- Open Access
Dose-response relationship for breast cancer induction at radiotherapy dose
© Schneider et al; licensee BioMed Central Ltd. 2011
Received: 23 March 2011
Accepted: 8 June 2011
Published: 8 June 2011
Cancer induction after radiation therapy is known as a severe side effect. It is therefore of interest to predict the probability of second cancer appearance for the patient to be treated including breast cancer.
Materials and methods
In this work a dose-response relationship for breast cancer is derived based on
(i) the analysis of breast cancer induction after Hodgkin's disease,
(ii) a cancer risk model developed for high doses including fractionation based on the linear quadratic model, and
(iii) the reconstruction of treatment plans for Hodgkin's patients treated with radiotherapy,
(iv) the breast cancer induction of the A-bomb survivor data.
The fitted model parameters for an α/β = 3 Gy were α = 0.067Gy -1 and R = 0.62. The risk for breast cancer is according to this model for small doses consistent with the finding of the A-bomb survivors, has a maximum at doses of around 20 Gy and drops off only slightly at larger doses. The predicted EAR for breast cancer after radiotherapy of Hodgkin's disease is 11.7/10000PY which can be compared to the findings of several epidemiological studies where EAR for breast cancer varies between 10.5 and 29.4/10000PY. The model was used to predict the impact of the reduction of radiation volume on breast cancer risk. It was estimated that mantle field irradiation is associated with a 3.2-fold increased risk compared with mediastinal irradiation alone, which is in agreement with a published value of 2.7. It was also shown that the modelled age dependency of breast cancer risk is in satisfying agreement with published data.
The dose-response relationship obtained in this report can be used for the prediction of radiation induced secondary breast cancer of radiotherapy patients.
Cancer induction after radiation therapy is known as a severe side effect. It is therefore of interest to predict the probability of second cancer appearance for the patient to be treated. For this purpose it is not sufficient to apply the results from epidemiological studies on cancer induction from more than 20 years ago to the patient treated today, since radiation therapy changed significantly in the last decades, for instance radiation type, treatment technique, application of treatment, treatment duration and 3D dose distributions.
As a consequence it is necessary to model cancer induction for patients undergoing radiotherapy and thus the underlying dose-response relationship [1–3]. Such modelling can be based on epidemiological studies of patients treated with old techniques. However, most of the epidemiological studies, which are published in large numbers, don't provide a correlation of cancer induction with dose. Unfortunately, if a dose correlation is deduced, cancer induction is usually related to the integral dose or average organ dose and thus implies a linear dose-response relationship. Therefore, such data cannot be used directly to obtain non-linear dose-response relationships. Up to now there are only few studies which correlate cancer induction in radiotherapy patients with point dose estimates at the location of secondary tumor growth [4–10].
Radiotherapy of patients with Hodgkin's disease is very successful, but women treated with mantle field radiation experience up to a 30-fold increased risks for breast cancer compared with their peers in the general population. Travis et al  for instance studied breast cancer induction for mantle field treatments of Hodgkin's disease. They reconstructed the point doses where the secondary breast cancer was located and performed a case/control study to stratify breast cancer risk as a function of dose.
The goal of this report is the derivation of a dose-response relationship for breast cancer induction based on the analysis of Hodgkin's disease patients by Travis et al  and breast cancer induction from the A-bomb survivors . A recently developed cancer induction model  including fractionation was fitted to the available data. The model was tested by predicting second cancer risk resulting from historical mantle field treatments for Hodgkin's disease and comparing them to published epidemiological data. In addition model predictions were compared to recently published second breast cancer risk for mediastinal involved field radiotherapy.
Materials and methods
where the sum is taken over all volume elements V i of the breast and V Breast is the total breast volume.
It is assumed here an α/β = 3 Gy for breast tissue. However, α/β = 1 Gy and α/β = 5 Gy were also used for optimization to test the robustness of the model.
where the age modelling was centered around 30 and 70 years, respectively. This risk representing the A-bomb survivor data is plotted with the corresponding error bar in all figures of this report as a dashed line.
Patient data and statistical analysis
Point dose estimates and related odd ratios for breast cancer after radiotherapy of Hodgkin's disease from Travis et al .
Median dose (range)[Gy]
Odds ratio (stand. dev.)
EAR optimized with A-bomb agex= 30 agea= 70, α/β= 3 (std. dev.)
The unadjusted odds ratio was computed from controls and cases, and the error factor and confidence levels were obtained using maximum likelihood estimates. The odds ratio, which approximates relative risk, is listed in Table 1.
