The Impact of Heterogeneous Cell Density in Hypoxic Tumors Treated with Radiotherapy.

Hypoxia is frequently found in solid tumors and is known to increase the resistance to several kinds of treatment modalities including radiation therapy. Besides, the treatment response is also largely determined by the total number of clonogenic cells, i.e., cells with unlimited proliferative capacity. Depending on the duration of hypoxia, the rate of proliferation and hence also the clonogen density could be expected to differ in hypoxic compartments. The combination at the microscale between heterogeneous tumor oxygenation and clonogen density could therefore be crucial with respect to the outcome of a radiotherapy treatment. In this study it was investigated the impact of heterogeneous clonogen density on the outcome of stereotactic radiotherapy treatments of hypoxic tumors. A recently developed three-dimensional model for tissue vasculature and oxygenation was used to create realistic in silico tumors with heterogeneous oxygenation. Stereotactic radiotherapy treatments were simulated, and cell survival was calculated on a voxel-level accounting for the oxygenation. For a tumor with a diameter of 1 cm and a baseline clonogenic density of 107/cm3 for the normoxic subvolume, when the relative density for the hypoxic cells drops by a factor of 10 the tumor control probability (TCP) decreases by about 10% when relatively small hypoxic volumes and few fractions are considered; longer treatments tend to level out the results. With increasing size of the hypoxic subvolume, the TCP decreased overall as expected, and the difference in TCP between a homogeneous and a heterogeneous distribution of cells increased. The results demonstrate a delicate interplay between the heterogeneous distribution of tumor oxygenation and clonogenic cells that could significantly impact on the treatment outcome of radiotherapy.

Hypoxia dose painting in SBRT - the virtual clinical trial approach.

BACKGROUND: Treating hypoxic tumours remains a challenge in radiotherapy as hypoxia leads to enhanced tumour aggressiveness and resistance to radiation. As escalating the doses is rarely feasible within the healthy tissue constraints, dose-painting strategies have been explored. Consensus about the best of care for hypoxic tumours has however not been reached because, among other reasons, the limits of current functional in-vivo imaging systems in resolving the details and dynamics of oxygen transport in tissue. Computational modelling of the tumour microenvironment enables the design and conduction of virtual clinical trials by providing relationships between biological features and treatment outcomes. This study presents a framework for assessing the therapeutic influence of the individual characteristics of the vasculature and the resulting oxygenation of hypoxic tumours in a virtual clinical trial on dose painting in stereotactic body radiotherapy (SBRT) circumventing the limitations of the imaging systems. MATERIAL AND METHODS: The homogeneous doses required to overcome hypoxia in simulated SBRT treatments of 1, 3 or 5 fractions were calculated for tumours with heterogeneous oxygenation derived from virtual vascular networks. The tumour control probability (TCP) was calculated for different scenarios for oxygenation dynamics resulting on cellular reoxygenation. RESULTS: A three-fractions SBRT treatment delivering 41.9 Gy (SD 2.8) and 26.5 Gy (SD 0.1) achieved only 21% (SD 12) and 48% (SD 17) control in the hypoxic and normoxic subvolumes, respectively whereas fast reoxygenation improved the control by 30% to 50%. TCP values for the individual tumours with similar characteristics, however, might differ substantially, highlighting the crucial role of the magnitude and time evolution of hypoxia at the microscale. CONCLUSION: The results show that local microvascular heterogeneities may affect the predicted outcome in the hypoxic core despite escalated doses, emphasizing the role of theoretical modelling in understanding of and accounting for the dominant factors of the tumour microenvironment.

Perfusion-Limited Hypoxia Determines the Outcome of Radiation Therapy of Hypoxic Tumours.

