Effects of dose and dose-averaged linear energy transfer on pelvic insufﬁciency fractures after carbon-ion radiotherapy for uterine carcinoma

Background and Purpose: The correlation between dose-averaged linear energy transfer (LETd) and its therapeutic or adverse effects, especially in carbon-ion radiotherapy (CIRT), remains controversial. This study aimed to investigate the effects of LETd and dose on pelvic insufﬁciency fractures after CIRT. Material and Methods: Among patients who underwent CIRT for uterine carcinoma, 101 who were followed up for > 6 months without any other therapy were retrospectively analyzed. The sacrum insufﬁ- ciency fractures (SIFs) were graded according to the Radiation Therapy Oncology Group/European Organization for Research and Treatment of Cancer toxicity criteria. The correlations between the relative biological effectiveness (RBE)-weighted dose, LETd, physical dose, clinical factors, and SIFs were evalu-ated. In addition, we analyzed the association of SIF with LETd, physical dose, and clinical factors in cases where the sacrum D50% RBE-weighted dose was above the median dose. Results: At the last follow-up, 19 patients developed SIFs. Receiver operating characteristic curve analysis revealed that the sacrum D50% RBE-weighted dose was a valuable predictor of SIF. Univariate analyses suggested that LETd V10 keV/ l m, physical dose V5 Gy, and smoking status were associated with SIF. Cox regression analysis in patients over 50 years of age validated that current smoking habit was the sole risk factor for SIF. Therefore, LETd or physical dose parameters were not associated with SIF prediction. Conclusion

an effective treatment method for gynecological tumors. As with conventional RT, managing adverse events (AEs) after CIRT is considered vital.
Proctitis and cystitis are the most frequent late AEs after RT in the pelvic region [10]. Pelvic insufficiency fractures (PIFs) are also late AEs after RT and CIRT in the pelvic region [11,12]. RT for premenopausal women results in direct bone damage from radiation and indirect bone damage due to decreased ovarian function [13]. Pelvic injuries significantly decrease a patient's quality of life and increase mortality [14]. Thus, PIF is a significant AE after RT. Regarding the risk analysis for PIF after conventional RT, Ramlov et al. reported that patients aged > 50 years and the dose irradiated to 50 % of the volume (D50%) of the sacrum were predictors of PIF [15]. However, given the differences in terms of biological effectiveness between photon beams and carbon-ion beams, these predictors are unlikely to be applied in CIRT. Linear energy transfer (LET) is the amount of energy an ionizing particle transfers to the material traversed per unit distance. CIRT originally possesses a high LET; therefore, it is highly effective against cancer cells because it induces complex deoxyribonucleic acid (DNA) doublestrand breaks, dysfunction of the G2/MÀphase checkpoint, and mitotic catastrophes at a high rate [16,17]. Therefore, the socalled ''clinical dose" in CIRT is defined based on this biological effect, representing the relative biological effectiveness (RBE)weighted dose [18][19][20][21].
Of note, LET has been suggested to be more critical than the RBE-weighted dose, Gray (Gy) (RBE), in the anti-tumor effect of CIRT. Hagiwara et al. reported that the minimum dose-averaged LET (LETd) within the tumor was significantly associated with LC in primary pancreatic cancers [22]. In addition, Matsumoto et al. reported that local recurrence was not observed when the effective minimum LETd value exceeded 40 keV/lm after CIRT for chondrosarcoma [23]. Meanwhile, our previous study found no correlations between severe rectal toxicities and LETd alone or physical dose per se after CIRT for uterine carcinoma [24]. In a study, Niemierko et al. reported that LET adjusted for dose was not associated with the risk of brain necrosis in proton beam therapy [25]. Thus, the correlation between LETd and its therapeutic effects along with AEs, especially in CIRT, is controversial. Therefore, the purpose of this study was to comprehensively investigate the effects of dose and LETd on PIFs following CIRT for uterine carcinoma.

Materials and methods
The present single-institution retrospective observational study commenced following institutional review board approval (QST 18-015). Owing to the retrospective nature of the study, the requirement for written informed consent was waived. A document establishing an opt-out policy was uploaded to the institution's website, allowing patients and their families to opt-out of the study. The study adhered to the principles of the Declaration of Helsinki.

