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The current knowledge on biological effects associated with proton therapy is limited. Therefore, we investigated the distributions of dose, dose-averaged linear energy transfer (LETd), and the product between dose and LETd (DLETd) for a patient cohort treated with proton therapy. Different treatment planning system features and visualization tools were explored.
Methods and Materials
For a cohort of 24 patients with brain tumors, the LETd, DLETd, and dose was calculated for a fixed relative biological effectiveness value and 2 variable models: plan-based and phenomenological. Dose threshold levels of 0, 5, and 20 Gy were imposed for LETd visualization. The relationship between physical dose and LETd and the frequency of LETd hotspots were investigated.
Results
The phenomenological relative biological effectiveness model presented consistently higher dose values. For lower dose thresholds, the LETd distribution was steered toward higher values related to low treatment doses. Differences up to 26.0% were found according to the threshold. Maximum LETd values were identified in the brain, periventricular space, and ventricles. An inverse relationship between LETd and dose was observed. Frequency information to the domain of dose and LETd allowed for the identification of clusters, which steer the mean LETd values, and the identification of higher, but sparse, LETd values.
Conclusions
Identifying, quantifying, and recording LET distributions in a standardized fashion is necessary, because concern exists over a link between toxicity and LET hotspots. Visualizing DLETd or dose × LETd during treatment planning could allow for clinicians to make informed decisions.
Introduction
The decreased integral dose of ion therapy with respect to photon therapy, combined with recent technological advances, contributed to the significant growth of particle treatments in the last decades. Physically, the finite range of protons and the Bragg peak, with a sharp dose falloff after the target volume, enables better organ-at-risk (OAR) sparing and conformal dose around the target. Biologically, protons cause cellular damage more effectively than photons. Therefore, a conversion factor, relative biological effectiveness (RBE), is used for treatment and comparison between modalities.
However, biological effects of proton therapy (PT), in particular those associated with RBE, are less understood than those of photons, triggering discussions on its intrinsic uncertainty.
For the clinical energy range, RBE and linear energy transfer (LET), a nonstochastic quantity used to characterize the quality of a beam, present a monotonic correlation, which increases toward the distal edge of the Bragg peak, reaching a maximum at the falloff region. As energy decreases, energy deposition occurs more densely around the protons’ tracks, which causes more confined and complex damage.
Relative biological effectiveness variation along monoenergetic and modulated Bragg peaks of a 62-MeV therapeutic proton beam: A preclinical assessment.
Although a constant average value allows for ubiquitous treatment standardization and disregards RBE uncertainties, neglecting RBE variation might lead to the underestimation of normal tissue complication probability, because highly modulated fields may result in inhomogeneous LET distributions.
How can scanned proton beam treatment planning for low-grade glioma cope with increased distal RBE and locally increased radiosensitivity for late MR-detected brain lesions?.
Late contrast enhancing brain lesions in proton-treated patients with low-grade glioma: Clinical evidence for increased periventricular sensitivity and variable RBE.
Correlation of LET with MRI changes in brain and potential implications for normal tissue complication probability for patients with meningioma treated with pencil beam scanning proton therapy.
LET is defined at a point and describes the average energy transfer from electronic interactions per unit length traveled by charged primary particles.
Dose-averaged LET (LETd) is a frequently used quantity that considers the stopping power of each individual particle, weighted by its contribution to the local dose.
Mixed effect modeling of dose and linear energy transfer correlations with brain image changes after intensity modulated proton therapy for skull base head and neck cancer.
Relative biological effectiveness (RBE) values for proton beam therapy. Variations as a function of biological endpoint, dose, and linear energy transfer.
To avoid RBE uncertainty while reducing biological variability in treatment planning, metrics based on computable physical parameters (eg, dose and LET-RBE dependence [as a proxy for response]) have been suggested (eg, product between dose and LETd [DLETd]).
