As hypoxic cells are more resistant to photon radiation, it is desirable to obtain information about the oxygen distribution in tumors prior to the radiation treatment. Noninvasive techniques are currently not able to provide reliable oxygenation maps with sufficient spatial resolution; therefore mathematical models may help to simulate microvascular architectures and the resulting oxygen distributions in the surrounding tissue. Here, the authors present a new computer model, which uses the vascular fraction of tumor voxels, in principle measurable noninvasivelyin vivo, as input parameter for simulating realistic PO2 histograms in tumors, assuming certain 3D vascular architectures.
Oxygen distributions were calculated by solving a reaction-diffusion equation in a reference volume using the particle strength exchange method. Different types of vessel architectures as well as different degrees of vascular heterogeneities are considered. Two types of acute hypoxia (ischemic and hypoxemic) occurring additionally to diffusion-limited (chronic) hypoxia were implemented as well.
No statistically significant differences were observed when comparing 2D- and 3D-vessel architectures (p > 0.79 in all cases) and highly heterogeneously distributed linear vessels show good agreement, when comparing with published experimental intervessel distance distributions and PO2 histograms. It could be shown that, if information about additional acute hypoxia is available, its contribution to the hypoxic fraction (HF) can be simulated as well. Increases of 128% and 168% in the HF were obtained when representative cases of ischemic and hypoxemic acute hypoxia, respectively, were considered in the simulations.
The presented model is able to simulate realistic microscopic oxygen distributions in tumors assuming reasonable vessel architectures and using the vascular fraction as macroscopic input parameter. The model may be used to generate PO2 histograms, which are needed as input in models predicting the radiation response of hypoxic tumors.
This work was supported by a grand of the Ministry of Education of Chile, Programa MECE Educación Superior (2). The authors have no conflict of interest.
II. METHODS AND MATERIALS
II.A. Oxygen reaction-diffusion equation
II.B. Vascular architecture
II.B.1. Point-like vessels
II.B.2. Parallel linear vessels
II.B.3. Linear vessels in 3D
II.C. Simulation of oxygen distributions
II.C.1. Test of the implemented algorithm
II.C.2. Oxygen distribution for different vascular architectures and vascular fractions
II.C.3. Oxygen distributions for different vascular heterogeneities and vascular fractions
II.C.4. Acute hypoxia
II.C.5. Conditions of simulation
II.D. Comparison of IVD distributions with published experimental data
III.A. Test of the implemented algorithm
III.B. Oxygen distribution for different vascular architectures and vascular fractions
III.C. Oxygen distributions for different vascular heterogeneities and vascular fractions
III.D. Acute hypoxia
III.E. Comparison of IVD distributions with published experimental data
IV.B. Model assumptions
Data & Media loading...
Article metrics loading...
Full text loading...