Patient eligibility criteria
Between June 1995 and January 2010, 134 patients with uterine carcinoma underwent definitive CIRT as part of four clinical trials [3][4][5][6]. None of the patients in this cohort received concurrent chemotherapy or brachytherapy because of the regulation of these clinical trials. Of the 134 patients, 102 who were followed up for > 6 months with no other external beam RT in the pelvic region were enrolled. We analyzed all patients except one whose LETd data could not be retrieved; therefore, we analyzed a total of 101 patients. The patient cohort was the same as that used in a previ-ous study [12]. However, there was a longer follow-up period in this study.

Treatment outlines for carbon-ion radiotherapy
The modified microdosimetric kinetic model (MKM) was applied for CIRT RBE-weighted dose calculation at our institution, which was expressed in Gy (RBE) [18][19][20]. The RBE calculation based on MKM involves in vitro data on the 10 % survival rate of human salivary gland tumor cells under aerobic conditions and clinical experience with fast neutron beam therapy [26]. Details of CIRT for uterine carcinoma can be found in our previous studies [3][4][5][6]. In brief, the prescribed dose ranged from 52.8 to 74.4 Gy (RBE), which was determined due to the involvement of patients enrolled in dose-escalation clinical trials [3][4][5][6]. The patients received 20 or 24 fractions of CIRT for 5-6 weeks. The irradiation field size decreased in a stepwise manner from irradiating the whole pelvis to the tumor. All treatments were performed using passive beam irradiation, and no dose constraints were set for the pelvic bone of patients in this study. This study defined Gy (RBE) as the RBE-weighted dose to clarify definitions.

LETd distributions
The data acquisition method for the LETd distribution was similar to that in our previous study [24]. The RBE-weighted dose distributions based on modified MKM were calculated using the treatment planning system, XiO-N (Mitsubishi Electric, Tokyo), and the LETd was calculated from RBE and physical dose [27]. Additionally, primary carbon ions and secondary and tertiary projectile nuclear fragments were counted in the LETd using the Sihver model [28]. The LETd at location r was calculated as follows: where Di(r) denotes the physical dose distribution for beam i, ni denotes the beam fraction, and Li(r) denotes the LET distribution for beam i. Li in the equation is the LETd of the i-th beam at location r. The LET for this study was defined by the following settings: unrestricted, LET for water, and no density normalization [29]. As illustrated in Fig. 1, the calculated LETd distribution was superimposed on planning computed tomography (CT).

Data acquisition
Our previous study examined the preferred PIF site after CIRT for gynecologic tumors and revealed that the sacrum insufficiency fracture (SIF) site was the most predominant one [12]. Therefore, we collected data on the RBE-weighted dose, LETd, and physical doses to the sacrum in this study. The contour of the sacrum was delineated on XiO-N. The outer line of the bone was defined as the outer edge of the sacrum, without distinguishing between the bony cortex and trabecular bone.
Next, dose parameters were determined using dose-volume histograms (DVHs) [30]. The RBE-weighted dose parameters, including V10-40, D50%, D5cc, and D2cc, were obtained from DVHs using XiO-N. Vx Gy (RBE) in this context means the volume of the sacrum that received an RBE-weighted dose of Â Gy (RBE) or more. D RBE Â cc represents the minimum RBE-weighted dose to which a volume of Â cc has been irradiated. D RBE 50% indicates the dose irradiated to 50 % of the volume of the sacrum. The D50% of the sacrum is a relative value that has been reported by Ramlov et al. as a significant risk factor for PIFs in photon beam therapy [15]. We subsequently obtained LETd parameters, including V L 10-40 keV/lm, L50%, L5cc, and L2cc in keV/lm, as described previously [24]. V L Â keV/lm in this context means the volume of the sacrum that received an LETd of Â keV/lm or more. Lx cc represents the minimum LETd value to which a volume of Â cc has been exposed. L50% represents the LETd value exposed to 50 % of the volume of the sacrum. The physical dose distributions were generated through the RBE-weighted dose calculation on XiO-N, and the parameters, including V P 5-15, D P 50%, D P 5cc, and D P 2cc in Gy, were also determined. V P Â Gy in this context means the volume of the sacrum that received a physical dose of Â Gy or more. D P Â cc represents the minimum physical dose to which a volume of Â cc has been irradiated. D P 50% indicates the physical dose irradiated to 50 % of the volume of the sacrum. These parameters and clinical factors, such as age, smoking history, alcohol consumption, and body mass index, were analyzed as risk predictors of SIF.
The diagnostic criteria of SIFs included findings of T1hypointense and T2-hyperintense lesions on MRI and/or fracture lines or sclerotic changes without osteolytic lesions on CT images and no evidence of bone metastasis, similar to the previously reported findings [12].

