Dose prescription complexity versus tumor control probability in biologically conformal radiotherapy

The technical feasibility and potential benefits of voxel-based nonuniform dose prescriptions for biologically heterogeneous tumors have been widely demonstrated. In some cases, an "ideal" dose prescription has been generated by individualizing the dose to every voxel within the target, but often this voxel-based prescription has been discretized into a small number of compartments. The number of dose levels utilized and the methods used for prescribing doses and assigning tumor voxels to different dose compartments have varied significantly. The authors present an investigation into the relationship between the complexity of the dose prescription and the tumor control probability (TCP) for a number of these methods. The linear quadratic model of cell killing was used in conjunction with a number of modeled tumors heterogeneous in clonogen density, oxygenation, or proliferation. Models based on simple mathematical functions, published biological data, and biological image data were investigated. Target voxels were assigned to dose compartments using (i) simple rules based on the initial biological distribution, (ii) iterative methods designed to maximize the achievable TCP, or (iii) methods based on an ideal dose prescription. The relative performance of the simple rules was found to depend on the form of heterogeneity of the tumor, while the iterative and ideal dose methods performed comparably for all models investigated. In all cases the maximum achievable TCP was approached within the first few (typically two to five) compartments. Results suggest that irrespective of the pattern of heterogeneity, the optimal dose prescription can be well approximated using only a few dose levels but only if both the compartment boundaries and prescribed dose levels are well chosen.