## Introduction

Based on biological models, the excess absolute risk (EAR) of a second cancer occurring after exposure to radiation can be estimated from dose-volume histograms (DVH). Studies have compared different treatment techniques to determine the EAR after radiation therapy for breast cancer10,11,12,13. The EARs in the contralateral breast (CB) and the lungs have been compared between IMRT, VMAT, and tangential field techniques14. The thoracic size determines the distance between the breast and the body of the sternum, with affects the dose to the CB and lungs, even for the same treatment protocol. Secondary doses are inversely proportional to the distance from the treatment site. However, detailed and accurate data on radiation-induced secondary cancer risks to healthy organs after breast radiotherapy are lacking, and this information could provide guidance for the choice of radiotherapy techniques for breast cancer. On the other hand, because of the effect of respiratory motion, systematic error, and random error, the setup errors in breast cancer may be up to 5 mm or even larger than 5 mm in three dimensional directions during radiation therapy15. This introduces variation in the secondary dose to the CB and lungs in breast cancer treated with different modalities. Therefore, the risk of second cancer can increase or decrease, or show unobvious changes. In this study, we calculated and compared the secondary cancer risks associated with 3D-CRT, IMRT, and VMAT for the treatment of breast cancer after considering the effect of setup error and the distance between the breast and the body of the sternum. The concept of organ equivalent dose (OED) was used for the linear-exponential, plateau, and full mechanistic dose-response models11,13 to evaluate the secondary cancer risks to the CB, contralateral lung (CL), and ipsilateral lung (IL) after radiation therapy for breast cancer.

## Methods

### Patients

Computed tomography (CT) data of 26 patients who underwent breast cancer surgery were randomly selected from our database for a retrospective planning study. The median age was 41.6 years (range, 30–50 years). The ratio of right-sided to left-sided breast cancer was 1:1. Approval for retrospective analysis of patient data was obtained from the ethics committee of the Affiliated Cancer Hospital and Institute of Guangzhou Medical University.

Patients were divided into three groups according to the distance between the contralateral breast and the body of the sternum (Fig. 1) as follows: patients with a distance of <2 cm were classified into group 1 (G1); patients with a distance of 2–3 cm were classified into group 2 (G2); and patients with a distance of >3 cm were included in group 3 (G3). The G1:G2:G3 patient ratio was 4:5:4. Additionally, each group contained right-sided and left-sided breast cancer.

### Treatment planning

Patients were placed in the supine position with the ipsilateral arm in abduction above the head and scanned with 5 mm slice spacing. The target volumes and organs were delineated by clinical oncologists. The clinical target volume (CTV) included the whole breast. The planning target volume (PTV) was defined as the CTV with a 5–10 mm margin to the delineated target volume to compensate for treatment setup variability and internal organ motion but did not exceed the body. The organs at risk (OARs) included the heart, CB, CL, and IL. The PTV did not include the nodal for irradiation. Tumor bed boosts were not considered at this time.

Four treatment plans were designed for each patient using three different treatment techniques, such as tangential field 3D-CRT with hard-wedges (W-TF), tangential field IMRT (2F-IMRT), multiple field IMRT (6F-IMRT), and double partial arcs (VMAT). W-TF was used for 3D-CRT with hard-wedges (15° or 30°) and consisted of two parallel opposed tangential beams. The gantry and collimator angles were chosen to obtain the best target coverage and completely avoid the CB while minimizing exposure to the IL. The wedge angle, the beam weights, and the leaf openings were manually adjusted to optimize the target coverage and minimize the dose to the OARs. The corresponding 2F-IMRT was generated using the same tangential beams used for 3D-CRT but without wedges. The number of segments for 2F-IMRT was kept as low as possible, generally between 8–15 segments. The minimum segment area was set to 10 cm2, and the minimum segment monitor unit was set to 10 monitor units (MU). The 6F-IMRT consisted of multiple co-planar beams including three fields on the outer and inner sides of the breast, such as φ−25°, φ, φ + 25° and ν, ν + 10°, ν + 20°, where the φ and ν on both sides were set according to the tangential field from 3D-CRT. The total number of segments was ≤50, but the segment area and segment monitor unit were the same as those used for 2F-IMRT. The VMAT was created using double coplanar partial arcs with collimator angles of 15° or 345°. One arc was set up in a clockwise (CW) direction from φ to ν, whereas the second arc was performed in a counterclockwise (CCW) direction from ν to φ. The gantry spacing was 4°. The number of iterations for dose calculation did not exceed 100 during the IMRT and VMAT planning processes. All radiotherapy techniques were planned and calculated on the Pinnacle3 treatment planning system (TPS, version 9.10, Philips Medical Systems, Fitchburg, WI, USA) using a Collapsed Cone algorithm.

