Introduction
Breast cancer poses a significant global health burden, with over 2 million new cases diagnosed annually worldwide. Reference Sung, Ferlay and Siegel1,Reference Firouzjah, Banaei, Farhood and Bakhshandeh2 Radiotherapy plays a crucial role in both curative and palliative care of breast cancer. Reference Nadi, Abedi-Firouzjah, Banaei, Bijari and Elahi3–Reference Speers and Pierce5 While treatment technical developments have improved clinical outcomes, optimising the radiotherapy regimen remains challenging due to differences in individual risks and responses. Reference Yarnold, Bentzen, Coles and Haviland6 Hypo-fractionated radiotherapy (HypoRT) has emerged as a prominent approach, characterised by shorter treatment durations and escalated higher fractional doses. Reference Kim and Kim7
Clinical trials have underscored the safety and efficacy of hypofractionation in the treatment of breast cancer, with some studies even reporting ultra-HypoRT involving just five fractions. Reference Kim and Kim7 The low α/β ratio of breast cancer cells suggests heightened sensitivity to higher fractional doses (higher dose in each fraction), further validating the HypoRT strategy. Reference Van Leeuwen, Oei and Crezee8 Furthermore, multiple clinical trials over the past 10 years support the application of shorter treatment fractions with higher fractional doses for breast cancer radiotherapy. Reference Kim and Kim7 Recent clinical trials have demonstrated that HypoRT yields comparable outcomes in terms of survival, local control and acute toxicity when compared to conventionally fractionated radiotherapy. Reference Gay and Niemierko9 Furthermore, HypoRT suggests advantages in terms of treatment efficiency and reduced time commitment for patients. The selection of the optimal fractionation scheme remains a crucial clinical decision, considering individual patient factors. Reference Offersen, Alsner and Nielsen10
Radiobiological modelling is a multidimensional challenge that can help personalise radiation prescriptions and compare different treatment plans. Reference Toma-Dasu and Dasu11 In this model, both aspects of an appropriate treatment including tumour control probability (TCP) and normal tissue complication probability (NTCP) need to be predicted for comparison and evaluation. These probabilities are obtained from the dose distributions of target volume and organs at risk (OARs), considering previously obtained radiobiological dose-response parameters obtained from large groups of patients treated with radiation and receiving different doses. Therefore, the dose distribution must be calculated accurately and described with appropriate metrics. Reference Gulliford, El Naqa, El Naqa and Murphy12
Although advanced radiotherapy techniques such as volumetric modulated arc therapy, intensity-modulated radiotherapy (IMRT) and tomotherapy improve tumour control and spare normal tissues, conventional radiotherapy remains a standard treatment technique in breast cancer. Reference Heymann, Dipasquale and Nguyen13 Conventionally, whole breast radiotherapy involves 50 Gy over 5 weeks Reference Speers and Pierce5 ; however, HypoRT regimens with lower total doses and fractions have shown comparable efficacy with reduced workload. Reference Eraso, Sanz and Mollà14 This approach, introduced experimentally in the UK and Canada decades ago, includes dose regimens of 41·6 Gy in 13 sessions, 39 Gy in 13 sessions and 40 Gy in 15 sessions. Reference Haviland, Owen and Dewar15–Reference Haviland, Bentzen, Bliss, Yarnold and Group17
While conventional treatment planning systems can calculate equivalent doses, our study offers a unique and clinically relevant contribution by employing a comparative approach within the same patient group. We leverage radiobiological models, including the Lyman-Kutcher-Burman LKB, EUD and Poisson models, to predict and compare both TCP and NTCP for different hypo-fractionated regimens (41·6 Gy in 13 sessions, 39 Gy in 13 sessions and 40 Gy in 15 sessions). This approach allows us to assess the relative performance of each model in predicting not only tumour control but also the potential for complications in healthy tissues. By comparing the models’ predictive power for both TCP and NTCP within a consistent clinical context, our study offers a more robust and internally controlled evaluation compared to analyses across diverse patient populations.
