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Research Papers

Comparison of Models of Post-Hyperthermia Cell Survival

[+] Author and Article Information

Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48864
e-mail: ntwright@msu.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received October 5, 2011; final manuscript received March 5, 2013; accepted manuscript posted March 8, 2013; published online April 23, 2013. Assoc. Editor: John C. Bischof.

J Biomech Eng 135(5), 051001 (Apr 23, 2013) (9 pages) Paper No: BIO-11-1419; doi: 10.1115/1.4023981 History: Received October 05, 2011; Revised March 05, 2013

Several existing mathematical models of the survival of mammalian cells in culture following heating are compared. These models describe the fraction of cells that survive in a normal culture environment following a relatively brief period of heating between approximately 43 °C and 60 °C. The models have been developed either from rate process or mechanistic arguments. Little quantitative comparison between such models has been made using the same sets of data. The models are compared using the Akaike Information Criterion (AICc) after the model parameters have been estimated for two sets of existing data: human prostate cancer cells and Chinese hamster ovary cells. Most of the models capture the cell survival response. Scaled sensitivity coefficients show that some of the models have parameters that are difficult to estimate reliably. Relatively small variations in the AICc suggest that more measurements are needed before ranking the models.

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Copyright © 2013 by ASME
Topics: Temperature , Heating , Cancer
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References

Rosenberg, B., Kemeny, G., Switzer, R. C., and Hamilton, T. C., 1971, “Quantitative Evidence for Protein Denaturation as the Cause of Thermal Death,” Nature, 232, pp. 471–473. [CrossRef] [PubMed]
Johnson, H. A., and Pavelec, M., 1972, “Thermal Injury Due to Normal Body Temperature,” Am. J. Pathol., 66, pp. 557–564. [PubMed]
Lepock, J., 2003, “Cellular Effects of Hyperthermia: Relevance to the Minimum Dose for Thermal Damage,” Int. J. Hyperthermia, 19(3), pp. 252–266. [CrossRef] [PubMed]
RotiRoti, J. L., 2008, “Cellular Responses to Hyperthermia (40–46 °C): Cell Killing and Molecular Events,” Int. J. Hyperthermia, 24(1), pp. 3–15. [CrossRef] [PubMed]
He, X., and Bischof, J. C., 2003, “Quantification of Temperature and Injury Response in Thermal Therapy and Cryosurgery,” Crit. Rev. Biomed. Eng., 31(5), pp. 355–422. [CrossRef] [PubMed]
He, X., Bhowmick, S., and Bischof, J., 2009, “Thermal Therapy in Urologic Systems: A Comparison of Arrhenius and Thermal Isoeffective Dose Models in Predicting Hyperthermic Injury,” ASME J. Biomech. Eng., 131, p. 074507. [CrossRef]
Bauer, K. D., and Henle, K. J., 1979, “Arrhenius Analysis of Heat Survival Curves From Normal and Thermotolerant Cho Cells,” Radiat. Res., 78, pp. 251–263. [CrossRef] [PubMed]
Jung, H., 1991, “A Generalized Concept for Cell Killing by Heat: Effect of Chronically Induced Thermotolerance,” Radiat. Res., 127, pp. 235–242. [CrossRef] [PubMed]
Akaiki, H., 1974, “A New Look at the Statistical Model Identification,” IEEE Trans. Autom. Control, 19, pp. 716–723. [CrossRef]
Anderson, D. R., 2008, Model Based Inference in the Life Sciences, Springer, New York.
Beck, J., and Arnold, K., 1977, Parameter Estimation in Engineering and Science, Wiley, New York.
Feng, Y., Oden, J. T., and Rylander, M. N., 2008, “A Two-State Cell Damage Model Under Hyperthermic Conditions: Theory and In Vitro Experiments,” J. Biomech. Eng., 130, p. 041016. [CrossRef] [PubMed]
Westra, A., and Dewey, W., 1971, “Variation in Sensitivity to Heat Shock During the Cell Cycle of Chinese Hamster Cells In Vitro,” Int. J. Radiat. Biol., 19, pp. 467–477. [CrossRef]
Henle, K. J., and Dethlefsen, L. A., 1980, “Time-Temperature Relationships for Heat-Induced Killing of Mammalian Cells,” Ann. N.Y. Acad. Sci., 335, pp. 234–253. [CrossRef] [PubMed]
Dewey, W., Hopwood, L., Sapareto, S., and Gerweck, L., 1977, “Cellular Responses to Combinations of Hyperthermia and Radiation,” Radiology, 123, pp. 463–479. [PubMed]
Hahn, G. M., 1982, Hyperthermia and Cancer, Plenum, New York.
Kellerer, A., and Rossi, H., 1971, “RBE and the Primary Mechanics of Radiation Action,” Radiat. Res., 47, pp. 15–34. [CrossRef] [PubMed]
Roti Roti, J. L., and Henle, K., 1980, “Comparison of Two Mathematical Models for Describing Heat-Induced Cell Killing,” Radiat. Res., 81, pp. 374–383. [CrossRef] [PubMed]
Jung, H., 1986, “A Generalized Concept for Cell Killing by Heat,” Radiat. Res., 106, pp. 56–72. [CrossRef] [PubMed]
Mackey, M. A., and Roti Roti, J. L., 1992, “A Model of Heat-Induced Clonogenic Cell Death,” J. Theor. Biol., 156(1), pp. 133–146. [CrossRef] [PubMed]
O'Neill, D. P., Peng, T., Stiegler, P., Mayrhauser, U., Koestenbauer, S., Tscheiliessnigg, K., and Payne, S. J., 2011, “A Three-State Mathematical Model of Hyperthermic Cell Death,” Ann. Biomed. Eng., 39(1), pp. 570–579. [CrossRef] [PubMed]
Beck, J., McMasters, R., Dowding, K., and Amos, D., 2006, “Intrinsic Verification Methods in Linear Heat Conduction,” Int. J. Heat Mass Transfer, 49, pp. 2984–2994. [CrossRef]
Mackey, M. A., and Roti Roti, J. L., 2000, “Biophysical Injury Mechanisms in Electrical Shock Trauma,” Ann. Rev. Biomed. Eng., 2, pp. 477–509. [CrossRef]
Brown, F., and Diller, K. R., 2008, “Calculating the Optimum Temperature for Serving Hot Beverages,” Burns, 34, pp. 648–654. [CrossRef] [PubMed]
Henriques, F. C. Jr., and Moritz, J., A. R., 1947, “Studies of Thermal Injury. I. The Conduction of Heat to and Through Skin and the Temperatures Attained Therein,” Am. J. Pathol., 23, pp. 531–549.
Henriques, F. C. Jr., 1947, “Studies of Thermal Injury V. the Predictability and the Significance of Thermally Induced Rate Processes Leading to Irreversible Epidermal Injury,” Arch. Pathol., 43, pp. 489–502.
Pearce, J. A., and Thomsen, S., 1995, “Rate Process Analysis of Thermal Damage,” Optical and Thermal Response of Laser-Irradiated Tissue, A. J.Welch and M. J. C.van Germert, eds., Plenum, New York, pp. 561–606.

