In Vitro Measurement and Mathematical Modeling of Thermally-Induced Injury in Pancreatic Cancer Cells

Abstract

Thermal therapies are under investigation as part of multi-modality strategies for the treatment of pancreatic cancer. In the present study, we determined the kinetics of thermal injury to pancreatic cancer cells in vitro and evaluated predictive models for thermal injury. Cell viability was measured in two murine pancreatic cancer cell lines (KPC, Pan02) and a normal fibroblast (STO) cell line following in vitro heating in the range 42.5-50 °C for 3-60 min. Based on measured viability data, the kinetic parameters of thermal injury were used to predict the extent of heat-induced damage. Of the three thermal injury models considered in this study, the Arrhenius model with time delay provided the most accurate prediction (root mean square error = 8.48%) for all cell lines. Pan02 and STO cells were the most resistant and susceptible to hyperthermia treatments, respectively. The presented data may contribute to studies investigating the use of thermal therapies as part of pancreatic cancer treatment strategies and inform the design of treatment planning strategies.

Keywords: Arrhenius injury model; cell death; hyperthermia; pancreatic cancer; thermal damage.

Figure 1

(a) Dummy plate design with five thermocouples for monitoring temperature during hyperthermia sealed within four corner wells and one central well. (b) Photograph of a thermocouple sealed within a well. (c) Cell-containing plate (plate 2) and dummy plate (plate 1) immersed within the water bath during hyperthermia.

Figure 2

(a) Illustration of temperature recorded by thermocouples in the dummy plate during a 46 °C, 40 min hyperthermia exposure (b) illustration of temperatures over 1 min of the steady-state phase (c) illustration of temperatures during the cool-down phase, and (d) illustration of temperatures during the heat-up phase.

Figure 3

Measured cell viability for all three cell lines normalized to 37 °C control for different recovery times. Error bars represent one standard deviation.

Figure 4

(a) Correlation between the kinetic coefficients, ln (A) and E_a (KPC + Pan02 + STO), (b) comparison between the Wright’s plot (relationship between Arrhenius coefficients based on the literature) shown in solid black square markers and obtained Arrhenius coefficients for three different cell lines in our study. Hollow black, red and green square markers indicate the obtained Arrhenius coefficients for STO, KPC and Pan02 cells, respectively at 24 h post treatment in our study.

Figure 5

Cell viability assessed at 24 h post in vitro hyperthermia exposure in KPC, Pan02, and STO cell lines. Markers indicate measured data points. (a) Solid lines represent the simple Arrhenius model; (b), solid lines represent the improved Arrhenius model with time delay; (c) solid lines represent the predictive two- state model.

Figure 6

(a) Simulated temperature map in perfused pancreas tissue following 40 W, 10 min MWA, the black contour indicates the regions where 50 °C was achieved while the green circle and red x illustrate two positions along the periphery of the ablation zone where time-temperature history over 10 min was analyzed; (b) temperature profiles calculated from the bio-heat transfer model (shown in dashed lines) during 10 min MWA as well as experimentally measured temperatures in vitro during water bath hyperthermia (solid lines); (c) comparison between measured and calculated cell survival.