Materials and Methods
Patients
This cross-sectional study was conducted under the recommendations and regulations of the national ethical committee. The consent forms were waived due to the retrospective nature of the study. In this study, 30 patients in T2 and T3 stages without positive nodes and metastasis (N0M0) were selected who had been diagnosed with early-stage invasive ductal carcinoma of the left-sided breast cancer and showed no signs of involvement in the supraclavicular and axillary lymph nodes. The patient’s computed tomography images (Somatom Sensation 16, Siemens Healthcare, Erlangen, Germany), treatment plans, calculated dose distributions and demographic information were obtained from the radiation oncology department of Golestan Ahvaz Hospital (Ahvaz, Iran).
Treatment approach
The selected patients received whole breast radiation therapy using the 3D-conformal technique (3D-CRT). The whole breast with 2 cm inferior to the inframammary line and 1 cm superiorly above the breast tissue superiorly was considered as the planning target volume. The medial and lateral margins for PTV were defined as the mid-sternum and mid-axillary lines, respectively. The ipsilateral lung and heart were also contoured adhering to the criteria outlined by Radiation Therapy Oncology Group. Reference Mathew, Chao and Lapuz18 The entire treatment planning process was carried out using ISOgray treatment planning system (DOSI soft corporation, edition 4·2·3·65L, France). One treatment plan for each patient was considered and the prescribed dose was altered to obtain the HypoRT, determining the dose distribution of the target volume and OARs. Details of the treatment planning can be found in Banaei et al.’s study. Reference Banaei, Hashemi and Bakhshandeh4 The prescribed conventional treatment regimen consisted of a total dose of 50 Gy, administered in 25 fractions, using photon irradiation with the energy of 6 MV and employing two tangential fields (medial and lateral fields). Furthermore, three commonly used HypoRT regimens, Reference Koulis, Phan and Olivotto19 with the dose levels of 41·6 Gy (13 fractions), 39 Gy (13 fractions) and 40 Gy (15 fractions) were considered for patients. It should be noted that we did not evaluate the ultra- HypoRT regimens (such as five fraction short-course techniques) in the current study. Regarding the calculated dose distribution, 95% of the PTV received 95% of the prescribed dose in all the patients. After the planning procedure and dose calculations, dose-volume histograms (DVHs) for each patient in various treatment regimens were exported as the input data for TCP and NTCP calculations.
Radiobiological modelling and parameters
To assess the radiobiological impact of treatment regimens on the target volume and OARs (lung and heart), TCP and NTCP values were calculated using various models regarding the DVHs derived from the treatment plans as the input data. Two models based on equivalent uniform dose (EUD) and the Poisson model for TCP and two models based on EUD and LKB for NTCP calculations were considered.
NTCP and TCP: EUD model-based
EUD can be computed from the dose distribution of a structure and is defined as a uniform dose that produces similar biological effects to an actually delivered non-uniform dose distribution for the structure. It can be used when dealing with inhomogeneous dose distributions in tissues and is essentially regarded as a uniform dosage that mimics the same radiobiological effects of a non-uniform dose distribution. To adapt the concept of EUD for normal tissues, Niemierko Reference Niemierko20 introduced a mathematical formula (Equation 1):
In this formula, v i signifies the fraction of the i th volume of an organ receiving a dose of D i , while M represents the number of histograms. The parameter ‘a’ is a dimensionless factor characterised by a negative value for tumour tissues and a positive value for normal tissues, reflecting its volumetric impact.
Based on this formulation, a methodology was proposed for calculating the probability of producing complications in healthy tissues and assessing TCP. Reference Gay and Niemierko9 This calculation relies on the concept of EUD and was introduced in the following equations (Equation 2):
Where TD50 is the uniform tolerance dose of normal tissues that leads to a 50% of complications within a specified time interval. TCD50 is the tumour control dose that, if uniformly delivered to the tumour, achieves 50% control, and γ50 is a dimensionless parameter that represents the slope of the dose-response curve at the point of TD50 dose.
