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.

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.

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.

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.