
==== Front
Phys Imaging Radiat Oncol
Phys Imaging Radiat Oncol
Physics and Imaging in Radiation Oncology
2405-6316
Elsevier

S2405-6316(24)00102-7
10.1016/j.phro.2024.100632
100632
Original Research Article
Benefit of range uncertainty reduction in robust optimisation for proton therapy of brain, head-and-neck and breast cancer patients
Tarp Ivanka Sojat ivatar@rm.dk
⁎
Taasti Vicki Trier
Jensen Maria Fuglsang
Vestergaard Anne
Jensen Kenneth
Danish Centre for Particle Therapy, Aarhus University Hospital, Aarhus, Denmark
⁎ Corresponding author at: Danish Centre for Particle Therapy, Palle Juul Jensens Boulevard 25, 8200 Aarhus N, Denmark. ivatar@rm.dk
21 8 2024
7 2024
21 8 2024
31 10063216 4 2024
14 8 2024
18 8 2024
© 2024 The Authors. Published by Elsevier B.V. on behalf of European Society of Radiotherapy & Oncology.
2024

https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Highlights

• Reducing the range uncertainty in proton therapy may reduce dose to healthy tissue.

• Treatment plans were re-optimized with different levels of range uncertainty.

• Reduction in dose-volume parameters were evaluated.

• Reduced dose to normal tissue in brain, head-and-neck and breast cancer patients.

Background and Purpose

The primary cause of range uncertainty in proton therapy is inaccuracy in estimating the stopping-power ratio from computed tomography. This study examined the impact on dose-volume metrics by reducing range uncertainty in robust optimisation for a diverse patient cohort and determined the level of range uncertainty that resulted in a relevant reduction in doses to organs-at-risk (OARs).

Materials and Methods

The effect of reducing range uncertainty on OAR doses was evaluated by robustly optimising six proton plans with varying range uncertainty levels (ranging from 3.5% in the original plan to 1.0%), keeping setup uncertainty fixed. All plans used the initial clinical treatment plan’s beam directions and optimisation objectives and were optimised until a clinically acceptable plan was achieved across all setup and range scenarios. The effect of reduced range uncertainty on dose-volume metrics for OARs near the target was evaluated. This study included 30 brain cancer patients, as well as five head-and-neck and five breast cancer patients, investigating the relevance of reducing range uncertainty when different setup uncertainties were used.

Results

Lowering range uncertainty slightly reduced the nominal dose to surrounding tissue. For body volume receiving 80% of the prescribed dose, reducing range uncertainty from 3.5% to 2.0% resulted in a median decrease of 4 cm3 for the brain, 17 cm3 for head-and-neck, and 27 cm3 for breast cancer patients.

Conclusions

Reducing range uncertainty in robust optimisation showed a reduction in dose to OARs. The clinical relevance depends on the affected organs and the clinical dose constraints.

Keywords

Proton therapy
Range uncertainty reduction
Robust optimisation
==== Body
pmc1 Introduction

Proton therapy enables delivery of a highly conformal dose distribution to the target volume. The dose to healthy tissue and organs-at-risk (OARs) surrounding the target is reduced compared to conventional photon therapy [1]. Protons have a finite range when travelling through matter, eliminating the exit dose in the patient. Therefore, the exact proton range in the patient is of great importance. The proton range depends on the energy of the proton beam and the density of the traversed tissues [2]. These dependencies are given by the proton stopping-power of the tissue. In proton therapy, the stopping-power ratio (SPR) relative to water is typically estimated based on a computed tomography (CT) scan of the patient by applying a predetermined empirical piecewise linear relationship between CT numbers and SPRs, a so-called Hounsfield look-up table (HLUT) [3], [4]. The state-of-the-art approach for estimation of the SPR from CT numbers based on single-energy CT (SECT) is the stoichiometric calibration method proposed by Schneider et al. [3] and described in detail in a recent consensus guide [4]. This method depends on the choice of calibration phantom, CT scanner hardware and CT scanning and reconstruction protocol used. Recent studies have shown a large variation in SPR prediction between European particle therapy centres and large inter-centre discrepancies in SPR accuracy [5].