Figures

Grahic Jump Location
Fig. 1

Panel (a) displays PC3 data from [12], while panel (b) shows CHO data from [13]. The PC3 data are for heating from 44≤T≤56 °C. Data are taken for up to 30 mins of heating. Panel (b) is for heating from 43.5≤T≤46.5 °C, with heating of up to 105 mins. Note that the dotted lines are not model results, but meant as a visual aid.

Grahic Jump Location
Fig. 2

The PC3 data fit by the models (a) first-order, (b) Johnson and Pavelec, (c) Kellerer and Rossi, (d) Jung, (e) Mackey and Roti Roti, and (f) Feng et al. The circles represent 44 °C, the squares 46 °C, the diamonds represent 48 °C, the triangles 50 °C, and the inverted triangles 54 °C. The 56 °C data were not used. The 56 °C data were not used.

Grahic Jump Location
Fig. 3

The difference between the measured and predicted survival are shown in the residuals (S-S∧). For the predictions of the PC3 cells heated at 48 °C these are for the first-order model (solid circle), Johnson and Pavelec model (solid square), Kellerer and Rossi (solid triangle), Jung model (open circle), Mackey and Roti Roti model (open square), and Feng et al. model (open triangle).

Grahic Jump Location
Fig. 4

Scaled sensitivity coefficients of the (a) first-order model (k–dashed), (b) Johnson and Pavelec model (kj–dashed, nj–dot-dash), (c) Kellerer and Rossi model (ak–dashed, bk–dot-dash), (d) Jung model (p–dashed, c–dot-dash), (e) Mackey and Roti Roti model (ɛf–dashed, kr–dot-dash), and (f) Feng et al. model (α–dashed, β–dot-dash, γ–dotted) for PC3 cells heated at 48 °C. The solid line in each panel is the model prediction for S at 48 °C, for reference.

Grahic Jump Location
Fig. 5

The CHO data fit by the models (a) first-order, (b) Johnson and Pavelec, (c) Kellerer and Rossi, (d) Jung, (e) Mackey and Roti Roti, and (f) Feng et al. The solid circles represent 43.5 °C, the solid squares 44 °C, the diamonds represent 44.5 °C, the triangles 45 °C, the inverted triangles 45.5 °C, the open circles 46 °C, and the open squares 46.5 °C.

Grahic Jump Location
Fig. 6

The difference between the measured and predicted survival are shown in the residuals (S-S∧) for the CHO cells at 45 °C. The residual are for the the first-order model (solid circle), Johnson and Pavelec model (solid square), Kellerer and Rossi (solid triangle), Jung model (open circle), Mackey and Roti Roti model (open square), and Feng et al. model (open triangle).

Grahic Jump Location
Fig. 7

Scaled sensitivity coefficients of the (a) first-order model (k–dashed), (b) Johnson and Pavelec model (kj–dashed, nj–dot-dash), (c) Kellerer and Rossi model (ak–dashed, bk–dot-dash), (d) Jung model (p–dashed, c–dot-dash), (e) Mackey and Roti Roti model (ɛf–dashed, kr–dot-dash), and (f) Feng et al. model (α–dashed, β–dot-dash, γ–dotted) for CHO cells heated at 45 °C. The solid line in each panel is the model prediction for S at 45 °C, for reference.

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