Robust optimization to reduce the impact of biological effect variation from physical uncertainties in intensity-modulated proton therapy

Abstract

12Purpose: Robust optimization (RO) methods are applied to intensity-modulated proton therapy (IMPT) 13 treatment plans to ensure their robustness in the face of treatment delivery uncertainties, such as 14 proton range and patient setup errors. However, the impact of those uncertainties on the biological 15 effect of protons has not been specifically considered. In this study, we added biological effect-based 16 objectives into a conventional RO cost function for IMPT optimization to minimize the variation in 17 biological effect. 18 Methods: One brain tumor case, one prostate tumor case and one head & neck tumor case were 19 selected for this study. Three plans were generated for each case using three different optimization 20 approaches: planning target volume (PTV)-based optimization, conventional RO, and RO incorporating 21 biological effect (BioRO). In BioRO, the variation in biological effect caused by IMPT delivery 22 uncertainties was minimized for voxels in both target volumes and critical structures, in addition to a 23 conventional voxel-based worst-case RO objective function. The biological effect was approximated by 24 the product of dose-averaged linear energy transfer (LET) and physical dose. All plans were normalized 25 to give the same target dose coverage, assuming a constant relative biological effectiveness (RBE) of 1.1. 26 Dose, biological effect, and their uncertainties were evaluated and compared among the three 27 optimization approaches for each patient case. 28Results: Compared with PTV-based plans, RO plans achieved more robust target dose coverage and 29 reduced biological effect hot spots in critical structures near the target. Moreover, with their sustained 30 robust dose distributions, BioRO plans not only reduced variations in biological effect in target and 31 normal tissues but also further reduced biological effect hot spots in critical structures compared with 32 RO plans. 33 Conclusion:Our findings indicate that IMPT could benefit from the use of conventional RO, which would 34 reduce the biological effect in normal tissues and produce more robust dose distributions than those of 35 PTV-based optimization. More importantly, this study provides a proof of concept that incorporating 36 biological effect uncertainty gap into conventional RO would not only control the IMPT plan robustness 37 in terms of physical dose and biological effect but also achieve further reduction of biological effect in 38 normal tissues. 39

Difference in LET‐based biological doses between IMPT optimization techniques: Robust and PTV‐based optimizations

“…3), which indicates that the biological dose derived by the TPS is closer to the “true” biological dose, and thus is more reliable in robust plans than in PTV‐based plans. A similar trend was observed in the biological surrogate according to the study conducted by X. Bai et al With this, the authors carried out further analysis of the correlation between the difference of among the optimization techniques and the CTV‐to‐OAR distance, which showed a large value when the OAR was closer to the CTV.…”

“…Thus far, a good number of research works have conducted a comparative study of biological surrogate and LET distributions among different optimization techniques. If the optimization techniques are confined to only those available in commercial TPS, then the recent study by X. Bai et al shows that robust optimization can reduce both the biological surrogate and the LET at OARs, causing less biological damage to the OARs than PTV‐based plans because the former tends to use lateral fall‐off to spare the OARs rather than the distal edge . D. Giantsoudi et al demonstrated a series of Pareto‐optimal IMPT base plans showing substantial LET variations, which leads to potentially considerable differences in RBE‐weighted doses in terms of multicriteria optimization .…”

Impact of range uncertainty on clinical distributions of linear energy transfer and biological effectiveness in proton therapy

“…35 LET d distributions differ between those two treatment planning approaches. 20 However, the optimization strategy in this study, using either SFO or MFO, had neither a relevant impact on absolute LET d values in OARs and CTVs nor on their sensitivity to range uncertainties when applying robust dose optimization. LET d distributions in the target volumes of all entities were rather homogeneous, comparable in LET d magnitude, and essentially insensitive against the uncertainty in range prediction.…”

“…This includes the use of robust dose optimization, 19 which results in LET d distributions differing from those based on the traditional concept using a planning target volume. 20 Furthermore, a comprehensive LET d quantification with uncertainty estimates for relevant patient cases is vital before explicitly including the LET d in future clinical proton treatment planning. Biological dose distributions in organs at risk (OARs) estimated by RBE models based on in vitro data need to be complemented with clinically derived models for normal tissue complication probability (NTCP) and their uncertainties to facilitate the translation of improved biological dose concepts.…”

A biological effect‐guided optimization approach using beam distal‐edge avoidance for intensity‐modulated proton therapy

“…Inaniwa et al 19 minimized the physical dose and LET d based on prescribed values in a quadratic cost function, while Cao et al 20 added two terms for maximizing LET-weighted dose in the target and minimizing it in OARs without considering any prescription. To deal with plan robustness under proton range and patient setup uncertainties, An et al 21 minimized the highest LET in OARs while maintaining the same dose coverage and robustness in tumor targets as the conventional robust IMPT treatment plan model, while Bai et al 22 penalized the sum of the differences between the highest and lowest biological effect in each voxel, approximated by the product of dose and LET, to achieve robust biological effect and physical dose distributions in both target and critical structures. However, these approaches typically used optimization priorities to control the trade-off dynamic between dose and LET criteria.…”