Can the mean linear energy transfer of organs be directly related to patient toxicities for current head and neck cancer intensity-modulated proton therapy practice?

Open AccessPublished:September 14, 2021DOI:https://doi.org/10.1016/j.radonc.2021.09.003

      Highlights

      • Relating organ LET to head and neck toxicity not feasible for current practice.
      • Does not contradict previous evidence for increased RBE for high LET.
      • Lack of variation in LET causes high required sample size.
      • Other methods to investigate RBE and LET in clinical practice are suggested.

      Abstract

      Background and purpose

      The relative biological effectiveness (RBE) of proton therapy is predicted to vary with the dose-weighted average linear energy transfer (LETd). However, RBE values may substantially vary for different clinical endpoints. Therefore, the aim of this study was to assess the feasibility of relating mean D⋅LETd parameters to patient toxicity for HNC patients treated with proton therapy.

      Materials and methods

      The delivered physical dose (D) and the voxel-wise product of D and LETd (D⋅LETd) distributions were calculated for 100 head and neck cancer (HNC) proton therapy patients using our TPS (Raystation v6R). The means and covariance matrix of the accumulated D and D⋅LETd of all relevant organs-at-risk (OARs) were used to simulate 2.500 data sets of different sizes. For each dataset, an attempt was made to add mean D⋅LETd parameters to a multivariable NTCP model based on mean D parameters of the same OAR for xerostomia, tube feeding and dysphagia. The likelihood of creating an NTCP model with statistically significant parameters (i.e. power) was calculated as a function of the simulated sample size for various RBE models.

      Results

      The sample size required to have a power of at least 80% to show an independent effect of mean D⋅LETd parameters on toxicity is over 15,000 patients for all toxicities.

      Conclusion

      For current clinical practice, it is not feasible to directly model NTCP with both mean D and mean D⋅LETd of OARs. These findings should not be interpreted as a contradiction of previous evidence for the relationship between RBE and LETd.

      Keywords

      The biological damage of proton therapy is generally considered to be higher than that of conventional X-ray radiotherapy of the same physical dose for tumors and healthy tissues [
      • Paganetti H.
      • Niemierko A.
      • Ancukiewicz M.
      • Gerweck L.E.
      • Goitein M.
      • Loeffler J.S.
      • et al.
      Relative biological effectiveness (RBE) values for proton beam therapy.
      ]. Current guidelines recommend a constant relative biological effectiveness (RBE) model equal to 1.1 for clinical proton therapy treatments, meaning the equivalent physical photon dose equals 1.1 times the physical proton dose [

      ICRU. Prescribing, Recording, and Reporting Proton-Beam. ICRU Report 78. vol. 7. 2007. 10.1093/jicru/ndi004.

