Estimation of cell survival in tumours heated to nonuniform temperature distributions

A stochastic model describing the probability of cell survival as a function of thermal exposure was developed and fit to data arising from studies of CHO cell survival under hyperthermic conditions. This model characterizes the separate risks of temperature-induced cell death and induction of thermotolerance during heating. Tumour cells are assumed to be affected independently of each other by hyperthermia. Tumour geometry, perfusion and power deposition affect hyperthermia-induced temperature distributions in tumours, producing nonuniform temperatures. Two tumours may respond to hyperthermia slightly differently because of differences in tumour geometry, perfusion, power deposition, or by chance alone and the approach presented here incorporates chance and these other factors explicitly. The results: (1) the time-temperature history is important for estimating tumour cell survival; (2) tumour temperature heterogeneity leaves more surviving cells at a given T₉₀ temperature than would be expected if the entire tumour were uniformly heated to that same temperature; and (3) changes in the shape of the temperature distribution because of tumour geometry and perfusion distribution greatly influence cell survival between tumours, even when the standard temperature descriptors, such as T₉₀, are fixed. The simulations also showed a modest effect on cell kill attributable to varying the lengths of the warm-up and the cool-down periods. These simulations indicate that these types of sensitivity studies can be used to investigate relationships between various modifiers of temperature distributions achieved when treating tumours with hyperthermia and to assess their potential therapeutic impact in clinical trials.