### Evaluation of plans

The total prescribed dose was 50 Gy to the PTV, which was delivered at 2 Gy per fraction16,17,18. The plans were optimized to cover at least 95% of each PTV by administering 95% of the prescribed dose. Dose constraints for the IL were set at V10 < 30%, V20 < 20%, and V30 < 10%, and the average dose Dmean < 15 Gy. Dose constrains for the ipsilateral heart were set at V10 < 20%, V20 < 15%, and V30 < 20%, and V5 < 15% was set for the contralateral heart with a maximum dose Dmax < 40 Gy for the spinal cord16,17,18. The VX Gy referred to the volume receiving more than x Gy. Doses to the CB and lungs were kept as low as possible without compromising target coverage. All plans were optimized and evaluated for optimal target coverage, conformity, homogeneity, and dose limits of OARs. The conformity index (CI)19, which is a measure of target volume dose distribution conformity, was defined as CI = VT,ref/VT × VT,ref /Vref, where VT,ref is the target volume covered by reference isodose, VT is the target volume, and Vref is the volume of the reference isodose. A CI closer to 1 indicated better dose conformity. The homogeneity index (HI)20, which is a measure of the evenness of dose distribution, was defined as HI = (D2–D98)/D50, where D2, D98, and D50 are the doses covering 2%, 98%, and 50% of the PTV, respectively. HI = 0 is considered the ideal value. Analysis of the OARs included the maximum dose, mean dose, and a set of appropriate define (Vx) and define (Dy) values.

### Secondary cancer risk assessment

Several risk models had been developed to estimate secondary cancer risk, as detailed in Supplementary data. Based on the exported differential DVHs, secondary cancer risks in OARs were calculated using Schneider’s OED concept13, which included the impact of fractionation and incorporated a repair and population parameter. The OED was calculated for the linear-exponential, plateau, and full mechanistic dose-response models10,11,12,13. Assuming that the dose-response was linear to the dose exposition, the linear model OEDlin for an organ would be calculated as follows:

$${{\rm{OED}}}_{lin}=\frac{1}{{{\rm{V}}}_{0}}\sum _{i}{V}_{Di}Di$$
(1)

Considering that the probability for cell killing increased exponentially with the dose, which would decrease the risk of cancer induction due to the killing of mutated cells, the linear-exponential model OEDlinear-exp for an organ would be calculated as follows:

$${{\rm{OED}}}_{linear-exp}=\frac{1}{{V}_{0}}\sum _{i}{V}_{Di}Di\,exp(-\alpha ^{\prime} Di)$$
(2)

If it was assumed that the dose-response had reached a plateau after increasing linearly up to a certain dose because of the balance between cell killing and recovery effects in a fractionated scheme, the plateau model OEDplateau for an organ would be calculated as follows:

$${{\rm{OED}}}_{plateau}=\frac{1}{{V}_{0}}\sum _{i}{V}_{Di}\frac{1-{\exp }(-\alpha ^{\prime} Di)}{\alpha ^{\prime} }$$
(3)

When there was an enhancement of the linear exponential model and plateau model and considering the number of fractions in the fractionated therapy, the full mechanistic model OEDmechanistic for an organ was calculated as follows:

$${{\rm{OED}}}_{mechanistic}=\frac{1}{{V}_{0}}\sum _{i}{V}_{Di}\frac{exp(-\alpha ^{\prime} Di)}{\alpha ^{\prime} R}+\left[1-2R+{R}^{2}exp(\alpha ^{\prime} Di)-{(1-R)}^{2}exp\left(-\frac{\alpha ^{\prime} R}{1-R}Di\right)\right]\,$$
(4)