In this retrospective study, we investigated the distributions of LETd, dose (with different RBE models) and DLETd in a cohort of patients with brain tumors treated between 2019 and 2020 at our institute. Distributions were quantified and analyzed focusing on hotspots adjacent to the clinical target volumes (CTVs) and inside the OARs. The Monte Carlo (MC) engine from our treatment planning system (TPS) was used for all calculations. Although common practice, judging a physical dose is less intuitive for LETd distributions. The lack of knowledge and experience with this quantity (and its units) pose an additional challenge. To interpret these results, we propose various visualization tools to improve the perception and acquaintance regarding the relationship between treatment planning dose and LETd distribution.
Methods and Materials
Cohort of neurologic patients
A cohort of 24 patients with brain tumors who received PT between September 2019 and July 2020 was selected for this study. Institutional review board approval (W-210700059) was obtained for this retrospective analysis. Table 1 presents the characteristics of the cohort and treatment planning parameters.
Table 1Cohort description, including number of patients, treatment parameters, tumor type, and location
Patients
Treatment
Total number
24
Prescription
Dose, Gy
Fractions
Incidence
50.4
28
75.0%
Female
54.2%
54
30
4.2%
Male
45.8%
59.4
33
20.8%
Average age and range, y
44.5 (24-61)
Number of beams
3
75.0%
Pathology
95.8%
4
25.0%
Chemotherapy
75.0%
Dose per fraction, Gy
1.8
Treatment time, d
40.8 (37-50)
Distal layers for Monte Carlo optimization
3
Tumor
Central nervous system WHO grade
Location
Frontal
62.5%
Type
Oligodendroglioma
37.5%
II (67%), III (33%)
Parietal
12.5%
Astrocytoma
37.5%
II (100%)
Temporal
12.5%
Craniopharyngioma
4.2%
II (100%)
Overlapping
12.5%
Meningioma
20.8%
I (20%), II (20%)
Laterality
Right
50.0%
60%: no pathology available
Left
45.8%
Midline
4.2%
WHO Eastern Cooperative Oncology Group performance status
During radiation therapy
0
1
2
After radiation therapy
0
1
2
27.4%
64.0%
8.6%
30.0%
64.0%
6.0%
Abbreviation: WHO = World Health Organization.
Values were calculated considering the entire study population. The performance status grades from the WHO Eastern Cooperative Oncology Group correspond to (0) fully active, normal; (1) symptomatic and ambulatory, cares for self; and (2) ambulatory >50% of the time; occasional assistance needed.
The MC algorithm of RayStation (RaySearch, Sweden) was used for dose calculations with uncertainty set to 1%. All plans were robustly optimized (voxel-wise-minimum-maximum)
with range uncertainty set to 3% and universal uncertainty to 1 mm. The TPS optimization for our Mevion S250i Hyperscan PT system (Mevion, Littleton, MA) allows for a number of proximal and distal energy layers to be set. CTV coverage was evaluated on the voxel-wise-minimum and -maximum doses to OAR and on the voxel-wise-maximum and mean doses on the nominal plan, considering constraints according to Lambrecht et al.
Target volumes were delineated by experienced radiation oncologists according to national guidelines and OARs according to the European Particle Therapy Network neurocontouring atlas.
The periventricular space (PVS) and brain ventricles were also included in this analysis, although not yet contoured at our clinical practice. Besides the CTV, a selection of critical OARs for dosimetric analysis included the brain, brain stem, chiasm, pituitary, left and right (LR) optic nerve, LR cochlea, LR cornea, LR hippocampus, LR lacrimal gland, LR lens, and LR retina. The OAR contours, dose, RBE, and LET distributions were extracted from the TPS for further statistical analysis.
