The impact of including spatially longitudinal heterogeneities of vessel oxygen content and vascular fraction in 3D tumor oxygenation models on predicted radiation sensitivity
Authors: Lagerlöf Jakob H. , Kindblom Jon , Bernhardt Peter 
Published: March 2014

Purpose:

Oxygen distribution models have been used to analyze the influences of oxygen tensions on tissue response after radiotherapy. These distributions are often generated assuming constant oxygen tension in the blood vessels. However, as red blood cells progress through the vessels, oxygen is continuously released into the plasma and the surrounding tissue, resulting in longitudinally varying oxygen levels in the blood vessels. In the present study, the authors investigated whether a tumor oxygenation model that incorporated longitudinally varying oxygen levels would provide different predictions of necrotic fractions and radiosensitivity compared to commonly used models with a constant oxygen pressure.

Methods:

Our models simulated oxygen diffusion based on a Greenˈs function approach and oxygen consumption according to the Michaelis‐Menten equation. The authors constructed tumor models with different vascular fractions (VFs), from which they generated depth oxygenation curves and a look‐up table of oxygen pressure gradients. The authors evaluated models of spherical tumors of various sizes, from 1 to 104 mg. The authors compared the results from a model with constant vessel oxygen (CVO) pressure to those from models with longitudinal variations in oxygen saturation and either a constant VF (CVF) or variable VF (VVF) within the tumor tissue. The authors monitored the necrotic fractions, defined as tumor regions with an oxygen pressure below 1 mmHg. Tumor radiation sensitivity was expressed as D99, the homogeneous radiation dose required for a tumor control probability of 0.99.

Results:

In the CVO saturation model, no necrosis was observed, and decreasing the VF could only decrease the D99 by up to 10%. Furthermore, the D99 vs VF dependence was similar for different tumor masses. Compared to the CVO model, the extended CVF and VVF models provided clearly different results, including pronounced effects of VF and tumor size on the necrotic fraction and D99, necrotic fractions ranging from 0% to 97%, and a maximal D99 increment of 57%. Only minor differences were observed between different vessel architectures, i.e., CVF vs VVF. In the smallest tumor with a low necrotic fraction, the D99 strictly decreased with increasing blood velocity. Increasing blood velocity also decreased the necrotic fraction in all tumor sizes. VF had the most profound influence on both the necrotic fraction and on D99.

Conclusions:

Our present analysis of necrotic formation and the impact of tumor oxygenation on D99 demonstrated the importance of including longitudinal variations in vessel oxygen content in tumor models. For small tumors, radiosensitivity was particularly dependent on VF and slightly dependent on the blood velocity and vessel arrangement. These dependences decreased with increasing tumor size, because the necrotic fraction also increased, thereby decreasing the number of viable tumor cells that required sterilization. The authors anticipate that the present model will be useful for estimating tumor oxygenation and radiation response in future detailed studies.