Despite advancements in functional imaging, the resolution of modern techniques is still limited with respect to the tumour microenvironment. Radiotherapy strategies to counteract e.g., tumour hypoxia based on functional imaging therefore carry an inherent uncertainty that could compromise the outcome of the treatment. It was the aim of this study to investigate the impact of variations in the radiosensitivity of hypoxic tumours in small regions in comparison to the resolution of current imaging techniques on the probability of obtaining tumour control. A novel in silico model of three-dimensional tumour vasculature and oxygenation was used to model three tumours with different combinations of diffusion-limited, perfusion-limited and anaemic hypoxia. Specifically, cells in the transition region from a tumour core with diffusion-limited hypoxia to the well-oxygenated tumour rim were considered with respect to their differential radiosensitivity depending on the character of the hypoxia. The results showed that if the cells in the transition region were under perfusion-limited hypoxia, the tumour control probability was substantially lower in comparison to the case when the cells were anaemic (or under diffusion-limited hypoxia). This study therefore demonstrates the importance of differentiating between different forms of hypoxia on a scale currently unattainable to functional imaging techniques, lending support to the use and importance of radiobiological modelling of the cellular radiosensitivity and response at microscale.

Towards the virtual tumor for optimizing radiotherapy treatments of hypoxic tumors: A novel model of heterogeneous tissue vasculature and oxygenation.

PURPOSE: Tumor oxygenation is one of the key features influencing the response of cells to radiation and chemo therapies. This study presents a novel in silico tumor model simulating realistic 3D microvascular structures and related oxygenation maps, featuring regions with different levels and typologies of hypoxia (chronic, acute and anemic). Such model, if integrated into a treatment planning system, could allow evaluations and comparisons of various scenarios when deciding the therapy to administer. METHODS AND MATERIALS: Spherical tumors between 0.6 and 1.5 cm in diameter encompassed uniformly by vascular trees generated starting from pseudo-fractal principles were simulated with a voxel resolution of 10 µm. The approach ensures a continuous transition from a well-perfused rim to a core with poor vascularization. The oxygen diffusion equation in the tumor is solved by a finite difference method. Several quantities, such as the fractal dimension (FD), the microvascular density (MVD) and the hypoxic fraction (HF) were assessed and compared. RESULTS: Different tumors with various degrees of chronic hypoxia were simulated by varying the tumor size and the number of bifurcations in the vascular networks. The simulations showed that for the case of chronically hypoxic tumors, in well-oxygenated volumes FD = 2.53 ± 0.07, MVD = 3460 ± 2180 vessels/mm3 and HF = 4.0 ± 3.4%, while in hypoxic volumes FD = 2.34 ± 0.09, MVD = 365 ± 156 vessels/mm3, HF = 49.8 ± 18.3%. The superimposition of acute or anemic hypoxia accentuated the oxygen deprivation in the core of the volumes. CONCLUSIONS: Tumors varying in diameter and extension of their vasculature were simulated, showing features that define two distinctive subvolumes in terms of oxygenation. The model could be regarded as a testbed for simulations of key radiobiological features governing the tumor response to radio- and chemotherapy and thus for treatment outcome simulations.

Assessment of the Probability of Tumour Control for Prescribed Doses Based on Imaging of Oxygen Partial Pressure.

In radiotherapy, hypoxia is a known negative factor, occurring especially in solid malignant tumours. Nitroimidazole-based positron emission tomography (PET) tracers, due to their selective binding to hypoxic cells, could be used as surrogates to image and quantify the underlying oxygen distributions in tissues. The spatial resolution of a clinical PET image, however, is much larger than the cellular spatial scale where hypoxia occurs. A question therefore arises regarding the possibility of quantifying different hypoxia levels based on PET images, and the aim of the present study is the prescription of corresponding therapeutic doses and its exploration.A tumour oxygenation model was created consisting of two concentric spheres with different oxygen partial pressure (pO2) distributions. In order to mimic a PET image of the simulated tumour, given the relation between uptake and pO2, fundamental effects that limit spatial resolution in a PET imaging system were considered: the uptake distribution was processed with a Gaussian 3D filter, and a re-binning to reach a typical PET image voxel size was performed. Prescription doses to overcome tumour hypoxia and predicted tumour control probability (TCP) were calculated based on the processed images for several fractionation schemes. Knowing the underlying oxygenation at microscopic scale, the actual TCP expected after the delivery of the calculated prescription doses was evaluated. Results are presented for three different dose painting strategies: by numbers, by contours and by using a voxel grouping-based approach.The differences between predicted TCP and evaluated TCP indicate that careful consideration must be taken on the dose prescription strategy and the selection of the number of fractions, depending on the severity of hypoxia.