NTCP: LKB model-based
In our effort to compare the outcomes derived from the EUD model when estimating the complication probability in healthy tissues, we turned to the LKB model. This model features a volume-dose relationship that effectively characterises these side effects. Reference Lyman21,Reference Burman, Kutcher, Emami and Goitein22 The complication probability for a uniform dose (D) to the total volume of normal tissue (V total ) is expressed by the Equation 3:
Where TD50 is the dose to the total volume of the organ that leads to 50% complication and m is a parameter that describes the slope of the dose-response curve. This model integrates fractionation and DVH parameters and takes into account the uniform irradiation of a portion of normal tissue (v i ). This involves calculating the effective volume (V eff ) and the tolerance dose for the effective volume, TD(V eff ). This calculation is outlined in the following equation (Equation 4):
$$\eqalign{ & {V_{eff}} = \sum\limits_{i = 1}^M {{v_i}{{\left( {{{{D_i}} \over D} \times {{1 + \left[ {{d_i}/\left( {\alpha /\beta } \right)} \right]} \over {1 + \left[ {d/\left( {\alpha /\beta } \right)} \right]}}} \right)}^{1/n}}} \cr & T{D_{50}}\left( {{V_{eff}}} \right) = {{T{D_{50}}\left( {{V_{total}}} \right)} \over {{V_{eff}}^n}} \cr} $$
Where v i denotes the fraction of volume that receives total doe D i and dose per fraction d i , M is the number of fractional volumes and n is a parameter that represents the volume’s power, relating the tolerance doses to the total organ volume and a portion of the organ volume that is irradiated. Reference Kuperman23 The parameter ‘a’ (Equation 1) and the parameter ‘n’ from the LKB model have an inverse relationship with each other, expressed as ‘a = 1/n’.
TCP: Poisson model-based
To compare the results obtained from the EUD model for tumour control calculations, the Poisson model was used, and the results were compared with available clinical trial data. This model is based on the assumption that the remaining clonogenic cells in the tumour after receiving a uniform dose D follow a Poisson distribution. The Poisson linear-quadratic (Poisson LQ) radiobiological model Reference Laboratories24 considers that the probability of overall tumour control is equal to the product of the probabilities of controlling each voxel as follows (Equation 5):
$$TCP = {\prod\limits_{i = 1}^M {\left[ {\exp \left( { - {N_0}\exp \left( {\sum\limits_{k = 1}^{Fr} {\{ - \alpha {d_{k,i}} - \beta d_{k,i}^2\} } } \right)} \right)} \right]} ^{{v_i}}}$$
Where v i denotes the fraction of volume that receives dose D i , M is the number of volumes, D k,i , is the dose delivered to the i th voxel within k th fraction and Fr is the total number of fractions. α and β stand for the LQ model parameters, and N 0 signifies the initial number of cells. The exact value of N 0 is often unclear, thus, we adopted the following equation for TCP estimation (Equation 6):
$$TCP = {\prod\limits_{i = 1}^M {\left[ {\exp \left( { - \exp \left( {e.\gamma - {{EQ{D_{2,i}}} \over {T{D_{50}}}}\left( {e.\gamma - \ln \left( {\ln 2} \right)} \right)} \right)} \right)} \right]} ^{{v_i}}}$$
Where TD50 corresponds to the dose yielding a 50% response probability, γ denotes the maximum normalised gradient of the dose-response curve, and EQD2,i represents the equivalent dose in voxel i when delivered in a 2 Gy per fraction regimen.
Table 1 depicts the parameters used for the radiobiological models for calculating the side effects on healthy heart and lung tissues as well as tumour control for the left breast tissue. Reference Gay and Niemierko9,Reference Burman, Kutcher, Emami and Goitein22,Reference Owen, Ashton and Bliss25–Reference Kwa, Lebesque and Theuws28 The endpoints of the NTCP models for the heart and lung were pericarditis and pneumonitis, respectively. BIOPLAN version 1·3·3 (BIOlogical evaluation of PLANs) was used for TCP and NTCP calculation.
