Validation of a model for physical dose variations in irregularly moving targets treated with carbon ion beams

In particle therapy, conventional treatment planning systems rely on an imaging representation of the irradiated region to compute the dose. For irregular breathing, when an imaging dataset describing the actual motion is not available, a different approach for dose estimation is needed. To this aim, we validate a method for the estimation of physical dose variations in gated carbon ion treatments, providing also a demonstration of the feasibility of physical dose metrics to assess the method performance. Finally, we describe a sample use case, in which this method is used to assess plan robustness with respect to undetected irregular tumor motion.

The method entails the definition of a patient- and beam-specific water equivalent depth (WED) space, the simulation of motion as a translation equal to tumor displacement, and the reconstruction of the altered dose. We validated the approach using four-dimensional computed tomographies (4DCTs) and clinical plans in 12 patients, treated with respiratory gated carbon ion beams at the National Centre for Oncological Hadrontherapy (Pavia, Italy). Using the end-exhale CT and dose distribution as a reference, the physical dose delivered at the end-inhale tumor position was estimated and compared to the ground-truth dose recalculation on the end-inhale CT. Biologically effective and physical dose variations between the plan and the recalculation were compared as well. As a use case, we evaluated dose changes caused by simulated irregular tumor motion, that is, linear and nonlinear baseline shifts and/or amplitude variations with hysteresis.

The ratio between biologically effective and physical equivalent uniform dose (EUD) variations due to end-exhale to end-inhale motion was less than one for 96% of investigated structures. In the validation study, we found a median error corresponding to a 14% EUD overestimation for the tumor and 4% EUD underestimation for a subgroup of organs at risk, together with a high EUD variation due to motion [median 352% EUD variation between end-exhale and end-inhale doses in the planning tumor volume (PTV)]. Considering relevant dose-volume histogram (DVH) metrics, the median difference between estimated and ground truth doses was ≤ 4%. Gamma analysis between estimated and recalculated dose distributions resulted in a pass rate > 80% for 83% of the target volumes. For the two patients selected for the sample use case, a patient-specific assessment of the method performance was performed on the 4DCT and it was possible to relate EUD variations of both tumor and organs at risk to the simulated target motion.

The physical dose distribution was found to be more sensitive to motion with respect to the biologically effective one, suggesting the suitability of the physical dose metrics for the WED-space method validation. We showed that the method can compensate for intra-fractional tumor motion with proper accuracy in the selected patient group, although its use is recommended when limited deformations are expected. In conclusion, the WED-space method can provide simulations of dose alteration due to irregular breathing when imaging data are lacking, and, once integrated with relative biological effectiveness (RBE) modeling, it would be useful in evaluating the robustness of carbon ion treatment plans.