Mathematical Models Describing Chinese Hamster Ovary Cell Death Due to Electroporation In Vitro
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Electroporation is a phenomenon used in the treatment of tumors by electrochemotherapy, non-thermal ablation with irreversible electroporation, and gene therapy. When treating patients, either predefined or variable electrode geometry is used. Optimal pulse parameters are predetermined for predefined electrode geometry, while they must be calculated for each specific case for variable electrode geometry. The position and number of electrodes are also determined for each patient. It is currently assumed that above a certain experimentally determined value of electric field, all cells are permeabilized/destroyed and under it they are unaffected. In this paper, mathematical models of survival in which the probability of cell death is continuously distributed from 0 to 100 % are proposed and evaluated. Experiments were performed on cell suspensions using electrical parameters similar to standard electrochemotherapy and irreversible electroporation parameters. The proportion of surviving cells was determined using clonogenic assay for assessing the ability of a cell to grow into a colony. Various mathematical models (first-order kinetics, Hülsheger, Peleg-Fermi, Weibull, logistic, adapted Gompertz, Geeraerd) were fitted to experimental data using a non-linear least-squares method. The fit was evaluated by calculating goodness of fit and by observing the trend of values of models’ parameters. The most appropriate models of cell survival as a function of treatment time were the adapted Gompertz and the Geeraerd models and, as a function of the electric field, the logistic, adapted Gompertz and Peleg-Fermi models. The next steps to be performed are validation of the most appropriate models on tissues and determination of the models’ predictive power.
KeywordsClonogenic assay Cell death probability Treatment planning Electrochemotherapy Predictive models Non-thermal irreversible electroporation
This study was supported by the Slovenian Research Agency (ARRS) and conducted within the scope of the Electroporation in Biology and Medicine European Associated Laboratory (LEA-EBAM). Experimental work was performed in the infrastructure center ‘Cellular Electrical Engineering’ IP-0510. The authors would like to thank Dr. Bor Kos for his helpful comments about fitting of the models and numerical modeling and Lea Vukanović for her help with the experiments in the laboratory.
- Edhemović I, Brecelj E, Gasljevič G, Marolt Mušič M, Gorjup V, Mali B, Jarm T, Kos B, Pavliha D, Grčar Kuzmanov B, Čemažar M, Snoj M, Miklavčič D, Gadžijev EM, Serša G (2014) Intraoperative electrochemotherapy of colorectal liver metastases: electrochemotherapy of liver metastases. J Surg Oncol 110:320–327CrossRefPubMedGoogle Scholar
- Garcia PA, Pancotto T, Rossmeisl JH, Henao-Guerrero N, Gustafson NR, Daniel GB, Robertson JL, Ellis TL, Davalos RV (2011a) Non-thermal irreversible electroporation (N-TIRE) and adjuvant fractionated radiotherapeutic multimodal therapy for intracranial malignant glioma in a canine patient. Technol Cancer Res Treat 10:73–83PubMedCentralPubMedGoogle Scholar
- Linton RH (1994) Use of the Gompertz Equation to Model Non-linear Survival Curves and Predict Temperature, pH, and Sodium Chloride Effects for Listeria monocytogenes Scott A. Faculty of the Virginia Polytechnic Institute and State University, BlacksburgGoogle Scholar
- Miklavčič D, Serša 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 50:1213–1225. doi: 10.1007/s11517-012-0991-8 PubMedCentralCrossRefPubMedGoogle Scholar
- Mir LM, Gehl J, Serša G, Collins CG, Garbay J-R, Billard V, Geertsen PF, Rudolf Z, O’Sullivan GC, Marty M (2006) Standard operating procedures of the electrochemotherapy: instructions for the use of bleomycin or cisplatin administered either systemically or locally and electric pulses delivered by the CliniporatorTM by means of invasive or non-invasive electrodes. Eur J Cancer Suppl 4:14–25CrossRefGoogle Scholar
- Neal RE 2nd, Rossmeisl JH, Robertson JL, Arena CB, Davis EM, Singh RN, Stallings J, Davalos RV (2013) Improved local and systemic anti-tumor efficacy for irreversible electroporation in immunocompetent versus immunodeficient mice. PLoS ONE 8:e64559. doi: 10.1371/journal.pone.0064559 PubMedCentralCrossRefPubMedGoogle Scholar
- Neal RE 2nd, Millar JL, Kavnoudias H, Royce P, Rosenfeldt F, Pham A, Smith R, Davalos RV, Thomson KR (2014) In vivo characterization and numerical simulation of prostate properties for non-thermal irreversible electroporation ablation: characterized and Simulated Prostate IRE. Prostate. doi: 10.1002/pros.22760 PubMedGoogle Scholar
- Neal RE 2nd, Garcia PA, Kavnoudias H, Rosenfeldt F, Mclean CA, Earl V, Bergman J, Davalos RV, Thomson KR (2015) In vivo irreversible electroporation kidney ablation: experimentally correlated numerical models. IEEE Trans Biomed Eng 62:561–569. doi: 10.1109/TBME.2014.2360374 CrossRefPubMedGoogle Scholar
- Sack M, Sigler J, Frenzel S, Eing C, Arnold J, Michelberger T, Frey W, Attmann F, Stukenbrock L, Müller G (2010) Research on industrial-scale electroporation devices fostering the extraction of substances from biological tissue. Food Eng Rev 2:147–156. doi: 10.1007/s12393-010-9017-1 CrossRefGoogle Scholar
- Serša G, Miklavčič D, Čemažar M, Belehradek J, Jarm T, Mir LM (1997) Electrochemotherapy with CDDP on LPB sarcoma: comparison of the anti-tumor effectiveness in immunocompetent and immunodeficient mice. Bioelectrochem Bioenerg 43:270–283Google Scholar
- Županič A, Miklavčič D (2011) Tissue heating during tumor ablation with irreversible electroporation. Elektrotehniški Vestn Engl Ed 78:42–47Google Scholar