Robust optimization for intensity modulated radiation therapy treatment planning under uncertainty

Abstract

The recent development of intensity modulated radiation therapy (IMRT) allows the dose distribution to be tailored to match the tumour's shape and position, avoiding damage to healthy tissue to a greater extent than previously possible. Traditional treatment plans assume that the target structure remains in a fixed location throughout treatment. However, many studies have shown that because of organ motion, inconsistencies in patient positioning over the weeks of treatment, etc, the tumour location is not stationary. We present a probabilistic model for the IMRT inverse problem and show that it is identical to using robust optimization techniques, under certain assumptions. For a sample prostate case, our computational results show that this method is computationally feasible and promising-compared to traditional methods, our model has the potential to find treatment plans that are more adept at sparing healthy tissue while maintaining the prescribed dose to the target.

Adaptive and robust radiation therapy optimization for lung cancer

“…In Chu et al [2005], tumour position uncertainty due to interfraction motion and setup error was modelled using an ellipsoidal uncertainty set and the authors showed that the resulting robust solution achieves the same level of tumour coverage as a clinical margin solution, in which the volume that receives the prescription dose is expanded to account for changes in position, but with less healthy tissue dose. InÓlafsson and Wright [2006], the uncertainty due to dose calculation error and interfraction organ motion was also modelled using an ellipsoidal uncertainty set, and the authors showed for a nasopharyngeal case that a robust solution achieves better tumour coverage than the nominal solution (one which assumes a dose matrix known with certainty) and leads to better organ sparing than the margin solution that was clinically prescribed for the case.…”

On the Robustness of Global Optima and Stationary Solutions to Stochastic Mathematical Programs with Equilibrium Constraints, Part 2: Applications

“…Combining the two, we get a position uncertainty which can be represented by a stochastic influence matrix K(ω). Olafsson and Wright [42] and Chu et al [13], assume that the doses are stochastic, and use probabilistic constraints to control the dose levels in the target and in the organs at risk. Chan et al [12] use a motion probability mass function, and assumes that the probability itself is uncertain.…”

Efficient schemes for robust IMRT treatment planning

“…Chu et al (2005) reported run times of 3.3 h for a formulation similar to (2.8), while the corresponding nominal LP required about 17 min.…”

“…This term is quite similar to the variance term considered in Chu et al (2005), since it is based on the same position uncertainty model and contains no dose calculation errors. Therefore, we simply adopt the rationale of Chu et al (2005), which is based on the central limit theorem, in computing this contribution to the variance. We conclude that where i is defined in (2.6b).…”