Survival and tumour control probability in tumours with heterogeneous oxygenation: A comparison between the linear-quadratic and the universal survival curve models for high doses

<div><p></p><p><b>Background.</b> The validity of the linear-quadratic (LQ) model at high doses has been questioned due to a decreasing agreement between predicted survival and experimental cell survival data. A frequently proposed alternative is the universal survival curve (USC) model, thought to provide a better fit in the high-dose region. The comparison between the predictions of the models has mostly been performed for uniform populations of cells with respect to sensitivity to radiation. This study aimed to compare the two models in terms of cell survival and tumour control probability (TCP) for cell populations with mixed sensitivities related to their oxygenation.</p><p><b>Methods.</b> The study was performed in two parts. For the first part, cell survival curves were calculated with both models assuming various homogeneous populations of cells irradiated with uniform doses. For the second part, a realistic three-dimensional (3D) model of complex tumour oxygenation was used to study the impact of the differences in cell survival on the modelled TCP. Cellular response was assessed with the LQ and USC models at voxel level and a Poisson TCP model at tumour level.</p><p><b>Results.</b> For hypoxic tumours, the disputed continuous bend of the LQ survival curve was counteracted by the increased radioresistance of the hypoxic cells and the survival curves started to diverge only at much higher doses than for oxic tumours. This was also reflected by the TCP curves for hypoxic tumours for which the difference in <i>D</i>₅₀ values for the LQ and USC models was reduced from 5.4 to 0.2 Gy for 1 and 3 fractions, respectively, in a tumour with only 1.1% hypoxia and from 9.5 to 0.4 Gy in a tumour with 11.1% hypoxia.</p><p><b>Conclusions.</b> For a large range of fractional doses including hypofractionated schemes, the difference in predicted survival and TCP between the LQ and USC models for tumours with heterogeneous oxygenation was found to be negligible.</p></div

Defining the hypoxic target volume based on positron emission tomography for image guided radiotherapy – the influence of the choice of the reference region and conversion function

<p><b>Background:</b> Hypoxia imaged by positron emission tomography (PET) is a potential target for optimization in radiotherapy. However, the implementation of this approach with respect to the conversion of intensities in the images into oxygenation and radiosensitivity maps is not straightforward. This study investigated the feasibility of applying two conversion approaches previously derived for ¹⁸F-labeled fluoromisonidazole (¹⁸F-FMISO)-PET images for the hypoxia tracer ¹⁸F-flortanidazole (¹⁸F-HX4).</p> <p><b>Material and methods:</b> Ten non-small-cell lung cancer patients imaged with ¹⁸F-HX4 before the start of radiotherapy were considered in this study. PET image uptake was normalized to a well-oxygenated reference region and subsequently linear and non-linear conversions were used to determine tissue oxygenations maps. These were subsequently used to delineate hypoxic volumes based partial oxygen pressure (pO₂) thresholds. The results were compared to hypoxic volumes segmented using a tissue-to-background ratio of 1.4 for ¹⁸F-HX4 uptake.</p> <p><b>Results:</b> While the linear conversion function was not found to result in realistic oxygenation maps, the non-linear function resulted in reasonably sized sub-volumes in good agreement with uptake-based segmented volumes for a limited range of pO₂ thresholds. However, the pO₂ values corresponding to this range were significantly higher than what is normally considered as hypoxia. The similarity in size, shape, and relative location between uptake-based sub-volumes and volumes based on the conversion to pO₂ suggests that the relationship between uptake and pO₂ is similar for ¹⁸F-FMISO and ¹⁸F-HX4, but that the model parameters need to be adjusted for the latter.</p> <p><b>Conclusions:</b> A non-linear conversion function between uptake and oxygen partial pressure for ¹⁸F-FMISO-PET could be applied to ¹⁸F-HX4 images to delineate hypoxic sub-volumes of similar size, shape, and relative location as based directly on the uptake. In order to apply the model for e.g., dose-painting, new parameters need to be derived for the accurate calculation of dose-modifying factors for this tracer.</p