      ]. The RBE is used to calculate the RBE-weighted dose (DRBE) which is the multiplication of physical dose D and RBE. The DRBE has the unit GyRBE and represents the equivalent photon dose in Gy. However, a large body of preclinical evidence suggests the RBE varies and multiple variable RBE models have been suggested based on the dose-weighted average linear energy transfer (LETd), fraction dose and tissue-specific α/β value [
      • Paganetti H.
      Relative biological effectiveness (RBE) values for proton beam therapy. Variations as a function of biological endpoint, dose, and linear energy transfer.
      ,
      • Rørvik E.
      • Fjæra L.F.
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      • Dale J.E.
      • Engeseth G.M.
      • Stokkevåg C.H.
      • et al.
      Exploration and application of phenomenological RBE models for proton therapy.
      ,
      • Wedenberg M.
      • Lind B.K.
      • Hårdemark B.
      A model for the relative biological effectiveness of protons: the tissue specific parameter α/β of photons is a predictor for the sensitivity to LET changes.
      ,
      • McNamara A.L.
      • Schuemann J.
      • Paganetti H.
      A phenomenological relative biological effectiveness (RBE) model for proton therapy based on all published in vitro cell survival data.
      ].
      Better understanding of the role of LETd is necessary to give patients the best possible radiation treatment in the near future. Several recent studies have shown the benefit of integrating LETd into treatment planning optimization in terms of RBE-weighted dose when a variable RBE model is assumed [
      • Traneus E.
      • Ödén J.
      Introducing proton track-end objectives in intensity modulated proton therapy optimization to reduce linear energy transfer and relative biological effectiveness in critical structures.
      ,
      • Unkelbach J.
      • Botas P.
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      • Gorissen B.L.
      • Paganetti H.
      Reoptimization of intensity modulated proton therapy plans based on linear energy transfer.
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      • Cao W.
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      • Lee A.
      • Li Y.
      • Liu W.
      • Ronald Zhu X.
      • et al.
      Uncertainty incorporated beam angle optimization for IMPT treatment planning.
      ,
      • Liu C.
      • Patel S.H.
      • Shan J.
      • Schild S.E.
      • Vargas C.E.
      • Wong W.W.
      • et al.
      Robust optimization for intensity modulated proton therapy to redistribute high linear energy transfer from nearby critical organs to tumors in head and neck cancer.
      ,
      • Bai X.
      • Lim G.
      • Grosshans D.
      • Mohan R.
      • Cao W.
      A biological effect-guided optimization approach using beam distal-edge avoidance for intensity-modulated proton therapy.
      ]. Once these tools become available in commercial treatment planning systems (TPS), treatment planners will have the ability to manipulate the clinical LETd distribution. Consequently, clinically validated variable RBE models will be required to decide between planning strategies with different LETd and dose distributions [
      • Paganetti H.
      • Blakely E.
      • Carabe-Fernandez A.
      • Carlson D.J.
      • Das I.J.
      • Dong L.
      • et al.
      Report of the AAPM TG-256 on the relative biological effectiveness of proton beams in radiation therapy.
      ].
      The evidence for the variability of RBE for in-vitro cell kill is convincing. However, the RBE for cell kill is not necessarily equivalent to the RBE for clinically relevant endpoints such as patient toxicity [
      • Paganetti H.
      • Blakely E.
      • Carabe-Fernandez A.
      • Carlson D.J.
      • Das I.J.
      • Dong L.
      • et al.
      Report of the AAPM TG-256 on the relative biological effectiveness of proton beams in radiation therapy.
      ]. Therefore, a recent report by the American Association of Physics in Medicine recommended that variable RBE models need to be cross-validated against clinically relevant endpoints before introduction into clinical treatment planning and optimization [
      • Paganetti H.
      • Blakely E.
      • Carabe-Fernandez A.
      • Carlson D.J.
      • Das I.J.
      • Dong L.
      • et al.
      Report of the AAPM TG-256 on the relative biological effectiveness of proton beams in radiation therapy.
      ]. Previous in-patients retrospective investigations showed that the formation of contrast-enhancing brain lesions visible on MRI were independently related to both dose (D) and the voxel-wise product of D and LETd, (D⋅LETd) [
      • Bahn E.
      • Bauer J.
      • Harrabi S.
      • Herfarth K.
      • Debus J.J.
      • Alber M.
      Late contrast enhancing brain lesions in proton treated low-grade glioma patients: clinical evidence for increased periventricular sensitivity and variable RBE.
      ,
      • Eulitz J.
      • Troost E.G.C.
      • Raschke F.
      • Schulz E.
      • Lutz B.
      • Dutz A.
      • et al.
      Predicting late magnetic resonance image changes in glioma patients after proton therapy.
      ]. The contribution of D⋅LETd to contrast-enhancing brain lesions was in agreement with predictions from an existing variable RBE model [
      • Wedenberg M.
      • Lind B.K.
      • Hårdemark B.
      A model for the relative biological effectiveness of protons: the tissue specific parameter α/β of photons is a predictor for the sensitivity to LET changes.
      ,
      • Bahn E.
      • Bauer J.
      • Harrabi S.
      • Herfarth K.
      • Debus J.J.
      • Alber M.
      Late contrast enhancing brain lesions in proton treated low-grade glioma patients: clinical evidence for increased periventricular sensitivity and variable RBE.
      ]. While contrast-enhancing brain lesions may be considered an adverse event, they are not typically accompanied by clinical symptoms. This indicates that while this endpoint might be a useful surrogate, it is not a clinically relevant outcome itself.
      Treatment of head and neck cancer (HNC) typically involves the irradiation of several healthy tissues and organs-at-risk (OARs), as these are often in close proximity to the tumor. Therefore, HNC patients commonly suffer from multiple radiotherapy-induced side effects such as xerostomia, dysphagia and sticky saliva, which can start within the first year of follow-up and may persist for years after treatment [
      • Christianen M.E.M.C.
      • Schilstra C.
      • Beetz I.
      • Muijs C.T.
      • Chouvalova O.
      • Burlage F.R.
      • et al.
      Predictive modelling for swallowing dysfunction after primary (chemo)radiation: results of a prospective observational study.
      ,
      • Beetz I.
      • Schilstra C.
      • van der Schaaf A.
      • van den Heuvel E.R.
      • Doornaert P.
      • van Luijk P.
      • et al.
      NTCP models for patient-rated xerostomia and sticky saliva after treatment with intensity modulated radiotherapy for head and neck cancer: the role of dosimetric and clinical factors.
      ]. In the Netherlands, HNC patients are treated with proton therapy after model-based selection and their toxicities are prospectively scored [

      Landelijk Platform Protonentherapie, Protonentherapie LP. Landelijk Indicatie Protocol Protonen Therapie Hoofd-halstumoren. 2017.