The model parameters α and R of Eq.2 were optimized by a variation in the interval [0,1] for both case-control studies independently. For any combination of (α,R)∈ [0,1] the relative risks of Travis et al  were converted to excess absolute risk. The risk for radiation induced cancer after radiation therapy is better modelled using excess absolute risk (EAR) as expressed by Eq. 2, since relative risk estimates make only sense when patients with the same dose distributions are compared and this is most often not the case for radiotherapy patients. As EAR defined by Eq. 2 approaches for small dose the LNT model it was assumed that the risk of the lowest dose category corresponds to the findings of the A-bomb survivor data. This correspondence was used to transform the Travis data, expressed in odds ratios, into EAR. However, the LNT risk for breast cancer (μ = 4.8/10000PY/Gy according to Eq. 4) is subject to an uncertainty between 3.5 and 6.2/10000PY/Gy (95% CI-interval according to ). This uncertainty was included in the model fit for the lowest dose category.
Fitted model parameters with the corresponding standard deviation for different α/β-values.
0.067 (0.033-0.112 )
Dose reconstruction for risk predictions
Dose distributions were reconstructed, which were characteristic for a large patient collective of Hodgkin's disease patients. We calculated the dose distributions in an Alderson Rando Phantom with a 200 ml breast attachment.
Typical treatment techniques for Hodgkin's disease radiotherapy were reconstructed. Treatment planning was performed on the basis of the review by Hoppe  and the German Hodgkin disease study protocols (http://www.ghsg.org). We used for treatment planning the Eclipse External Beam Planning system version 8.6 (Varian Oncology Systems, Palo Alto, CA) using the AAA-algorithm (version 8.6.14). Treatment plans were computed which included mantle field treatment and treatment of supraclavicular, axillary and mediastinal lymph nodes for both, left and right location. All plans were calculated with 6 MV photons and consisted of two opposed fields. The technique for shaping large fields included divergent lead blocks. Treatment was performed at a distance of 100 cm (SSD). Anterior-posterior (ap/pa) opposed field treatment techniques were applied to insure dose homogeneity.
The mantle field included the bilateral cervical, supraclavicular, axillary, infraclavicular, mediastinal and pulmonary hilar lymph nodes. The unblocked field size was 34 cm × 33 cm with equal field weights from 0° and 180°. The superior border of the mantle was located along the base of the mandible, and the inferior border was at the level of the insertion of the diaphragm (T10 vertebra). Blocks were placed over the lung and the humeral heads both anteriorly and posteriorly. Spinal cord blocking was not needed, since the planned total dose was 38 Gy, which is the average dose of the patients studied by Travis et al . All blocks were contoured by hand.
The pelvic field included bilateral iliac and inguinal lymph nodes with 2 cm safety margins laterally. The superior border was drawn at the L4-5 interspace, the inferior border was bilateral at the inferior border of the obturatorial foramen.
The supraclavicular field included the ipsilateral supraclavicular fossa and the lower cervical lymph nodes, that means from the inferior border of the hyoid bone to 1.5 - 2 cm below the clavicle.
The axillarv field encompassed the axillar lymph nodes. It included the periclavicular region and reached caudally to the 6th rib. A small peripheral lung zone of 1.5 cm was included. We used a block over the humeral head. The mediastinal field included both the superior and inferior mediastinal and hilar lymph nodes in addition to the lower cervical and supraclavicular lymph nodes (medial 2/3 of clavicula). The upper border was the hyoid bone, the lower border the insertion of the diaphragm. The field border was on each site 1.5 cm inferior to the clavicule, along transversal processi and 1.5 cm laterally from each hilus.
Results of the model fit
Comparison of modelled breast cancer risk with published results of mantle field treatment
The dose-response relationship for breast cancer induction obtained in this work was used to predict female breast cancer risk resulting from independent epidemiological studies of mantle field treatments of Hodgkin's disease.
Cohort size (number of patients), median age at exposure and attained age for the published breast cancer rates after Hodgkin's disease radiotherapy.
Modelled breast cancer risk for different α/β-values for mantle field treatment of Hodgkin's disease and comparison with published data.
EAR [/10000 PY]
Dores et al
Hancock and Hoppe
Swerdlow et al
α/β = 1 Gy
α/β = 3 Gy
11.8 (9.2 -15.8)
α/β = 5 Gy
It should be noted here that the statistical power of the published data is quite different due to the different cohort sizes (Table 3) involved. The data from Dores et al  are by far the most reliable since the number of observed persons is six-times larger than the second largest group.
Comparison of modelled breast cancer risk with published results for involved field treatment
Comparison of modelled and observed relative breast cancer risk for involved field radiotherapy.
Used Treament plans
Weighting according to # treated patients
Relative OED (Travis fit)
Observed relative risk
Mantle field alone
Axillary + Mediastinal/homolat
Axillary + Mediastinal/bilat
Axillary, no Media.
