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Hypofractionation of partial breast irradiation using radiobiological models
Physica Medica 31 (2015) 1022–1028
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Physica Medica j o u r n a l h o m e p a g e : h t t p : / / w w w. p h y s i c a m e d i c a . c o m
Original Paper
Hypofractionation of partial breast irradiation using radiobiological models Michele Avanzo a,*, Marco Trovo b, Joseph Stancanello c, Rajesh Jena d, Mario Roncadin b, Giulia Toffoli e, Chiara Zuiani e, Elvira Capra a a
Medical Physics Department, CRO Aviano, 33081 Aviano, Italy Radiation Oncology Department, CRO Aviano, 33081 Aviano, Italy c MRI Applications and Workflow, General Electric, 78533 Buc, France d Department of Oncology, University of Cambridge, Cambridge CB2 0QQ, UK e Institute of Diagnostic Radiology, Department of Medical and Biological Sciences, University of Udine, 33100 Udine, Italy b
A R T I C L E
I N F O
Article history: Received 20 April 2015 Received in revised form 10 July 2015 Accepted 3 August 2015 Available online 23 October 2015 Keywords: Hypofractionation Partial breast irradiation NTCP TCP Breast Fibrosis
A B S T R A C T
Purpose: To reduce the fraction number in Partial Breast Irradiation (PBI) with initial prescription of 40 Gy in 10 fractions using radiobiological models with specific focus on risk of moderate/severe radiationinduced fibrosis (RIF) and report clinical results. Methods and materials: 68 patients (patient group A) were treated with 40 Gy in 10 fractions delivered by field-in-field, forward-planned IMRT. Isotoxic regimens with decreasing number of fractions were calculated using Biological Effective Dose (BED) to the breast. Risk for RIF in hypofractionated treatment was predicted by calculating NTCP from DVHs of group A rescaled to fractions and dose of novel regimens. Moderate/severe RIF was prospectively scored during follow-up. Various NTCP models, with and without incomplete repair correction, were assessed from difference to observed incidence of RIF. In order to verify the value for α/β of 3 Gy assumed for breast, we fitted α/β to observed incidences of moderate/ severe RIF. Results: Treatments with 35 Gy/7f and 28 Gy/4f were selected for the fraction reduction protocol. 75 patients (group B) were treated in 35 Gy/7f. Incidence of moderate/severe RIF was 5.9% in group A, 5.3% in group B. The NTCP model with correction for incomplete repair had lowest difference from observed RIF. The α/β obtained from fitting was 2.8 (95%CIs 1.1–10.7) Gy. Conclusions: The hypofractionated regimen was well tolerated. The model for NTCP corrected for incomplete repair was the most accurate and an assumed α/β value of 3 Gy is consistent with our patient data. The hypofractionation protocol is continuing with patients treated with 28 Gy/4f. © 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Introduction In recent years partial breast irradiation (PBI) performed with external photon beams has gained acceptance in the post-operative management of early stage breast cancer after breast conserving surgery [1–4]. In our hospital, PBI treatments were delivered following a novel protocol consisting of 40 Gy in 10 daily fractions of 4 Gy over two weeks which produced good cosmetic results [5]. In radiotherapy (RT) treatments it is desirable to reduce the overall treatment time to enhance convenience to the patient as well as reduce the treatment burden of breast radiotherapy in busy treatment centers. Strategies to shorten treatment time include reducing the number of fractions (hypofractionation) and increasing the
* Corresponding author. Medical Physics Unit, CRO Aviano National Cancer Institute, 33081 Aviano, Italy. Tel.: +39 0434659175; fax: +39 0434659524. E-mail address: [email protected] (M. Avanzo).
number of fractions per day (accelerated treatment). Good results in terms of side effect profile and local control rate [1] have been generally reported with accelerated PBI (APBI), which is delivered in twice daily fractions but, in two APBI studies, significant short term toxicities have been observed [3,4]. On the other hand, trials of whole breast RT hypofractionation provided evidence that lower total doses of RT delivered in fewer fractions with larger doses per fraction are as safe and effective as conventional regimens (50 Gy in 25 fractions) for women after primary surgery for early breast cancer [6,7]. A strategy to reduce fraction number was therefore adopted in our hospital to reduce the duration of PBI from the consolidated regimen of 40 Gy/10 fractions. A clinically acceptable hypofractionation regimen should yield equivalent effect to the tumor and risk of normal tissue toxicity. These goals can be achieved using the concept of Biologically Effective Dose (BED), which accounts for the effect of fractionation on clinical outcome, and analytical models of Normal Tissue Complication Probability (NTCP), which correlate outcome of RT with
http://dx.doi.org/10.1016/j.ejmp.2015.08.016 1120-1797/© 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
M. Avanzo et al./Physica Medica 31 (2015) 1022–1028
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Table 1 Models for NTCP and BED, and radiobiological parameters used in the present study. Model, description, reference
Parameter values
(1) Model for moderate/severe RIF prediction model accounting for incomplete repair and latency of effect, derived from published average clinical and dosimetrical data of PBI and WBI [9] (1a) Model 1, calculated from average DVH and average follow-up time of the patient groups (1b) Model 1, with α/β = 2.8 Gy derived from fitting clinical results in the present study (2) Model for moderate/severe RIF accounting for latency of effect, derived from published average clinical and dosimetrical data of PBI and WBI [9] (3) Moderate/severe RIF prediction model, derived from analysis of pooled individual patient clinical data of EORTC and START trials, with two-compartment DVH model [10] (4) Moderate/severe RIF prediction model, derived from published clinical data of PBI and WBI and DVHs from in-phantom generated treatments [8] (5) Biologically effective dose (BED) for breast cancer based on linear quadratic model and Poisson statistics [15]
dose-volume data and fractionation scheme [8–11]. These predictive models have now been implemented in clinical practice, specifically as a tool for comparison of treatment schedules [12,13]. To model toxicity, we use models of NTCP for subcutaneous radiation induced fibrosis (RIF). RIF is characterized by progressive induration, edema formation, and thickening of the dermis and subcutaneous tissue. It is considered one of key side effects of PBI influencing cosmetic outcome [14]. We recently derived NTCP models for the risk of severe (grade 2 or more) RIF from published incidences of RIF on PBI [9]. The best fit parameters for the model were estimated using average dosimetric parameters (prescription dose, fraction dose, mean follow up time) from published Whole Breast Irradiation (WBI) studies and external beam PBI studies. The purpose of this study was to derive consistent fraction reduction protocol for PBI using radiobiological models and report clinical results on patients treated with the newly designed regimen. In our previous work, verification of NTCP models for RIF used to design the hypofractionation protocol could be made in a very limited dataset with limited follow-up time (35 patients with 12 months average follow up) [9]. As follow up data for incidence of side effects were prospectively collected in the present work, the accuracy of NTCP models can be tested against a more diverse and mature dataset. Moreover, since in NTCP modeling of RIF the value of α/β of RIF was assumed as 3 Gy, we want to test the validity of this assumption by fitting α/β to incidences of severe RIF in the hypofractionation study already available at our institution.
