A Three-State Mathematical Model of Hyperthermic Cell Death

Thermal treatments for tissue ablation rely upon the heating of cells past a threshold beyond which the cells are considered destroyed, denatured, or killed. In this article, a novel three-state model for cell death is proposed where there exists a vulnerable state positioned between the alive and dead states used in a number of existing cell death models. Proposed rate coefficients include temperature dependence and the model is fitted to experimental data of heated co-cultures of hepatocytes and lung fibroblasts with very small RMS error. The experimental data utilized include further reductions in cell viabilities over 24 and 48 h post-heating and these data are used to extend the three-state model to account for slow cell death. For the two cell lines employed in the experimental data, the three parameters for fast cell death appear to be linearly increasing with % content of lung fibroblast, while the sparse nature of the data did not indicate any co-culture make-up dependence for the parameters for slow cell death. A critical post-heating cell viability threshold is proposed beyond which cells progress to death; and these results are of practical importance with potential for more accurate prediction of cell death.