Robust spatiotemporal fractionation schemes in the presence of patient setup uncertainty

Spatiotemporal fractionation schemes for photon radiotherapy have recently arisen as a promising technique for healthy tissue sparing. Because spatiotemporally fractionated treatments have a characteristic pattern of delivering high doses to different parts of the tumor in each fraction, uncertainty in patient positioning is an even more pressing concern than in conventional uniform fractionation. Until now, such concerns in patient setup uncertainty have not been addressed in the context of spatiotemporal fractionation.

A stochastic optimization model is used to incorporate patient setup uncertainty to optimize spatiotemporally fractionated plans using expected penalties for deviations from prescription values. First, a robust uniform reference plan is optimized with a stochastic optimization model. Then, a spatiotemporal plan is optimized with a constrained stochastic optimization model that minimizes a primary clinical objective and constrains the spatiotemporal plan to be at least as good as the uniform reference plan with respect to all other objectives. A discrete probability distribution is defined to characterize the random setup error occurring in each fraction. For the optimization of uniform plans, the expected penalties are computed exactly by exploiting the symmetry of the fractions, and for the spatiotemporal plans, quasi-Monte Carlo sampling is used to approximate the expectation.

Using five clinical liver cases, it is demonstrated that spatiotemporally fractionated treatment plans maintain the same robust tumor coverage as a stochastic uniform reference plan and exhibit a reduction in the expected mean BED of the uninvolved liver. This is observed for a spectrum of probability distributions of random setup errors with shifts in the patient position of up to 5 mm from the nominal position. For probability distributions with small variance in the patient position, the spatiotemporal plans exhibit an 8-30% reduction in expected mean BED in the healthy liver tissue for shifts up to 2.5 mm and reductions of 5-25% for shifts up to 5 mm.

In the presence of patient setup uncertainty, spatiotemporally fractionated treatment plans exhibit the same robust tumor coverage as their uniformly fractionated counterparts and still retain the benefit in sparing healthy tissues.