      ,
      • Langendijk J.A.
      • Boersma L.J.
      • Rasch C.R.N.
      • van Vulpen M.
      • Reitsma J.B.
      • van der Schaaf A.
      • et al.
      Clinical trial strategies to compare protons with photons.
      ,
      • Tambas M.
      • Steenbakkers R.J.H.M.
      • van der Laan H.P.
      • Wolters A.M.
      • Kierkels R.G.J.
      • Scandurra D.
      • et al.
      First experience with model-based selection of head and neck cancer patients for proton therapy.
      ]. The effect of RBE variability on HNC toxicity may be studied by combining variable RBE models with normal tissue complication probability (NTCP) models based on X-ray radiotherapy [
      • Wedenberg M.
      • Lind B.K.
      • Hårdemark B.
      A model for the relative biological effectiveness of protons: the tissue specific parameter α/β of photons is a predictor for the sensitivity to LET changes.
      ,
      • McNamara A.L.
      • Schuemann J.
      • Paganetti H.
      A phenomenological relative biological effectiveness (RBE) model for proton therapy based on all published in vitro cell survival data.
      ,
      • Christianen M.E.M.C.
      • Schilstra C.
      • Beetz I.
      • Muijs C.T.
      • Chouvalova O.
      • Burlage F.R.
      • et al.
      Predictive modelling for swallowing dysfunction after primary (chemo)radiation: results of a prospective observational study.
      ,
      • Beetz I.
      • Schilstra C.
      • van der Schaaf A.
      • van den Heuvel E.R.
      • Doornaert P.
      • van Luijk P.
      • et al.
      NTCP models for patient-rated xerostomia and sticky saliva after treatment with intensity modulated radiotherapy for head and neck cancer: the role of dosimetric and clinical factors.
      ].
      In short, there is a strong need for validation of variable RBE models for clinically relevant endpoints such as patient toxicity. However, methodologies relating LETd OAR parameters to patient toxicity are still to be investigated as it is not clear yet if such an analysis would be possible. Therefore, the aim of this study was to assess the feasibility of independently relating the mean D⋅LETd of OARs to observed patient toxicity for HNC patients treated with proton therapy.

      Materials and methods

       Study population

      The first 100 consecutive adult HNC patients treated with pencil beam scanning intensity-modulated proton therapy (IMPT) at the University Medical Center Groningen were included in this study. In the Netherlands, patients are selected for proton therapy using a model-based approach. In the model-based clinic, a patient is selected for proton therapy if the ΔNTCP between the proton and photon treatment plans exceeds a certain indication-specific threshold [

      Landelijk Platform Protonentherapie, Protonentherapie LP. Landelijk Indicatie Protocol Protonen Therapie Hoofd-halstumoren. 2017.

      ]. The ΔNTCP thresholds used for HNC patients are 10% for grade II xerostomia or dysphagia, 15% for the combined total of grade II xerostomia and dysphagia, or 5% for grade III tube feeding dependence [

      Landelijk Platform Protonentherapie, Protonentherapie LP. Landelijk Indicatie Protocol Protonen Therapie Hoofd-halstumoren. 2017.

      ,
      • Langendijk J.A.
      • Boersma L.J.
      • Rasch C.R.N.
      • van Vulpen M.
      • Reitsma J.B.
      • van der Schaaf A.
      • et al.
      Clinical trial strategies to compare protons with photons.
      ,
      • Tambas M.
      • Steenbakkers R.J.H.M.
      • van der Laan H.P.
      • Wolters A.M.
      • Kierkels R.G.J.
      • Scandurra D.
      • et al.
      First experience with model-based selection of head and neck cancer patients for proton therapy.
      ].
      Patients were treated with an RBE weighted dose (DRBE) of 70 GyRBE to the primary clinical target volume (CTV) and 54.25 GyRBE to the prophylactic CTV in 35 fractions with 5 fractions per week using IMPT and assuming a constant RBE of 1.1 (Proteus ®Plus, IBA, Ottignies-Louvain-la-Neuve, Belgium). Patients were immobilized using a 5-point mask (HP Pro, Orfit Industries, Wijnegem, Belgium) and aligned daily using a 6-D robotic table with translations and rotations based on cone-beam CT (CBCT) scans. Potential anatomical changes were monitored with daily online CBCTs and weekly offline verification CTs with the patient immobilized and aligned in treatment position.
      Clinical treatment plans were generated using robust optimization employing the treatment planning system (TPS) (RayStation v6 and v9, RaySearch Laboratories, Stockholm, Sweden). Robustness optimization settings were initially a 3% range and 5 mm setup uncertainty which was reduced to a 3 mm setup uncertainty as our clinical experience matured [
      • Wagenaar D.
      • Kierkels R.G.J.
      • van der Schaaf A.
      • Meijers A.
      • Scandurra D.
      • Sijtsema N.M.
      • et al.
      Head and neck IMPT probabilistic dose accumulation: Feasibility of a 2 mm setup uncertainty setting.
      ]. Target coverage was assessed using the voxel-wise minimum robustness (multi-scenario) evaluation approach, where the coverage criteria was that 95% of the volume of both CTVs should receive at least 98% of the prescribed dose (i.e. V95% > 98%) in the voxel-wise minimum of all robustness scenarios, as described in a previous publication [
      • Korevaar E.W.
      • Habraken S.J.M.
      • Scandurra D.
      • Kierkels R.G.J.
      • Unipan M.
      • Eenink M.G.C.
      • et al.
      Practical robustness evaluation in radiotherapy - A photon and proton-proof alternative to PTV-based plan evaluation.
      ].