n = 0.15, m = 0.22, BEUD50 = 105.8 Gy, α/β = 3 Gy, μ = 0.46 years, σ = 1.27 years
n = 0.06, m = 0.22, BEUD50 = 107.2 Gy, α/β = 3 Gy, μ = 0.46 years, σ = 1.27 years n = 0.012, m = 0.35, BEUD50 = 132 Gy, α/β = 3 Gy n = 0.78, m = 0.27, BEUD50 = 104 Gy, α/β = 3 Gy α = 0.27 Gy−1, α/β = 4 Gy, Tpot = 15 days, Tk = 0
to study the average NTCP as a function of dose and fraction number. These patients, previously treated by breast conserving surgery for an early stage ductal carcinoma, underwent non-accelerated external PBI with prescribed dose of 40 Gy in 10 daily fractions of 4 Gy over two weeks [5]. Patient characteristics are shown in Table 2. The clinical target volume (CTV) consisted of the lumpectomy cavity and the Planning Target Volume (PTV) consisted of the CTV plus 1 cm margin. Breast tissue visible on the computed tomography simulation scan was outlined. The RT technique consisted of “field-infield” planning (forward-planned intensity modulated RT) [16] using
Methods and materials Hypofractionation modeling The hypofractionated treatments were designed with the aim of being isotoxic, that is, of providing the same biological dose for the effect of moderate/severe RIF. A formula of BED based on the linear quadratic model was used to derive equivalent prescribed doses, with a value for α/β of 3 Gy for breast tissue (Eq. A1 in Appendix A.1). Hypofractionated treatments were required to have the same BED to the breast as the initial treatment of 40 Gy in 10 fractions. In order to evaluate the effect of change of regimen on the tumor, a formula corrected for repopulation of tumor cells was used to calculate tumor BED as described by Eq. (A2) in Appendix A.1. The radiobiological parameters of models are shown in Table 1. The total dose with the same BED as the initial treatment with 40 Gy in 10 fractions was plotted versus decreasing number of fractions in Fig. 1. NTCP for severe RIF in the hypofractionated regimens was preliminarily estimated from data of patients already treated with 40 Gy/ 10f using a model originally derived from literature data on PBI [9] as described in Appendix A.2. Data from 68 patients (patient group A) treated with PBI between July 2008 and June 2012 were used
Figure 1. Design of hypofractionation protocol of PBI. The red dashed lines represent the prescribed dose giving the same tumor BED as the initial treatment of 40 Gy in 10 fractions for decreasing number of fractions. Levels of average NTCPIR of moderate/severe RIF (green areas) are calculated from DVHs of patients previously treated with the initial regimen of 40 Gy/10 fractions rescaled to different doses and fractions. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 2 Characteristics of patients treated at our institution with PBI in the initial (Group A) and hypofractionated regimens (Groups B and C). Incidence of fibrosis is not assessed in the third group due to short follow-up time. Patient and treatment characteristics
Mean value (range) Group A
Group B
Group C
Prescribed dose [Gy] Fractions [number] Patients [number] Age [years] Follow-up [months] RIF grade ≥ 2 [yes/no]
40 Gy 10 68 71 (61–83) 53 (17–23) 4/64
35 Gy 7 75 70 (61–85) 26 (9–38) 4/71
28 4 15 70.5 (60–81) 3 [0–6] /
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Clinical results
Figure 2. DVHs of patients treated with the original PBI regimen of 40 Gy/ fractions and the hypofractionated regimens of 35 Gy/7 fractions and 28 Gy/4 fractions.
A second group of 75 patients (Group B), whose characteristics are summarized in Table 2, was treated using the first hypofractionated regimen of 35 Gy in 7 fractions. For these treatments, image guidance based on daily orthogonal antero-posterior and lateral kV images and 3 fiducial markers placed on the tumor bed was performed before each fraction. This permitted safe reduction of the PTV margin to 5 mm. Maximal toxicity was evaluated during post-treatment follow-up visits that occurred after 1, 3, 6 and 12 months for the first year, and then once a year. The DVHs of patients treated with are shown in Fig. 2. With the approval of our Institutional Review Board and after obtaining informed consent from each patient, the dosimetric data and follow-up data were reviewed. Patients were seen at regular intervals to determine the presence of symptoms, and one physician (M.T.) evaluated the toxicity by the RTOG scale and by the CTCAE (version 3.0) [17]. The presence of RIF (grade 2 or more) was reported at the end of treatment, 1 month and every 3 months after the completion of radiation course, and scored in a prospective database. In order to describe the statistical uncertainty on the incidence of moderate/severe RIF in our patient population, confidence intervals for the observed incidences of toxicities were calculated using the Clopper–Pearson Binomial interval [18]. Verification of radiobiological models
multiple planar and non-coplanar 6 MV photon beams. All treatments were developed using the Eclipse treatment planning system (version 8.9.08, Varian Medical Systems, Palo Alto, CA), and dose calculations were carried out using the anisotropic analytical algorithm (AAA) with a grid resolution of 2.5 mm, taking into account heterogeneity correction. For every patient, individual (percentage breast volume vs dose in Gy) differential DVHs of the ipsilateral breast and follow up times (time from end of RT to last follow-up visit) were recorded. The differential DVHs were exported in a text format with dose bins of 0.05 Gy. The average value of NTCP in patient group A versus the total prescribed dose D and number of fractions N was calculated (Fig. 1). In the model, termed NTCPIR, a correction for incomplete repair between two fractions delivered in the same day can be included in order to account for the effect of accelerated regimens (Eqs. A8–A9 in Appendix A.2). A correction for latency of the toxicity event was also included to account for events that are censored due to incomplete follow-up and result in decreased number of observed toxicities. This correction factor (Eq. A11, Appendix A.3) was calculated for each patient from the individual follow-up time, defined as the time between end of the treatment and last follow-up visit, and represents the probability that the side effect is developed before last follow-up visit [11]. NTCPIR iso-level curves were then calculated and plotted in the same graph of total dose versus fraction number (Fig. 1), in order to assess equivalent dose to the tumor and, at the same time, the risk of moderate/severe RIF deriving from changing prescription dose and fractions.
As the first toxicity data have been collected we tested the NTCP models used for hypofractionation protocol design, the predictive capability of different NTCP models was tested by comparison of average NTCP against observed incidence of RIF in the patients treated with 40 Gy/10f and 35 Gy/7f PBI. As combined difference between model predictions and incidence of toxicity, we used the square root of the sum of squared differences between NTCP and RIF in the two cohorts. The first test was to check if the NTCPIR works when calculated from individual patient data, as it was originally derived from average dosimetrical and follow up data reported in literature on breast radiotherapy [9]. To this purpose, the average DVH was calculated for each of the two patient groups. NTCPIR was calculated from average DVHs and follow-up times of the two patient groups (Model 1a in Table 1) and compared against average NTCPs calculated from individual data (Model 1). As a result, no significant difference was found, as shown in Table 3, indicating that the two methods provide equivalent estimates of risk of the side effect. Second, NTCPIR results were compared against other models of NTCP for severe/moderate RIF available in literature, all of which do not incorporate incomplete repair correction, as shown in Table 1. In order to verify the value for α/β of 3 Gy assumed for breast, the α/β for RIF was derived by fitting the model with the best predictive power, NTCPIR, to observed incidences of RIF. The weighted least squares method was used to determine the best fit α/β value, assuming the number of patients in each dataset as weights. The
Table 3 Results of calculation of NTCP with different models described in Table 1 and differences from observed incidences of RIF. For each model used, the average NTCP value on patient groups is reported with 95%CIs. Treatment
40 Gy/10f 35 Gy/7f
Incidence of RIF
5.9 (1.6–14.4)% 5.3 (1.6–14.4)% Combined difference of NTCP from incidences of RIF:
NTCP mean value (95% CIs) Model 1
Model 1a
Model 1b
Model 2
Model 3
Model 4
5.6 (2.5–9.6)% 1.6 (0.25–3.2)% 3.7%
5.5% 1.7% 3.7%
6.9 (3.1–11.9)% 2.0 (0.3–4.1)% 3.5%
12.4 (5.8–16.6)% 5.2 (1.3–8.3)% 6.6%
18.5 (15.3–21.02)% 10.7 (6.1–13.3)% 13%
1.1 (0.2–4.2)% 0.2 (0.1–0.5)% 7.0%
M. Avanzo et al./Physica Medica 31 (2015) 1022–1028
