Background: 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.

Methods: 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 3D-model of complex tumour oxygenation was used to study the impact of the differences in cell survival on the modelled tumour control probability. Cellular response was assessed with the LQ and USC models at voxel level and a Poisson TCP model at tumour level.

Results: For hypoxic tumours, the disputed continuous bend of the LQ survival curve was counteracted by the increased radio-resistance 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 D₅₀ 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.

Conclusions: For a large range of fractional doses including hypofractionated schemes, the difference in predicted survival and tumour control probability between the LQ and USC models for tumours with heterogeneous oxygenation was found to be negligible.

The progress in functional imaging and dose delivery has opened the possibility of targeting tumour hypoxia with radiotherapy. Advanced approaches apply quantitative information on tumour oxygenation retrieved from imaging in dose prescription. These do not, however, take into account the potential difference in radiosensitivity of chronically and acutely hypoxic cells. It was the aim of this study to evaluate the implications of assuming the same or different sensitivities for the hypoxic cells. An in silico 3D-model of a hypoxic tumour with heterogeneous oxygenation was used to model the probabilities of tumour control with different radiotherapy regimens. The results show that by taking into account the potential lower radioresistance of chronically hypoxic cells deprived of oxygen and nutrients, the total dose required to achieve a certain level of control is substantially reduced for a given fractionation scheme in comparison to the case when chronically and acutely hypoxic cells are assumed to have similar features. The results also suggest that the presence of chronic hypoxia could explain the success of radiotherapy for some hypoxic tumours. Given the implications for clinical dose escalation trials, further exploration of the influence of the different forms of hypoxia on treatment outcome is therefore warranted.

Background: Stereotactic body radiotherapy (SBRT) for non-small-cell lung cancer (NSCLC) has led to promising local control and overall survival for fractionation schemes with increasingly high fractional doses. A point has however been reached where the number of fractions used might be too low to allow efficient local inter-fraction reoxygenation of the hypoxic cells residing in the tumour. It was therefore the purpose of this study to investigate the impact of hypoxia and extreme hypofractionation on the tumour control probability (TCP) from SBRT.

Methods: A three-dimensional model of tumour oxygenation able to simulate oxygenation changes on the microscale was used. The TCP was determined for clinically relevant SBRT fractionation schedules of 1, 3 and 5 fractions assuming either static tumour oxygenation or that the oxygenation changes locally between fractions due to fast reoxygenation of acute hypoxia without an overall reduction in chronic hypoxia.

Results: For the schedules applying three or five fractions the doses required to achieve satisfying levels of TCP were considerably lower when local oxygenation changes were assumed compared to the case of static oxygenation; a decrease in D₅₀ of 17.7 Gy was observed for a five-fractions schedule applied to a 20% hypoxic tumour when fast reoxygenation was modelled. Assuming local oxygenation changes, the total doses required for a tumor control probability of 50% were of similar size for one, three and five fractions.

Conclusions: Although attractive from a practical point of view, extreme hypofractionation using just one single fraction may result in impaired local control of hypoxic tumours, as it eliminates the possibility for any kind of reoxygenation.

Background. Conventionally fractionated radiotherapy (CFRT) has proven ineffective in treating non-small cell lung cancer while more promising results have been obtained with stereotactic body radiotherapy (SBRT). Hypoxic tumours, however, might present a challenge to extremely hypofractionated schedules due to the decreased possibility for inter-fraction fast reoxygenation. A potentially successful compromise might be found in schedules employing several fractions of varying fractional doses. In this modelling study, a wide range of fractionation schedules from single-fraction treatments to heterogeneous, multifraction schedules taking into account repair, repopulation, reoxygenation and radiosensitivity of the tumour cells, has been explored with respect to the probability of controlling lung tumours.

Material and methods. The response to radiation of tumours with heterogeneous spatial and temporal oxygenation was simulated including the effects of accelerated repopulation and intra-fraction repair. Various treatments with respect to time, dose and fractionation were considered and the outcome was estimated as Poisson-based tumour control probability for local control.

Results. For well oxygenated tumours, heterogeneous fractionation could increase local control while hypoxic tumours are not efficiently targeted by such treatments despite reoxygenation. For hypofractionated treatments employing large doses per fraction, a synergistic effect was observed between intra-fraction repair and inter-fraction fast reoxygenation of the hypoxic cells as demonstrated by a reduction in D₅₀ from 53.3 Gy for 2 fractions to 52.7 Gy for 5 fractions.

Conclusions. For well oxygenated tumours, heterogeneous fractionation schedules could increase local control rates substantially compared to CFRT. For hypoxic tumours, SBRT-like hypofractionated schedules might be optimal despite the increased risk of intra-fraction repair due to a synergistic effect with inter-fraction reoxygenation.

Background: 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).

Material and methods: 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.

Results: 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.

Conclusions: 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.

Background: Tumour hypoxia is associated with increased radioresistance and poor response to radiotherapy. Pre-treatment assessment of tumour oxygenation could therefore give the possibility to tailor the treatment by calculating the required boost dose needed to overcome the increased radioresistance in hypoxic tumours. This study concerned the derivation of a non-linear conversion function between the uptake of the hypoxia-PET tracer ¹⁸F-HX4 and oxygen partial pressure (pO₂).

Material and methods: Building on previous experience with FMISO including experimental data on tracer uptake and pO₂, tracer-specific model parameters were derived for converting the normalised HX4-uptake at the optimal imaging time point to pO₂. The conversion function was implemented in a Python-based computational platform utilising the scripting and the registration modules of the treatment planning system RayStation. Subsequently, the conversion function was applied to determine the pO₂ in eight non-small-cell lung cancer (NSCLC) patients imaged with HX4-PET before the start of radiotherapy. Automatic segmentation of hypoxic target volumes (HTVs) was then performed using thresholds around 10 mmHg. The HTVs were compared to sub-volumes segmented based on a tumour-to-blood ratio (TBR) of 1.4 using the aortic arch as the reference oxygenated region. The boost dose required to achieve 95% local control was then calculated based on the calibrated levels of hypoxia, assuming inter-fraction reoxygenation due to changes in acute hypoxia but no overall improvement of the oxygenation status.

Results: Using the developed conversion tool, HTVs could be obtained using pO₂ a threshold of 10 mmHg which were in agreement with the TBR segmentation. The dose levels required to the HTVs to achieve local control were feasible, being around 70–80 Gy in 24 fractions.

Conclusions: Non-linear conversion of tracer uptake to pO₂ in NSCLC imaged with HX4-PET allows a quantitative determination of the dose-boost needed to achieve a high probability of local control.