       LETd calculation and longitudinal dose accumulation

      For the purpose of this study, the LETd distributions were calculated for protons in a development version of the TPS (RayStation v9R), previously validated for clinical use by our group [
      • Wagenaar D.
      • Tran L.T.
      • Meijers A.
      • Marmitt G.G.
      • Souris K.
      • Bolst D.
      • et al.
      Validation of linear energy transfer computed in a Monte Carlo dose engine of a commercial treatment planning system.
      ].
      The physical dose (D) and D⋅LETd were calculated on all weekly verification CTs. The D⋅LETd is the voxel-wise multiplication of dose and LETd and therefore different form the LETd itself. The D and D⋅LETd distributions were deformed to the planning CT and summed to get the accumulated distributions, using the deformable image registration algorithm built into the TPS [
      • Weistrand O.
      • Svensson S.
      The ANACONDA algorithm for deformable image registration in radiotherapy.
      ].

       Dataset simulation and testing

      We simulate the feasibility of relating mean voxel-wise product of D and LETd (D⋅LETd) of organs-at-risk (OARs) to observed patient toxicity for HNC patients treated with proton therapy in the future. The workflow for simulating and testing datasets is illustrated in Fig. 1. A dataset was gathered of 100 HNC patients including the continuous parameters mean dose (D) and D⋅LETd for OARs and categorical parameters used in NTCP models (e.g. baseline xerostomia).
      Figure thumbnail gr1
      Fig. 1Schematic representation of the workflow for generating and testing datasets. A dataset was gathered of 100 HNC patients including the continuous parameters mean dose (D) and voxel-wise product of D and LETd (D⋅LETd) for all organs-at-risk and categorical parameters used in NTCP models (e.g. baseline xerostomia). This dataset was used to simulate datasets and estimate the statistical power for various assumed RBE models. See the manuscript text for a detailed explanation of the workflow steps.
      Step 1: A multivariate Gaussian distribution was fitted to the continuous parameters determining their standard deviations and covariances. A frequency table was generated for categorical parameters.
      Step 2: From the multivariate distribution and frequency table, an unlimited number of realistic patients can be simulated for which the covariance between different continuous parameters is identical to that of the original dataset. A sample size N of up to 100,000 was simulated and each N was simulated 2500 times resulting in 60,000 datasets of various sizes.
      Step 3: The RBE-weighted dose (DRBE) is calculated assuming a linear RBE model of the form RBE=1+c·LETd, where c is the slope of the RBE-LETd relation so that DRBE=D+c·D·LETd. In our study we performed the analysis for RBE models with different RBE-LETd slopes. Once with a RBE-LETd slope c of 0.04 (keV/μm)−1 as a low estimate which results in a clinical RBE of 1.1 in the target and once with a RBE-LETd slope c of 0.1 (keV/μm)−1 as a high estimate, as this value was found in a recent study [
      • Bahn E.
      • Bauer J.
      • Harrabi S.
      • Herfarth K.
      • Debus J.J.
      • Alber M.
      Late contrast enhancing brain lesions in proton treated low-grade glioma patients: clinical evidence for increased periventricular sensitivity and variable RBE.
      ,
      • Unkelbach J.
      • Chan T.C.Y.
      • Bortfeld T.
      Accounting for range uncertainties in the optimization of intensity modulated proton therapy.
      ].
      The DRBE parameters are used to calculate an NTCP-profile based on previously published models for xerostomia, grade 2–4 dysphagia, and tube feeding dependence [
      • Christianen M.E.M.C.
      • Schilstra C.
      • Beetz I.
      • Muijs C.T.
      • Chouvalova O.
      • Burlage F.R.
      • et al.
      Predictive modelling for swallowing dysfunction after primary (chemo)radiation: results of a prospective observational study.
      ,
      • Beetz I.
      • Schilstra C.
      • van der Schaaf A.
      • van den Heuvel E.R.
      • Doornaert P.
      • van Luijk P.
      • et al.
      NTCP models for patient-rated xerostomia and sticky saliva after treatment with intensity modulated radiotherapy for head and neck cancer: the role of dosimetric and clinical factors.
      ,

      Landelijk Platform Protonentherapie, Protonentherapie LP. Landelijk Indicatie Protocol Protonen Therapie Hoofd-halstumoren. 2017.