The treatment planning system (TPS) uses the SPR map to compute a patient-specific dose distribution. To account for range and setup uncertainties, proton treatment plans can be robustly optimised to obtain a good trade-off between target coverage and dose tolerance of the OARs [6]. Range uncertainty margins used in proton treatment planning are institution-dependent and span from 2.5% to 3.5% of the proton range [7], [8]. Including range uncertainty in the plan optimisation to ensure full target coverage leads to an expansion of the irradiated volume and, thereby, an increased dose to OARs, which limits the full exploitation of the benefit of proton therapy. In a study by Tattenberg et al. which investigated the effect of range reduction on ten skull base patients, they observed a favourable outcome across all levels of range uncertainty reduction concerning normal tissue complication probability (NTCP) for brainstem and chiasm. The conclusion was that even a minor reduction in range uncertainty may be beneficial [9]. Furthermore, reduced uncertainty in the proton range may allow for exploring alternative beam arrangements that position OARs in the distal edge of the beam, which could decrease the normal tissue complication probability (NTCP) [10].

Advanced CT imaging techniques, such as dual-energy CT (DECT), have improved precision in estimating the SPR, resulting in a reduced range uncertainty of 2% [11], [12]. Another technology that could reduce range uncertainty is proton CT, which offers a direct measure of the SPR in the patient using the proton beam, thereby overcoming uncertainties in the conversion from X-ray attenuation to proton SPR [13]. With the advent of these imaging techniques and other new technologies, it is relevant to investigate the dose-volume metric benefit of reducing range uncertainty in robust proton treatment planning. In this study, we therefore examined the effect on the dose-volume metrics when reducing range uncertainty as the only changing parameter on a diverse patient population, and we determined the level of range uncertainty that resulted in a relevant dose reduction to OARs.

2 Material and methods

2.1 Patient cohort, dose prescription and CT scan settings

This study is based on original patient CT imaging data, treatment plans, optimisation and evaluation parameters used in our clinical proton therapy facility. In our current clinical practice, all proton dose calculations assume a constant relative biological effect (RBE) of 1.1 to account for the differences between photon and proton irradiation [14]. In this study, all reported doses are given in GyRBE.

The study evaluated 30 brain cancer patients, divided into three groups of ten patients each, receiving a prescribed dose of 50.4 GyRBE in 28 fractions, 54 GyRBE in 30 fractions, or 59.4 GyRBE in 33 fractions to the clinical target volume (CTV). The robust proton plans for this patient group were based on a setup uncertainty of 2 mm. To evaluate the effect of reducing range uncertainty when applying larger setup uncertainties, we additionally included five head-and-neck (HN) and five breast cancer patients, as these were robustly optimised with a setup uncertainty of 4 or 5 mm, respectively. The HN cancer patient cohort included five oropharynx cancer patients, all treated in 34 fractions with a prescription dose of 68, 60 and 50 GyRBE to CTV1, CTV2 and CTV3, respectively. The breast cancer patient cohort consisted of five consecutive patients who fulfilled the following criteria: left-sided breast tumour, lumpectomised tumour, lymph node irradiation, no breast implants, and a prescribed dose of 40 GyRBE in 15 fractions [15]. The study was approved by Aarhus University Hospital institutional review board.

