A regularized-multi-field optimization algorithm for robust IMPT

Treatment planning in proton therapy aims to deliver a conformal dose to the target while sparing normal healthy tissues. However, the range uncertainty of CT values and patient motion during delivery may compromise both target dose coverage and organ-at-risk (OAR) sparing.

This study proposes a novel optimization method, Regularized-Multi-Field Optimization (R-MFO). R-MFO which incorporates the single-field uniform dose as a regularization term in the multi-field optimization (MFO). The proposed method seeks to reduce the sensitivity to uncertainties while maintaining the high plan quality as MFO plans.

R-MFO combines the uniform dose distribution with the flexibility of MFO plans through an iterative process. Specifically, a dose equality constraint in the target volume for each field is introduced as a regularized term in the conventional MFO at every certain iteration. Robust optimization is performed with the range uncertainty of 3.5% and setup uncertainty of 3mm for the head and neck (HN) case and 5mm for the liver and lung cases. Due to the nonconvex constraints associated with minimum monitor unit (MMU) and active set, R-MFO optimization is solved by iterative convex relaxation (ICR) and alternating direction method of multipliers (ADMM) algorithms. To demonstrate the effectiveness of our proposed R-MFO, plan quality and robustness are compared with R-MFO, MFO, and single-field optimizations (SFO) across three clinical cases: HN, liver, and lung.

R-MFO demonstrated significantly enhanced robustness compared to MFO, with narrower uncertainty bands (e.g., RV₉₅: 7.8-10.0 vs. 9.6-10.5) and superior high-dose tail performance, though slightly inferior to SFO in RV₁₀₀ (26.2-31.5 vs. 19.2-26.9). Plan quality analysis revealed R-MFO achieved higher conformity indices (CI: 0.65-0.79) and improved dose coverage (D₉₅ ≥99.15%, D_max ≤111.90%) compared to SFO, approaching MFO performance. For OARs, both MFO and R-MFO reduced esophageal D_max, D_mean, and D_5cc in the lung case by leveraging dose distribution flexibility. However, R-MFO incurred the longest computational time due to comprehensive voxel-level optimization, whereas MFO remained the most time-efficient.

The proposed R-MFO method successfully integrates the uniform dose characteristics of SFO with the flexibility of MFO, achieving enhanced robustness compared to MFO and superior plan quality compared to SFO.