LET and RBE calculations
LETd, DLETd, and RBE were calculated using the Raystation-9AR-IONPG-Research with the MC engine commissioned for our Mevion system and in-house developed scripts. LETd, the unrestricted mass stopping power scored in the medium and normalized to unity density, was calculated according to:
(1)
where is the unrestricted electronic stopping power, the dose of the ion type , the kinetic energy of the ion, the position of the ion, and the ion type. LETd was computed for primary and secondary protons with its maximum displayed value set to 50 keV/µm. LETd was calculated for all dose levels within the voxelized geometry and, because high LETd at low planning doses is not clinically relevant, 3 dose threshold levels were defined at 0, 5, and 20 Gy. Here, LETd was calculated for the voxels with a dose value above the threshold, otherwise LETd was set to 0. DLETd was computed through the voxel-wise product between the planning dose and LETd distribution through scripting within the TPS.
For the RBE calculation, 2 models were investigated (Unkelbach [UNK]
), with the set to 2 Gy and fixed to all voxels. Although UNK is a dose-scaling, nontissue, dependent model, MCN is a phenomenological model that considers all published RBE experimental measurements up to 2014.
Visualizing distributions
For each patient, the 3-dimensional distributions of physical dose with RBE of 1.1 (RBE1.1), UNK and MCN RBE maps and weighted dose, LETd (dose threshold of 0, 5, and 20 Gy), and DLETd were generated. The distributions were displayed as auxiliary doses or additional plans within the TPS and further exported and processed through scripting. To visualize and compare distributions of similar quantities, raincloud plots were chosen to provide a transparent visualization of raw distributions combined with probability density and statistics.
Bivariate histograms were used to map the relationship between physical dose and LETd and to highlight the frequency of the hotspots.
Results
RBE, LETd, and DLETd were calculated for all patients considered in the cohort.
RBE models
Considering the entire population, MCN presented the highest dose values for OARs, followed by UNK and RBE1.1 (Fig. 1). For small structures (eg, chiasm and pituitary gland), an average increase of 19.3% and 25.5% for MCN and 5.2% and 7.3% for UNK, respectively, was identified with respect to RBE1.1. For larger structures and the CTV, the difference was less pronounced (eg, brain and PVS: 2.9% and 18.3% for MCN, and 1.0% and 4.8% for UNK, respectively). The mean RBE1.1, MCN, and UNK CTV doses were 52.1 Gy (±2.5; range, 41.8-63.5), 52.1 Gy (±2.7; range, 42.4-67.6), and 57.2 Gy (±3.1; range, 46.5-75.7), respectively.
Figure 1Relative biological effectiveness (RBE) dose distributions for a selection of organs at risk, calculated using the constant clinical factor of 1.1 (red), McNamara's model (green; α/β of 2 Gy), and Unkelbach's model (blue). Both histograms and bars present the frequency distribution (differential dose and number of voxels per unit of RBE dose). The boxplots show the interquartile range, median, and outliers.
The choice of a clinically meaningful dose threshold caused a substantial effect on the LETd results. The avoidance of voxels with lower doses greatly affected the LETd distribution in OARs. When no dose limit was imposed, the distribution was steered toward higher LETd values, which arose from very low treatment doses (red plots [LET0] of Fig. 2). LET5 and LET20 showed that the threshold magnitude affects the mean LET values. Differences were found up to 26.0% (for the retina).
Figure 2Dose-averaged linear energy transfer (LETd) distributions for a selection of organs at risk, calculated using dose thresholds of 0 Gy (red), 5 Gy (blue), and 20 Gy (green). Both histograms and bars present the frequency distribution, or the number of voxels per unit of LETd value. The boxplots show the interquartile range, median, and outliers according to the individual distribution.
Although the largest average values were found for the chiasm (LET20: 3.1 ± 1.8 keV/µm; LET5: 3.5 ± 1.8 keV/µm; LET0: 4.4 ± 2.1 keV/µm) and pituitary (LET20: 3.0 ± 2.2 keV/µm; LET5: 4.0 ± 2.0 keV/µm; LET0: 4.8 ± 1.7 keV/µm), the maximum LETd values were identified in the brain, PVS, and ventricles (LET20: 8.6 ± 1.0 keV/µm; LET5: 10.5 ± 1.5 keV/µm). For LET0, the maximum values coincided with the maximum displayed setting of 50 keV/µm for most structures.