The VDi was the volume of the DVH bin receiving dose Di, and V0 was the total volume of the organ. For the full mechanistic model, the parameters α′ = 0.044 Gy–1 and R = 0.15 for a female breast, and α′ = 0.042 Gy–1 and R = 0.83 for the lungs were derived from a combined fit to the data of atomic bomb survivors and data of Hodgkin’s patients treated with single doses of 2 up to 40 Gy assuming an α/β value of 3 Gy. Similarly, α′ = 0.041 Gy–1 for the linear-exponential model and α′ = 0.115 Gy–1 for the plateau model were used in regard to a female breast, whereas α′ = 0.022 Gy–1 for the linear-exponential model and α′ = 0.056 Gy–1 for the plateau model were used in regard to the lungs.

The EAR described the absolute difference in cancer rates between persons exposed to a dose d and those not exposed to a dose beyond the natural dose exposure per 10,000 person-years per Gy. The EAR was calculated as follows12:

$${\rm{EAR}}={{\rm{EAR}}}_{0}\times {\rm{OED}}$$
(5)

EAR0 represented the initial slope of the dose-response curve at a low dose and included population-related parameters, such as age at exposure (agex), sex (s) and attained age (agea), namely EAR0(agex, s, agea). The EAR of developing a second cancer in one of the investigated organs was calculated as follows:

$${\rm{EAR}}={\rm{OED}}\beta ^{\prime} exp[{\gamma }_{e}(agex-30)+{\gamma }_{a}\,\mathrm{ln}(agea/70)]$$
(6)

β′ was the initial slope for the dose-response relationship of second cancer induction, γe and γa were the age-modifying factors. All parameters for EAR calculation were from Schneider. All EARs were initially calculated based on patients irradiated at the actual age and assumed to reach an age of 70 years. To remove the EAR variability related to the varying age of irradiated patients, the EAR was recalculated based on all patients who were irradiated at age 30 years and reached an age of 70 years.

### Setup error simulations

The effect of setup error on the variation of secondary doses to organs was simulated by moving the isocenter and recalculating the dose distribution without changing the field fluence distribution21. When the isocenter was moved, it was assumed that all beams were incorrectly positioned in the same direction for all fractions during treatment, namely systematic setup error. According to Hurkmans’ work, the systematic setup error in the study was 5 mm in the different directions, such as left–right (L-R), superior–inferior (S-I), and anterior–posterior (A-P). Random errors were ignored at this time.

### Statistical analysis

Statistical analysis was performed using SPSS 19.0 (SPSS Inc., Chicago, IL, USA). Data were expressed as the mean ± standard deviation. Data for dosimetric factors, OEDs, and EARs obtained from different plans were evaluated and compared using Wilcoxon’s signed rank test. Multiple groups of means were compared by one-way analysis of variance (ANOVA) after testing for equality of variance. Homogeneity of variance was assessed using Levene’s test. Differences were considered statistically significant when P < 0.05.

### Ethical approval and informed consent

All experimental protocols used in this study were approved by the Institutional Review Board of Affiliated Cancer Hospital and Institute of Guangzhou Medical University. The requirement for patient informed consent was waived by the Institutional Review Board, and all experiments were performed in accordance with relevant international and national guidelines and regulations.

## Results

### Dosimetry for PTVs and OARs

The IMRT and VMAT plans resulted in significantly lower mean doses to OARs and equivalent doses to the PTV than 3D-CRT plans. A representative dose distribution for the four treatment plans is presented in Fig. S1 (Supplementary data). Both 6F-IMRT and VMAT significantly reduced hot spots. The dosimetric parameters and the number of monitor units for all alternative techniques are shown in Figs. 2 and 3. The CI and HI for the PTV were optimal in VMAT, followed by 6F-IMRT, whereas the CI and HI showed the worst values in 3D-CRT’ (P < 0.05). The CI obtained from 6F-IMRT was superior to that from 2F-IMRT, whereas the HI was similar between the two techniques. The minimum low dose volumes to OARs were observed in 2F-IMRT, and VMAT frequently resulted in more low-dose volumes than 2F-IMRT, followed by 3D-CRT and 6F-IMRT (P < 0.05). The low dose volumes from 3D-CRT were similar or inferior to those from 6F-IMRT, whereas the high dose volumes to the IL and heart obtained from VMAT were reduced to some extent. The treatment MUs were lower with 2F-IMRT than with the other three treatment modalities, whereas the treatment MUs were comparable between the other three treatment modalities (P > 0.05).

