Intra-voxel heterogeneity influences the dose prescription for dose-painting with radiotherapy: a modelling study.

The purpose of this study was to increase the potential of dose redistribution by incorporating estimates of oxygen heterogeneity within imaging voxels for optimal dose determination. Cellular oxygen tension (pO(2)) distributions were estimated for imaging-size-based voxels by solving oxygen diffusion-consumption equations around capillaries placed at random locations. The linear-quadratic model was used to determine cell survival in the voxels as a function of pO(2) and dose. The dose distribution across the tumour was optimized to yield minimal survival after 30 x 2 Gy fractions by redistributing the dose based on differences in oxygen levels. Eppendorf data of a series of 69 tumours were used as a surrogate of what might be expected from oxygen imaging datasets. Dose optimizations were performed both taking into account cellular heterogeneity in oxygenation within voxels and assuming a homogeneous cellular distribution of oxygen. Our simulations show that dose redistribution based on derived cellular oxygen distributions within voxels result in dose distributions that require less total dose to obtain the same degree of cell kill as dose distributions that were optimized with a model that considered voxels as homogeneous with respect to oxygen. Moderately hypoxic tumours are expected to gain most from dose redistribution. Incorporating cellular-based distributions of radiosensitivity into dose-planning algorithms theoretically improves the potential gains from dose redistribution algorithms.