Energy layer optimization strategies for intensity-modulated proton therapy of lung cancer patients.

PURPOSE: When treating lung cancer patients with intensity-modulated proton therapy (IMPT), target coverage can only be guaranteed when utilizing motion mitigation. The three motion mitigation techniques, gating, breath-hold, and dose repainting, all benefit from a more rapid application of the treatment plan. A lower limit for the ungated treatment time is defined by the number of energy layers in the IMPT plan. By limiting this number during treatment planning, IMPT could become more viable for lung cancer patients. We investigate to what extend the number of layers can be reduced in single-field optimization (SFO) and multifield optimization (MFO) plans and which implications it has on the plan quality and robustness. METHODS: We have implemented three distinct layer-reducing strategies in the treatment planning system Hyperion; constant energy steps, exponential energy steps, and an adaptive strategy, where the spot weights are exposed to a group sparsity penalty in combination with layer exclusion during optimization. Four levels of increasing layer removal are planned for each strategy. SFO and MFO plans with three treatment fields are created for eleven locally advanced NSCLC patients on the midventilation 4DCT phase to simulate a breath-hold. A minimum dose to the target is ensured for each degree of layer reduction, reflecting the plan quality in the homogeneity index (HI). Plan quality was also assessed by a robustness evaluation, where the patient setup was shifted 2 mm or 4 mm in six directions. RESULTS: The three strategies result in very similar target coverages and robustness levels as a function of removed layers. The HI increases unacceptably for all the SFO plans after 50% layer removal as compared to the reference plan, while all the MFO plans are clinically acceptable with up to a highest removed percentage of 75%. The robustness level is constant as a function of removed layers. The SFO plans are significantly more robust than the MFO plans with all P-values below 0.001 (Wilcoxon signed-rank). The overall mean D98% CTV dose difference is at 2-mm setup error amplitude: 0.7 Gy (SFO) and 1.9 Gy (MFO), and at 4 mm: 3.2 Gy (SFO) and 5.4 Gy (MFO), respectively. CONCLUSIONS: The number of layers in MFO plans can be reduced substantially more than in SFO plans without compromising plan quality. Furthermore, as the robustness is independent of the number of layers, it follows that if the level of robustness is acceptable or enforced via robust optimization, MFO plans could be candidates for treatment time reductions via energy layer reductions.

Surface band-gap narrowing in quantized electron accumulation layers.

An energy gap between the valence and the conduction band is the defining property of a semiconductor, and the gap size plays a crucial role in the design of semiconductor devices. We show that the presence of a two-dimensional electron gas near to the surface of a semiconductor can significantly alter the size of its band gap through many-body effects caused by its high electron density, resulting in a surface band gap that is much smaller than that in the bulk. Apart from reconciling a number of disparate previous experimental findings, the results suggest an entirely new route to spatially inhomogeneous band-gap engineering.