### Secondary cancer risk

The risks of radiation-induced secondary cancers for all alternative techniques relative to that for 2F-IMRT are shown in Fig. 4. The OEDs to the CB and CL were significantly higher for VMAT than for 2F-IMRT, followed by 6F-IMRT and W-TF. However, the OEDs to the IL were lower for VMAT (P < 0.05) and comparable between the other three treatment modalities (P > 0.05). The corresponding EARs in all organs are shown in Fig. 5. The effect of the age of irradiated patients was eliminated to reduce the variability in EAR. Table S1 shows the OEDs and EARs to organs, which were calculated using linear-exponential and plateau dose-response models (see Supplementary data). The other three alternative techniques had higher secondary cancer risks than 2F-IMRT for most patients. However, when either W-TF or 2F-IMRT was compared with 6F-IMRT or VMAT, the OEDs and EARs for W-TF or 2F-IMRT in all patients were smaller than those of 6F-IMRT or VMAT except in the IL.

After adjusting for the effect of the distance between the CB and the body of the sternum, the OEDs and EARs to organs in the different groups are shown in Fig. 6, Table S2, and Table S3. In the CB, the OEDs and EARs decreased significantly in correlation with increased distance for all alternative techniques. The OEDs and EARs to the CB were similar between W-TF and 6F-IMRT when the distance was <2 cm (P > 0.05), whereas the OEDs and EARs were higher for 6F-IMRT than for W-TF when the distance was >2 cm (P < 0.05). For the EARs at different distances, higher secondary cancer risks were observed for VMAT, such as an EAR of 103.311/10,000 PY, whereas secondary cancer risks were lower for 2F-IMRT, such as an EAR of 18.214/10,000 PY. Conversely, secondary cancer risks to the CL were almost independent from distance, and depended mainly on radiotherapy techniques. The EARs to the CL were significantly higher for VMAT than for the other three alternative techniques (P < 0.05), increasing the risks by 6.545-, 16.545-, and 3.664-fold over those for W-TF, 2F-IMRT, and 6F-IMRT, respectively. For the IL, the OEDs and EARs were significantly lower for all alternative techniques when the distance was >3 cm. However, VMAT was associated with lower OEDs and EARs than those of the other three alternative techniques in this case.

### Effects of setup error on secondary cancer risk

The maximum differences of OEDs and EARs to organs for all alternative techniques determined after setup error simulations are shown in Table 1 and Table S4. Compared with W-TF, the OEDs and EARs for the other three treatment modalities showed a greater effect of setup error, especially 2F-IMRT, which changed by 198.82% in the CB and 122.77% in the CL. The OEDs and EARs to the CL showed a lower effect of setup error without significant differences (P > 0.05). There was no significant difference in the increments of change in OEDs and EARs for the CB and IL between 2F-IMRT, 6F-IMRT, and VMAT. In contrast, the increments of change in OEDs and EARs for the CL were significantly different between all alternative techniques, increasing in the order of W-TF, 2F-IMRT, 6F-IMRT, and VMAT.