The parameters used for the radiobiological models. The reference numbers are presented in the parenthesis
TCD50/TD50 is derived from clinical data based on conventional fractionation (typically 2 Gy per fraction). Therefore, it adjusted for a specific HypoRT regimen using an equivalent uniform dose (EQD) concept (Eq. 2).
Statistical analysis
We used the SPSS version 26 software (IBM Corporation, USA) to analyse our radiobiological results and previous clinical data. A normality statistical assessment was conducted using the Kolmogorov-Smirnov test. Since all data exhibited a normal distribution, we applied the Repeated Measurement statistical test to compare the different treatment regimens. The significance level, namely, a P-value was considered to be lower than 0·05.
Results
Table 2 presents the mean ± standard deviation values of TCP in addition to 95% confidence interval (between brackets) values obtained from Poisson and EUD models for two different sets of radiobiological parameter values (including
${\raise0.7ex\hbox{$\alpha $} \!\mathord{\left/ {\vphantom {\alpha \beta }}\right.}\!\lower0.7ex\hbox{$\beta $}}\left( {Gy} \right),\;TC{D_{50}}\left( {Gy} \right),\;{\gamma _{50}},\;and\;a$
across the evaluated breast radiotherapy regimens, along with comparison results among treatment regimen.
Mean ± standard deviation values of TCP in addition to 95% confidence interval
The statistical analysis showed that the differences between the TCP values obtained from Poisson and EUD models were significant (p < 0·001) in both sets of radiobiological parameter values. The results showed that different radiotherapy regimens had significant differences in TCP values. The dose fractionation of 50 Gy in 25 fractions had the highest TCP values in both EUD and Poisson-based calculation models. Furthermore, delivering 41·6 Gy in 13 fractions had the lowest TCP values in both of TCP models and considering the radiobiological parameters of
${\raise0.7ex\hbox{$\alpha $} \!\mathord{\left/ {\vphantom {\alpha \beta }}\right.}\!\lower0.7ex\hbox{$\beta $}} = 4Gy,\;TC{D_{50}} = 28Gy,\;{\gamma _{50}} = 2,\;and\;a = - 7.2.$
In the other set of radiobiological parameters, the 41·6 Gy in 13 fractions had the lowest TCP values in the EUD-based model; without a significant difference with 40 Gy in 15 fractions.
The mean and standard deviation values (as error bars) of ipsilateral lung NTCP values obtained from LKB and EUD models for the evaluated breast radiotherapy regimens, along with comparison results among these regimens are provided in Figure 1. The results showed that all the NTCP values obtained from the LKB model had significantly higher values compared to values obtained with the EUD model (p < 0·001). The 50 Gy in 25 fraction regimens showed significantly higher lung NTCP values compared to 39 Gy in 13 fraction regimens for EUD NTCP modelling. In addition, for LKB NTCP modelling, the 50 Gy/25 fractions regimen had significantly higher values compared to the 40 Gy/15 fractions regimen. Other radiotherapy regimens had no significant differences between these regimens and each other.
Mean and standard deviation values (as error bars) of ipsilateral lung NTCP values obtained from EUD (a) and LKB (b) models for the evaluated breast radiotherapy regimens, along with comparison of radiobiological models among these regimens (c).
Heart NTCP values were also calculated based on the EUD, and LKB models. The obtained heart NTCP values for LKB model were zero for all the evaluated radiotherapy regimens. Therefore, we only presented the NTCP values obtained from EUD NTCP modelling (Figure 2). Although the heart NTCP values were very low and negligible, the statistical analysis showed that the radiotherapy regimen with 50 Gy dose delivered in 25 fractions had the highest heart NTCP compared to other regimens (p < 0·01).
Mean and standard deviation values (as error bars) of heart NTCP values obtained from EUD radiobiological model for the evaluated breast radiotherapy regimens.
