Introduction 6 1 10 25 18 18 24 20 18 12 18 17 in vitro et al. 7 in vitro et al. 13 15 et al. 19 et al. 5 22 11 15 4 in vitro 2 3 15 A key difference of high temperature–short time thermal therapy protocols from the traditional hyperthermia protocols is the significant injury accumulation during the non-isothermal portion of the thermal history (heating up/cooling down period). Therefore, injury accumulation tends to be a complex function of hold time as well ramp up and cooling time. Hence, accurate prediction of the cell injury kinetics requires the knowledge of heating/cooling rates in addition to peak temperatures (PTs) and hold/total time. This model also better represents the thermo-clinical applications because the rate at which the PTs are achieved at different locations inside the tumor vary with the applicator location and plays a paramount role in determining the amount of injury accumulated. The knowledge of the injury accumulated in reaching a PT or the PT required to obtain a desired injury under different heating rates (HRs) are some of the very important parameters in designing better and optimal clinical protocols. E −1 A −1 16 E A E E −1 Materials and methods HEPG2 Cell Culture and Sample Preparation 2 2 Heating Stage 1 1 k p k d −1 Figure 1. Block diagram of the amplifying OPAMP circuit and feedback control of the heating stage. The OPAMP circuit amplifies the voltage signal from the data acquisition board to heat the stage, while the feedback control system, through the VB code, controls the amount of voltage based on the instantaneous temperature of the stage.  Table 1. k p k d -1 PT (°C) k p k d 100 60 0.0155 0.0925 65 0.0155 0.0925 70 0.0155 0.0925 200 60 0.035 0.108 65 0.035 0.108 70 0.035 0.121 300 60 0.085 0.255 65 0.085 0.255 70 0.0903 0.275 Heating Studies and Ethd-1 Dye Uptake Assay  −1 −1 Cellular injury post heating for isothermal and non-isothermal studies was quantified using Ethd-1 (Sigma-Aldrich, MO) vital dye assay by counting the number of cells stained with Ethd-1 dye (dead only) and the total number of the cells stained with Hoechst (Sigma-Aldrich). Thermally treated cell samples were placed in a 50 μl drop of 2.5 μM Ethd-1 and 10 μM Hoechst dye solution in a 35-mm Petri dish and incubated for 3 h. The incubation time of 3 h was based on the experiments conducted after 1, 2 and 3 h of incubation (data not included), which confirmed that membrane damage equilibrates within this period and a significant amount of media is pulled between the cover glasses to stain the cells. Control samples underwent the same procedure without heating. After 3 h, the dead and the total number of cells were counted with a fluorescent microscope (Nikon Eclipse TS 100, Tokyo) using a 20× objective. Multiple fields with at least 150–300 cells were counted for each run. Normalized Cell Survival S e 1 \documentclass[12pt]{minimal}
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$$ S_{\rm{e}}\ { = }\,{{\left[ {{\rm{(}}N_{{\rm{H,t}}} \, - \,N_{{\rm{E,t}}} {\rm{)/}}N_{{\rm{H,t}}} } \right]} \mathord{\left/ {\vphantom {{\left[ {{\rm{(}}N_{{\rm{H,t}}} \, - \,N_{{\rm{E,t}}} {\rm{)/}}N_{{\rm{H,t}}} } \right]} {\left[ {{\rm{(}}N_{{\rm{H,c}}} \, - \,N_{{\rm{E,c}}} {\rm{)/}}N_{{\rm{H,c}}} } \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {{\rm{(}}N_{{\rm{H,c}}} \, - \,N_{{\rm{E,c}}} {\rm{)/}}N_{{\rm{H,c}}} } \right]}} $$\end{document} N H N E The Cell Injury Model 2 \documentclass[12pt]{minimal}
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$$ V\,\xrightarrow{k}\,I{\text{ }} $$\end{document} V I k S c 3 \documentclass[12pt]{minimal}
