Medical & Biological Engineering & Computing

, Volume 55, Issue 7, pp 1085–1096 | Cite as

Mathematical model of tumor volume dynamics in mice treated with electrochemotherapy

  • Tadeja Forjanič
  • Damijan Miklavčič
Special Issue – Original Article


The effectiveness of electrochemotherapy, a local treatment using electric pulses to increase the uptake of chemotherapeutic drug, includes several antitumor mechanisms. In addition to the cytotoxic action of chemotherapeutic drug, treatment outcome also depends on antitumor immune response. In order to assess the contribution of different antitumor mechanisms to the observed treatment outcome, we designed a model of tumor volume dynamics, which is able to quantify early and late treatment effects. Model integrates characteristics of both main posttreatment processes, namely removal of lethally damaged cells from tumor volume and tumor–immune interaction. Fitting to individual responses gives the insight into the dynamics of tumor cell elimination. Two more or less clearly separable peaks can be observed from these dynamics. Model was used to quantify responses obtained after chemotherapy and electrochemotherapy with bleomycin and cisplatin in immunocompetent and immunodeficient mice. As expected, electrochemotherapy resulted in higher number of lethally damaged cells as well as in stronger immune response compared to chemotherapy alone. Additionally, bleomycin-treated tumors proved to be more immunogenic than cisplatin-treated tumors in the given range of doses.


Electroporation Electrochemotherapy Mathematical model Tumor growth 



This work was supported by the Slovenian Research Agency (ARRS) and conducted within the scope of Electroporation in Biology and Medicine (EBAM) European Associated Laboratory (LEA) and the COST Action TD1104 (in particular by a short-term scientific mission COST-STSM-TD1104-21001). Authors would like to thank Gregor Sersa from Institute of Oncology Ljubljana for providing us with the raw data.