      ]. These NTCP models are based on actual patient toxicity datasets of over 350 photon therapy patients each. The resulting models depend on demographic and DRBE parameters which are summarized in Table 1. Toxicity scores were simulated by assigning a toxicity if the NTCP was higher than a random number drawn from a uniform distribution between 0 and 1 independently for each simulated patient and toxicity.
      Table 1Normal tissue complication models used in this study. These models are taken from the Dutch national proton therapy indication protocol

      Landelijk Platform Protonentherapie, Protonentherapie LP. Landelijk Indicatie Protocol Protonen Therapie Hoofd-halstumoren. 2017.

      . Using these parameters NTCP is calculated as NTCP = 1/(1 + exp(−S)) where the linear predictor S is defined as S = β0 + ΣβiXi.
      OutcomeParameterEstimate
      XerostomiaβX0Intercept−1.507
      βX1Baseline xerostomia: a bit0.525
      βX2Baseline xerostomia: moderate to severe1.482
      βX3Mean dose to contralateral parotid gland0.052
      DysphagiaβD0Intercept−3.303
      βD1Baseline dysphagia grade 2–30.967
      βD2Mean dose to superior pharyngeal constrictor muscle0.024
      βD3Mean dose to oral cavity0.024
      Tube feedingβT0Intercept−6.849
      βT1Tumor stage 3–40.68
      βT2Weight loss 1–10%0.317
      βT3Weight loss > 10%1.178
      βT4Modality: Accelerated0.198
      βT5Modality: Chemoradiation1.716
      βT6Modality: Bioradiation1.101
      βT7Mean dose to superior pharyngeal constrictor muscle0.030
      βT8Mean dose to inferior pharyngeal constrictor muscle0.013
      βT9Mean dose to contralateral parotid gland0.022
      βT10Mean dose to cricopharyngeal muscle0.008
      Step 4: A logistic regression analysis was used to test the hypothesis that the RBE depends on the LETd in each simulated dataset for each toxicity. For a model consisting of one predicting demographic parameter (Xdemographic) and one dose parameter (XD) the NTCP function is:
      NTCPS=11+exp-S
      (1)


      S=β0+β1·Xdemographic+β2·XD
      (2)


      To include a variable RBE, a mean D⋅LETd parameter is added for each OAR with a mean dose parameter
      S'=β0+β1·Xdemographic+β2·XD+c·β2·XD·LETd
      (3)


      The adjusted S′-function is identical to S when the RBE-LETd slope c is 0 (Table 2). Inserting S′ into the NTCP function, with the beta values and c as the only free parameters, and fitting to the data results in an estimate and standard error of the RBE-LETd slope c. This procedure allows the refitting of the parameter in the NTCP model as well as the RBE-LETd slope c. Refitting all NTCP parameters eliminates the possibility of model inaccuracies being mistaken for LETd effects. This procedure adds mean D⋅LETd parameters of OARs to the linear predictor S. This is similar to, but slightly different from, adding a LETd parameter as an effect moderator on the dose–effect relation of these OARs. When considering the mean D⋅LETd, LETd is only taken into account in areas where there is dose, which is where it is clinically relevant.
      Table 2Definitions of the S′ functions for all normal tissue complication probability models. The normal tissue complication probability can be calculated from these linear predictor functions using formula 1. The demographic parameters were categorized as described by Langendijk et al.

      Landelijk Platform Protonentherapie, Protonentherapie LP. Landelijk Indicatie Protocol Protonen Therapie Hoofd-halstumoren. 2017.

      .
      ModelS-functions
      Xerostomia
      S'=βX0+βX1·basexer=1+β2·basexer2+β3·Dpgcontra+c·β3·DLETpgcontra
      Dysphagia
      S'=βD0+βD1·basedys2+βD2·Dpcmsuperior+βD3·Doralcavity+c·βD2·DLETpcmsuperior+βD3·DLEToralcavity
      Tube feeding
      S'=βT0+βT1·T-stage3+βT2·1Weightloss10%+βT3·Weightloss>10%+βT4·Modality=Accelarated+βT5·Modality=Chemoradiation+βT6·Modality=Bioradiation+βT7·Dpcmsuperior+βT8·Dpcminferior+βT9·Dpgcontra+βT10·Dcpm+c·βT7·DLETpcmsuperior+βT8·DLETpcminferior+βT9·DLETpgcontra+βT10·DLETcpm
      Base xer: Baseline Xerostomia score on a 4-point scale where 0 is ‘none’, 1 is ‘a little’, 2 is ‘moderate’ and 3 is ‘severe’.



      Base dys: Baseline dysphagia grade scored between 0 and 4.

      Pcm: pharynx constrictor muscle.

      Pg contra: The parotid gland contralateral to the target.

