Volume effects in the TCP for hypoxic and oxygenated tumors

Purpose Clinical studies in radiation therapy with conventional fractionation show a reduction in the tumor control probability (TCP) with an increase in the total and hypoxic tumor volumes. The main objective of this article is to derive an analytical relationship between the TCP and the hypoxic and total tumor volumes. This relationship is applied to clinical data on the TCP reduction with increasing total tumor volume and, also, dose escalation to target tumor hypoxia. Methods The TCP equation derived from the Poisson probability distribution predicts that both (a) an increase in the number of tumor clonogens and (b) an increase in the average cell surviving fraction are the factors contributing to the loss of local control. Using asymptotic mathematical properties of the TCP formula and the linear quadratic (LQ) cell survival model with two levels of hypoxic and oxygenated cells, we separated the TCP dependence on the total and hypoxic tumor volumes. The predicted trends in the local control as a function of total and hypoxic tumor volumes were evaluated in radiotherapy model problems with conventional dose fractionation for head and neck and non‐small cell lung cancers. Tumor‐specific parameters in the LQ model and the density of clonogens in the TCP model were taken from published data on predictive assays and the plating efficiency measurements, respectively. Results Our simulations show that, at the dose levels used in conventional radiation therapy for head and neck and non‐small cell lung cancers, the TCP dependence on the total tumor volume is negligible for completely oxygenated tumors. However, the presented results demonstrate that tumor hypoxia introduces a significant volume effect into estimates of the TCP. The extent of tumor hypoxia is a plausible mechanism to explain the TCP reduction with increasing total tumor volume observed in clinical studies. To achieve the same level of tumor control in a hypoxic tumor region relative to well oxygenated tumor regions, the delivered dose should, in principle, be escalated by a factor equal to the oxygen enhancement ratio (OER). The theoretically required hypoxia‐targeted dose escalation could be as large as 100% because it has been estimated that hypoxic tumor regions may have an OER = 2 for conventional fractionation. However, our results indicate that clinically acceptable values of the TCP would require much lower hypoxia‐targeted dose escalation (<50%) when the effects of total and hypoxic tumor volumes are taken into account. Conclusions The reported studies and models suggest that the effect of total tumor volume on the TCP is negligible for oxygenated head and neck and non‐small cell lung tumors treated with conventional fractionation. According to our simulations, the volume effects in the TCP observed in clinical studies are defined primarily by the hypoxic volume. This information can be useful for the analysis of treatment outcomes and the dose escalation to target tumor hypoxia.