The routine treatment planning was based on a CT scan acquired at a SOMATOM Definition Edge CT scanner (Siemens Healthineers, Forchheim, Germany). For all scans, a quantitative kernel, Qr40, and iterative reconstruction, ADMIRE strength 3, with beam hardening correction for bone, were applied. The scans were acquired in DECT TwinBeam mode for brain and HN patients, where the X-ray beam of 120 kVp was split into low and high energy datasets by a gold and tin filter before reaching the patient [16], [17]. The proton treatment plans were based on a virtual monoenergetic image at 90 keV [18]. The datasets were reconstructed with a slice thickness of 1.5 mm for brain cancer patients and 2 mm for HN cancer patients. For breast cancer patients, a SECT scan was acquired at 120 kVp reconstructed with 2 mm slice thickness.

2.2 Plan optimisation and evaluation

To assess the effect on dose-volume metrics of reduced range uncertainties, proton plans were robustly optimised using the Eclipse TPS (Varian Medical Systems, Palo Alto, CA, USA). For most patients, the spot spacing was defined as 0.425 times the full width at half maximum (FWHM) of the spot size in air at the isocenter at the given energy. The spot size without a range shifter varied from 7 mm at the highest energy to 15 mm at the lowest energy. All treatment plans used the Proton Convolution Superposition (PCS) v16.1 algorithm from Varian. The calculation grid was isotropic with a side length of 1 mm for brain, 1.5 mm for HN, and 2.5 mm for breast cancer patients. The spot pattern was hexagonal with an energy layer spacing of 3.3 MeV. Six treatment plans were created for each patient, with a range uncertainty of 3.5% (original plan), 3.0%, 2.5%, 2.0%, 1.5% and 1.0%, respectively. The setup error was kept constant. A total of fourteen error scenarios, with either no, or a positive or negative setup shift in each of the three dimensions combined with either a positive or negative range error, were included in robust optimisation and robust evaluation of each plan.

Each plan was optimised using multi-field optimisation for brain and HN cases and single-field optimisation for breast cases until a clinically acceptable plan was achieved for all fourteen error scenarios. Optimisation constraints and priorities for target coverage and OARs adhered to local clinical guidelines, based on the original proton plan objectives. The objective functions included mean and maximum doses to the OARs, alongside constraints that ensured the required target coverage for each target volume (Table 1). Maximum doses to the body structure did not exceed 107% of the prescribed dose. The beam angles were kept equal to those of the original clinical plan tailored individually based on tumour location and size. The plans consisted of three (N = 29) or four (N = 1) beams for brain cancer patients, five for HN cancer patients, and two for breast cancer patients. The 3.5%-plan was optimised first, followed by the other plans in descending order of range uncertainty. The optimisation was re-started for each new plan, keeping the optimisation objectives for the OARs the same as in the 3.5%-plan. Only the applied range uncertainty was changed between the individual plans. All plans were optimised by the same planner. Four breast cancer patients initially had target under-dosage in the 3.5% plan, a tendency observed in subsequent plans with reduced range. Additional optimisation corrected these issues ensuring adequate target coverage to maintain a fair comparison of the plans. Following the optimisation, the plans were normalised to ensure that the mean dose within the CTV was equal to the prescription dose.Table 1 Constraints for targets and organs-at-risk (OARs) evaluated in this study. Abbreviations: CTV – clinical target volume; L – left; R – right; PCM_Low, PCM_Mid, PCM_Up – pharyngeal constrictor muscle; IMN – internal mammary lymph nodes.

Treated anatomy	Structure	Constraint	
Brain	CTV
Brainstem	V95% > 98%
Dmax ≤ 54 GyRBE	
	Chiasm	Dmax ≤ 54 GyRBE	
	Optic Nerve L/R
Brain − CTV	Dmax ≤ 54 GyRBE
V50% ≤ 30 GyRBE
	


	
Head-and-neck	CTV1
CTV2
CTV3
Oral Cavity	V95%>99% and V90%>100%
V95%>98%
V95%>98%
Dmean ≤ 30 GyRBE	
	PCM_Low, PCM_Mid, PCM_Up	Dmean ≤ 55 GyRBE	
	Submandibular L/R	Dmean ≤ 35 GyRBE	
	Parotid L/R	Dmean ≤ 20 GyRBE
	