      Cpm: Cricopharyngeal muscle
      Step 5: These simulations were performed 2500 times for sample sizes up to 100,000 patients for a RBE-LETd slope c of 0, 0.04 and 0.10 (keV/μm)−1 as described in the dataset simulation subsection above. The power was defined as the proportion of simulations for which the RBE-LETd slope c was statistically significantly larger than 0. Statistical testing was done using an alpha (probability of type I error) of 0.05 to test the null-hypothesis that the RBE-LETd slope is 0.
      For 2500 simulations the standard error of the power is at most 1.0%. All analyses were performed in Matlab 2018b. The required computation time for all simulations was 83 hours. All Matlab code was reviewed by the second author (AS) and is included in the supplementary material.

      Results

      The mean dose D and mean D⋅LETd parameters of different OARs of the 100 included patients are shown in Fig. 2 and their demographic characteristics are summarized in Table 3.
      Figure thumbnail gr2
      Fig. 2Distributions of mean dose D and voxel-wise product of D and LETd (D⋅LETd) to organs-at-risk for head and neck cancer patients treated with proton therapy (N = 100) The line plot represents the 90%-confidence threshold of the two-dimensional Gaussian fit. The Pearson correlations were 0.90 for the contralateral parotid, 0.95 for the oral cavity, 0.85 for the cricopharyngeal muscle, 0.85 for the superior pharynx constrictor muscle and 0.85 for the inferior pharynx constrictor muscle.
      Table 3Demographic characteristics of the patient population (N = 100).
      CharacteristicFrequency
      T-stage
       T1–T234
       T3–T466
      Baseline xerostomia
       None59
       A bit27
       Moderate-severe14
      Weight loss
       None55
       1–10%27
       >10%18
      Modality
       Conventional RT23
       Accelerated RT35
       Chemoradiation8
       Bioradiation34
      Baseline dysphagia
       Grade 0–160
       Grade 2–340
      NTCPMean (%)
       Xerostomia40.3
       Dysphagia20.7
       Tube feeding dependence6.1
      The demographic characteristics were scored according with the Dutch National indication protocol

      Landelijk Platform Protonentherapie, Protonentherapie LP. Landelijk Indicatie Protocol Protonen Therapie Hoofd-halstumoren. 2017.

      .
      The proportion of simulations for which a statistically significant independent relation was found (i.e. power) between toxicity and mean D⋅LETd for OARs is shown in Fig. 3. For a sample size of 5000 patients, the maximum power was 22%. For an assumed RBE-LETd slope c of 0.10 (keV/μm)–1, the required number of patients to reach 80% power was 28568, 30,000 and 24,058 for xerostomia, dysphagia and tube feeding respectively. For a RBE-LETd slope c of 0.04 (keV/μm)−1, none of the toxicities reached 80% power in our simulations.
      Figure thumbnail gr3
      Fig. 3Statistical power of showing an independent relation between toxicity and voxel-wise product of D and LETd (D⋅LETd) for an assumed RBE-LETd slope c of 0.04 or 0.1 (keV/μm)−1. Each toxicity has two line plots associated with it. The lower and higher estimates were for 0.04 and 0.1 (keV/μm)−1 respectively.
      For simulations with a RBE-LETd slope c of 0 (keV/μm)−1, the power was found to be 6.8%, 9.5% and 24.4% for xerostomia, dysphagia and tube feeding respectively with no clear dependence on sample size (Supplementary materials fig. S1).
      When the alpha was increased from 0.05 to 0.10 and testing was performed one-tailed instead of two-tailed, the required number of patients was decreased to 15,120, 17,350 and 14,341 for xerostomia, dysphagia and tube feeding respectively for a RBE-LETd slope c of 0.10 (keV/μm)−1 and 85,000, >100,000 and >100,000 respectively for a RBE-LETd slope c of 0.04 (keV/μm)−1.