Besides the skin, brain, CTV, PVS, and ventricles, when a dose threshold was imposed, most patients exhibited 0 LET distributions for all other structures (eg, for left lacrimal gland, retina, and cochlea). Only 2 patients presented LET distributions >0, and the entire cohort presented a 0 LET distribution for the spinal cord, lenses, and corneas. When considering all OARs, a mean organ-wise LETd of 0.8 keV/µm (±0.9; range, 0.0-3.1 keV/µm), 1.26 keV/µm (±1.11; range, 0.0-4.0 keV/µm), and 4.12 keV/µm (±0.72; range, 2.9-5.6 keV/µm) was found for the highest to lowest dose threshold and a consistent value of 2.51 keV/µm (±0.4; range, 1.2-6.0 keV/µm) for the CTV, independent of the threshold.
Dose-LETd relationships
Different dose cutoffs affected DLETd distributions to a lesser extent, because this quantity prevents high LET spikes in low-dose regions (Fig. 3). When considering DLETd values >0 (Fig. 3), for the 20 Gy threshold, mean DLETd results ranged from 74 Gy·keV/µm (±27; range, 32-143 Gy·keV/µm) to 174 Gy·keV/µm (±28; range, 69-267 Gy·keV/µm) for the right lacrimal gland and brain stem, respectively. The maximum values were found in the PVS, ventricles, brain, skin, and CTV (306 ± 28 to 354 ± 45 Gy·keV/µm).
Figure 3Product between dose and dose-averaged linear energy transfer (DLETd) distributions for a selection of organs at risk, calculated using 0 Gy (red), 5 Gy (blue), and 20 Gy (green) relative biological effectiveness dose threshold. Both histograms and bars present the frequency distribution, or the number of voxels per unit of DLETd value. The boxplots show the interquartile range, median, and outliers according to the individual distribution.
Throughout the population, an inverse relationship between LETd and dose was observed. For some structures (eg, chiasm and pituitary), this relationship was more evident (Fig. 4). These structures abut the CTV and several distal layers are used for treatment optimization; thus, higher LETd regions may arise beyond the OARs in regions not considered during optimization, such as the PVS.
Figure 4(A) Example patient with planning dose, dose-averaged linear energy transfer (LETd), and product between dose and dose-averaged linear energy transfer (DLETd) distributions with the optic chiasm contoured in yellow. (B) Distribution of dose and LETd values for the chiasm (orange) and pituitary (blue) for all patients (N = 24) in the study. (C, D) Relationship between mean values of dose, LETd, and DLETd (for dose threshold of 20 Gy) for the chiasm and pituitary gland. Dose, LETd, and DLETd are represented by the blue, red, and green axes, respectively.
Figure 4B presents an overview of the relationship between LETd and dose. Additional frequency information was visualized using the dose and LETd, on a structure (Fig. 5) or patient (Fig. 6) basis. Such enhanced visualization allows for the identification and interpretation of clusters, which steer the mean LETd values and identification of the higher, but sparse, LETd values. For this cohort (Fig. 5), LETd values exceeding 6 keV/µm were only present for half of the investigated OARs and always <5% of the structure's voxels (1.2% on average). Although the pituitary presented 4.2% of its voxels >6 keV/µm (mean, 6.3 ± 0.2; range, 6.0-6.9 keV/µm, corresponding to a mean dose of 27.2 ± 3.5 keV/µm), the PVS and brain presented with 0.7% (mean, 6.5 ± 0.5, 6.0-8.6; mean dose, 29.2 ± 5.3 keV/µm) and 0.2% (mean, 6.5 ± 0.4, 6.0-8.6; mean dose, 28.4 ± 5.1 keV/µm), respectively.