Breast cancer risk for the cohort analysed by De Bruin et al  was modelled using the dose-volume histograms for the left and right breast obtained from the treatment plans listed in Table 5. OED was calculated using Eqs. 2-4 with an α/β = 3 Gy using the fitted model parameters from Table 2. Since OED is additive the total OED for a treatment technique was determined using the weighting of the treatment fields of Table 5.
Comparison of modelled age dependence of breast cancer risk with clinical results
The aim of this study was the determination of model parameters for a dose-response relationship for breast cancer covering dose levels relevant for radiotherapy. In addition a model for the age dependence of breast cancer risk was verified. The model was tested with epidemiological data on second breast cancer of historic mantle field treatments and high dose involved field radiotherapy. Satisfying agreement was found. In the limit of small dose the model approaches the LNT-model for cancer induction.
In this report a cancer induction model for the radiotherapy dose range was used. Several assumptions had to be made to simplify the biological processes leading to cancer induction . This includes the design of tissues, the repopulation process and processes which result in the formation of a tumor cell. This was done to keep the number of model parameters at a minimum. However, this is associated with uncertainties.
When interpreting the results of this study, certain limitations should be taken into account. The model was fitted to epidemiological data describing breast cancer risk after radiotherapy of Hodgkin's disease. Several assumptions were made to use these data for model fitting. It has been hypothesized that the age parameters of the complete patient cohorts can be applied to the patients grouped in different dose categories. In addition the median/averages of the characteristic age parameters were used knowing that the ages can vary significantly and that the age dependence is in general non-linear.
In addition the impact of ovarian function on breast cancer induction is not included in the model. Chemotherapy and pelvic radiotherapy could have a protective effect regarding breast cancer induction. However, in the publication of De Bruin et al  such an effect was not found.
In this work EAR has been used to quantify radiation-induced cancer. Usually excess relative risk (ERR) is recommended for transferring risk from the Japanese population to other populations. EAR is used here, since the risk calculations of the Hodgkin's cohort are based on extremely inhomogeneous dose distributions. Currently there is no method available for obtaining analogous organ risks using ERR. As the difference between the Japanese and the US population in EAR for all solid tumors is less than 10% the use of EAR is probably justifiable.
Additionally, as the results of this report are expressed in terms of EAR, it is also difficult to compare them with the findings of Sachs and Brenner  who fitted an algebraic model of cancer induction to breast cancer risk. The risk ratio between historic mantle field treatments and high dose involved field radiotherapy is however comparable with other ERR models .
The treatment plans calculated in this work were computed using 6 MV photons. Apparently, patients treated in a time period of nearly 30 years were irradiated with x-ray beams of various energies. Since De Bruin et al  presented no information on the range of treatment energies, it was decided to use 6 MV photons. However, this could have an impact on the calculated dose distributions in particular on the deposited energy from scattered radiation.
In this work a dose-response relationship for breast cancer was derived based on the analysis of breast cancer induction after Hodgkin's disease, a cancer risk model developed for high doses including fractionation based on the linear quadratic model, and the reconstruction of treatment plans for Hodgkin's patients treated with radiotherapy.
The fitted model parameters for an α/β = 3 Gy and μ = 4.8/10000PY/Gy were α = 0.067 Gy-1 and R = 0.62. Breast cancer risk is according to this model for small doses consistent with the findings of the A-bomb survivors, has a maximum at doses of around 20 Gy and drops off only slightly at larger doses. The predicted EAR for breast cancer after radiotherapy of Hodgkin's disease is 11.7/10000PY which can be compared to the findings of several epidemiological studies were EAR for breast varies between 10.5 and 29.4/10000PY. The model was used to predict the impact of the reduction of radiation volume on breast cancer risk. It was predicted that mantle field irradiation is associated with a 3.2-fold increased risk compared with mediastinal irradiation alone. This is comparable to the findings of De Bruin et al  who found a 2.7-fold increase.
It was also shown that the modelled age dependency of breast cancer risk based on the A-bomb survivor data is in satisfying agreement with published data on breast cancer risk after radiotherapy of Hodgkin's disease. The work presented here might provide the first direct evidence that cancer risk age modelling based on the A-bomb survivor data can be applied to radiotherapy patients.
The dose-response relationship obtained in this report can be used for the prediction of radiation induced secondary breast cancer of radiotherapy patients. It might be used to further optimize radiation therapy of Hodgkin's disease with regard to second breast cancer. In addition the obtained α-value for breast tissue can be used for applications of the linear-quadratic model in radiotherapy.
This study was supported in part financially by the European Commission with ALLEGRO grant No. 231965.
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