A temporo-spatial description of moving tumor and organs by the probability of presence time proportion: concept and implementation for 4D dose calculation and optimization

Objective. The binary definition of the internal target volume (ITV) artificially separates tumor from healthy organs at motion overlapping area for dose evaluation and optimization, bringing confusion about taking partial organs as tumor or adversely. In this work, the probability of presence time (PPT) proportion of a moving anatomic voxel at a geometric voxel is defined to construct a temporo-spatial description of moving objects. The geometric overlapping of tumor and organs in 3D space is distinguished by individual residence time proportion. The dose deposition at a geometric voxel is decomposed into individual dose delivered to tumor and organs for accumulative dose calculation and optimization. Approach. A novel PPT-based plan optimization strategy is proposed to generate an optimized non-uniform dose distribution based on the temporo-spatial relationship between tumor and organs. Main results. Results from a simulation study on phantoms show that the proposed method provides promising performance for surrounding organs at risk (OAR) avoidance with a reduction of mean and maximum dose at a range of 22.6%–23.1% and 23.6%–28.3% compared with ITV-based plans under different geometric conditions, while keeping the clinical target volume dose as prescription. Significance. The PPT definition constructs a unified framework to deal with the 4D temporo-spatial distribution, accumulative dose calculation and optimization of moving tumor and organs. The advantages of the PPT-based dose calculation and optimization approach are demonstrated by simulation study with significant reduction of OARs dose level compared with conventional ITV-based plan.