  1. 1.
    Adkins I, Fucikova J, Garg AD, Agostinis P, Spisek R (2015) Physical modalities inducing immunogenic tumor cell death for cancer immunotherapy. Oncoimmunology 3:e968434CrossRefPubMedPubMedCentralGoogle Scholar
  2. 2.
    Bugaut H , Bruchard M, Berger H, Derangere V, Odoul L, Euvrard R, Ladoire S, Chalmin F, Vegran F, Rebe C, Apetoh L, Ghiringhelli F, Mignot G (2013) Bleomycin exerts ambivalent antitumor immune effect by triggering both immunogenic cell death and proliferation of regulatory T cells. PLoS One 8:e65181CrossRefPubMedPubMedCentralGoogle Scholar
  3. 3.
    Calvet CY, Famin D, Andre FM, Mir LM (2014) Electrochemotherapy with bleomycin induces hallmarks of immunogenic cell death in murine colon cancer cells. Oncoimmunology 3:e28131CrossRefPubMedPubMedCentralGoogle Scholar
  4. 4.
    Cemazar M, Miklavcic D, Sersa G (1998) Intrinsic sensitivity of tumor cells to bleomycin as an indicator of tumor response to electrochemotherapy. Jpn J Cancer Res 89:328–333CrossRefPubMedGoogle Scholar
  5. 5.
    Cemazar M, Parkins CS, Holder AL, Kranjc S, Chaplin DJ, Sersa G (2001) Cytotoxicity of bioreductive drug tirapazamine is increased by application of electric pulses in SA-1 tumours in mice. Anticancer Res 21:1151–1156PubMedGoogle Scholar
  6. 6.
    Corovic S, Lackovic I, Sustaric P, Sustar T, Rodic T, Miklavcic D (2013) Modeling of electric field distribution in tissues during electroporation. Biomed Eng Online 12:16CrossRefPubMedPubMedCentralGoogle Scholar
  7. 7.
    Domenge C, Orlowski S, Luboinski B, De Baere T, Schwaab G, Belehradek J, Mir LM (1996) Antitumor electrochemotherapy: new advances in the clinical protocol. Cancer 77:956–963CrossRefPubMedGoogle Scholar
  8. 8.
    Edhemovic I, Brecelj E, Gasljevic G, Marolt Music M, Gorjup V, Mali B, Jarm T, Kos B, Pavliha D, Grcar Kuzmanov B, Cemazar M, Snoj M, Miklavcic D, Gadzijev EM, Sersa G (2014) Intraoperative electrochemotherapy of colorectal liver metastases. J Surg Oncol 110:320–327CrossRefPubMedGoogle Scholar
  9. 9.
    Gay HA, Taylor QQ, Kiriyama F, Dieck GT, Jenkins T, Walker P, Allison RR, Ubezio P (2013) Modeling of non-small cell lung cancer volume changes during CT-based image guided radiotherapy: patterns observed and clinical implications. Comput Math Methods Med 2013:637181CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Golden EB, Apetoh L (2015) Radiotherapy and immunogenic cell death. Semin Radiat Oncol 25:11–17CrossRefPubMedGoogle Scholar
  11. 11.
    Jarm T, Cemazar M, Miklavcic D, Sersa G (2010) Antivascular effects of electrochemotherapy: implications in treatment of bleeding metastases. Expert Rev Anticancer Ther 10:729–746CrossRefPubMedGoogle Scholar
  12. 12.
    Koch G, Walz A, Lahu G, Schropp J (2009) Modeling of tumor growth and anticancer effects of combination therapy. J Pharmacokinet Pharmacodyn 36:179–197CrossRefPubMedGoogle Scholar
  13. 13.
    Kotnik T, Kramar P, Pucihar G, Miklavcic D, Tarek M (2012) Cell membrane electroporation- Part 1: The phenomenon. IEEE Electr Insul Mag 28:14–23CrossRefGoogle Scholar
  14. 14.
    Kuznetsov V, Makalkin I, Taylor M, Perelson A (1994) Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull Math Biol 56:295–321CrossRefPubMedGoogle Scholar
  15. 15.
    Krysko DV, Garg AD, Kaczmarek A, Krysko O, Agostinis P, Vandenabeele P (2012) Immunogenic cell death and DAMPs in cancer therapy. Nat Rev Cancer 12:860–875CrossRefPubMedGoogle Scholar
  16. 16.
    Markelc B, Bellard E, Sersa G, Pelofy S, Teissie J, Coer A, Golzio M, Cemazar M (2012) In vivo molecular imaging and histological analysis of changes induced by electric pulses used for plasmid DNA electrotransfer to the skin: a study in a dorsal window chamber in mice. J Membr Biol 245:545–554CrossRefPubMedPubMedCentralGoogle Scholar
  17. 17.
    Markelc B, Sersa G, Cemazar M (2013) Differential mechanisms associated with vascular disrupting action of electrochemotherapy: intravital microscopy on the level of single normal and tumor blood vessels. PLoS One 8:e59557CrossRefPubMedPubMedCentralGoogle Scholar
  18. 18.
    Marty M, Sersa G, Garbay JR, Gehl J, Collins CG, Snoj M, Billard V, Geertsen PF, Larkin JO, Miklavcic D, Pavlovic I, Paulin-Kosir SM, Cemazar M, Morsli N, Soden DM, Rudolf Z, Robert C, O’Sullivan GC, Mir LM (2006) Electrochemotherapy—an easy, highly effective and safe treatment of cutaneous and subcutaneous metastases: results of ESOPE (European Standard Operating Procedures of Electrochemotherapy) study. Eur J Cancer Suppl 4:3–13CrossRefGoogle Scholar
