Realistic Cellular Oxygen Model Reveals High Potential Gains With Dose Painting and Offers a General Solution for Incorporating Cellular Distributions That Underlie Imaging Data

Article Outline

• Purpose/Objective(s)
• Materials/Methods
• Results
• Conclusions
• Copyright

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Purpose/Objective(s) 

Oxygenation, proliferation and clonogen cell density are often heterogeneous within tumor tissue. Knowledge of the spatial differences in these parameters can theoretically be used to redistribute dose across the tumor volume so as to achieve a better therapeutic result. Previous approaches for dose optimization based on 3D imaging data have assumed that each imaging voxel is homogeneous with respect to the imaging parameter of interest, e.g. oxygenation. However the imaging resolution is typically 100 times lower than the cellular scale at which large variations in these parameters can occur. The goal of this study is to estimate and incorporate the micro-environmental heterogeneity present within imaging voxels to construct an optimal dose painting algorithm. We focus on tumor oxygenation.

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Materials/Methods 

To estimate the underlying cellular oxygen partial pressure (pO₂) distribution within a voxel with a given measured pO₂, an oxygen diffusion-consumption equation was solved on a 2 dimensional surface with capillaries placed orthogonally at random locations. Capillaries are added and/or removed at random to achieve a mean pO₂ equal to the voxel pO₂. Multiple simulations are performed to obtain a representative average cellular pO₂ distribution. The linear quadratic model was used to describe survival at the cellular level as a function of pO₂ and dose. The overall response of the tumor after 30 fractions was minimized by an optimization algorithm that allowed the dose to the voxels to vary between set limits. The dose distributions were optimized for 69 head and neck tumors of which oxygenation data was available. Optimizations were performed using both the described heterogeneous voxel model (HeVM) and a homogeneous voxel model (HoVM).

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Results 

The HoVM underestimates the amount and impact of tumor hypoxia. Simulations with the HEVM illustrate that an “aerobic” tumor voxel with a mean pO₂ of 20 mmHg contains, on average, 8% of cells with pO₂ ≤ 5 mmHg. This results in an underestimation of survival by up to 1.8 logs after 60 Gy when using the HoVM. Depending on the individual tumor, dose redistribution increases the effective dose by 0 to 31 Gy (mean 13.8 Gy) with the HoVM and 0 to 38 Gy (mean 17.4 Gy) with the HeVM, with 70% of the analyzed tumors gaining more than 10 Gy. In all cases the total tumor dose was equal to 60 Gy. On average, dose redistribution with the HeVM results in an equivalent dose that is 3.4 Gy larger than the HoVM. Furthermore, when voxel heterogeneity is ignored, large errors (up to 16 Gy) occur in the therapeutic gain that can be expected by dose redistribution.

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Conclusions 

Dose redistribution based on oxygenation can result in large gains in terms of cell kill. Failure to recognize voxel heterogeneity results in errors in both the best way to redistribute dose and to the expected gains by such a redistribution. This study focuses on oxygenation, but the concept can be used as well for other imaging parameters in which heterogeneity is expected (e.g. clonogen density or proliferation).