Figure 5Dose and dose-averaged linear energy transfer (LETd) histograms of a selection of investigated structures for a single patient. Dose and LETd values are represented on the x- and y-axes, respectively, for each subplot. Next to each structure name, the percentage of voxels >0 is indicated, as used for the graph. The color bar on the right indicates the frequency in the same scale for all plots.
Figure 6(A) Clinical target volume (CTV; gray color map) and periventricular space (PVS; multiple colors) dose-averaged linear energy transfer (LETd) distribution spatial representation. (B) Dose–LETd histograms of the PVS for different patients. Dose and LETd values are represented on the x- and y-axes, respectively, for each subplot. The color bar on the right indicates the frequency in the same scale for all plots.
As a patient-based approach, planning quality for individual anatomies promoted an organ-based visualization of LET gradients (Fig. 6). Similar histograms associated with each OAR (eg, PVS) promoted the identification of variation within the cohort and the identification of outliers and higher LETd distributions.
Discussion
An approach was presented for visualization and explorative investigations of RBE-weighted doses, LETd, and DLETd for multiple OARs of patients with tumors in different regions of the brain. For the considered RBE models, MCN values were consistently higher than UNK, which has been shown in other studies.
For brain structures associated with cognition, the average RBE values of 1.54 (0.13) and 1.09 (0.02) found for MCN and UNK, respectively, agree with the reported values of 1.21 and 1.09.
Although UNK performs LET optimization based on objective functions evaluated for DLETd (scaled down by a factor and considered as a measure of the additional biological dose caused by high LET), MCN is a variable phenomenological model.
For simplicity and consistency (α/β) was defined as 2 Gy. This assumption possibly affected the MCN results, which predict the highest RBE for low (α/β) values. Moreover, brain tumors likely have high (α/β) values,
predict large RBE differences when the difference in (α/β) is large between adjacent structures. A recent review reported target values between 3.1 and 12.5 Gy for glioma and 3.3 and 3.8 Gy for meningioma, as well as for OAR endpoints between 2 and 3 for chiasm (loss of vision), optic nerve (neuropathy), and brain (necrosis).
Besides the investigated models, many others exist with various levels of complexity, regression techniques, and experimental data sets. However, the correlation between RBE variation and outcome data are still impaired by a lack of current in vivo data with up-to-date fractionation schedules, modulation techniques, and evidence from randomized clinical trials.
Relative biological effectiveness (RBE) values for proton beam therapy. Variations as a function of biological endpoint, dose, and linear energy transfer.
Moreover, RBE is intrinsically a quantity conceived for comparing radiation qualities. Thus, the conservative clinical recommendation of using the 1.1 constant factor still simplifies clinical routine, ensures tumor control, and promotes clinical consistency and shared experience across the PT field.
How can scanned proton beam treatment planning for low-grade glioma cope with increased distal RBE and locally increased radiosensitivity for late MR-detected brain lesions?.
A thorough RBE review presented average values of 1.1, 1.15, 1.35, and 1.7 at the entrance, center, distal edge, and distal falloff of the spread-out Bragg peak, respectively.
Relative biological effectiveness (RBE) values for proton beam therapy. Variations as a function of biological endpoint, dose, and linear energy transfer.
This consideration is relevant for neurologic cases, because increased tissue homogeneity, positioning accuracy, less range straggling, and shallower tumors promote sharper dose distributions; thus, OARs close to the target could be affected.
A preliminary analysis showed that the majority of patients presented herein reported little or no acute toxicity and normal performance during and up to 2 years after treatment. However, 2 years could be too early to detect any observable toxicities. Although PT radiation-induced brain lesions have been associated with increased RBE and LET values,
Further outcome investigations (eg, periodic functional imaging to track changes in brain anatomy), along with cognitive tests for protons, photons, and correlation with LETd distributions for large patient cohorts selected with specific criteria could improve the current knowledge. However, a full analysis of the current visualization techniques related to treatment side effects is outside of the scope of the current study and subject to further analysis.