Statistical analysis
Comparisons of RBE-weighted DVH parameters between patients with and without SIFs were performed by the Mann-Whitney U test. The optimal cut-off values for the RBE-weighted dose of SIFs were determined using receiver operating characteristic (ROC) curve analysis. Additionally, the area under the ROC curve (AUC) values were calculated. The log-rank test was used for univariate analyses. The factors with a p-value < 0.1 by univariate analysis were included in the Cox regression analysis. For multiple factors with p-value < 0.1 in each category, that is, LETd, physical dose, and clinical factors, a multivariate analysis was performed using factors with the lowest p-value from the univariate analysis to avoid confounding of factors. A correlation analysis was used to evaluate the correlation between the two values.
Firstly, we specifically identified the parameters for SIF based on the RBE-weighted dose using the Mann-Whitney U test. Thereafter, we validated the reliability of these parameters in predicting SIF by ROC analysis. We dichotomized the patient groups based on the RBE-weighted dose parameter(s) and determined whether LETd, physical dose, or clinical factors were associated with SIF in each group. Univariate and multivariate analyses were used for these validations. Additionally, we used 50 years as the cut-off age for multivariate analysis, as reported in a previous study on pelvic insufficiency fractures [15].
All test results were considered statistically significant at a twosided p-value < 0.05. SPSS 27.0 (for Mac) was used for statistical analyses (Armonk, NY: IBM Corp, USA). Table 1 shows the patient and tumor characteristics in this study. The median follow-up time was 66 months (range, 8-297 months), and the median age at diagnosis was 58 years (range, 28-85 years). SIFs were observed in 19 patients during the last follow-up. Fig. 2A shows the DVH of each patient's RBE-weighted dose to the sacrum in the groups with SIF and without SIF. The averaged DVHs in the groups with SIF and without SIF are shown in Fig. 2B. When comparing DVH parameters between patients  with and without SIFs, the patients with SIFs showed a statistically significant difference in V10 Gy (RBE), V20 Gy (RBE), V30 Gy (RBE), D RBE 50%, D RBE 5cc, and D RBE 2cc compared to those of patients without SIF (Mann-Whitney U tests) (Table 2A). When dichotomized by the median of each parameter, the Mann-Whitney U test showed a statistically significant difference in the incidence of SIF for all parameters except D RBE 5cc, which was particularly significant for D RBE 50% and V20 Gy (RBE) (p < 0.001, each) (Table 2B). ROC analyses showed that AUCs ranged from 0.682 to 0.755, and the AUCs of D RBE 50% and V20 Gy (RBE) were particularly high for these factors (0.755 and 0.753, respectively), suggesting that they are valuable risk predictors for SIF (Fig. 2C). As shown in Table 2B, however, even in these groups with high D RBE 50% or V20 Gy (RBE), there were cases with and without SIF. Therefore, univariate and multivariate analyses were performed to further examine the effects of physical dose, LETd, and clinical factors on SIF in the groups. Next, we examined the factors influencing SIF in 51 patients whose D RBE 50% was beyond the median. The characteristics of 51 patients are shown in Supplementary Table 1. Among these 51 patients, 17 developed SIF at the last follow-up. Table 3 shows the univariate analysis to assess the risk factors of SIF. The V10 keV/lm in LETd and the V5 Gy in physical dose showed significant differences according to log-rank tests, suggesting that they are   (Table 4B). Therefore, parameters of LETd or physical dose were not predictive of SIF.

