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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

Abstract

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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Topics: Temperature , Heating , Cancer

Figures

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.

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.

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).

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.

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.

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).

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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