	
Breast	CTV chest wall
CTV IMN
Heart	V95%>95%
V90%>95%
V35 GyRBE ≤ 5%	
	

Lung_ipsilateral
	V17 GyRBE ≤ 10%
Dmean ≤ 5 GyRBE
V17 GyRBE ≤ 35%
Dmean ≤ 18 GyRBE	

The plans were robustly evaluated using the same range uncertainty as applied for robust optimisation, e.g. plans robustly optimised with a 3% range uncertainty were also evaluated with a 3% range uncertainty.

The dose distribution in the CTVs and OARs was assessed by inspecting dose-volume-histogram (DVH) parameters, conformity index (CI) [19], and by visual inspection of the dose-colour-wash at 95% of the prescribed dose. The 3.5% range uncertainty plan, seen as the reference, was compared to the plans with reduced range uncertainties. Near maximum doses (D0.03 cm3) to brainstem, chiasm and optic nerves were extracted from the nominal and worst-case scenarios for brain cancer patients. Additionally, V30GyRBE to the brain tissue outside the CTV was evaluated for the nominal scenario according to our clinical practise. For HN cancer patients, the mean doses for pharyngeal constrictor muscle (PCM; up, mid, low) and oral cavity were extracted from the nominal scenario. The NTCP model used in DAHANCA35 [20] was applied to calculate NTCP differences between the 3.5%-plan and the other plans. For the breast cancer patients, the mean doses to the heart and V17GyRBE to the ipsilateral lung were extracted from the nominal scenario. Furthermore, the V80% for the body contour, including the target, was extracted for all patients. The differences in dose to the OARs were expressed as an absolute dose difference. The OARs evaluated in this study follow the recommendations issued by the national protocols and are listed in Table 1. Statistical significance was tested using the Wilcoxon signed rank test, applying the signrank function in Matlab version 2023B (The MathWorks Inc., Natick, MA, USA).

3 Results

All plans fulfilled the required constraints for all CTV and OAR structures described in Table 1. Examples of dose distribution differences for axial, coronal and sagittal view between the 3.5%-plan (reference) and the 2%-plan for a single slice in the centre of the CTV region are shown in Fig. 1 for one brain cancer patient.Fig. 1 Difference in dose distribution between 3.5% and 2% range uncertainty plans for axial, coronal and sagittal views in brain cancer patients. The CTV is depicted by the magenta contour. Positive dose difference indicates the advantage of the 2%-plan. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

For patients with brain cancer, minimising range uncertainty resulted in a reduced OAR dose, with statistically significant reductions observed in most cases (Fig. 2). Decreasing range uncertainty from 3.5% to e.g. 2% resulted in a median reduction of 4 cm3 (range: −0.8 to 31.9 cm3) in V80% for the body contour for brain cancer patients (Table 2). For further range uncertainty reduction, V80% continued to decrease, showing the advantage of reducing range uncertainty as less dose was deposited in the patient. Reducing the range uncertainty to 2.0% also resulted in a median reduction of 4.3 cm3 in V30GyRBE for the brain tissue outside the CTV (Brain-CTV). The median of maximum dose (specified as D0.03 cm3) to the brainstem did not markedly change between the plans, however, for 20 patients (67%), a dose reduction was observed in both nominal and worst-case scenarios. For eight patients (27%), the reduction exceeded 0.5 GyRBE in the nominal scenario (average 0.8 GyRBE), and for 12 patients, the average reduction was 3.1 GyRBE in the worst-case scenario.Fig. 2 Boxplot of absolute dose-volume-histogram (DVH) differences compared to the reference plan (3.5% range uncertainty) for the brain cancer patients. Positive values indicate a benefit of the specific range uncertainty level. All results were extracted from the nominal scenario (nom) shown by the blue boxplots. For the maximum dose (given by D0.03 cm3) to the brainstem, the results were additionally extracted from the worst-case-scenario (WC) shown by the purple boxplots, to follow the clinical evaluation procedure. The boxes show the interquartile range from the 25th to the 75th percentile, the line inside each box indicates the sample median, while outliers are represented by circles. Differences which were statically significant (i.e. p < 0.05) are marked with an asterisk. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 2 Median (range) dose-volume-histogram (DVH) metrics for the OARs across the three treatment sites for plans with a range uncertainty of 3.5% and 2.0%, as well as the differences between these two plans. The DVH metrics are either extracted from the nominal dose distribution or the worst-case error scenario.

