Impact of LET-modifying planning objectives on the optimization of mixed-modality proton-photon treatments

The linear energy transfer (LET) correlates with the relative biological effectiveness (RBE); thus, the increase of LET in depth in proton therapy leads to elevated RBE and a higher risk of toxicity in healthy tissue beyond the target. Jointly optimized combined proton-photon treatments may serve as a means to redistribute LET and avoid high-LET regions in organs at risk (OARs).

To mitigate LET-related toxicity in OARs, this work leverages combined treatments by direct integration of LET in the joint optimization process. To this end, LET-modifying objective functions and variable RBE models are used within a joint optimization framework for combined proton-photon treatments. This approach combines the properties of both modalities to achieve LET-shaping and satisfy biological dose objectives in the target and OAR.

LET-modifying objective (LMO) functions based on the dose-weighted LET (LETxDose) and on dirty dose-defined as high-LET dose above a defined LET-threshold- were integrated into joint optimization within the open source toolkit matRad (v2.10.1). Treatment plans with phantom and clinical test cases were optimized and evaluated, consistently using the same dose objectives in each plan. The compared plans use the following: (1) constant RBE model, (2) variable RBE models, (3) dirty dose objectives, (4) LETxDose (LxD) objectives. Furthermore, sensitivity analysis was performed for various penalty weights, different proton beam angles and $\alpha$ - $\beta$ ratios. The plans were assessed for target coverage, dose conformity, and LET reduction in OARs, combining five proton fractions with 25 photon fractions.

LET-modifying objectives enabled localized reduction of high-LET exposition in OARs by redistributing dose contributions of both modalities. Protons provided superior tumor-targeted dose delivery and reduced integral dose, while photons mitigated high-LET at the distal edge without compromising dose conformity in the tumor. Beam alignment had a greater influence on enhancing the LMO effect than the number of proton beams. The dirty dose to $2\%$ of brain stem volume was reduced when using joint LET optimization approaches. LET-modifying squared underdosing objectives increased the dirty dose in the GTV by up to $102\%$ compared with the reference joint plan, whereas squared overdosing objectives reduced the dirty dose in the brain stem by $96\%$ . Their combination achieved a $94\%$ increase of dirty dose in the GTV with a corresponding reduction in the brain stem. Despite $2\mathrm{Gy}$ per fraction, the proton-only plan resulted with a $7.5$ times higher dirty dose per fraction in a joint optimized plan using dirty dose objectives, approximately $5\mathrm{Gy}$ locally per fraction. Using LETxDose objectives, it was $3.3$ times higher. Dirty dose objectives provided more explicit LET control than LETxDose, with minimal compromise in target coverage.

Integrating LET-based objectives into a jointly optimized proton-photon system allows for direct steering of the combined LET, improving dose conformity and reducing high-LET exposure in critical regions. This approach leverages modality-specific strengths and offers a practical route toward LET-optimized multimodality radiotherapy for safer, more effective treatments.