When considering the distances, the maximum differences of OEDs and EARs to organs after setup error simulations are shown in Table 2, Table 3, Table S5, and Table S6. For the CL, the OEDs and EARs after adjusting for distance showed a lower effect of setup error for all alternative techniques. For the CB and IL, the OEDs and EARs after adjusting for distance also showed a greater effect of setup error except for W-TF. Furthermore, there was a significant difference in the increments of change in OEDs and EARs for the CB at different distances, but not for the IL. If the distance was <2 cm, the change of EAR was 83.168/10,000 PY in the CB after setup error simulation, except for W-TF. If the distance was >3 cm, the effect of setup error on the secondary cancer risk to the CB was significantly decreased, except for VMAT. The total absolute risk of secondary cancer according to distance was determined by adding the EARs to the CB and CL based on pre- and post-simulated setup error for all alternative techniques, as illustrated in Fig. 7. On average, the cumulative EARs for 2F-IMRT were lower before setup error simulation, although there was a small increase in secondary cancer risk for 2F-IMRT and an increase of 159% and 318% for 6F-IMRT and VMAT, respectively, compared with W-TF after setup error simulation. After setup error simulation, if the distance was <2 cm, there was no significant difference in EARs between 2F-IMRT and 6F-IMRT, whereas there was an approximately 38% higher overall EAR for 6F-IMRT than for 2F-IMRT.

## Discussion

In radiation therapy for breast cancer, 3D-CRT with tangential fields, even when used with hard-wedges or dynamic-wedges, is generally used to improve the dose uniformity to the tumor22. IMRT and VMAT have been increasingly used to provide a higher conformal dose distribution in the radiation treatment of breast cancer17. Compared with 3D-CRT, IMRT and VMAT showed excellent results regarding tumor target conformity and homogeneity, especially 6F-IMRT and VMAT, which is consistent with other studies17,18. However, for organs proximal to the fields, such as the CB, CL, IL, and heart, the low dose volumes were considerably higher with 6F-IMRT and VMAT than with 3D-CRT, which are associated with radiation-induced risk of secondary cancer6. Along with improved long-term survival rates in breast cancer, the secondary cancer risk after radiation therapy is becoming critical. Approximately 80% of secondary cancers are located either within the radiation field or in the beam-bordering regions23. However, accurate prediction of radiation-induced cancer risk is complex because of the lack of long-term follow-up and epidemiological data. Although several risk models have been developed to estimate secondary cancer risks, the incidence rates of radiation-induced cancer are not necessarily a linear function of dose. The dose-risk relationship is linear at lower doses (<2 Gy) for all solid organs and at higher doses (up to 40 Gy) for the breast and lung24,25. Previous studies demonstrated that the linear-exponential, plateau, and full mechanistic dose-response models provide a better description of the dose-risk relationship than other linear models for inhomogeneous dose distributions (>2 Gy)10,12. However, detailed and accurate data on radiation-induced secondary cancer risks to healthy organs after breast radiotherapy are lacking.

Because the Monte Carlo calculation for 3D-CRT and wedge planning is lacking in commercial planning systems, the Collapsed Cone algorithm was used for all radiotherapy techniques in this study26. This may result in inaccuracies in the estimates with respect to the Monte Carlo algorithm27,28. In this study, the EARs for 6F-IMRT and VMAT were significantly higher than those for W-TF and 2F-IMRT. These results were consistent with those of previous studies6,29,30,31. VMAT is associated with an especially high risk of secondary cancer relative to multi-field IMRT; similarly, multi-field IMRT is associated with a higher risk of secondary cancer than 3D-CRT without external wedges30. By contrast, tangential IMRT has a lower risk of secondary cancer than 3D-CRT with external wedges31. This was attributed to the leakage of radiation outside the field, which increased in correlation with increased field numbers and MUs. For example, the MUs were considerably higher for 6F-IMRT and VMAT. The mean secondary cancer risk for 2F-IMRT was slightly lower than that for W-TF, although this was not true for every patient. A similar trend was observed when comparing 6F-IMRT and VMAT. Therefore, when determining which modality has a higher secondary cancer risk, we must consider differences between individual patients. The differences between the linear-exponential, plateau, and full mechanistic dose-response models were smaller, except for the IL. Because the IL constitutes the target volume or is close to the target, it receives high doses to achieve tumor control. The higher doses to the IL lead to larger differences between the models. This warrants special consideration when estimating the secondary cancer risk to the IL. When organs located in the high dose regions are considered in the risk calculations, the leakage radiation dose has a negligible impact on the calculated risks.