	3.5% Median	2.0% Median	Δ Median	
Brain				
Body V80% [cm3] (Nominal)	285.2 (34.9;831.5)	278.2 (33.3;815.9)	3.9 (−0.8;31.9)	
BrainCTV V30GyRBE [cm3] (Nominal)	132.8 (25.6;381.7)	125.4 (23.3–385.5)	4.3 (−3.8;13.2)	
Brainstem [GyRBE] (Nominal)	50.9 (0.0;58.7)	50.5 (0.0;53.5)	0.2 (−1.9;3.6)	
Brainstem [GyRBE] (Worst-case)	51.5 (0.0;60.4)	51.4 (0.0;54.8)	0.2 (−1.7;13.1)	
Chiasm [GyRBE] (Nominal)	5.4 (0.0;50.2)	13.4 (0.0;51.7)	0.0 (−0.6;4.0)	
Chiasm [GyRBE] (Worst-case)	8.9 (0.0;51.1)	20.0 (0.0;52.1)	0.2 (−0.4;5.2)	


	
Head-and-neck				
Body V80% [cm3] (Nominal)	808.5 (700.6;1629.9)	786.2 (686.2;1599.6)	16.8 (14.4;30.3)	
OralCavity Dmean [GyRBE] (Nominal)	28.4 (22.0;47.2)	28.0 (22.0;47.0)	0.2 (0.1;0.5)	
OralCavity Dmean [GyRBE] (Worst-case)	33.9 (26.6;52.7)	32.4 (26.1;51.3)	1.4 (0.5;2.2)	
PCM Up Dmean [GyRBE] (Nominal)	53.8 (35.2;60.6)	53.9 (34.3;60.4)	0.1 (0.0;0.3)	
PCM Up Dmean [GyRBE] (Worst-case)	57.4 (39.4;62.4)	56.6 (38.9;62.1)	0.6 (0.2;1.1)	
PCM Mid Dmean [GyRBE] (Nominal)	58.7 (34.6;61.5)	58.8 (33.3;61.2)	0.2 (−0.8;1.4)	
PCM Mid Dmean [GyRBE] (Worst-case)	63.2 (44.5;64.4)	63.1 (42.7;64.1)	0.6 (0.2;1.9)	
PCM Low Dmean [GyRBE] (Nominal)	20.4 (12.4;37.1)	20.2 (12.1;36.5)	0.2 (−0.4;0.7)	
PCM Low Dmean [GyRBE] (Worst-case)	25.5 (18.2;48.4)	24.0 (16.7;46.8)	1.5 (0.0;1.7)	