Radiation-induced Vascular Damage and the Impact on the Treatment Outcome of Stereotactic Body Radiotherapy.

BACKGROUND/AIM: The aim of this study was to investigate radiation-induced tumour vascular damage and its impact thereof on the outcome of stereotactic body radiotherapy (SBRT). MATERIALS AND METHODS: Vessel densities in animal tumours before and after a single dose of 20 Gy were quantified and used as input for simulations of three-dimensional tumours with heterogeneous oxygenation. SBRT treatments of the modelled tumours in 1-8 fractions were simulated. The impact of vessel collapse on the outcome of SBRT was investigated by calculating tumour control probability (TCP) and the dose required to obtain a TCP of 50% (D50). RESULTS: A radiation-induced increase of acute hypoxia in tumours during SBRT treatment could be simulated based on the experimental data. The D50 values for these tumours were higher than for the simulated tumours without vessel collapse. CONCLUSION: The vascular changes after high doses of radiation could compromise the outcome of SBRT by increasing tumour hypoxia.

Hypoxia Induced by Vascular Damage at High Doses Could Compromise the Outcome of Radiotherapy.

BACKGROUND/AIM: This study investigated the impact of temporary vascular collapse on tumour control probability (TCP) in stereotactic body radiotherapy (SBRT), taking into account different radiosensitivities of chronically and acutely hypoxic cells. MATERIALS AND METHODS: Three-dimensional tumours with heterogeneous oxygenation were simulated assuming different fractions of collapsed vessels at every treatment fraction. The modelled tumours contained a chronically hypoxic subvolume of 30-60% of the tumour diameter, and a hypoxic fraction ≤5 mm Hg of 30-50%. The rest of the tumours were well-oxygenated at the start of the simulated treatment. RESULTS: For all simulated cases, the largest reduction in TCP from 97% to 2% was found in a tumour with a small chronically hypoxic core treated with 60 Gy in eight fractions and assuming a treatment-induced vascular collapse of 35% in the well-oxygenated region. CONCLUSION: The timing of SBRT fractions should be considered together with the tumour oxygenation to avoid loss of TCP in SBRT.

Impact of SBRT fractionation in hypoxia dose painting - Accounting for heterogeneous and dynamic tumor oxygenation.

PURPOSE: Tumor hypoxia, often found in nonsmall cell lung cancer (NSCLC), implies an increased resistance to radiotherapy. Pretreatment assessment of tumor oxygenation is, therefore, warranted in these patients, as functional imaging of hypoxia could be used as a basis for dose painting. This study aimed at investigating the feasibility of using a method for calculating the dose required in hypoxic subvolumes segmented on 18 F-HX4 positron emission tomography (PET) imaging of NSCLC. METHODS: Positron emission tomography imaging data based on the hypoxia tracer 18 F-HX4 of 19 NSCLC patients were included in the study. Normalized tracer uptake was converted to oxygen partial pressure (pO2 ) and hypoxic target volumes (HTVs) were segmented using a threshold of 10 mmHg. Uniform doses required to overcome the hypoxic resistance in the target volumes were calculated based on a previously proposed method taking into account the effect of interfraction reoxygenation, for fractionation schedules ranging from extremely hypofractionated stereotactic body radiotherapy (SBRT) to conventionally fractionated radiotherapy. RESULTS: Gross target volumes ranged between 6.2 and 859.6 cm3 , and the hypoxic fraction < 10 mmHg between 1.2% and 72.4%. The calculated doses for overcoming the resistance of cells in the HTVs were comparable to those currently prescribed in clinical practice as well as those previously tested in feasibility studies on dose escalation in NSCLC. Depending on the size of the HTV and the distribution of pO2 , HTV doses were calculated as 43.6-48.4 Gy for a three-fraction schedule, 51.7-57.6 Gy for five fractions, and 59.5-66.4 Gy for eight fractions. For patients in whom the HTV pO2 distribution was more favorable, a lower dose was required despite a bigger volume. Tumor control probability was lower for single-fraction schedules, while higher levels of tumor control probability were found for schedules employing several fractions. CONCLUSIONS: The method to account for heterogeneous and dynamic hypoxia in target volume segmentation and dose prescription based on 18 F-HX4-PET imaging appears feasible in NSCLC patients. The distribution of oxygen partial pressure within HTV could impact the required prescribed dose more than the size of the volume.