lsqcurvefit MATLAB instruction was used which employs the “trustregion-reflective” algorithm for large scale optimization by Coleman and Li [19]. The cost function in the optimization process was the sum of squares of percent differences between observed incidences of RIF and NTCP in the two patient groups. The optimization stopped when the change of the cost function was less than 0.01% or the change of the variable α/β was less than 0.01 Gy. The asymptotic 95% confidence intervals for the estimated parameters and 95% prediction intervals for the fitted function were evaluated, assuming the asymptotic normal distribution for the parameter estimates, from the Jacobian matrix and the residuals of fit [20]. Results Hypofractionation modeling The regimens with total prescribed doses of 35, and 28 Gy in 7 and 4 fractions, respectively, were selected for the clinical study of fraction reduction. Using α/β of 3 Gy for moderate/severe RIF, both treatments are equivalent to 40 Gy in 10 fractions for subcutaneous tissue. These treatments are equivalent, for the tumor, to 39.9 Gy and 39.4 Gy in 10 fractions, respectively. Hypofractionated treatments, equivalent in terms of tumor control to the initial treatment, yielded a predicted toxicity level between 5 and 10% for the endpoint of Grade 2+ RIF, as shown in Fig. 1. Clinical results 75 patients were then treated with 35 Gy in 7 fractions. The mean follow-up was 26 months (range, 9–38 months), and therefore all patients were assessable for late toxicity. The proposed fractionation scheme was very well tolerated, and grade ≥2 fibrosis was observed only in 4 (5.3%) patients with 95% CIs of 1.6–14.4%. Verification of radiobiological models The differences between NTCP calculated with available models for moderate/severe RIF and observed incidences of side-effects in patients treated with 40 Gy/10f and 35 Gy/7f are shown in Table 3. The incidences of RIF were 4/68 (5.9% with 95% CIs of 1.6–14.4) and 4/75 (5.3%, 95% CIs of 1.6–14.4%) among patients treated with 40/ 10f and 35/7f, respectively. Combined difference of average NTCP from RIF was 3.9% with the NTCPIR model, which scored better than all other NTCP models without incomplete repair correction. The α/β was obtained from fitting after three optimization iterations and was 2.8 Gy with 95% CIs of 1.1–10.7 Gy. The combined difference of NTCP IR model from RIF incidence with this value for α/β decreased to 3.5%. Using this α/β for fibrosis, the 37/7f and 28/4f hypofractionated treatments are equivalent to 40.1 and 40.2 Gy in 10 fractions for subcutaneous tissue. Discussion Hypofractionation modeling Radiobiological models for patient outcome have been used to study the feasibility of hypofractionated regimens [21,22]. The usual method involves determining equivalent doses such as normalized total doses (NTDs) at fractions of 2 Gy or BED to the tumor and the most critical organ at risk at various fraction numbers or fraction size in order to determine isotoxic and/or isoeffective regimens [21]. In this study, we used BED to the breast tissue as the objective was to produce isotoxic treatments. Given that tumor has α/β ratio similar to that of breast tissue, treatments were equivalent also for the tumor, as they yielded equivalent doses to the tumor very
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close to the initial prescription. As a consequence, treatments can be considered to be isoeffective and isotoxic. Before beginning the reduction of fractions, we estimated the risk for RIF in hypofractionated treatments by calculating NTCPIR using individual dosimetrical data of patients treated with the initial regimen (group A) rescaled to doses and fractions of the new regimens. The model NTCPIR included the correction for latency of the side-effect calculated from individual follow-up times. The predicted incidence of RIF using the NTCPIR model was 5.3% with 35/7 and 4.9% with 28/4, as shown in Fig. 1. This approach provides a preliminary estimate of toxicity in a novel regimen which accounts for the dose distribution generated from the treatment technique in use. The limit of this approach is that it does not account for a change in treatment technique in the new regimens. In our case the PTV margins were reduced from 1 cm to 0.5 cm as the use of fiducial markers and portal imaging resulted in more accurate patient setup. Therefore the irradiated breast volumes decreased from patient group A to group B (Fig. 2). Because of the reduction of irradiated volumes, the NTCPIR in the 35/7f regimen calculated from actual DVHs decreased to 1.6%. This result confirms that the DVH rescaling method serves only for preliminary estimate of the risk of side effects, and NTCP should be recalculated using actual DVHs as soon as dosimetrical data from patients are available. Clinical results The data collected in the present work have many favorable characteristics for the analysis of side effects and NTCP modeling. All patients had been CT-planned and treated with forward-planned IMRT, had individual dosimetrical data and prospectively scored toxicity. Toxicity was prospectively evaluated and the clinical results were reported. All the treatments were delivered using the same forward planned IMRT technique, and individual DVHs of the subcutaneous breast tissue were available for each patient. In mostly historical datasets from PBI individual dose-volume data are not available and toxicity is retrospectively analyzed [10]. Moreover, our datasets have two distinct fractionation regimens allowing studying the robustness of NTCP models to a change of dose per fraction. By using DVH data from individual patients, and standardizing the treatment planning and delivery techniques in each hypofractionation strategy, we reduce the uncertainties in NTCP estimation that are inherent in retrospective evaluation of published treatment schedules. Overall, dosimetric and clinical data from 143 patients were collected prospectively. Average follow-up on all the patients was 40 months (3.3 years). This dataset compares well against the study by Chen et al. [1] where 93 patients were treated with median follow up of 4.2 years, and is the largest report on clinical results of PBI at our best knowledge. Authors reported an incidence of RIF of grade 2 or more in 8/93 patients (8.6%) which agrees well with our results of 5.9% (95%CIs 1.6–14.4%) and 5.3% (95%CIs 1.6–14.4%) in the two patient groups. The major limitation of this study is that, whilst the fractionation regimens are assumed to be iso-effective according to tumor BED, patients do not have a complete follow-up to confirm longterm tumor control. The number of RIF events (8 over 143 patients treated) is also too limited to assess models for predicting individual risk for RIF, and the models used here must therefore be used for prediction of average risk of RIF in patient groups. RIF is a late effect and has long time for latency. The follow-up time (average 53 and 26 months in the two patient groups) is not complete for assessment of late moderate/severe RIF and its incidence is expected to increase with longer follow-up. In the model the influence of incomplete follow up time was accounted for using the latency function, and the average corrections to NTCP on the two patient groups A and B were 0.79 and 0.60. Therefore, when the
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follow-up for late effects will be complete, the incidence of grade 2 or more RIF is estimated to increase to 7.6% in group A and 8.8% in group B, which are acceptable rates of toxicity and confirm good tolerability of the treatment.
Verification of radiobiological models In the present work, models for predicting the risk of RIF derived from literature data were used to assess the feasibility of hypofractionated regimens for PBI. The NTCPIR includes a correction term to the BEUD, h, for incomplete recovery between fractions. According to this model the APBI regimen, typically delivering treatment in 10 fractions over 5 days with two fractions per day, increases the risk of RIF because incomplete recovery from sub-lethal damage occurs between the two daily fractions. This is in agreement with recent clinical findings, as in two recent APBI studies, significant short term toxicities have been observed [3,4]. In case of non-accelerated treatment, as for the patients considered in the present study, the h term is set to zero, so that NTCPIR has the same analytical form as the classical NTCP Lyman model (Appendix A.2). The model parameters are different between the two models 1 and 2 in Table 1, as they were derived from published clinical data in which some datasets had accelerated treatments. As a consequence, the fitting process yielded different radiobiological parameter sets for the two models. In our results NTCPIR reproduced clinical results better than other models (Models 2–5 in Table 1) currently available for prediction of moderate/severe RIF, none of which included the correction for incomplete repair. These results suggest that incomplete recovery should be accounted for in predictive models for RIF. After fitting of the α/β value to our clinical results, the difference of NTCPIR from severe/moderate RIF decreased to 3.5%. This residual difference can be explained with other clinical factors affecting the incidence of RIF and not modeled in NTCPIR, such as administration of tamoxifen, co-morbidity or patient variability in radiosensitivity [9]. NTCPIR has relatively low value of volume effect parameters, in contrast with previous investigations [8] based on WBI data (Model 4 in Table 1). As in our clinical data NTCPIR obtained the best prediction performance between all models, results seem to confirm the hypothesis of a low volume effect for fibrosis. Other investigators analyzed pooled data of 5856 patients from the START and EORTC trials and derived an even lower volume effect of n = 0.012 for the Lyman NTCP model [10]. Their model (Model 3 in Table 1), however, overestimated the incidence of RIF in our patients. A possible explanation could be that, for some patients in the START and EORTC clinical trials, fibrosis was assessed early during follow-up so that post-operative induration may have been scored as severe/ moderate RIF (Mukesh MB and Coles CE, personal communication). The design of isotoxic regimens was based on BED calculation using an α/β value of 3 Gy for breast tissue. We refitted this parameter using the least-square method on our clinical results to test the validity of our assumption, and the value obtained, 2.8 Gy with 95%CIs of 1.1–10.7 Gy, does not differ significantly from the value of 3 Gy that we used. Values of 3.5 and 3.1 Gy have been derived from the analysis of clinical data of WBI data [6] and of WBI and PBI [9] data which also agree well with our result. For these reasons, and considering also the good prediction results obtained with NTCPIR, we decided to continue the hypofractionation protocol. PBI is presently delivered with the second hypofractionated regimen of 28 Gy in 4 fractions. So far, 15 patients have been treated following this regimen although their average follow-up of three months is currently too short to assess fibrosis (Group C in Table 2). Hopefully, when the fraction reduction trial will be completed with complete follow-up on patients treated with three fractionation regimens, our data will yield a more precise estimate of α/β.
