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

Abstract

PurposeTumor 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.