	
Breast				
Body V80% [cm3] (Nominal)	2108.6 (1108.7;4291.2)	2081.7 (1109.4;4261.7)	26.9 (−5.0;59.0)	
Heart Mean Dose [GyRBE] (Nominal)	1.0 (0.8;1.2)	1.0 (0.9;1.3)	−0.1 (−0.1;0.0)	
Heart Mean Dose [GyRBE] (Worst-case)	1.5 (1.4;1.7)	1.4 (1.3;1.6)	0.1 (0.1;0.2)	
Heart V30Gy [cm3] (Nominal)	6.0 (1.8;7.1)	5.9 (1.7;7.4)	0.1 (−0.3;0.2)	
Heart V30Gy [cm3] (Worst-case)	9.6 (4.1;11.8)	8.3 (3.5;10.3)	1.5 (0.6;2.0)	
Lung Mean Dose [GyRBE] (Nominal)	5.7 (3.9;10.7)	5.7 (4.1;10.9)	−0.1 (−0.2;0.1)	
Lung Mean Dose [GyRBE] (Worst-case)	9.8 (6.6;14.2)	8.8 (6.1;13.6)	0.6 (0.5;1.7)	
Lung V17Gy [cm3] (Nominal)	143.8 (73.1;226.8)	147.4 (76.1;231.2)	−3.0 (−4.4;5.7)	
Lung V17Gy [cm3] (Worst-case)	246.1 (140.1;420.2)	228.2 (127.4;353.5)	18.0 (12.7;66.7)	

The effect of reducing range uncertainty in patients robustly optimised with a larger setup uncertainty was assessed based on HN and breast cancer patients (Fig. 3). Similarly to the results observed for brain cancer patients, a reduction was seen in V80% for the body contour for both the HN and breast cancer patients. For HN cancer patients, there was a reduction of 17 cm3 (range: 14.4 to 30.3 cm3), while for breast cancer patients, the reduction amounted to 27 cm3 (range: −5.0 to 59.0 cm3) (Fig. 4).Fig. 3 Dose difference distribution between the 3.5%- and 2%-plan for a HN (left) and a breast (right) cancer patient. In the HN case the magenta-coloured structure represents CTV3, while in the breast case it represents the CTV. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4 Boxplot of absolute dose-volume-histogram (DVH) differences compared to the reference plan (3.5% range uncertainty) for HN and breast cancer patients. The boxes show the interquartile range from the 25th to the 75th percentile, the line inside each box indicates the sample median, while outliers are represented by circles. No statistical tests were performed due to the small sample size.

The dose differences for OARs in the HN cancer patients translated into an average reduction of dysphagia NTCP between the 3.5%-plan and the 2.0%-plan of 0.2 percentage points (pp) for the nominal scenario and 1.3 pp for the worst-case scenario. As the range uncertainty was further reduced, the NTCP continued to decrease.

There was a reduction in the median volume in V17GyRBE for the lung tissue by 18 cm3 in the worst-case scenario among the five breast patients. The mean heart dose for all five patients remained below 2 GyRBE in all plans, including the 3.5%-plan, with only minor dose differences observed, although a slight increase was noted for the nominal case scenarios. Median values for evaluated OARs are listed in Table 2.

4 Discussion

This study investigated the dose reduction to OARs when the range uncertainty was reduced as the only parameter changed in the robust optimisation process, to ensure a fair comparison between the plans. For all patients included in the study, the re-optimised plans with reduced range uncertainty fulfilled the dose constraints for target coverage and for the OAR doses. Our results showed a decrease in the overall dose to healthy tissue (quantified by the V80% to the body contour) when decreasing the range uncertainty for all treatment sites included in this study.

There was minimal or no change in the maximum dose to brainstem, optic chiasm and optic nerves for brain cancer patients, as the patients were not selected by having tumours adjacent to these OARs. However, an average reduction of 3.1 GyRBE was observed for the brainstem in 12 patients in the worst-case scenario. This could result from the current clinical beam arrangement utilising the lateral, less steep dose fall-off to conform the dose distribution towards the critical organs rather than the distal beam edge. This approach aims to prevent placing the sharp dose fall-off in the OAR minimising the risk of over-dosage of the OAR. However, reducing the range uncertainty leads to the feasibility of novel beam arrangements that take advantage of the sharp dose fall-off in the distal beam edge, as investigated by Tattenberg et al. [10]. Their study showed a decrease of OAR NTCP and the volume of healthy tissue receiving 70% of the prescribed dose.