Conclusions A fraction reduction study was designed based on radiobiological models. Prospective patient data, analyzed in terms of toxicity, demonstrated that the new hypofractionated regimen is well tolerated. The model for NTCPIR which includes incomplete repair between fractions in accelerated regimens reproduces better the observed incidences of RIF. The currently assumed value of α/β of 3 Gy was found consistent with the value obtained by fitting patient data obtained from our institutional hypofractionated trial. The hypofractionation protocol is continuing with patients treated with 28 Gy/4f. Appendix A.1 Biologically effective dose (BED) Biologically effective dose (BED) for an organ at risk is calculated, based on the linear quadratic model [21], as:
⎛ ⎜ D BED = D ⎜ 1 + ⎜ N⋅ α ⎜ β ⎝
⎞ ⎟ ⎟ ⎟ ⎟ ⎠
(A1)
where D is the prescribed dose, N the number of fractions in the RT treatment, and α and β account for the radiosensitivity of tissue. BED for the tumor, based on linear quadratic model and Poisson statistics, is [21]:
⎛ ⎜ D BED = D ⎜ 1 + ⎜ N⋅α ⎜ β ⎝
⎞ ⎟ loge 2 ⎟− ( T − Tk ) ⎟ α Tp ⎟ ⎠
(A2)
The BED formula accounts for repopulation during the treatment with overall treatment time, T, in days. The onset or kick-off time of repopulation is at Tk days and the cell number doubling time is Tp (days). The parameters from [15] were used for calculation of BED for breast tumor. A.2 NTCP models In order to describe NTCP in a population of patients versus the prescribed dose and number of fractions, the absolute doses Di in the patient differential ipsilateral breast DVHs are described as the product of the relative dose in the DVH bin, d%,i, and the nominal prescribed dose in the treatment, D. From these quantities, the EUD is defined for the patient j as a function of the prescribed dose D, as [23]: 1 ⎛ ⎞ EUD j ( D ) = ⎜ ∑ v j,i ⋅ ( d%,i D ) n ⎟ ⎝ i ⎠
n
(A3)
where vji is the i-th fractional sub-volume of the organ irradiated with percent dose d%,i for the patient j and the parameter n describes the volume effect of the irradiated organ or tissue. Biologically effective uniform dose to the breast tissue for patient j in a regimen with prescribed dose D in N fractions, BEUDj(D,N), is defined using the BED formula for an organ at risk (Eq. A1) with EUDj(D) (Eq. A3) in place of D [24]:
⎛ ⎞ ⎜ EUD j ( D ) ⎟ BEUD j ( D, N ) = EUD j ( D ) ⎜ 1 + ⎟ α ⎟ ⎜ N⋅ ⎜ ⎟ β ⎠ ⎝
(A4)
M. Avanzo et al./Physica Medica 31 (2015) 1022–1028
where the α/β ratio is the parameter of the linear-quadratic model for the breast. For dose response modeling, we used previously established NTCP model [8–10]. In the Lyman-BEUD model, the probability of side-effect is calculated from BEUD (see Eq. A2) using equations:
NTCPj ( D, N ) =
x=
1 2π
X
∫e
⎛ x2 ⎞ −⎜⎜ ⎟⎟ ⎝ 2 ⎠
dt
(A5)
−∞
BEUD j − TD50 mTD50
(A6)
where TD50 is the dose resulting in a 50% complication probability and m describes the slope of the NTCP curve at TD50. In the model corrected for incomplete repair NTCPIR, a correction factor, h, to the quadratic term in Eq. (A1) is introduced [25] for incomplete repair from sublethal damage between fractions:
⎛ EUD ( j, D ) ⎞ BEUD j ( D, N ) = EUD j ( D ) ⎜ 1 + [1 + h] ⎟ N ⋅α β ⎝ ⎠
(A7)
In the original incomplete recovery model it was assumed that, for treatments in which more than one fraction per day is delivered, complete repair occurs overnight. The model was then generalized without this assumption, as described in detail in [26]. In the generalized model, incomplete repair during the time between two fractions delivered in the same day and also during the overnight interval contributes to the biological effect:
h ≡ (1 + ϑ 2 )
N ϑ * ⎛⎜ 2 ⎡ 1 − (ϑ ⋅ ϑ * ) 2 ⎤⎥ ⎞⎟ ⋅ 1+ ⎢ +ϑ 1 + ϑϑ * ⎜ N ⎢ 1 − ϑ ⋅ ϑ * ⎥ ⎟ ⎣ ⎦⎠ ⎝
(A8)
where
ln 2 ⎞ ln 2 ⎞ ⎛ ϑ = exp ⎛⎜ −Δt ⋅ ⎟; ϑ * = exp ⎜ − ( 24 − Δt ) ⋅ ⎟ τ ⎠ τ ⎠ ⎝ ⎝
(A9)
Δt is the inter-fraction time between two fractions delivered in the same day averaged on the whole treatment course in hours, 24-Δt is the over-night interval, and τ is the recovery half-time of the subcutaneous tissue in hours. The probability of side effect is calculated from BEUD using Eqs. (A4) and (A5), so that when a treatment is not accelerated, the h term is zero, and the NTCPIR model has the same analytical form of the NTCP model.
A.3 Correction for the latency of the effect NTCP in Eqs. (A5)–(A6) represents the probability that a complication occurs and the patient is followed for a sufficient amount of time to develop the toxicity. When a patient has incomplete follow-up, a toxicity event may be not scored (“censored”) because the toxicity has not developed before last follow-up visit and, as a consequence, the observed incidence of side effects decreases. This is modeled using the distribution of times needed to develop toxicity in a population of patients, or latency function, which is assumed to follow a log-normal distribution [11]:
f (t ) =
− 1 e σ t 2π
(ln(t )− μ )2 2σ 2
(A10)
where t is the time after the end of RT at which the toxicity occurs in years, and σ and μ are the parameters of the distribution of latency times in years. For RIF, values of μ = 0.47 years and σ = 1.27 years have been derived [9]. The probability that toxicity occurs before
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the last follow-up visit and thus is scored, for the patient with followup time Tj, is the cumulative distribution of times to toxicities: Tj
Fj = ∫ f ( t ) dt
(A11)
0
where Tj is defined as the time between the end of RT and the last follow-up visit for the patient j in years. The NTCP corrected for the latency of the effect is the crude incidence of toxicity, NTCPj (Eqs. A5–A6), multiplied by the probability that the toxicity has occurred before the last follow-up visit, Fj (Eq. A11):
NTCPj ( D, N ) = NTCPj ( D, N ) ⋅ Fj
(A12)
References [1] Chen PY, Wallace M, Mitchell C, Grills I, Kestin L, Fowler A, et al. Four-year efficacy, cosmesis, and toxicity using three-dimensional conformal external beam radiation therapy to deliver accelerated partial breast irradiation. Int J Radiat Oncol Biol Phys 2010;76:991–7. [2] Formenti SC, Truong MT, Goldberg JD, Mukhi V, Rosenstein B, Roses D, et al. Prone accelerated partial breast irradiation after breast-conserving surgery: preliminary clinical results and dose-volume histogram analysis. Int J Radiat Oncol Biol Phys 2004;60:493–504. [3] Hepel JT, Tokita M, MacAusland SG, Evans SB, Hiatt JR, Price LL, et al. Toxicity of three-dimensional conformal radiotherapy for accelerated partial breast irradiation. Int J Radiat Oncol Biol Phys 2009;75:1290–6. [4] Jagsi R, Ben-David MA, Moran JM, Marsh RB, Griffith KA, Hayman JA, et al. Unacceptable cosmesis in a protocol investigating intensity-modulated radiotherapy with active breathing control for accelerated partial-breast irradiation. Int J Radiat Oncol Biol Phys 2010;76:71–8. [5] Trovo M, Roncadin M, Polesel J, Piccoli E, Mileto M, Micheli E, et al. Toxicity and cosmesis following partial breast irradiation consisting of 40 Gy in 10 daily fractions. Breast 2013;22:744–7. [6] FAST Trialists Group, Agrawal RK, Alhasso A, Barrett-Lee PJ, Bliss JM, Bliss P, et al. First results of the randomised UK FAST Trial of radiotherapy hypofractionation for treatment of early breast cancer (CRUKE/04/015). Radiother Oncol 2011;100:93–100. [7] Haviland JS, Owen JR, Dewar JA, Agrawal RK, Barrett J, Barrett-Lee PJ, et al. The UK Standardisation of Breast Radiotherapy (START) trials of radiotherapy hypofractionation for treatment of early breast cancer: 10-year follow-up results of two randomised controlled trials. Lancet Oncol 2013;14:1086–94. [8] Alexander MA, Brooks WA, Blake SW. Normal tissue complication probability modelling of tissue fibrosis following breast radiotherapy. Phys Med Biol 2007;52:1831–43. [9] Avanzo M, Stancanello J, Trovo M, Jena R, Roncadin M, Trovo MG, et al. Complication probability model for subcutaneous fibrosis based on published data of partial and whole breast irradiation. Phys Med 2012;28:296–306. [10] Mukesh MB, Harris E, Collette S, Coles CE, Bartelink H, Wilkinson J, et al. Normal tissue complication probability (NTCP) parameters for breast fibrosis: pooled results from two randomised trials. Radiother Oncol 2013;108:293–8. [11] Tucker SL, Liu HH, Liao Z, Wei X, Wang S, Jin H, et al. Analysis of radiation pneumonitis risk using a generalized Lyman model. Int J Radiat Oncol Biol Phys 2008;72:568–74. [12] Wu Q, Mohan R, Niemierko A, Schmidt-Ullrich R. Optimization of intensitymodulated radiotherapy plans based on the equivalent uniform dose. Int J Radiat Oncol Biol Phys 2002;52:224–35. [13] Jothy Basu KS, Bahl A, Subramani V, Sharma DN, Rath GK, Julka PK. Normal tissue complication probability of fibrosis in radiotherapy of breast cancer: accelerated partial breast irradiation vs conventional external-beam radiotherapy. J Cancer Res Ther 2008;4:126–30. [14] Archambeau JO, Pezner R, Wasserman T. Pathophysiology of irradiated skin and breast. Int J Radiat Oncol Biol Phys 1995;31:1171–85. [15] Wyatt RM, Beddoe AH, Dale RG. The effects of delays in radiotherapy treatment on tumour control. Phys Med Biol 2003;48:139–55. [16] Haciislamoglu E, Colak F, Canyilmaz E, Dirican B, Gurdalli S, Yilmaz AH, et al. Dosimetric comparison of left-sided whole-breast irradiation with 3DCRT, forward-planned IMRT, inverse-planned IMRT, helical tomotherapy, and volumetric arc therapy. Phys Med 2015;31:360–7. [17] National Cancer Institute. Common Terminology Criteria for Adverse Events v3.0 (CTCAE),; 2006. [18] Wallis S. Binomial confidence intervals and contingency tests: mathematical fundamentals and the evaluation of alternative methods. J Quant Linguist 2013;20:178–208. [19] Coleman T, Li Y. An interior trust region approach for nonlinear minimization subject to bounds. SIAM J Optim 1996;6:418–45. [20] Seber GAF, Wild CJ. Estimation methods. In: Nonlinear regression. Hoboken, NJ: John Wiley & Sons, Inc.; 1989. p. 21. [21] Fowler JF. Is there an optimum overall time for head and neck radiotherapy? A review, with new modelling. Clin Oncol (R Coll Radiol) 2007;19:8–22.
