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Research Papers

# A Two-State Cell Damage Model Under Hyperthermic Conditions: Theory and In Vitro Experiments

[+] Author and Article Information
Yusheng Feng

Computational Bioengineering and Nanotechnology Laboratory, Department of Mechanical Engineering, The University of Texas at San Antonio, San Antonio, TX 78249yusheng.feng@utsa.edu

J. Tinsley Oden

Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712oden@ices.utexas.edu

Marissa Nichole Rylander

Department of Mechanical Engineering, and School of Biomedical Engineering and Sciences, Virginia Tech, Blacksburg, VA 24061mnr@vt.edu

J Biomech Eng 130(4), 041016 (Jun 20, 2008) (10 pages) doi:10.1115/1.2947320 History: Received May 30, 2007; Revised May 20, 2008; Published June 20, 2008

## Abstract

The ultimate goal of cancer treatment utilizing thermotherapy is to eradicate tumors and minimize damage to surrounding host tissues. To achieve this goal, it is important to develop an accurate cell damage model to characterize the population of cell death under various thermal conditions. The traditional Arrhenius model is often used to characterize the damaged cell population under the assumption that the rate of cell damage is proportional to $exp(−Ea∕RT)$, where $Ea$ is the activation energy, $R$ is the universal gas constant, and $T$ is the absolute temperature. However, this model is unable to capture transition phenomena over the entire hyperthermia and ablation temperature range, particularly during the initial stage of heating. Inspired by classical statistical thermodynamic principles, we propose a general two-state model to characterize the entire cell population with two distinct and measurable subpopulations of cells, in which each cell is in one of the two microstates, viable (live) and damaged (dead), respectively. The resulting cell viability can be expressed as $C(τ,T)=exp(−Φ(τ,T)∕kT)∕(1+exp(−Φ(τ,T)∕kT))$, where $k$ is a constant. The in vitro cell viability experiments revealed that the function $Φ(τ,T)$ can be defined as a function that is linear in exposure time $τ$ when the temperature $T$ is fixed, and linear as well in terms of the reciprocal of temperature $T$ when the variable $τ$ is held as constant. To determine parameters in the function $Φ(τ,T)$, we use in vitro cell viability data from the experiments conducted with human prostate cancerous (PC3) and normal (RWPE-1) cells exposed to thermotherapeutic protocols to correlate with the proposed cell damage model. Very good agreement between experimental data and the derived damage model is obtained. In addition, the new two-state model has the advantage that is less sensitive and more robust due to its well behaved model parameters.

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Copyright © 2008 by American Society of Mechanical Engineers
Topics: Temperature , Heating
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## Figures

Figure 1

Flow cytometric analysis of cell viability. (a) control (unheated), (b) methanol treated, (c) severely heat-shocked (52°C, 6min), and (d) typical heated sample (44°C, 15min).

Figure 2

Experimental measured cell viability for (a) PC3 cells and (b) RWPE-1 cells under various hyperthermic protocols consisting of temperature ranges of 44–60°C and exposure durations of 1–30min.

Figure 3

Illustration of the transformation by introducing a z-variable that converts a curved surface for cell viability C to a flat plane for bilinear regression. (a) Three-dimensional surface plot of cell viability C in terms of 1∕T and τ. (b) Three-dimensional surface plot of z-variable, which is defined as ln[(1−C)∕C], in terms of 1∕T and τ.

Figure 4

Comparison of the two-state model with the traditional Arrhenius model at T=44–56°C for PC3 cells. The solid line represents the two-state model, the dashed line represents the traditional Arrhenius model, and the boxes with error bars indicate measurement data over three experiments.

Figure 5

Comparison of the two-state model with the traditional Arrhenius model at T=44–56°C for RWPE-1 cells. The solid line represents the two-state model, the dashed line represents the traditional Arrhenius model, and the boxes with error bars indicate measurement data over three experiments.

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