Robust optimization for intensity-modulated proton therapy with soft spot sensitivity regularization

Purpose Proton dose distribution is sensitive to uncertainties in range estimation and patient positioning. Currently, the proton robustness is managed by worst-case scenario optimization methods, which are computationally inefficient. To overcome these challenges, we develop a novel intensity-modulated proton therapy (IMPT) optimization method that integrates dose fidelity with a sensitivity term that describes dose perturbation as the result of range and positioning uncertainties. Methods In the integrated optimization framework, the optimization cost function is formulated to include two terms: a dose fidelity term and a robustness term penalizing the inner product of the scanning spot sensitivity and intensity. The sensitivity of an IMPT scanning spot to perturbations is defined as the dose distribution variation induced by range and positioning errors. To evaluate the sensitivity, the spatial gradient of the dose distribution of a specific spot is first calculated. The spot sensitivity is then determined by the total absolute value of the directional gradients of all affected voxels. The fast iterative shrinkage-thresholding algorithm is used to solve the optimization problem. This method was tested on three skull base tumor (SBT) patients and three bilateral head-and-neck (H&N) patients. The proposed sensitivity-regularized method (SenR) was implemented on both clinic target volume (CTV) and planning target volume (PTV). They were compared with conventional PTV-based optimization method (Conv) and CTV-based voxel-wise worst-case scenario optimization approach (WC). Results Under the nominal condition without uncertainties, the three methods achieved similar CTV dose coverage, while the CTV-based SenR approach better spared organs at risks (OARs) compared with the WC approach, with an average reduction of [Dmean, Dmax] of [4.72, 3.38] GyRBE for the SBT cases and [2.54, 3.33] GyRBE for the H&N cases. The OAR sparing of the PTV-based SenR method was comparable with the WC method. The WC method, and SenR approaches all improved the plan robustness from the conventional PTV-based method. On average, under range uncertainties, the lowest [D95%, V95%, V100%] of CTV were increased from [93.75%, 88.47%, 47.37%] in the Conv method, to [99.28%, 99.51%, 86.64%] in the WC method, [97.71%, 97.85%, 81.65%] in the SenR-CTV method and [98.77%, 99.30%, 85.12%] in the SenR-PTV method, respectively. Under setup uncertainties, the average lowest [D95%, V95%, V100%] of CTV were increased from [95.35%, 94.92%, 65.12%] in the Conv method, to [99.43%, 99.63%, 87.12%] in the WC method, [96.97%, 97.13%, 77.86%] in the SenR-CTV method, and [98.21%, 98.34%, 83.88%] in the SenR-PTV method, respectively. The runtime of the SenR optimization is eight times shorter than that of the voxel-wise worst-case method. Conclusion We developed a novel computationally efficient robust optimization method for IMPT. The robustness is calculated as the spot sensitivity to both range and shift perturbations. The dose fidelity term is then regularized by the sensitivity term for the flexibility and trade-off between the dosimetry and the robustness. In the stress test, SenR is more resilient to unexpected uncertainties. These advantages in combination with its fast computation time make it a viable candidate for clinical IMPT planning.