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[22] Yuan J, Wang JZ, Lo S, Grecula JC, Ammirati M, Montebello JF, et al. Hypofractionation regimens for stereotactic radiotherapy for large brain tumors. Int J Radiat Oncol Biol Phys 2008;72:390–7. [23] Gay HA, Niemierko A. A free program for calculating EUD-based NTCP and TCP in external beam radiotherapy. Phys Med 2007;23:115–25. [24] Vogelius IS, Westerly DC, Cannon GM, Bentzen SM. Hypofractionation does not increase radiation pneumonitis risk with modern conformal radiation delivery techniques. Acta Oncol 2010;49:1052–7.
[25] Thames HD. An ‘incomplete-repair’ model for survival after fractionated and continuous irradiations. Int J Radiat Biol Relat Stud Phys Chem Med 1985;47:319–39. [26] Guttenberger R, Thames HD, Ang KK. Is the experience with CHART compatible with experimental data? A new model of repair kinetics and computer simulations. Radiother Oncol 1992;25:280–6.
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Physica Medica j o u r n a l h o m e p a g e : h t t p : / / w w w. p h y s i c a m e d i c a . c o m
Original Paper
Hypofractionation of partial breast irradiation using radiobiological models Michele Avanzo a,*, Marco Trovo b, Joseph Stancanello c, Rajesh Jena d, Mario Roncadin b, Giulia Toffoli e, Chiara Zuiani e, Elvira Capra a a
Medical Physics Department, CRO Aviano, 33081 Aviano, Italy Radiation Oncology Department, CRO Aviano, 33081 Aviano, Italy c MRI Applications and Workflow, General Electric, 78533 Buc, France d Department of Oncology, University of Cambridge, Cambridge CB2 0QQ, UK e Institute of Diagnostic Radiology, Department of Medical and Biological Sciences, University of Udine, 33100 Udine, Italy b
A R T I C L E
I N F O
Article history: Received 20 April 2015 Received in revised form 10 July 2015 Accepted 3 August 2015 Available online 23 October 2015 Keywords: Hypofractionation Partial breast irradiation NTCP TCP Breast Fibrosis
A B S T R A C T
Purpose: To reduce the fraction number in Partial Breast Irradiation (PBI) with initial prescription of 40 Gy in 10 fractions using radiobiological models with specific focus on risk of moderate/severe radiationinduced fibrosis (RIF) and report clinical results. Methods and materials: 68 patients (patient group A) were treated with 40 Gy in 10 fractions delivered by field-in-field, forward-planned IMRT. Isotoxic regimens with decreasing number of fractions were calculated using Biological Effective Dose (BED) to the breast. Risk for RIF in hypofractionated treatment was predicted by calculating NTCP from DVHs of group A rescaled to fractions and dose of novel regimens. Moderate/severe RIF was prospectively scored during follow-up. Various NTCP models, with and without incomplete repair correction, were assessed from difference to observed incidence of RIF. In order to verify the value for α/β of 3 Gy assumed for breast, we fitted α/β to observed incidences of moderate/ severe RIF. Results: Treatments with 35 Gy/7f and 28 Gy/4f were selected for the fraction reduction protocol. 75 patients (group B) were treated in 35 Gy/7f. Incidence of moderate/severe RIF was 5.9% in group A, 5.3% in group B. The NTCP model with correction for incomplete repair had lowest difference from observed RIF. The α/β obtained from fitting was 2.8 (95%CIs 1.1–10.7) Gy. Conclusions: The hypofractionated regimen was well tolerated. The model for NTCP corrected for incomplete repair was the most accurate and an assumed α/β value of 3 Gy is consistent with our patient data. The hypofractionation protocol is continuing with patients treated with 28 Gy/4f. © 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Introduction In recent years partial breast irradiation (PBI) performed with external photon beams has gained acceptance in the post-operative management of early stage breast cancer after breast conserving surgery [1–4]. In our hospital, PBI treatments were delivered following a novel protocol consisting of 40 Gy in 10 daily fractions of 4 Gy over two weeks which produced good cosmetic results [5]. In radiotherapy (RT) treatments it is desirable to reduce the overall treatment time to enhance convenience to the patient as well as reduce the treatment burden of breast radiotherapy in busy treatment centers. Strategies to shorten treatment time include reducing the number of fractions (hypofractionation) and increasing the
* Corresponding author. Medical Physics Unit, CRO Aviano National Cancer Institute, 33081 Aviano, Italy. Tel.: +39 0434659175; fax: +39 0434659524. E-mail address: [email protected] (M. Avanzo).
number of fractions per day (accelerated treatment). Good results in terms of side effect profile and local control rate [1] have been generally reported with accelerated PBI (APBI), which is delivered in twice daily fractions but, in two APBI studies, significant short term toxicities have been observed [3,4]. On the other hand, trials of whole breast RT hypofractionation provided evidence that lower total doses of RT delivered in fewer fractions with larger doses per fraction are as safe and effective as conventional regimens (50 Gy in 25 fractions) for women after primary surgery for early breast cancer [6,7]. A strategy to reduce fraction number was therefore adopted in our hospital to reduce the duration of PBI from the consolidated regimen of 40 Gy/10 fractions. A clinically acceptable hypofractionation regimen should yield equivalent effect to the tumor and risk of normal tissue toxicity. These goals can be achieved using the concept of Biologically Effective Dose (BED), which accounts for the effect of fractionation on clinical outcome, and analytical models of Normal Tissue Complication Probability (NTCP), which correlate outcome of RT with
http://dx.doi.org/10.1016/j.ejmp.2015.08.016 1120-1797/© 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
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Table 1 Models for NTCP and BED, and radiobiological parameters used in the present study. Model, description, reference
Parameter values
(1) Model for moderate/severe RIF prediction model accounting for incomplete repair and latency of effect, derived from published average clinical and dosimetrical data of PBI and WBI [9] (1a) Model 1, calculated from average DVH and average follow-up time of the patient groups (1b) Model 1, with α/β = 2.8 Gy derived from fitting clinical results in the present study (2) Model for moderate/severe RIF accounting for latency of effect, derived from published average clinical and dosimetrical data of PBI and WBI [9] (3) Moderate/severe RIF prediction model, derived from analysis of pooled individual patient clinical data of EORTC and START trials, with two-compartment DVH model [10] (4) Moderate/severe RIF prediction model, derived from published clinical data of PBI and WBI and DVHs from in-phantom generated treatments [8] (5) Biologically effective dose (BED) for breast cancer based on linear quadratic model and Poisson statistics [15]
dose-volume data and fractionation scheme [8–11]. These predictive models have now been implemented in clinical practice, specifically as a tool for comparison of treatment schedules [12,13]. To model toxicity, we use models of NTCP for subcutaneous radiation induced fibrosis (RIF). RIF is characterized by progressive induration, edema formation, and thickening of the dermis and subcutaneous tissue. It is considered one of key side effects of PBI influencing cosmetic outcome [14]. We recently derived NTCP models for the risk of severe (grade 2 or more) RIF from published incidences of RIF on PBI [9]. The best fit parameters for the model were estimated using average dosimetric parameters (prescription dose, fraction dose, mean follow up time) from published Whole Breast Irradiation (WBI) studies and external beam PBI studies. The purpose of this study was to derive consistent fraction reduction protocol for PBI using radiobiological models and report clinical results on patients treated with the newly designed regimen. In our previous work, verification of NTCP models for RIF used to design the hypofractionation protocol could be made in a very limited dataset with limited follow-up time (35 patients with 12 months average follow up) [9]. As follow up data for incidence of side effects were prospectively collected in the present work, the accuracy of NTCP models can be tested against a more diverse and mature dataset. Moreover, since in NTCP modeling of RIF the value of α/β of RIF was assumed as 3 Gy, we want to test the validity of this assumption by fitting α/β to incidences of severe RIF in the hypofractionation study already available at our institution.