Results
To validate these findings that LETd or physical dose parameters were not risk predictors for SIF, we performed univariate analyses to assess the risk factors for SIF in the 50 patients whose D RBE 50% was less than the median. None of the dose parameters or clinical factors showed a significant difference according to the log-rank test (Supplementary Table 2).
As mentioned earlier, ROC analysis suggested that V20 Gy (RBE) was also a valuable predictor of SIF. Therefore, similar to the analysis based on D RBE 50%, we validated whether SIF was associated with LETd, physical dose, and clinical factors in patients with high V20 Gy (RBE). The characteristics of the 51 patients whose V20 Gy (RBE) was above the median are shown in Supplementary Table 3. Among these 51 patients, 17 developed SIF at the last follow-up. Supplementary Table 4 shows the results of univariate analyses of the risk factors for SIF; interestingly, neither LETd nor physical dose parameters showed significant differences with respect to SIF, suggesting that only smoking history was associated with SIF (p = 0.005). Cox regression analysis validated that current smoking habit was the sole risk factor for SIF (p = 0.006; HR = 5.188; 95 % CI: 1.593-16.900). Furthermore, the Cox regression analysis in the population over 50 years of age showed an even higher HR for current smoking habit with respect to SIF (p = 0.001; HR = 40.107; 95 % CI: 4.238-379.609) (Supplementary Table 5). Therefore, LETd or physical dose parameters were not found to be risk predictors of SIF, even with the analyses based on V20 Gy (RBE). The correlation analysis showed a high correlation between D RBE 50% and V20 Gy (RBE) (r = 0.891).

Discussion
To our knowledge, this is the first study to comprehensively examine the effects of the RBE-weighted dose, LETd, and physical dose on SIF development after CIRT for uterine carcinoma. Firstly, this study revealed D RBE 50% to be a valuable risk predictor of SIF. The V20 Gy (RBE) was also suggested to be a significant risk predictor of SIF. The median D RBE 50% in this study was 19.9 Gy (RBE); the two variables, D RBE 50% and V20 Gy (RBE), were highly correlated. Ramlov et al. reported that the sacral D50% was predictive of SIF in locally advanced cervical cancer patients over 50 years of age treated with radical chemoradiation using intensity-modulated RT [15]. Thus, our results support Ramlov's findings [15]. Unlike the rectum and bladder, where small volumes in the high dose Table 3 Univariate analyses of risk factors for sacrum insufficiency fracture in 51 patients whose D RBE 50% was above the median in the relative biological effectiveness-weighted dose. Analyzed by log-rank tests. * Data was not available in one patient. D RBE 50 %, the relative biological effectiveness-weighted dose irradiated to 50 % of the volume of the sacrum; SIF, sacrum insufficiency fracture; LETd, dose-averaged linear energy transfer; V L Â, the volume of the sacrum that received an LETd of Â keV/lm or more; SD, standard deviation; L50 %, the LETd value exposed to 50 % of the volume of the sacrum; Lx, the minimum LETd value to which a volume of Â cc has been exposed; V P x, the volume of the sacrum that received a physical dose of Â Gy or more; D P 50 %, the physical dose irradiated to 50 % of the volume of the sacrum; BMI, body mass index.

