Stochastic programming for off-line adaptive radiotherapy

In intensity-modulated radiotherapy (IMRT), a treatment is designed to deliver high radiation doses to tumors, while avoiding the healthy tissue. Optimizationbased treatment planning often produces sharp dose gradients between tumors and healthy tissue. Random shifts during treatment can cause significant differences between the dose in the “optimized” plan and the actual dose delivered to a patient. An IMRT treatment plan is delivered as a series of small daily dosages, or fractions, over a period of time (typically 35 days). It has recently become technically possible to measure variations in patient setup and the delivered doses after each fraction. We develop an optimization framework, which exploits the dynamic nature of radiotherapy and information gathering by adapting the treatment plan in response to temporal variations measured during the treatment course of a individual patient. The resulting (suboptimal) control policies, which re-optimize before each fraction, include two approximate dynamic programming schemes: certainty equivalent control (CEC) and open-loop feedback control (OLFC). Computational experiments show that resulting individualized adaptive radiotherapy plans promise to provide a considerable improvement compared to non-adaptive treatment plans, while remaining computationally feasible to implement.