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$$ S_{\text{c}} \, = \,\exp \left( { - \int\limits_0^\delta {k\,dt} } \right) $$\end{document} δ 16 14 21 4 \documentclass[12pt]{minimal}
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$$ k\, = \,A\,{\text{exp}}\left( {\frac{{ - E}} {{RT}}} \right) $$\end{document} A −1 E −1 R −1  −1 A E 15 5 \documentclass[12pt]{minimal}
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$$ {\text{ln}}\,{\text{(}}A{\text{)}}\,{\text{ = }}\,{\text{0}}{\text{.38}}\,{\text{E}}\, - \,{\text{9}}{\text{.36 }} $$\end{document} Determination of Arrhenius Model Parameters E A 15 6 \documentclass[12pt]{minimal}
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$$ f({\text{X}})\, = \,\left[ {\frac{1} {N}\,\sum\limits_{i = 1}^n {\left( {S_{{\text{e,}}i} {\text{(X)}}\, - \,S_{{\text{c,}}i} {\text{(X)}}} \right)^{\text{2}} } } \right]^{0.5} $$\end{document} N E A S e,i S c,i i R 2 7 \documentclass[12pt]{minimal}
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$$ R^2 \, = \,1 - \frac{{\sum \left({\left( {S_{{\text{e,}}i} {\text{(X)}}\, - \,S_{{\text{c,}}i} {\text{(X)}}} \right)^2 }\right) }} {{\sum \left({\left( {S_{{\text{e,}}i} {\text{(X)}}\, - \,S_{{\text{av}}} } \right)^2 }\right) }} $$\end{document} S av Results 2 2 2 2 Figure 2. Micrographs showing cell samples stained with Hoechst (Blue-all cells) and Ethd-1 (Red-dead cells only). (a and b) – control samples without heating; (c and d) – samples heated at 50°C for 9 min; (e and f) – samples heated at 70°C for 1 min.  Isothermal Heating Studies −1 −1 3 Figure 3. attached cells heated isothermally E A suspended cells heated isothermally E A t  The figures also show the effect of PTs on the slope of the survival curve. The drop in the survival with the increase in the hold time is slow at low PTs. The survival curve gets steeper as the PT increases. When heated at 50°C for up to 9 min, the cell survival is still higher than 0.43 for both suspended and attached cells. This trend changes for 55°C, where the cell survival drops to 0.03 after only 6 min of heating. This trend magnifies sharply as the PTs increases to 60, 65 and 70°C. For suspended cells, the survival at 60°C varies from 0.58 to almost zero survival as the hold time increases from 0.5 to 3 min. The survival dropped from 0.2 to 0.003 for an increase in the hold time from 15 s to a min at 70°C. The attached cells also showed a similar trend with slightly higher survival than the suspended cells for all the data points. t 3 p  p  −3 p- E A E A 2 E A −1 31  −1 −1 36 −1 E A 3 Table 2. E − 1 A − 1 −1 E −1 A -1 100 272.4 40 200 262.02 39 300 257.38 38 525 (Isothermal – Attached) 248.64 36 525 (Isothermal – Suspended) 229.46 31 Non-Isothermal Heating Studies −1 4 −1 −1 −1 −1 −1 −1 −1 −1 −1 Figure 4. −1 −1 −1  E A 2 E A −1 −1 −1 −1 −1 −1 −1 5 Figure 5. min  min  min min  Relation Between Activation Energy and HRs 2 −1 8 \documentclass[12pt]{minimal}
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$$ E\, = \,0.0001\,(HR)^2 \, - \,0.1173\,(HR)\, + \,282.67 $$\end{document} E −1 −1 −1 Effects of PTs, HRs and Hold Time on the Cell Survival E A −1  E 5 −1 −1 −1 −1 −1 −1  −1  −1  −1 −1 5 Hold and Total Injury Time for Complete Cell Destruction 6 −1 Figure 6. attached HepG2 cells −1 attached HepG2 cells −1  6 −1 −1 −1  −1 6 −1 −1 −1 −1 −1 −1 −1 −1 Discussion Injury Kinetics of Attached and Suspended Cells 3 15 Comparison with Previous Hyperthermic Studies 9 23 9 Comparison of Arrhenius Parameters −1  −1  −1 −1 4 −1 15 −1 11 4 22 −1 Clinical Relevance 8 −1 −1 15 −1 −1 −1 −1 E E A k p k d 5 6 5 5 −1  −1  −1 5 6 −1 −1 6 −1 −1 −1 −1  6 −1 −1 6 −1 −1 6 in vitro in vivo Summary −1 E A E −1  −1 −1 −1 −1 −1 −1