Accounting for Two Forms of Hypoxia for Predicting Tumour Control Probability in Radiotherapy: An In Silico Study.

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.

Non-linear conversion of HX4 uptake for automatic segmentation of hypoxic volumes and dose prescription.

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.

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.

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.

High brachytherapy doses can counteract hypoxia in cervical cancer-a modelling study.

Tumour hypoxia is a well-known adverse factor for the outcome of radiotherapy. For cervical tumours in particular, several studies indicate large variability in tumour oxygenation. However, clinical evidence shows that the management of cervical cancer including brachytherapy leads to high rate of success. It was the purpose of this study to investigate whether the success of brachytherapy for cervical cancer, seemingly regardless of oxygenation status, could be explained by the characteristics of the brachytherapy dose distributions. To this end, a previously used in silico model of tumour oxygenation and radiation response was further developed to simulate the treatment of cervical cancer employing a combination of external beam radiotherapy and intracavitary brachytherapy. Using a clinically-derived brachytherapy dose distribution and assuming a homogeneous dose delivered by external radiotherapy, cell survival was assessed on voxel level by taking into account the variation of sensitivity with oxygenation as well as the effects of repair, repopulation and reoxygenation during treatment. Various scenarios were considered for the conformity of the brachytherapy dose distribution to the hypoxic region in the target. By using the clinically-prescribed brachytherapy dose distribution and varying the total dose delivered with external beam radiotherapy in 25 fractions, the resulting values of the dose for 50% tumour control, D 50, were in agreement with clinically-observed values for high cure rates if fast reoxygenation was assumed. The D 50 was furthermore similar for the different degrees of conformity of the brachytherapy dose distribution to the tumour, regardless of whether the hypoxic fraction was 10%, 25%, or 40%. To achieve 50% control with external RT only, a total dose of more than 70 Gy in 25 fractions would be required for all cases considered. It can thus be concluded that the high doses delivered in brachytherapy can counteract the increased radioresistance caused by hypoxia if fast reoxygenation is assumed.

Optimal fractionation in radiotherapy for non-small cell lung cancer--a modelling approach.

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.

Treatment fractionation for stereotactic radiotherapy of lung tumours: a modelling study of the influence of chronic and acute hypoxia on tumour control probability.

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.

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.

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 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. RESULTS: 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 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 TCP between the LQ and USC models for tumours with heterogeneous oxygenation was found to be negligible.

Clinical oxygen enhancement ratio of tumors in carbon ion radiotherapy: the influence of local oxygenation changes.

The effect of carbon ion radiotherapy on hypoxic tumors has recently been questioned because of low linear energy transfer (LET) values in the spread-out Bragg peak (SOBP). The aim of this study was to investigate the role of hypoxia and local oxygenation changes (LOCs) in fractionated carbon ion radiotherapy. Three-dimensional tumors with hypoxic subvolumes were simulated assuming interfraction LOCs. Different fractionations were applied using a clinically relevant treatment plan with a known LET distribution. The surviving fraction was calculated, taking oxygen tension, dose and LET into account, using the repairable-conditionally repairable (RCR) damage model with parameters for human salivary gland tumor cells. The clinical oxygen enhancement ratio (OER) was defined as the ratio of doses required for a tumor control probability of 50% for hypoxic and well-oxygenated tumors. The resulting OER was well above unity for all fractionations. For the hypoxic tumor, the tumor control probability was considerably higher if LOCs were assumed, rather than static oxygenation. The beneficial effect of LOCs increased with the number of fractions. However, for very low fraction doses, the improvement related to LOCs did not compensate for the increase in total dose required for tumor control. In conclusion, our results suggest that hypoxia can influence the outcome of carbon ion radiotherapy because of the non-negligible oxygen effect at the low LETs in the SOBP. However, if LOCs occur, a relatively high level of tumor control probability is achievable with a large range of fractionation schedules for tumors with hypoxic subvolumes, but both hyperfractionation and hypofractionation should be pursued with caution.