  19. 19.
    Miklavcic D, Mali B, Kos B, Heller R, Sersa G (2014) Electrochemotherapy: from the drawing board into medical practice. Biomed Eng Online 13:29CrossRefPubMedPubMedCentralGoogle Scholar
  20. 20.
    Miklavcic D, Sersa G, Brecelj E, Gehl J, Soden D, Bianchi G, Ruggieri P, Rossi CR, Campana LG, Jarm T (2012) Electrochemotherapy: technological advancements for efficient electroporation-based treatment of internal tumors. Med Biol Eng Comput 50:1213–1225CrossRefPubMedPubMedCentralGoogle Scholar
  21. 21.
    Miklavcic D, Beravs K, Semrov D, Cemazar M, Demsar F, Sersa G (1998) The importance of electric field distribution for effective in vivo electroporation of tissues. Biophys J 74:2152–2158CrossRefPubMedPubMedCentralGoogle Scholar
  22. 22.
    Mir LM, Orlowski S, Belehradek J, Paoletti C (1991) Electrochemotherapy potentiation of antitumour effect of bleomycin by local electric pulses. Eur J Cancer 27:68–72CrossRefPubMedGoogle Scholar
  23. 23.
    Mould DR, Walz A-C, Lave T, Gibbs JP, Frame B (2015) Developing exposure/response models for anticancer drug treatment: special considerations. CPT Pharmacomet Syst Pharmacol 4:e00016CrossRefGoogle Scholar
  24. 24.
    Pavselj N, Bregar Z, Cukjati D, Batiuskaite D, Mir LM, Miklavcic D (2005) The course of tissue permeabilization studied on a mathematical model of a subcutaneous tumor in small animals. IEEE Trans Biomed Eng 52:1373–1381CrossRefPubMedGoogle Scholar
  25. 25.
    Rocchetti M, Poggesi I, Germani M, Fiorentini F, Pellizzoni C, Zugnoni P, Pesenti E, Simeoni M, De Nicolao G (2005) A pharmacokinetic-pharmacodynamic model for predicting tumour growth inhibition in mice: a useful tool in oncology drug development. Basic Clin Pharmacol Toxicol 96:265–268CrossRefPubMedGoogle Scholar
  26. 26.
    Rockne R, Alvord EC, Rockhill JK, Swanson KR (2009) A mathematical model for brain tumor response to radiation therapy. J Math Biol 58:561–578CrossRefPubMedGoogle Scholar
  27. 27.
    Sersa G, Miklavcic D, Cemazar M, Belehradek J, Jarm T, Mir LM (1997) Electrochemotherapy with CDDP on LPB sarcoma: comparison of the anti-tumor effectiveness in immunocompotent and immunodeficient mice. Bioelectrochem Bioenerg 43:279–283CrossRefGoogle Scholar
  28. 28.
    Sersa G, Jarm T, Kotnik T, Coer A, Podkrajsek M, Sentjurc M, Miklavcic D, Kadivec M, Kranjc S, Secerov A, Cemazar M (2008) Vascular disrupting action of electroporation and electrochemotherapy with bleomycin in murine sarcoma. Br J Cancer 98:388–398CrossRefPubMedPubMedCentralGoogle Scholar
  29. 29.
    Sersa G, Teissie J, Cemazar M, Signori E, Kamensek U, Marshall G, Miklavcic D (2015) Electrochemotherapy of tumors as in situ vaccination boosted by immunogene electrotransfer. Cancer Immunol Immunother 64:1315–1327CrossRefPubMedPubMedCentralGoogle Scholar
  30. 30.
    Sersa G, Cemazar M, Miklavcic D (1995) Antitumor effectiveness of electrochemotherapy with cis-diamminedichloroplatinum(II) in mice. Cancer Res 55:3450–3455PubMedGoogle Scholar
  31. 31.
    Sersa G, Miklavcic D, Cemazar M, Rudolf Z, Pucihar G, Snoj M (2008) Electrochemotherapy in treatment of tumours. Eur J Surg Oncol 34:232–240CrossRefPubMedGoogle Scholar
  32. 32.
    Spratt DE, Gordon Spratt EA, Wu S, DeRosa A, Lee NY, Lacouture ME, Barker CA (2014) Efficacy of skin-directed therapy for cutaneous metastases from advanced cancer: a meta-analysis. J Clin Oncol 32:3144–3155CrossRefPubMedPubMedCentralGoogle Scholar
  33. 33.
    Todorovic V, Sersa G, Flisar K, Cemazar M (2009) Enhanced cytotoxicity of bleomycin and cisplatin after electroporation in murine colorectal carcinoma cells. Radiol Oncol 43:264–273CrossRefGoogle Scholar
  34. 34.
    Trdan O, Galmarini CM, Patel K, Tannock IF (2007) Drug resistance and the solid tumor microenvironment. J Natl Cancer Inst 99:1441–1454CrossRefGoogle Scholar
  35. 35.
    Zitvogel L, Apetoh L, Ghiringhelli F, Kroemer G (2008) Immunological aspects of cancer chemotherapy. Nat Rev Immunol 8:59–73CrossRefPubMedGoogle Scholar
  36. 36.
    Zitvogel L, Kepp O, Kroemer G (2011) Immune parameters affecting the efficacy of chemotherapeutic regimens. Nat Rev Clin Oncol 8:151–160CrossRefPubMedGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2016

Authors and Affiliations

  1. 1.Department for Biomedical Engineering, Faculty of Electrical EngineeringUniversity of LjubljanaLjubljanaSlovenia

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