Volume dependence in hypoxia-targeted dose escalation.

PURPOSE: Dose painting techniques based on dose escalation to hypoxic regions are usually governed by the spatial distribution of Oxygen Enhancement Ratio (OER) derived from PET or MRI images. The goal of this article is to show that the volume of the hypoxic region is also a parameter which may affect the radiobiological effectiveness of hypoxia-targeted dose escalation. METHODS: Our analysis is performed using the equation for Tumor Control Probability (TCP) derived from Poisson statistics. A tumor response model based on two levels of oxygenated and hypoxic cells with the survival curves described by the Linear Quadratic (LQ) model was used in the calculations. The model allows for analytical solutions which can be used for additional validation of our numerical simulations. The model was used to compute the average tumor cell survival that defines TCP. Dependence of average tumor cell survival on the relative hypoxic volume and dose escalation was computed for the conventional 30 × 2 Gy and hypofractionated 4 × 12 Gy dose regimens in a model problem with radiobiological parameters for nonsmall cell lung cancer. RESULTS: We show that equal average tumor cell survival and TCP can be achieved with smaller hypoxia-targeted dose escalation for smaller relative hypoxic volumes if the dose escalation does not exceed 50% of dose in the oxygenated region. This effect is explained by the dependence of average tumor cell survival and TCP mostly on the hypoxic tumor volume in this dose escalation range. Assuming a linear relationship between the number of clonogens and the hypoxic volume, smaller hypoxic volumes have smaller number of clonogens, therefore, smaller doses are needed to eradicate them. CONCLUSIONS: The theoretical analysis performed in this article predicts that tumors with smaller relative hypoxic volumes may require smaller hypoxia-targeted dose escalation to maintain equal TCP. The results of this research can be used for dose de-escalation strategies in dose painting techniques which may reduce dose to normal tissue and normal tissue complications without deterioration of TCP.