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.

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.

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.

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.

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.

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.

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 ¹⁸F‐HX4 positron emission tomography (PET) imaging of NSCLC.

Methods

Positron emission tomography imaging data based on the hypoxia tracer ¹⁸F‐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 ¹⁸F‐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.

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.

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: 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.