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    The Arrhenius model accurately predicts cell death above 55°C but overestimates it at hyperthermic temperatures (43-55°C). Adding a temperature-dependent time delay improves predictions for thermal damage and cell death processes.

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    Area of Science:

    • Biophysics
    • Biochemistry
    • Mathematical Biology

    Background:

    • The Arrhenius formulation is a long-standing model for unimolecular reactions, widely applied to thermal damage and cell death.
    • While accurate for high temperatures (>55°C), it overestimates cell death at hyperthermic temperatures (43-55°C), limiting its use in tumor treatment predictions.
    • Existing models struggle with the 'shoulder' region observed in cell death kinetics at hyperthermic temperatures, which arises from complex signaling delays.

    Purpose of the Study:

    • To enhance the accuracy of Arrhenius models for predicting thermal damage and cell death at hyperthermic temperatures.
    • To introduce a simpler, yet accurate, mathematical approach to model the 'shoulder' region in cell death kinetics.
    • To validate the improved model using experimental data and explore compensation law behavior.

    Main Methods:

    • Modified the standard Arrhenius formulation by incorporating a temperature-dependent time delay.
    • Determined kinetic coefficients and time delays from the constant-rate regions of measured cell survival curves.
    • Analyzed the correlation between kinetic coefficients (ln A and E(a)) to confirm compensation law behavior.

    Main Results:

    • The modified Arrhenius model with a time delay accurately predicts cell death fractions at hyperthermic temperatures, avoiding overestimation.
    • The model successfully represents the 'shoulder' region characteristic of transient intrinsic cell death processes.
    • Confirmed a strong correlation between kinetic coefficients, supporting compensation law behavior in cell death.

    Conclusions:

    • A modified Arrhenius model with a temperature-dependent time delay offers a practical and accurate alternative for predicting thermal cell death.
    • This approach improves the reliability of hyperthermia treatment efficacy predictions by accounting for initial delays in cell damage.
    • The findings support the application of compensation law principles to thermal cell death processes, linking kinetic parameters.