n = 0.15, m = 0.22, BEUD50 = 105.8 Gy, α/β = 3 Gy, μ = 0.46 years, σ = 1.27 years
n = 0.06, m = 0.22, BEUD50 = 107.2 Gy, α/β = 3 Gy, μ = 0.46 years, σ = 1.27 years n = 0.012, m = 0.35, BEUD50 = 132 Gy, α/β = 3 Gy n = 0.78, m = 0.27, BEUD50 = 104 Gy, α/β = 3 Gy α = 0.27 Gy−1, α/β = 4 Gy, Tpot = 15 days, Tk = 0
to study the average NTCP as a function of dose and fraction number. These patients, previously treated by breast conserving surgery for an early stage ductal carcinoma, underwent non-accelerated external PBI with prescribed dose of 40 Gy in 10 daily fractions of 4 Gy over two weeks [5]. Patient characteristics are shown in Table 2. The clinical target volume (CTV) consisted of the lumpectomy cavity and the Planning Target Volume (PTV) consisted of the CTV plus 1 cm margin. Breast tissue visible on the computed tomography simulation scan was outlined. The RT technique consisted of “field-infield” planning (forward-planned intensity modulated RT) [16] using
Methods and materials Hypofractionation modeling The hypofractionated treatments were designed with the aim of being isotoxic, that is, of providing the same biological dose for the effect of moderate/severe RIF. A formula of BED based on the linear quadratic model was used to derive equivalent prescribed doses, with a value for α/β of 3 Gy for breast tissue (Eq. A1 in Appendix A.1). Hypofractionated treatments were required to have the same BED to the breast as the initial treatment of 40 Gy in 10 fractions. In order to evaluate the effect of change of regimen on the tumor, a formula corrected for repopulation of tumor cells was used to calculate tumor BED as described by Eq. (A2) in Appendix A.1. The radiobiological parameters of models are shown in Table 1. The total dose with the same BED as the initial treatment with 40 Gy in 10 fractions was plotted versus decreasing number of fractions in Fig. 1. NTCP for severe RIF in the hypofractionated regimens was preliminarily estimated from data of patients already treated with 40 Gy/ 10f using a model originally derived from literature data on PBI [9] as described in Appendix A.2. Data from 68 patients (patient group A) treated with PBI between July 2008 and June 2012 were used
Figure 1. Design of hypofractionation protocol of PBI. The red dashed lines represent the prescribed dose giving the same tumor BED as the initial treatment of 40 Gy in 10 fractions for decreasing number of fractions. Levels of average NTCPIR of moderate/severe RIF (green areas) are calculated from DVHs of patients previously treated with the initial regimen of 40 Gy/10 fractions rescaled to different doses and fractions. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 2 Characteristics of patients treated at our institution with PBI in the initial (Group A) and hypofractionated regimens (Groups B and C). Incidence of fibrosis is not assessed in the third group due to short follow-up time. Patient and treatment characteristics
Mean value (range) Group A
Group B
Group C
Prescribed dose [Gy] Fractions [number] Patients [number] Age [years] Follow-up [months] RIF grade ≥ 2 [yes/no]
40 Gy 10 68 71 (61–83) 53 (17–23) 4/64
35 Gy 7 75 70 (61–85) 26 (9–38) 4/71
28 4 15 70.5 (60–81) 3 [0–6] /
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Clinical results
Figure 2. DVHs of patients treated with the original PBI regimen of 40 Gy/ fractions and the hypofractionated regimens of 35 Gy/7 fractions and 28 Gy/4 fractions.
A second group of 75 patients (Group B), whose characteristics are summarized in Table 2, was treated using the first hypofractionated regimen of 35 Gy in 7 fractions. For these treatments, image guidance based on daily orthogonal antero-posterior and lateral kV images and 3 fiducial markers placed on the tumor bed was performed before each fraction. This permitted safe reduction of the PTV margin to 5 mm. Maximal toxicity was evaluated during post-treatment follow-up visits that occurred after 1, 3, 6 and 12 months for the first year, and then once a year. The DVHs of patients treated with are shown in Fig. 2. With the approval of our Institutional Review Board and after obtaining informed consent from each patient, the dosimetric data and follow-up data were reviewed. Patients were seen at regular intervals to determine the presence of symptoms, and one physician (M.T.) evaluated the toxicity by the RTOG scale and by the CTCAE (version 3.0) [17]. The presence of RIF (grade 2 or more) was reported at the end of treatment, 1 month and every 3 months after the completion of radiation course, and scored in a prospective database. In order to describe the statistical uncertainty on the incidence of moderate/severe RIF in our patient population, confidence intervals for the observed incidences of toxicities were calculated using the Clopper–Pearson Binomial interval [18]. Verification of radiobiological models
multiple planar and non-coplanar 6 MV photon beams. All treatments were developed using the Eclipse treatment planning system (version 8.9.08, Varian Medical Systems, Palo Alto, CA), and dose calculations were carried out using the anisotropic analytical algorithm (AAA) with a grid resolution of 2.5 mm, taking into account heterogeneity correction. For every patient, individual (percentage breast volume vs dose in Gy) differential DVHs of the ipsilateral breast and follow up times (time from end of RT to last follow-up visit) were recorded. The differential DVHs were exported in a text format with dose bins of 0.05 Gy. The average value of NTCP in patient group A versus the total prescribed dose D and number of fractions N was calculated (Fig. 1). In the model, termed NTCPIR, a correction for incomplete repair between two fractions delivered in the same day can be included in order to account for the effect of accelerated regimens (Eqs. A8–A9 in Appendix A.2). A correction for latency of the toxicity event was also included to account for events that are censored due to incomplete follow-up and result in decreased number of observed toxicities. This correction factor (Eq. A11, Appendix A.3) was calculated for each patient from the individual follow-up time, defined as the time between end of the treatment and last follow-up visit, and represents the probability that the side effect is developed before last follow-up visit [11]. NTCPIR iso-level curves were then calculated and plotted in the same graph of total dose versus fraction number (Fig. 1), in order to assess equivalent dose to the tumor and, at the same time, the risk of moderate/severe RIF deriving from changing prescription dose and fractions.
