Impact of dose calculation accuracy on inverse linear energy transfer optimization for intensity‐modulated proton therapy

To determine the effect of dose calculation accuracy on inverse linear energy transfer (LET) optimization for intensity‐modulated proton therapy, and to determine whether adding more beams would improve the plan robustness to different dose calculation engines.


INTRODUCTION
As recommended by the International Commission on Radiation Units and Measurements, in clinical practice, proton therapy used a constant relative biological effectiveness (RBE) of 1.1, which assumes proton therapy is 10% more biologically effective than photon therapy. 1 However, experimental studies have shown that proton RBE value varies with physical and radiobiological parameters, such as linear energy transfer (LET), dose per fraction, the α/β ratio of the tissues, and the biological endpoint. [2][3][4] The use of biological optimization accounting for the variable RBE might have the potential to fully exploit the biological advantages of protons and improve the therapeutic index of proton therapy.
Owing to uncertainties in the radiobiological parameters and the discrepancy among different RBE calculation models, researchers proposed to optimize LET instead of the variable RBE-weighted dose based on the fact that RBE increases with LET. [5][6][7][8][9][10][11] The physical quantity of the averaged LET from the primary protons can be accurately predicted by Monte Carlo (MC) simulation or analytical modeling, [12][13][14][15][16][17] and modulated through planning in multi-field optimization intensitymodulated proton therapy (IMPT). Studies have shown that LET painting is an effective approach to boost the biological effects within the target and to overcome hypoxia, leading to increased tumor control probability. [18][19][20][21][22] The rule of thumb in LET painting is to bring the elevated LET around the Bragg peak region into the target. This planning technique is transitioning from forward optimization 21 to inverse optimization 10 based on the dose and LET distributions generated from MC simulations.
The validated MC algorithm is generally considered as the most accurate method in dose calculation, and has been introduced to commercial treatment planning systems (TPSs). 23,24 However, in clinical practice, the analytical pencil beam (PB) algorithm is commonly used in IMPT dose calculation because of its comparable accuracy and fast calculation speed. Recent studies have used MC calculations to examine the accuracy of PB algorithms for IMPT. [24][25][26] In the studies of clinical patient cases, dosimetric indices of the target agreed within 4% between PB and MC algorithms, 25,26 and a high discrepancy in dose was rarely reported.
Adding LET modulation to the conventional dose modulation could make the multi-field optimization IMPT plan optimization more com-

Dose calculation engine
The Eclipse TPS has been commissioned for clinical use at our institution, and the proton PB convolution superposition algorithm is used to calculate the dose distribution. 29 Figure 1 shows the workflow of creating and re-calculating the DoseOpt and LETOpt plans. In the first step, we created four plans with two, four, six, and nine coplanar beam angles in Eclipse, setting the STV as the beam-specific target for each beam (Table 1). An arrangement of  Table S1).

RESULTS
With regard to the dose distribution, the variation of MC-calculated  However, pronounced dose differences between algorithms were observed in the LETOpt plans. For target coverage, PB calculations compared with MC calculations showed degradation in the D98 of CTV at 11.1 ± 3.4%, 5.1 ± 2.6%, 4.2 ± 1.5%, and 6.7 ± 1.8% for the two-field, four-field, six-field, and nine-field plans, respectively. The D2 of CTV calculated by the PB algorithm was underestimated, relative to that of the MC algorithm, by 3.7 ± 1.7% for the two-field plan, but was severely overestimated by 10.6 ± 6.0%, 12.7 ± 8.3% and 15.9 ± 9.0% for the other three plans. The dose difference between the PB and MC calculations of D1cc of the rectum was as large as 7.5 ± 3.3% (6.0 ± 2.7 Gy [RBE]) in the nine-field plan. The maximum deviation in the D1cc of the bladder 13.9 ± 8.2% (11.4 ± 6.7 Gy [RBE]) was also found in the nine-field plan.

DISCUSSION
The current study sought to verify the dose calculation accuracy of LET-optimized IMPT. We focused on a type of LET manipulation known as the LET painting technique, whose priority is to deliver high LET  Abbreviations: CTV, clinical target volume; D1cc, maximum dose to 1 cc of the volume; D2, dose covering 2% of the volume; D98, dose covering 98% of the volume; Dmean, mean dose; PB, pencil beam; MC, Monte Carlo; RBE, relative biological effectiveness; Vp, coverage of the volume by the prescribed dose;. *Δ is the percentage difference in the dose indices between the PB-computed and MC-computed linear energy transfer-optimized plans.
DoseOpt plans were 2.6%, 1.3%, and 2.1 Gy (RBE), respectively. This significant dose discrepancy between two dose calculation engines for a relatively homogeneous treatment site warrants the careful use of LET-optimized IMPT plans with a high degree of intensity modulation.
For the DoseOpt plans, PB calculations agreed well with MC calculations, which was consistent with previous studies. 25,26 By using CTV-based robust optimization, 37,41 the optimizer tended to limit the dose coverage of the beam that was more sensitive to uncertainties than other beams were and to avoid a sharp dose gradient in the target region. Thus, the dose distribution in the target of each beam was globally uniform along the beam direction ( Figure 4A) and regionally uniform in the transverse direction ( Figure 3 in Reference 41 ). The difference between the PB and MC algorithms in the flat dose region was minimal ( Figure 4A), whereas a distinct difference has been observed in the distal fall-off region. 42 In our DoseOpt plans, the difference in the distal region between the two algorithms was spread out as the beams stop at the periphery of the target. As such, we did not observe a great discrepancy in the dosimetric indices of the target and OARs.
In contrast, the LETOpt plans manifested dose differences between the two algorithms due to the distal field patching and the less uni- The results for the four-field LETOpt plan (Figures 2 and 3, and Table 4) indicated that PB underestimated the dose for the two contralateral beams, but overestimated the dose for the oblique beams, and the overestimation outperformed the underestimation. With regard to the OAR protection, the LETOpt treatment planning compared with the DoseOpt planning also increased the difference between the two algorithms in the dose to rectum and bladder.
In addition to the plan robustness against different dose calculation engines, the robustness of the LETOpt plans against the setup and range uncertainties was also a clinical concern. We evaluated the robustness of the conventional and LET-optimized plans, in which eight perturbation scenarios were taken into account. As it is shown in Figure   S1, CTV in the LET-optimized two-field plan was not robust to range uncertainty as that was in the conventional plan. Bai et al. 44  Although the issues raised in the present study are specific to the current framework in the clinics, and although the dose uncertainties could be reduced with fast MC-based inverse treatment planning and final dose calculation in the future, the sensitivity of LET modulation to dose calculation errors persists, and the quality assurance for LEToptimized IMPT plans is warranted.

CONCLUSION
In conclusion, high modulation of LET requires high calculation accuracy of physical quantities in inverse treatment planning for IMPT.
Slight differences in the distal fall-off modeling could cause significant dose error under the circumstance of distal field patching, and the dose error could not be washed out by adding more beams. MC or improved PB algorithms are preferable, and the same dose calculation engine is recommended to be used in both the LET optimization and the final dose calculation.