoogle Scholar
  6. 6.
    Simeoni M, Nicolao GD, Magni P, Rocchetti M, Poggesi I. Modeling of human tumor xenografts and dose rationale in oncology. Drug Discov Today Technol. 2013;10(3):e365–72.CrossRefGoogle Scholar
  7. 7.
    Bernard A, Kimko H, Mital D, Poggesi I. Mathematical modeling of tumor growth and tumor growth inhibition in oncology drug development. Expert Opin Drug Metab Toxicol. 2012;8(9):1057–69.CrossRefGoogle Scholar
  8. 8.
    Simeoni M, Magni P, Cammia C, De Nicolao G, Croci V, Pesenti E, et al. Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Cancer Res. 2004;64(3):1094–101.CrossRefGoogle Scholar
  9. 9.
    Rocchetti M, Poggesi I, Germani M, Fiorentini F, Pellizzoni C, Zugnoni P, et al. A pharmacokinetic-pharmacodynamic model for predicting tumour growth inhibition in mice: a useful tool in oncology drug development. Basic Clin Pharmacol Toxicol. 2005;96(3):265–8.CrossRefGoogle Scholar
  10. 10.
    Garattini S. Pharmacokinetics in cancer chemotherapy. Eur J Cancer. 2007;43(2):271–82.CrossRefGoogle Scholar
  11. 11.
    Trédan O, Galmarini CM, Patel K, Tannock IF. Drug resistance and the solid tumor microenvironment. J Natl Cancer Inst. 2007;99(19):1441–54.CrossRefGoogle Scholar
  12. 12.
    Grantab R, Sivananthan S, Tannock IF. The penetration of anticancer drugs through tumor tissue as a function of cellular adhesion and packing density of tumor cells. Cancer Res. 2006;66(2):1033–9.CrossRefGoogle Scholar
  13. 13.
    Terranova N, Tosca EM, Pesenti E, Rocchetti M, Magni P. Modeling tumor growth inhibition and toxicity outcome after administration of anticancer agents in xenograft mice: a dynamic energy budget (DEB) approach. J Theor Biol. 2018;450:1–14.CrossRefGoogle Scholar
  14. 14.
    Van Leeuwen I, Kelpin F, Kooijman S. A mathematical model that accounts for the effects of caloric restriction on body weight and longevity. Biogerontology. 2002;3(6):373–81.CrossRefGoogle Scholar
  15. 15.
    Van Leeuwen I, Zonneveld C, Kooijman S. The embedded tumour: host physiology is important for the evaluation of tumour growth. Br J Cancer. 2003;89(12):2254–63.CrossRefPubMedGoogle Scholar
  16. 16.
    Pigatto MC, Roman RM, Carrara L, Buffon A, Magni P, Dalla Costa T. Pharmacokinetic/ pharmacodynamic modeling of etoposide tumor growth inhibitory effect in Walker-56 tumor-bearing rat model using free intratumoral drug concentrations. Eur J Pharm Sci. 2017;97:70–8.CrossRefGoogle Scholar
  17. 17.
    Kaul S, Igwemezie LN, Stewart DJ, Fields SZ, Kosty M, Levithan N, et al. Pharmacokinetics and bioequivalence of etoposide following intravenous administration of etoposide phosphate and etoposide in patients with solid tumors. J Clin Oncol. 1995;13(11):2835–41.CrossRefGoogle Scholar
  18. 18.
    Toffoli G, Corona G, Sorio R, Robieux I, Basso B, Colussi AM, et al. Population pharmacokinetics and pharmacodynamics of oral etoposide. Br J Clin Pharmacol. 2001;52(5):511–9.CrossRefPubMedGoogle Scholar
  19. 19.
    Brazil. Lei 11.794/2008: Procedimentos para Uso Cientifico de Animais; 2008. CXLV, 196, 1-2. Diario Oficial da Uniao, Secao 1 de 9 de outubro de 2008.Google Scholar
  20. 20.
    Brazil. Ministerio de Ciencia, Tecnologia e Inovacao Conselho Nacional de Controle de Experimentacao Animal; 2013. -CONCEA. Diretriz Brasileira para o cuidado e a utilizacao de animais para fins cientificos e didaticos- DBCA. Brasilia - DF.Google Scholar
  21. 21.
    NCI. 2012 Frederick ACUC Guidelines Involving Experimental Neoplasia Proposals in Mice and Rats; (accessed
  22. 22.
    Pigatto MC, de Araujo BV, Torres BGS, Schmidt S, Magni P, Dalla Costa T. Population pharmacokinetic modeling of etoposide free concentrations in solid tumor. Pharm Res. 2016;33(7):1657–70.CrossRefGoogle Scholar
  23. 23.
    Tuntland T, Ethell B, Kosake T, Blasco F, Zang RX, Jain M, et al. Implementation of pharmacokinetic and pharmacodynamic strategies in early research phases of drug discovery and development at Novartis Institute of Biomedical Research. Front Pharmacol. 2014;5:174.CrossRefPubMedGoogle Scholar
  24. 24.
    Li X, Yun JK, Choi JS. Effects of morin on the pharmacokinetics of etoposide in rats. Biopharm Drug Dispos. 2007;28(3):151–6.CrossRefGoogle Scholar
  25. 25.
    Lee CK, Ki SH, Choi JS. Effects of oral curcumin on the pharmacokinetics of intravenous and oral etoposide in rats: possible role of intestinal CYP3A and P-gp inhibition by curcumin. Biopharm Drug Dispos. 2011;32(4):245–51.CrossRefGoogle Scholar
  26. 26.
    Kooijman SALM. Dynamic energy budgets in biological systems. Cambridge university press; 1993.Google Scholar
  27. 27.
    Kooijman SALM. Dynamic energy and mass budgets in biological systems. Cambridge university press 2000.Google Scholar
  28. 28.
    Kooijman SALM. Quantitative aspects of metabolic organization: a discussion of concepts. Philosophical Transactions of the Royal Society of London B: Biological Sciences. 2001;356(1407):331–49.CrossRefGoogle Scholar
  29. 29.
    Lixoft. Monolix version 2016 R;
  30. 30.
    Lavielle M. Mixed effects models for the population approach: models, tasks, methods and tools. CRC press; 2014.Google Scholar
  31. 31.
    Hollingshead MG. Antitumor efficacy testing in rodents. JNCI: Journal of the National Cancer Institute. 2008;100(21):1500–10.CrossRefPubMedGoogle Scholar
  32. 32.
    Tannock IF, Lee CM, Tunggal JK, Cowan DS, Egorin MJ. Limited penetration of anticancer drugs through tumor tissue: a potential cause of resistance of solid tumors to chemotherapy. Clin Cancer Res. 2002;8(3):878–84.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Industriale e dell’InformazioneUniversita degli Studi di PaviaPaviaItaly
  2. 2.Pharmacokinetics and PK/PD Modeling Laboratory, Pharmaceutical Sciences Graduate Program, Faculty of PharmacyFederal University of Rio Grande do SulPorto AlegreBrazil
  3. 3.R&D DepartmentEurofarma Laboratories S.A.ItapeviBrazil

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