As the first toxicity data have been collected we tested the NTCP models used for hypofractionation protocol design, the predictive capability of different NTCP models was tested by comparison of average NTCP against observed incidence of RIF in the patients treated with 40 Gy/10f and 35 Gy/7f PBI. As combined difference between model predictions and incidence of toxicity, we used the square root of the sum of squared differences between NTCP and RIF in the two cohorts. The first test was to check if the NTCPIR works when calculated from individual patient data, as it was originally derived from average dosimetrical and follow up data reported in literature on breast radiotherapy [9]. To this purpose, the average DVH was calculated for each of the two patient groups. NTCPIR was calculated from average DVHs and follow-up times of the two patient groups (Model 1a in Table 1) and compared against average NTCPs calculated from individual data (Model 1). As a result, no significant difference was found, as shown in Table 3, indicating that the two methods provide equivalent estimates of risk of the side effect. Second, NTCPIR results were compared against other models of NTCP for severe/moderate RIF available in literature, all of which do not incorporate incomplete repair correction, as shown in Table 1. In order to verify the value for α/β of 3 Gy assumed for breast, the α/β for RIF was derived by fitting the model with the best predictive power, NTCPIR, to observed incidences of RIF. The weighted least squares method was used to determine the best fit α/β value, assuming the number of patients in each dataset as weights. The
Table 3 Results of calculation of NTCP with different models described in Table 1 and differences from observed incidences of RIF. For each model used, the average NTCP value on patient groups is reported with 95%CIs. Treatment
40 Gy/10f 35 Gy/7f
Incidence of RIF
5.9 (1.6–14.4)% 5.3 (1.6–14.4)% Combined difference of NTCP from incidences of RIF:
NTCP mean value (95% CIs) Model 1
Model 1a
Model 1b
Model 2
Model 3
Model 4
5.6 (2.5–9.6)% 1.6 (0.25–3.2)% 3.7%
5.5% 1.7% 3.7%
6.9 (3.1–11.9)% 2.0 (0.3–4.1)% 3.5%
12.4 (5.8–16.6)% 5.2 (1.3–8.3)% 6.6%
18.5 (15.3–21.02)% 10.7 (6.1–13.3)% 13%
1.1 (0.2–4.2)% 0.2 (0.1–0.5)% 7.0%
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lsqcurvefit MATLAB instruction was used which employs the “trustregion-reflective” algorithm for large scale optimization by Coleman and Li [19]. The cost function in the optimization process was the sum of squares of percent differences between observed incidences of RIF and NTCP in the two patient groups. The optimization stopped when the change of the cost function was less than 0.01% or the change of the variable α/β was less than 0.01 Gy. The asymptotic 95% confidence intervals for the estimated parameters and 95% prediction intervals for the fitted function were evaluated, assuming the asymptotic normal distribution for the parameter estimates, from the Jacobian matrix and the residuals of fit [20]. Results Hypofractionation modeling The regimens with total prescribed doses of 35, and 28 Gy in 7 and 4 fractions, respectively, were selected for the clinical study of fraction reduction. Using α/β of 3 Gy for moderate/severe RIF, both treatments are equivalent to 40 Gy in 10 fractions for subcutaneous tissue. These treatments are equivalent, for the tumor, to 39.9 Gy and 39.4 Gy in 10 fractions, respectively. Hypofractionated treatments, equivalent in terms of tumor control to the initial treatment, yielded a predicted toxicity level between 5 and 10% for the endpoint of Grade 2+ RIF, as shown in Fig. 1. Clinical results 75 patients were then treated with 35 Gy in 7 fractions. The mean follow-up was 26 months (range, 9–38 months), and therefore all patients were assessable for late toxicity. The proposed fractionation scheme was very well tolerated, and grade ≥2 fibrosis was observed only in 4 (5.3%) patients with 95% CIs of 1.6–14.4%. Verification of radiobiological models The differences between NTCP calculated with available models for moderate/severe RIF and observed incidences of side-effects in patients treated with 40 Gy/10f and 35 Gy/7f are shown in Table 3. The incidences of RIF were 4/68 (5.9% with 95% CIs of 1.6–14.4) and 4/75 (5.3%, 95% CIs of 1.6–14.4%) among patients treated with 40/ 10f and 35/7f, respectively. Combined difference of average NTCP from RIF was 3.9% with the NTCPIR model, which scored better than all other NTCP models without incomplete repair correction. The α/β was obtained from fitting after three optimization iterations and was 2.8 Gy with 95% CIs of 1.1–10.7 Gy. The combined difference of NTCP IR model from RIF incidence with this value for α/β decreased to 3.5%. Using this α/β for fibrosis, the 37/7f and 28/4f hypofractionated treatments are equivalent to 40.1 and 40.2 Gy in 10 fractions for subcutaneous tissue. Discussion Hypofractionation modeling Radiobiological models for patient outcome have been used to study the feasibility of hypofractionated regimens [21,22]. The usual method involves determining equivalent doses such as normalized total doses (NTDs) at fractions of 2 Gy or BED to the tumor and the most critical organ at risk at various fraction numbers or fraction size in order to determine isotoxic and/or isoeffective regimens [21]. In this study, we used BED to the breast tissue as the objective was to produce isotoxic treatments. Given that tumor has α/β ratio similar to that of breast tissue, treatments were equivalent also for the tumor, as they yielded equivalent doses to the tumor very
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close to the initial prescription. As a consequence, treatments can be considered to be isoeffective and isotoxic. Before beginning the reduction of fractions, we estimated the risk for RIF in hypofractionated treatments by calculating NTCPIR using individual dosimetrical data of patients treated with the initial regimen (group A) rescaled to doses and fractions of the new regimens. The model NTCPIR included the correction for latency of the side-effect calculated from individual follow-up times. The predicted incidence of RIF using the NTCPIR model was 5.3% with 35/7 and 4.9% with 28/4, as shown in Fig. 1. This approach provides a preliminary estimate of toxicity in a novel regimen which accounts for the dose distribution generated from the treatment technique in use. The limit of this approach is that it does not account for a change in treatment technique in the new regimens. In our case the PTV margins were reduced from 1 cm to 0.5 cm as the use of fiducial markers and portal imaging resulted in more accurate patient setup. Therefore the irradiated breast volumes decreased from patient group A to group B (Fig. 2). Because of the reduction of irradiated volumes, the NTCPIR in the 35/7f regimen calculated from actual DVHs decreased to 1.6%. This result confirms that the DVH rescaling method serves only for preliminary estimate of the risk of side effects, and NTCP should be recalculated using actual DVHs as soon as dosimetrical data from patients are available. Clinical results The data collected in the present work have many favorable characteristics for the analysis of side effects and NTCP modeling. All patients had been CT-planned and treated with forward-planned IMRT, had individual dosimetrical data and prospectively scored toxicity. Toxicity was prospectively evaluated and the clinical results were reported. All the treatments were delivered using the same forward planned IMRT technique, and individual DVHs of the subcutaneous breast tissue were available for each patient. In mostly historical datasets from PBI individual dose-volume data are not available and toxicity is retrospectively analyzed [10]. Moreover, our datasets have two distinct fractionation regimens allowing studying the robustness of NTCP models to a change of dose per fraction. By using DVH data from individual patients, and standardizing the treatment planning and delivery techniques in each hypofractionation strategy, we reduce the uncertainties in NTCP estimation that are inherent in retrospective evaluation of published treatment schedules. Overall, dosimetric and clinical data from 143 patients were collected prospectively. Average follow-up on all the patients was 40 months (3.3 years). This dataset compares well against the study by Chen et al. [1] where 93 patients were treated with median follow up of 4.2 years, and is the largest report on clinical results of PBI at our best knowledge. Authors reported an incidence of RIF of grade 2 or more in 8/93 patients (8.6%) which agrees well with our results of 5.9% (95%CIs 1.6–14.4%) and 5.3% (95%CIs 1.6–14.4%) in the two patient groups. The major limitation of this study is that, whilst the fractionation regimens are assumed to be iso-effective according to tumor BED, patients do not have a complete follow-up to confirm longterm tumor control. The number of RIF events (8 over 143 patients treated) is also too limited to assess models for predicting individual risk for RIF, and the models used here must therefore be used for prediction of average risk of RIF in patient groups. RIF is a late effect and has long time for latency. The follow-up time (average 53 and 26 months in the two patient groups) is not complete for assessment of late moderate/severe RIF and its incidence is expected to increase with longer follow-up. In the model the influence of incomplete follow up time was accounted for using the latency function, and the average corrections to NTCP on the two patient groups A and B were 0.79 and 0.60. Therefore, when the
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follow-up for late effects will be complete, the incidence of grade 2 or more RIF is estimated to increase to 7.6% in group A and 8.8% in group B, which are acceptable rates of toxicity and confirm good tolerability of the treatment.