The treatment plans created in this study were optimised using consistent predefined priorities and clinical constraints across all levels of range uncertainties. For the breast cancer patients, decreasing the range uncertainty led to a median reduction of 27 cm3 in the volume receiving 80% of the prescribed dose. However, the changes in the cost functions as a result of lowered range uncertainty may have led to another compromise between the target coverage of the internal mammary lymph nodes (IMN) and the mean heart dose (MHD) compared to the reference plan (3.5%). Furthermore, the tumour margin extended towards the heart creating an overlap area. Our findings showed a decrease in V80%, reduced monitor units (MU), and fewer energy layers (average reduction of one layer) when the range uncertainty was reduced. However, there was a slight increase in the MHD for the nominal scenario. The increase in the MHD could result from the subsequent changes in the cost function for the CTV and the heart during the optimisation process. The penalty for the MHD varied with the changes in range uncertainty, making it easier for the optimiser to fulfil the OAR constraints. The rise in MHD is a disadvantage of keeping the fixed priorities and constraints. In clinical practice, a typical approach involves additional priority on the OAR structures, aligning with the ALARA (As Low As Reasonably Achievable) principle. However, the MHD remained below 2 GyRBE for all five patients, with the observed difference being in the second decimal place, considered not clinically relevant.

A similar study examined the clinical benefits of range uncertainty reductions for the treatment of ten skull base tumours [9]. Their analysis found a decrease in the healthy volume receiving 70% of the prescribed dose to range from −7.8 to 24.1 cm3 in the nominal scenario for range uncertainty reduction from 5% to 1%. This agrees with our findings for the brain cancer patients (−0.8 to 31.9 cm3 at 80% of the prescribed).

A study by van de Water et al. suggested that the effects of patient setup uncertainty may be larger than that of range uncertainty reduction in terms of dose and NTCP reduction [21]. In a study based on 20 oropharyngeal cancer patients, they varied the setup and range uncertainties separately and found up to 7.5 pp difference in average NTCP-values for xerostomia, dysphagia, and larynx edema when varying the setup uncertainty from 1 to 7 mm. Varying the range uncertainty from 1% to 7% resulted in NTCP difference of 1.2 pp [21]. The present study only focused on reducing the range uncertainties, while the effects of setup uncertainties were not considered. Wagenaar et al. also found that reducing the range uncertainty led to a reduction of the OAR dose and NTCP [22].

The primary focus and the strength of this study lie in the large brain patient cohort, with additional examples drawn from HN and breast cancer cases to illustrate the effect of reduced range uncertainty in other treatment sites, despite the limited number of patients in these groups.

Conversion of the CT number into SPR is a major contributor to range uncertainties [7], and various approaches to improve SPR estimation accuracy have been investigated in previous studies. Most centres still use SECT for proton treatment planning [9]. A new consensus guide lists the best standards for calibrating a conversion curve for SECT, but this still does not necessarily lead to a reduction in range uncertainty [5]. However, newer imaging modalities such as DECT imaging techniques have been shown to enable a reduced proton range uncertainty [18], [23], [24]. More clinics have started to use DECT clinically for proton treatment planning [11], [25], [26]. Other potential candidates for a reduction in range uncertainty could be photon-counting CT [27], [28], proton CT [29], or range verification methods like positron emission tomography [30] or prompt gamma imaging [31]. Moreover, newer strategies to consider tissue-specific range uncertainty estimation have been suggested [32].

In conclusion, reducing the range uncertainty in robust optimisation leads to reduction in dose to OARs. Whether the reduction is clinically relevant needs to be seen in a context; if the dose to an OAR is close to the dose constraint, the potential dose reductions shown in this study are clinically relevant.

Declaration of Competing Interest

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.

Acknowledgement

This research was supported by 10.13039/100008363 Danish Cancer Society (grant no. R231-A14040 ) and 10.13039/100009007 Health Research Foundation of 10.13039/501100010078 Central Denmark Region .
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