Table 4
Assessment of risk factors by multivariate analysis.
(A) Cox regression analysis in 51 patients whose D RBE 50% was above the median in the relative biological effectiveness-weighted dose. range are associated with late AEs [31], the medium dose for the entire sacrum resulted in the development of SIFs. Therefore, it seems reasonable to lower the D RBE 50% to < 19.9 Gy (RBE) to prevent SIFs in CIRT. However, as shown in Table 2A, in addition to D RBE 50%, the RBE-weighted dose parameters of V10-30 Gy (RBE), D RBE 5cc, and D RBE 2cc also correlated with SIF. In an in vivo experiment, Schreurs et al. reported that radiation decreased the bone mass of trabecular bones but not that of dense bones [32]. Although dense and trabecular bones were not distinguished in this study, DVH analysis considering the bone structure may be warranted in the future.
The multivariate analysis in this study revealed that LETd or physical dose per se were not significant predictors of SIF development. This result supports the validity of the model we used to calculate the biological dose [18][19][20]. This result also agrees with the findings of our previous study on late rectal AEs in CIRT [24]. Recently, in proton beam therapy, it has been reported that the RBE-weighted dose considering the LETd, rather than the LETd or the physical dose per se, was helpful in predicting late AEs in the brain and ribs [25,[33][34][35]. Bahn et al. calculated the LETd distributions using the Monte Carlo method in patients treated with proton therapy for low-grade glioma and reported the degree of concordance of dose and LETd distribution with minor posttreatment brain necrosis [35]. Their study revealed that the dose distribution weighted by LETd correlated strongly with contrastenhancing brain lesions, which was suggestive of minor brain necrosis, but not with the LETd distribution itself. Taken together, these results suggest that LETd per se may not be consistent with late normal tissue response in CIRT or proton beam therapy. However, in CIRT for primary pancreatic cancer and chondrosarcoma, low LETd in the tumor has been reported to be associated with local recurrence [22,23]. To date, there is no clear explanation for the discrepancy between the behavior of LETd in normal tissues and tumors. Therefore, further comprehensive analysis of the significance of LETd in other normal tissues and tumors is needed.
Regarding the mechanism of accelerated bone fragility after irradiation, Alwood et al. reported the effects of irradiation on bone and bone marrow cells of mice, using proton radiation as low-LET radiation and iron ion radiation as high-LET radiation [36]. Their study revealed that 50 cGy proton irradiation did not cause significant changes in bone structure, but 50 cGy iron ion irradiation caused significant changes in bone structure, compared to those of the control. Additionally, gene expression in bone marrow cells after 200 cGy of iron ion irradiation showed an increase in the expression of Gadd45, which is involved in cell cycle arrest, and a decrease in the expression of Alpl, which is an osteoblast differentiation gene. However, no such changes were observed after proton beam irradiation [36]. Thus, high-LET radiation may strongly affect bone cells or their gene expression. However, the effects in the dose range of several tens of Gy, such as those used in RT, have not been clarified. Additionally, it is difficult to extrapolate the results of in vivo study to those of humans, considering the differences in bone metabolism and external forces on bone due to differences in the skeletal structure between mice and humans. Considering the recent advancements in changing the LETd in the irradiation field by mixing multiple ion species [37,38], further studies on the effects of such high-LET radiation on the bone are critical to establishing a method for preventing fractures after CIRT.
In this study, age, smoking habit, alcohol consumption, and BMI as risk factors for SIF did not show significant differences in the univariate analysis of D RBE 50%. However, multivariate analysis in the group restricted to patients aged 50 years and older suggested that smoking was the only factor associated with SIF. In addition, the univariate analysis of V20 Gy (RBE) showed that only smoking history was associated with SIF. Smoking, including regular cigarettes or e-cigarettes, increases the risk of fractures and adversely affects fracture healing [39]. Furthermore, smoking worsens the overall survival of patients with locally advanced cervical cancer undergoing RT [40]. It also increases the incidence of malignancy and ischemic heart disease and increases the risk of mortality by a factor of 1.48 in women, compared to that in non-smokers [41]. Therefore, in addition to the negative health effects of smoking, smoking cessation guidance for patients undergoing CIRT is vital, as smoking can increase SIF risk.
This study had several limitations. First, the potential for bias, stemming from the retrospective nature and the limited sample size needs to be considered. Therefore, our findings need to be validated by other studies. Second, the effect of dose fractionation on CIRT has not been studied. All patients enrolled in this study had been enrolled in clinical trials for the dose-escalation study of CIRT; therefore, there was no room for dose fractionation adjustment. The fractionation effect in CIRT is likely to be small because the direct effect on DNA damage is more substantial than that in Xray therapy [16]. However, further investigation into the effect of late AEs, including brittle bones, may be warranted. Third, a limitation due to the calculation model of CIRT was considered. This study applied a modified MKM for dose calculation [20]. Therefore, caution should be exercised in interpreting the results because the calculation method differs from that of the local effect model (LEM), which is mainly applied in European particle therapy facilities [42]. It would be worthwhile to validate the findings of this study with clinical data using LEM. Although the present study has these limitations, our results show that the risk factors in CIRT gynecologic tumors help prevent SIF and may contribute to the patient's quality of life after CIRT treatment. Additionally, the fact that LETd does not affect SIF may support the feasibility of LETmodulated RT [43].
In conclusion, this study showed that the D RBE 50% was a risk factor for SIF. Neither LETd nor physical dose parameters were significant risk factors for SIF, and the current smoking habit was the only factor contributing to SIF when stratified by age > 50 years.

Funding
This study was supported by management expenses grant from the National Institutes for Quantum Science and Technology.

Declaration of interest
Nobuyuki Kanematsu reports relationships with the Japan Society of Medical Physics (which includes board membership and travel reimbursement), Japan Radiology Congress (which includes board membership and travel reimbursement), Kanagawa Cancer Center (which includes consulting or advisory), Osaka International Cancer Treatment Foundation (which includes travel reimbursement), and the Association for Nuclear Technology in Medicine (which includes speaking and lecture fees). In addition, Nobuyuki Kanematsu has patents: #JP2020-044286A (pending), #JP6383429 (issued), #JP5954705 (with royalties paid), #JP5521225 (with royalties paid), and #JP4456045 (with royalties paid), all to the National Institutes for Quantum Science and Technology.