Abstract
Thermal treatments for tissue ablation rely upon the heating of cells past a threshold beyond which the cells are considered destroyed, denatured, or killed. In this article, a novel three-state model for cell death is proposed where there exists a vulnerable state positioned between the alive and dead states used in a number of existing cell death models. Proposed rate coefficients include temperature dependence and the model is fitted to experimental data of heated co-cultures of hepatocytes and lung fibroblasts with very small RMS error. The experimental data utilized include further reductions in cell viabilities over 24 and 48 h post-heating and these data are used to extend the three-state model to account for slow cell death. For the two cell lines employed in the experimental data, the three parameters for fast cell death appear to be linearly increasing with % content of lung fibroblast, while the sparse nature of the data did not indicate any co-culture make-up dependence for the parameters for slow cell death. A critical post-heating cell viability threshold is proposed beyond which cells progress to death; and these results are of practical importance with potential for more accurate prediction of cell death.
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Arkin, H., L. Xu, and K. Holmes. Recent developments in modeling heat transfer in blood perfused tissues. IEEE Trans. Biomed. Eng. 41(2):97–107, 1994.
Breen, M., X. Chen, D. Wilson, and G. Saidel. Modeling cellular thermal damage from radio-frequency ablation. In: Engineering in Medicine and Biology, 2002. 24th Annual Conference and the Annual Fall Meeting of the Biomedical Engineering Society, EMBS/BMES Conference 2002. Proceedings of the Second Joint, Vol. 1, 2002, p. 715.
Dewey, W. C., L. E. Hopwood, S. A. Sapareto, and L. E. Gerweck. Cellular responses to combinations of hyperthermia and radiation. Radiology 123(2):463–474, 1977.
Dickson, J., and S. Calderwood. Temperature range and selective sensitivity of tumors to hyperthermia: a critical review. Ann. NY Acad. Sci. 335:180–205, 1980.
Dienes, G. J. A kinetic model of biological radiation response. Radiat. Res. 28(2):183–202, 1966.
Fajardo, L. F. Pathological effects of hyperthermia in normal tissues. Cancer Res. 44(10 Suppl):4826s–4835s, 1984.
Feng, Y., J. T. Oden, and M. N. Rylander. A two-state cell damage model under hyperthermic conditions: theory and in vitro experiments. J. Biomech. Eng. 130(4):1–10, 2008.
Fowler, J. F. Differences in survival curve shapes for formal multi-target and multi-hit models. Phys. Med. Biol. 9(2):177–188, 1964.
Goldberg, S. N., M. C. Stein, G. S. Gazelle, R. G. Sheiman, J. B. Kruskal, and M. E. Clouse. Percutaneous radiofrequency tissue ablation: optimization of pulsed-radiofrequency technique to increase coagulation necrosis. J. Vasc. Interv. Radiol. 10(7):907–916, 1999.
Henriques, Jr. F., and A. Moritz. Studies of thermal injury: I. The conduction of heat to and through skin and the temperatures attained therein. A theoretical and an experimental investigation. Am. J. Pathol. 23(4):530–549, 1947.
Hildebrand, P., T. Leibecke, and M. Kleemann. Influence of operator experience in radiofrequency ablation of malignant liver tumours on treatment outcome. Eur. J. Surg. Oncol. 32(4):430–434, 2006.
Jung, H. A generalized concept for cell killing by heat. Radiat. Res. 106(1):56–72, 1986.
Jung, H. Step-down heating of CHO cells at 37.5–39°C. Int. J. Hyperth. 5(6):665–673, 1989.
Jung, H. A generalized concept for cell killing by heat: effect of chronically induced thermotolerance. Radiat. Res. 127(3):235–242, 1991.
Moritz, A. Studies of thermal injury: III. The pathology and pathogenesis of cutaneous burns. An experimental study. Am. J. Pathol. 23(6):915–941, 1947.
Moritz, A., and F. Henriques, Jr. Studies of thermal injury: II. The relative importance of time and surface temperature in the causation of cutaneous burns. Am. J. Pathol. 23(5):695–720, 1947.
O’Neill, D. P., T. Peng, and S. J. Payne. Comparison of two mathematical models for hyperthermic cell death. In: 6th World Congress of Biomechanics (WCB), August 1–6, 2010, Singapore.
Pearce, J. Models for thermal damage in tissues: processes and applications. Crit. Rev. Biomed. Eng. 38(1):1–20, 2010 (Special Issue).
Rosner, G. L., S. T. Clegg, D. M. Prescott, and M. W. Dewhirst. Estimation of cell survival in tumours heated to nonuniform temperature distributions. Int. J. Hyperth. 12(2):223–239, 1996.
Roti Roti, J., and K. Henle. Comparison of two mathematical models for describing heat-induced cell killing. Radiat. Res. 81(3):374–383, 1980.
Rylander, M. N., K. R. Diller, S. Wang, and S. J. Aggarwal. Correlation of HSP70 expression and cell viability following thermal stimulation of bovine aortic endothelial cells. J. Biomech. Eng. 127(5):751–757, 2005.
Sapareto, S., and W. Dewey. Thermal dose determination in cancer therapy. Int. J. Radiat. Oncol. Biol. Phys. 10(6):787–800, 1984.
Sapareto, S. A., L. E. Hopwood, W. C. Dewey, M. R. Raju, and J. W. Gray. Effects of hyperthermia on survival and progression of Chinese hamster ovary cells. Cancer Res. 38(2):393–400, 1978.
Sapareto, S. A., S. G. Raaphorst, and C. Dewey. Cell killing and the sequencing hyperthermia and radiation. Radiat. Oncol. 5:343–347, 1979.
Sapozhnikov, A. M., E. D. Ponomarev, T. N. Tarasenko, and W. G. Telford. Spontaneous apoptosis and expression of cell surface heat-shock proteins in cultured EL-4 lymphoma cells. Cell Prolif. 32(6):363–378, 1999.
Szasz, A., and G. Vincze. Dose concept of oncological hyperthermia: heat-equation considering the cell destruction. J. Cancer Res. Therap. 2(4):171–181, 2008.
Uchida, N., H. Kato, and T. Ishida. A model for cell killing by continuous heating. Med. Hypotheses 41(6):548–553, 1993.
Whayne, J., S. Nath, and D. E. Haines. Microwave catheter ablation of myocardium in vitro. Circulation 89:2390–2395, 1994.
Whiting, P., J. Dowden, and P. Kapadia. A mathematical analysis of the results of experiments on rats’ livers by local laser hyperthermia. Lasers Med. Sci. 4(1):55–64, 1989.
Acknowledgments
Katja Schick for her contributions to work in the cell culture. The research leading to these results has received funding from the European Community’s Seventh framework Programme under grant agreement no. 223877, project IMPPACT.
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Associate Editor Gerald Saidel oversaw the review of this article.
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O’Neill, D.P., Peng, T., Stiegler, P. et al. A Three-State Mathematical Model of Hyperthermic Cell Death. Ann Biomed Eng 39, 570–579 (2011). https://doi.org/10.1007/s10439-010-0177-1
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DOI: https://doi.org/10.1007/s10439-010-0177-1