      Discussion

      The number of patients required to independently relate the mean D⋅LETd of OARs to patient toxicity was found to be unfeasibly high for all considered toxicities. Even for 10,000 patients, the power was below 10% for all considered toxicities. This result was confirmed even when the alpha was increased to 0.10 and testing was performed one-tailed.
      These results indicate that an independent association between the mean D⋅LETd of OARs and patient toxicity is unlikely to be proven for the considered patient population. This also indicates that estimating the RBE from our current 100 patients would be very inaccurate. There have been previous publications relating patient toxicity to the DRBE calculated using a variable RBE [
      • Ödén J.
      • Toma‐Dasu I.
      • Witt Nyström P.
      • Traneus E.
      • Dasu A.
      Spatial correlation of linear energy transfer and relative biological effectiveness with suspected treatment-related toxicities following proton therapy for intracranial tumors.
      ,
      • Wang C.-C.
      • McNamara A.L.
      • Shin J.
      • Schuemann J.
      • Grassberger C.
      • Taghian A.G.
      • et al.
      End-of-range radiobiological effect on rib fractures in patients receiving proton therapy for breast cancer.
      ]. One such study, showed that the observed rib fracture rate after proton therapy of 6.4% for 203 breast cancer patients was in better agreement with photon therapy dose–response relations when considering a variable RBE than with a constant RBE of 1.1 [
      • Wang C.-C.
      • McNamara A.L.
      • Shin J.
      • Schuemann J.
      • Grassberger C.
      • Taghian A.G.
      • et al.
      End-of-range radiobiological effect on rib fractures in patients receiving proton therapy for breast cancer.
      ]. However, they did not show whether rib fractures were more likely to occur in ribs with higher LETd. As a result, other factors may have contributed to the difference in observed rib fracture rates between photons and protons. For example, many rib fractures are asymptomatic, so that their observed rates are greatly influenced by follow-up procedures which can be different between proton and photon therapy [
      • Kim D.W.
      • Kim S.J.
      • Kim K.
      • Shin K.H.
      Spontaneous rib fractures after breast cancer treatment based on bone scans: comparison of conventional versus hypofractionated radiotherapy.
      ]. Another study observed rib-fracture rates up to 18% in breast cancer patients who had undergone radiotherapy when evaluating bone scans every 12 months for at least three years [
      • Kim D.W.
      • Kim S.J.
      • Kim K.
      • Shin K.H.
      Spontaneous rib fractures after breast cancer treatment based on bone scans: comparison of conventional versus hypofractionated radiotherapy.
      ]. Even so, the relation between LETd and rib fracture is of potential interest as higher LETd can be expected in the ribs. Additionally, rib fracture is a clinical toxicity which is likely to be related to the maximum DRBE which possibly has less correlation with the mean D⋅LETd of OARs. Therefore, gathering the required sample size to formulate an NTCP model for rib fractures based on both mean D and mean D⋅LETd for OARs might still be feasible.
      Another way to investigate the relation between RBE and LETd in patients treated with proton therapy may be to consider a different endpoint. Several studies considered the relation between imaging changes and LETd at voxel level as an objective measure of biological damage which provides more spatial information on the damage [
      • Eulitz J.
      • Troost E.G.C.
      • Raschke F.
      • Schulz E.
      • Lutz B.
      • Dutz A.
      • et al.
      Predicting late magnetic resonance image changes in glioma patients after proton therapy.
      ,
      • Giantsoudi D.
      • Grassberger C.
      • Craft D.
      • Niemierko A.
      • Trofimov A.
      • Paganetti H.
      Linear energy transfer-guided optimization in intensity modulated proton therapy: feasibility study and clinical potential.
      ,
      • Bahn E.
      • Bauer J.
      • Harrabi S.
      • Herfarth K.
      • Debus J.
      • Alber M.
      Late contrast enhancing brain lesions in proton-treated patients with low-grade glioma: clinical evidence for increased periventricular sensitivity and variable RBE.
      ,
      • Peeler C.R.
      • Mirkovic D.
      • Titt U.
      • Blanchard P.
      • Gunther J.R.
      • Mahajan A.
      • et al.
      Clinical evidence of variable proton biological effectiveness in pediatric patients treated for ependymoma.
      ]. One such study by Bahn et al. analyzed 110 low-grade glioma patients with 67 contrast-enhancing brain lesions on follow-up MRI scans [
      • Bahn E.
      • Bauer J.
      • Harrabi S.
      • Herfarth K.
      • Debus J.J.
      • Alber M.
      Late contrast enhancing brain lesions in proton treated low-grade glioma patients: clinical evidence for increased periventricular sensitivity and variable RBE.
      ]. They found that the probability of lesions in a voxel was independently related to physical dose, D⋅LETd and proximity to the ventricular system. The fit parameters estimate an RBE-LETd slope of 0.1 (keV/μm)−1, a rate consistent with a variable RBE model with an α/β value of 2.0 Gy [
      • Wedenberg M.
      • Lind B.K.
      • Hårdemark B.
      A model for the relative biological effectiveness of protons: the tissue specific parameter α/β of photons is a predictor for the sensitivity to LET changes.
      ,
      • Bahn E.
      • Bauer J.
      • Harrabi S.
      • Herfarth K.
      • Debus J.J.
      • Alber M.
      Late contrast enhancing brain lesions in proton treated low-grade glioma patients: clinical evidence for increased periventricular sensitivity and variable RBE.
      ]. Another study by Peeler et al. investigated a cohort of 34 pediatric patients treated for ependymoma of which 14 showed hyperintensity on T2-FLAIR MRI scans. They related imaging change probability to physical dose and track-averaged linear energy transfer, but not to D⋅LETd [
      • Peeler C.R.
      • Mirkovic D.
      • Titt U.
      • Blanchard P.
      • Gunther J.R.
      • Mahajan A.
      • et al.
      Clinical evidence of variable proton biological effectiveness in pediatric patients treated for ependymoma.
      ].
      These studies show the potential of imaging to provide clinical evidence for the dependency of RBE on LETd. New imaging techniques may be even better suited to investigate RBE variations. With clinically used MRI scans, imaging changes are a dichotomous endpoint (i.e. changes are or are not observed). Diffusion tensor imaging (DTI) is an MRI technique able to detect the anisotropy of water diffusion, which is high in undamaged neural axons. The decrease in DTI values has been related to photon radiotherapy dose and can thus be used to quantify biological damage on a continuous scale [
      • Connor M.
      • Karunamuni R.
      • McDonald C.
      • White N.
      • Pettersson N.
      • Moiseenko V.
      • et al.
      Dose-dependent white matter damage after brain radiotherapy.
      ]. Similarly, the uptake of prostate specific membrane antigen (PSMA) in a PET scan has been related to salivary gland damage and may help localize salivary gland damage [