Additionally, there is a lack of consensus or guidelines on what configures LET hotspots. LET values of typical beam arrangements have been reported of approximately 2 to 4 keV/µm in the center of the beam, from the proximal to distal target regions, and >10 keV/µm at the distal falloff.
Relative biological effectiveness (RBE) values for proton beam therapy. Variations as a function of biological endpoint, dose, and linear energy transfer.
However, intensity modulated PT delivers highly inhomogeneous dose distributions outside of the target volume, and dose–response data has been reported for a broad range of LET values, which may not consider dose threshold and incorporate low-energy protons with increased LET.
Relative biological effectiveness (RBE) values for proton beam therapy. Variations as a function of biological endpoint, dose, and linear energy transfer.
Introducing proton track-end objectives in intensity modulated proton therapy optimization to reduce linear energy transfer and relative biological effectiveness in critical structures.
to the best of our knowledge, no agreement exists on cutoff doses below which no LET should be evaluated. MC methods unavoidably result in a number of voxels with few interactions and high statistical uncertainty. The choice of a 0-Gy threshold exemplifies this effect in low-dose and out-of-field regions. In this study, different thresholds were evaluated (Fig. 2) and, considering prescription dose and OAR constraints, the highest threshold (20 Gy) is likely to be more clinically relevant. Individual OAR radiosensitivity could also be considered to specify a constraint, because 20 Gy can be prohibiting for some OARs (eg, eye lenses). On the other hand, as we also consider stochastic nature radiation effects and a general unfamiliarity with underlying causes of late effects, a threshold becomes relevant for instant visualization, but full data should be preserved for future outcome analyses.
The chiasm (3.1 ± 1.8 keV/µm) and pituitary (3.0 ± 2.2 keV/µm) presented the largest averaged LETd values. For these and other small structures (eg, optic nerve and cochlea), decreasing LETd values with increasing dose were observed. Due to the limitations of this study (eg, cohort size and heterogeneous tumor sites and beam orientations), different OARs, and especially the smaller ones, received little or no dose. This aspect was considered in the statistical analysis but does not explain the larger differences found for smaller structures compared with the larger structures. Multiple distal layers are used during treatment optimization; thus, high LET values possibly fall beyond critical structures when they adjoin the CTV. These regions likely coincide with the ventricles and PVS, for which no clinical dose constraints are considered during optimization and where the maximum global LETd values were identified (8.6 ± 1.0 keV/µm).
Different studies have associated late radiation-induced brain lesions in regions of increased LETd, RBE, and radiosensitivity at the PVS.
How can scanned proton beam treatment planning for low-grade glioma cope with increased distal RBE and locally increased radiosensitivity for late MR-detected brain lesions?.
Late contrast enhancing brain lesions in proton-treated patients with low-grade glioma: Clinical evidence for increased periventricular sensitivity and variable RBE.
Our study also highlights this structure, considering that treatment planning strategies to neutralize increased RBE (or LET) focus on placing the distal edge outside OARs, which coincide with the periventricular region. A recent survey showed that, even though all European PT centers use a constant RBE factor of 1.1, they also apply measures to counteract variable RBE effects (ie, avoid beams stopping inside or in front of an OAR)
Considering the uncertainties on RBE models and the difficult interpretation of LET alone, the LET–RBE dependence has been used as a proxy for biological response (eg, in the product between dose and LET).
How can scanned proton beam treatment planning for low-grade glioma cope with increased distal RBE and locally increased radiosensitivity for late MR-detected brain lesions?.
Logically, a dose cutoff is not so relevant when the product itself attends the effect of LET spikes in low-dose regions. To avoid LET overestimation, McMahon et al. added a factor to LET-weighted doses, which performed well compared with several RBE models.
