Proton ARC based LATTICE radiation therapy: feasibility study, energy layer optimization and LET optimization

<i>Objective.</i>LATTICE, a spatially fractionated radiation therapy (SFRT) modality, is a 3D generalization of GRID and delivers highly modulated peak-valley spatial dose distribution to tumor targets, characterized by peak-to-valley dose ratio (PVDR). Proton LATTICE is highly desirable, because of the potential synergy of the benefit from protons compared to photons, and the benefit from LATTICE compared to GRID. Proton LATTICE using standard proton RT via intensity modulated proton therapy (IMPT) (with a few beam angles) can be problematic with poor target dose coverage and high dose spill to organs-at-risk (OAR). This work will develop novel proton LATTICE method via proton ARC (with many beam angles) to overcome these challenges in target coverage and OAR sparing, with optimized delivery efficiency via energy layer optimization and optimized biological dose distribution via linear energy transfer (LET) optimization, to enable the clinical use of proton LATTICE.<i>Approach.</i>ARC based proton LATTICE is formulated and solved with energy layer optimization, during which plan quality and delivery efficiency are jointly optimized. In particular, the number of energy jumps (NEJ) is explicitly modelled and minimized during plan optimization for improving delivery efficiency, while target dose conformality and OAR dose objectives are optimized. The plan deliverability is ensured by considering the minimum-monitor-unit (MMU) constraint, and the plan robustness is accounted for using robust optimization. The biological dose is optimized via LET optimization. The optimization solution algorithm utilizes iterative convex relaxation method to handle the dose-volume constraint and the MMU constraint, with spot-weight optimization subproblems solved by proximal descent method.<i>Main results.</i>ARC based proton LATTCE substantially improved plan quality from IMPT based proton LATTICE, such as (1) improved conformity index (CI) from 0.47 to 0.81 for the valley target dose and from 0.62 to 0.97 for the peak target dose, (2) reduced esophagus dose from 0.68 Gy to 0.44 Gy (a 12% reduction with respect to 2 Gy valley prescription dose) and (3) improved PVDR from 4.15 to 4.28 in the lung case. Moreover, energy layer optimization improved plan delivery efficiency for ARC based proton LATTICE, such as (1) reduced NEJ from 71 to 56 and (2) reduction of energy layer switching time by 65% and plan delivery time by 52% in the lung case. The biological target and OAR dose distributions were further enhanced via LET optimization. On the other hand, proton ARC LATTCE also substantially improved plan quality from VMAT LATTICE, such as (1) improved CI from 0.45 to 0.81 for the valley target dose and from 0.63 to 0.97 for the peak target dose, (2) reduced esophagus dose from 0.59 Gy to 0.38 Gy (a 10.5% reduction with respect to 2 Gy valley prescription dose) and (3) improved PVDR from 3.88 to 4.28 in the lung case.<i>Significance.</i>The feasibility of high-plan-quality proton LATTICE is demonstrated via proton ARC with substantially improved target dose coverage and OAR sparing compared to IMPT, while the plan delivery efficiency for ARC based proton LATTICE can be optimized using energy layer optimization.