      Mohan V, Vogel WV, Valk GD, de Boer JP, Lam MGEH, de Keizer B. PSMA PET/CT identifies intrapatient variation in salivary gland toxicity from iodine-131 therapy. Mol Imaging 2020;19:153601212093499. 10.1177/1536012120934992.

      ]. If imaging techniques are able to quantify localized biological damage, each voxel’s biological damage can be related to localized dose and LETd at different time points and in different organs-at-risk.
      We found a higher than expected false positive rate for simulations with a RBE-LETd slope c of 0. The false-positive rate was higher for NTCP models with more independent predictors. The larger number of predictors possibly reduced the accuracy of the model. The large false positive rate indicates the model tests may not have been conservative enough. As a consequence, the actual required number of patients could be higher, not lower. Therefore, this limitation impacts the accuracy of our estimated required sample size but does not impact the conclusions of this study.
      An important drawback of looking for evidence of RBE variability using imaging changes is that the endpoints are potentially less clinically relevant than patient toxicity. Our results show that using patient toxicity as an endpoint is not feasible for current clinical practice due to the high correlation between mean physical dose and mean D⋅LETd for the relevant OARs. This correlation is a consequence of a lack of variation in OAR LETd caused by similarities in beam setup between patients.
      To our knowledge, this is the first study to investigate whether we can expect to find evidence of RBE variability (i.e. using LETd during the clinical treatment planning process) from future analyses when more patients have been treated with proton therapy. However, some limitations of our study have to be taken into consideration. We limited our study to HNC patients only. A drawback of our approach is that it depends on accurate NTCP models which are not available for all toxicities. We expect the results of our current study in HNC to be valid for toxicities of other treatment sites which depend on mean OAR dose as we expect a similar correlation between mean D and mean D⋅LETd in OAR, however this was not investigated in our study. We only considered two variable RBE models (i.e. a linear dependency on LETd with two different RBE-LETd slopes c). While the calculation time would allow for more RBE models with intermediate RBE-LETd slopes to be included, this was unnecessary as the results based on the strongest dependency on LETd have already indicated an unfeasibly high required patient sample size. In our study the dosimetric parameters were described using a multivariate Gaussian distribution while some non-normality could be present and heteroscedasticity can be observed in Fig. 2. The power for simulations with no RBE-LET relation were higher than the alpha of 5%, indicating that the testing methodology may not have been conservative enough and the number of required patients may have been underestimated.

      Conclusions

      We conclude that directly relating radiation-induced toxicity to the mean D⋅LETd of OARs will not be feasible for HNC patients treated with proton therapy in current clinical practice. Future research could focus on the indirect relation between RBE and LETd through imaging changes using different imaging modalities as these can be used to consider the local dose instead of the mean OAR dose. The presented study in no way contradicts evidence for an increased RBE at the end of proton range. Even though no relation between mean D⋅LETd for OARs and radiation-induced toxicity is expected to be observed for HNC patients, the incease of RBE is is substantiated by a large body of preclinical evidence. The question how proton RBE exactly depends on LETd for toxicity is still relevant because it can confirm how LETd can be used for treatment plan evaluation and will help guide the future implementation of LETd optimization. Therefore, new methodologies to investigate the proton RBE for clinical endpoints need to be explored.

      Conflict of interest statement

      • A research collaboration exists between the Department of Radiation Oncology, University Medical Center Groningen, University of Groningen, Groningen, the Netherlands and the following entities
        • o
          IBA (Ottignies-Louvain-la-Neuve, Belgium)
        • o
          Philips (Eindhoven, the Netherlands)
        • o
          Mirada Medical (Oxford, England)
        • o
          RaySearch Laboratories (Stockholm, Sweden)
        • o
          Elekta (Stockholm, Sweden)
        • o
          Siemens (Munich, Germany)
      • The fourth author (JL) reports honorarium for consultancy paid to UMCG Research BV.

      Acknowledgements

      We would like to acknowledge the contributions of Gijs Katgert, Nísia Santos Fernandez and Chioma Onyia towards gathering the required data.

      Appendix A. Supplementary data

      The following are the Supplementary data to this article:

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