Although a thorough analysis might still be necessary, this factor represents a simple approach to readily identify high LET without the influence of low-dose values. Additional tools to promote a better visualization of the relationship between LET and dose are also helpful to estimate its magnitude, identify hotspots, and compare and characterize treatment planning quality considering inter- and intrapatient LET distributions.
The heat maps presented in this study show a low frequency of higher LET values in regions restricted to lower doses below known tolerances. This effect should become less pronounced when different treatment uncertainties are also considered, such as range straggling, imaging uncertainty, and treatment variation in anatomy, positioning, motion, setup, dose distribution, and tissue heterogeneity.
Nevertheless, LET-guided robust optimization is a growing field that focuses on maximizing LET to the target while minimizing LET in OARs, minimally affecting the clinical goals of the treatment plan.
Late contrast enhancing brain lesions in proton-treated patients with low-grade glioma: Clinical evidence for increased periventricular sensitivity and variable RBE.
Introducing proton track-end objectives in intensity modulated proton therapy optimization to reduce linear energy transfer and relative biological effectiveness in critical structures.
Robust optimization for intensity modulated proton therapy to redistribute high linear energy transfer from nearby critical organs to tumors in head and neck cancer.
Because the effect of high LET in normal tissue is not fully understood, there is growing concern over its management, as LET visualization and optimization tools are not yet fully implemented in clinical TPSs. This study presents visualization strategies to quantify OAR and patient treatment quality based on the relationship between dose and LET. Investing in such visualization tools and standardization of LET reporting is necessary
and could assist clinicians to identify and characterize hotspots in regions susceptible to damage, as well as examine LET distributions for new techniques (eg, proton arc).
Conclusion
From the analysis of RBE models, LETd, and DLETd derived from our TPS for patients with brain tumors, strategies were proposed to assess treatment quality considering regions with increased LETd. For clinical practice, identifying, quantifying, and recording LET distributions is important, because concern exists over a link between normal tissue toxicity and LET hotspots. LET calculation and reporting requires standardization. The lack of a uniform approach was exemplified by the effect of establishing dose thresholds, which modifies LET reporting, and should be considered with a clinical rationale. Visualizing the dose and LETd space during treatment planning can provide a prompt check of high-LET regions and allow for the clinician to decide if changes in the planning technique are necessary. Finally, systematically acquiring clinically relevant data for treatment and outcomes is necessary for a robust clinical analysis and comparison with photon treatments, as well as provide guidance on how to incorporate this information in clinical decision making.
Relative biological effectiveness variation along monoenergetic and modulated Bragg peaks of a 62-MeV therapeutic proton beam: A preclinical assessment.
How can scanned proton beam treatment planning for low-grade glioma cope with increased distal RBE and locally increased radiosensitivity for late MR-detected brain lesions?.
Late contrast enhancing brain lesions in proton-treated patients with low-grade glioma: Clinical evidence for increased periventricular sensitivity and variable RBE.
Correlation of LET with MRI changes in brain and potential implications for normal tissue complication probability for patients with meningioma treated with pencil beam scanning proton therapy.
Mixed effect modeling of dose and linear energy transfer correlations with brain image changes after intensity modulated proton therapy for skull base head and neck cancer.
Relative biological effectiveness (RBE) values for proton beam therapy. Variations as a function of biological endpoint, dose, and linear energy transfer.
Introducing proton track-end objectives in intensity modulated proton therapy optimization to reduce linear energy transfer and relative biological effectiveness in critical structures.
Robust optimization for intensity modulated proton therapy to redistribute high linear energy transfer from nearby critical organs to tumors in head and neck cancer.
Sources of support: Dr Di Perri is supported by a grant from Fondation Saint-Luc, Belgium.
Disclosures: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data sharing statement: Research data are stored in an institutional repository and will be shared upon request to the corresponding author.
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