Verification of radiobiological models In the present work, models for predicting the risk of RIF derived from literature data were used to assess the feasibility of hypofractionated regimens for PBI. The NTCPIR includes a correction term to the BEUD, h, for incomplete recovery between fractions. According to this model the APBI regimen, typically delivering treatment in 10 fractions over 5 days with two fractions per day, increases the risk of RIF because incomplete recovery from sub-lethal damage occurs between the two daily fractions. This is in agreement with recent clinical findings, as in two recent APBI studies, significant short term toxicities have been observed [3,4]. In case of non-accelerated treatment, as for the patients considered in the present study, the h term is set to zero, so that NTCPIR has the same analytical form as the classical NTCP Lyman model (Appendix A.2). The model parameters are different between the two models 1 and 2 in Table 1, as they were derived from published clinical data in which some datasets had accelerated treatments. As a consequence, the fitting process yielded different radiobiological parameter sets for the two models. In our results NTCPIR reproduced clinical results better than other models (Models 2–5 in Table 1) currently available for prediction of moderate/severe RIF, none of which included the correction for incomplete repair. These results suggest that incomplete recovery should be accounted for in predictive models for RIF. After fitting of the α/β value to our clinical results, the difference of NTCPIR from severe/moderate RIF decreased to 3.5%. This residual difference can be explained with other clinical factors affecting the incidence of RIF and not modeled in NTCPIR, such as administration of tamoxifen, co-morbidity or patient variability in radiosensitivity [9]. NTCPIR has relatively low value of volume effect parameters, in contrast with previous investigations [8] based on WBI data (Model 4 in Table 1). As in our clinical data NTCPIR obtained the best prediction performance between all models, results seem to confirm the hypothesis of a low volume effect for fibrosis. Other investigators analyzed pooled data of 5856 patients from the START and EORTC trials and derived an even lower volume effect of n = 0.012 for the Lyman NTCP model [10]. Their model (Model 3 in Table 1), however, overestimated the incidence of RIF in our patients. A possible explanation could be that, for some patients in the START and EORTC clinical trials, fibrosis was assessed early during follow-up so that post-operative induration may have been scored as severe/ moderate RIF (Mukesh MB and Coles CE, personal communication). The design of isotoxic regimens was based on BED calculation using an α/β value of 3 Gy for breast tissue. We refitted this parameter using the least-square method on our clinical results to test the validity of our assumption, and the value obtained, 2.8 Gy with 95%CIs of 1.1–10.7 Gy, does not differ significantly from the value of 3 Gy that we used. Values of 3.5 and 3.1 Gy have been derived from the analysis of clinical data of WBI data [6] and of WBI and PBI [9] data which also agree well with our result. For these reasons, and considering also the good prediction results obtained with NTCPIR, we decided to continue the hypofractionation protocol. PBI is presently delivered with the second hypofractionated regimen of 28 Gy in 4 fractions. So far, 15 patients have been treated following this regimen although their average follow-up of three months is currently too short to assess fibrosis (Group C in Table 2). Hopefully, when the fraction reduction trial will be completed with complete follow-up on patients treated with three fractionation regimens, our data will yield a more precise estimate of α/β.
Conclusions A fraction reduction study was designed based on radiobiological models. Prospective patient data, analyzed in terms of toxicity, demonstrated that the new hypofractionated regimen is well tolerated. The model for NTCPIR which includes incomplete repair between fractions in accelerated regimens reproduces better the observed incidences of RIF. The currently assumed value of α/β of 3 Gy was found consistent with the value obtained by fitting patient data obtained from our institutional hypofractionated trial. The hypofractionation protocol is continuing with patients treated with 28 Gy/4f. Appendix A.1 Biologically effective dose (BED) Biologically effective dose (BED) for an organ at risk is calculated, based on the linear quadratic model [21], as:
⎛ ⎜ D BED = D ⎜ 1 + ⎜ N⋅ α ⎜ β ⎝
⎞ ⎟ ⎟ ⎟ ⎟ ⎠
(A1)
where D is the prescribed dose, N the number of fractions in the RT treatment, and α and β account for the radiosensitivity of tissue. BED for the tumor, based on linear quadratic model and Poisson statistics, is [21]:
⎛ ⎜ D BED = D ⎜ 1 + ⎜ N⋅α ⎜ β ⎝
⎞ ⎟ loge 2 ⎟− ( T − Tk ) ⎟ α Tp ⎟ ⎠
(A2)
The BED formula accounts for repopulation during the treatment with overall treatment time, T, in days. The onset or kick-off time of repopulation is at Tk days and the cell number doubling time is Tp (days). The parameters from [15] were used for calculation of BED for breast tumor. A.2 NTCP models In order to describe NTCP in a population of patients versus the prescribed dose and number of fractions, the absolute doses Di in the patient differential ipsilateral breast DVHs are described as the product of the relative dose in the DVH bin, d%,i, and the nominal prescribed dose in the treatment, D. From these quantities, the EUD is defined for the patient j as a function of the prescribed dose D, as [23]: 1 ⎛ ⎞ EUD j ( D ) = ⎜ ∑ v j,i ⋅ ( d%,i D ) n ⎟ ⎝ i ⎠
n
(A3)
where vji is the i-th fractional sub-volume of the organ irradiated with percent dose d%,i for the patient j and the parameter n describes the volume effect of the irradiated organ or tissue. Biologically effective uniform dose to the breast tissue for patient j in a regimen with prescribed dose D in N fractions, BEUDj(D,N), is defined using the BED formula for an organ at risk (Eq. A1) with EUDj(D) (Eq. A3) in place of D [24]:
⎛ ⎞ ⎜ EUD j ( D ) ⎟ BEUD j ( D, N ) = EUD j ( D ) ⎜ 1 + ⎟ α ⎟ ⎜ N⋅ ⎜ ⎟ β ⎠ ⎝
(A4)
M. Avanzo et al./Physica Medica 31 (2015) 1022–1028
where the α/β ratio is the parameter of the linear-quadratic model for the breast. For dose response modeling, we used previously established NTCP model [8–10]. In the Lyman-BEUD model, the probability of side-effect is calculated from BEUD (see Eq. A2) using equations:
NTCPj ( D, N ) =
x=
1 2π
X
∫e
⎛ x2 ⎞ −⎜⎜ ⎟⎟ ⎝ 2 ⎠
dt
(A5)
−∞
BEUD j − TD50 mTD50
(A6)
where TD50 is the dose resulting in a 50% complication probability and m describes the slope of the NTCP curve at TD50. In the model corrected for incomplete repair NTCPIR, a correction factor, h, to the quadratic term in Eq. (A1) is introduced [25] for incomplete repair from sublethal damage between fractions:
⎛ EUD ( j, D ) ⎞ BEUD j ( D, N ) = EUD j ( D ) ⎜ 1 + [1 + h] ⎟ N ⋅α β ⎝ ⎠
(A7)
In the original incomplete recovery model it was assumed that, for treatments in which more than one fraction per day is delivered, complete repair occurs overnight. The model was then generalized without this assumption, as described in detail in [26]. In the generalized model, incomplete repair during the time between two fractions delivered in the same day and also during the overnight interval contributes to the biological effect:
h ≡ (1 + ϑ 2 )
N ϑ * ⎛⎜ 2 ⎡ 1 − (ϑ ⋅ ϑ * ) 2 ⎤⎥ ⎞⎟ ⋅ 1+ ⎢ +ϑ 1 + ϑϑ * ⎜ N ⎢ 1 − ϑ ⋅ ϑ * ⎥ ⎟ ⎣ ⎦⎠ ⎝
(A8)
where
ln 2 ⎞ ln 2 ⎞ ⎛ ϑ = exp ⎛⎜ −Δt ⋅ ⎟; ϑ * = exp ⎜ − ( 24 − Δt ) ⋅ ⎟ τ ⎠ τ ⎠ ⎝ ⎝
(A9)
Δt is the inter-fraction time between two fractions delivered in the same day averaged on the whole treatment course in hours, 24-Δt is the over-night interval, and τ is the recovery half-time of the subcutaneous tissue in hours. The probability of side effect is calculated from BEUD using Eqs. (A4) and (A5), so that when a treatment is not accelerated, the h term is zero, and the NTCPIR model has the same analytical form of the NTCP model.
A.3 Correction for the latency of the effect NTCP in Eqs. (A5)–(A6) represents the probability that a complication occurs and the patient is followed for a sufficient amount of time to develop the toxicity. When a patient has incomplete follow-up, a toxicity event may be not scored (“censored”) because the toxicity has not developed before last follow-up visit and, as a consequence, the observed incidence of side effects decreases. This is modeled using the distribution of times needed to develop toxicity in a population of patients, or latency function, which is assumed to follow a log-normal distribution [11]:
f (t ) =
− 1 e σ t 2π
(ln(t )− μ )2 2σ 2
(A10)
where t is the time after the end of RT at which the toxicity occurs in years, and σ and μ are the parameters of the distribution of latency times in years. For RIF, values of μ = 0.47 years and σ = 1.27 years have been derived [9]. The probability that toxicity occurs before
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the last follow-up visit and thus is scored, for the patient with followup time Tj, is the cumulative distribution of times to toxicities: Tj
Fj = ∫ f ( t ) dt
(A11)
0
where Tj is defined as the time between the end of RT and the last follow-up visit for the patient j in years. The NTCP corrected for the latency of the effect is the crude incidence of toxicity, NTCPj (Eqs. A5–A6), multiplied by the probability that the toxicity has occurred before the last follow-up visit, Fj (Eq. A11):
NTCPj ( D, N ) = NTCPj ( D, N ) ⋅ Fj
(A12)
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