Discussion
Radiobiological models like the ones employed in this study (Poisson and EUD) offer valuable tools for evaluating the impact of different fractionation regimens on TCP and NTCP in various cancers. Reference Van Leeuwen, Oei and Crezee8 Our study aimed to assess these radiobiological effects using standardised treatment plans with identical target coverage and dose homogeneity across all fractionation schemes. While this approach allowed us to isolate the influence of fractionation on TCP and NTCP predictions, it did not account for potential variations in dosimetric parameters for OARs like the ipsilateral lung and heart. These OAR parameters, such as mean dose and volume receiving specific doses, are known to influence NTCP. Reference Gay and Niemierko9 Therefore, we focused on presenting the radiobiological results (TCP and NTCP) in this analysis.
Randomised trials involving over 7,000 patients have demonstrated no significant differences in treatment efficacy, late post-radiotherapy complications, or cosmetic effects between standard and moderately HypoRT regimens with 5–10 year follow-up. Reference Dearnaley, Syndikus and Mossop29–Reference Zhou, Mei and Chen31 Notably, Miller et al.’s Reference Miller, Wall, Baines, Sun, To and Narod32 extended follow-up strengthens the evidence supporting the non-inferiority of HypoRT compared to conventional fractionation. These findings are further reinforced by results from three large UK research projects. Reference Dearnaley, Syndikus and Mossop29–Reference Zhou, Mei and Chen31 While these studies provide robust evidence for the safety and efficacy of HypoRT in many patients, some ongoing research areas remain. Potential long-term effects of administering only five large fractions over five weeks require further investigation. Additionally, specific patient sub-groups, such as those with underlying health conditions or certain tumour characteristics, may warrant a more cautious approach to HypoRT implementation. Future research should focus on these areas to refine patient selection criteria and optimise treatment personalisation.
Our study compared the performance of the Poisson and EUD models in predicting TCP for breast cancer patients undergoing conservative radiotherapy. When benchmarked against data from the START trial, Reference Eraso, Sanz and Mollà14 the Poisson model yielded superior predictive accuracy. The START trial reported a HypoRT regimen (40 Gy in 15 fractions) as having the highest TCP (96%), while the 39 Gy regimen achieved the lowest (92%). Reference Haviland, Owen and Dewar15 In contrast, our findings using the Poisson model showed a narrower range of TCP values (3%) across the evaluated fractionation schemes. Conversely, the EUD model exhibited a wider range of TCP values (over 11%) between regimens. This discrepancy may be attributed to differences in the ‘a’ parameter, which plays a critical role in how each model responds to changes in fractionation.
We observed further discrepancies in TCP predictions when comparing our results to previous studies. Shirani et al. Reference Abi, Habibian, Salimi, Shakeri, Mojahed and Gharaati33 reported a TCP of 82·8% using the Poisson model for a conventional regimen in 10 patients. In contrast, our study using the same model yielded a higher TCP (92·5%) for the conventional regimen. Similarly, Astudillo-Velázquez et al. Reference Astudillo-Velazquez, Paredes-Gutiérrez and Reséndiz-González16 reported lower TCP values (56·04% and 55·41%) for conventional and HypoRT regimens, respectively, using the Poisson model in 10 patients. Our findings, however, showed higher TCP values (92·5% and 88·7%) for the same regimens. These discrepancies could stem from variations in model parameters, radiotherapy plans, dose distributions and fractionation. While there was a trend towards lower TCP for hypofractionation compared to conventional regimens in our study, further investigation with larger patient cohorts is warranted.
Results of the previous studies indicated a lower probability of tumour control for the hypofractionation method compared to the conventional method; and we also observed similar findings. However, we found higher NTCP values for the lung and heart in conventional fractionation. The results of Kazemzadeh et al. Reference Kazemzadeh, Abedi, Amouheidari and Shirvany34 showed lower NTCP values for the lung in conventional fractionation compared to the hypofractionation regimen. In contrast, Astudillo-Velázquez et al. Reference Astudillo-Velazquez, Paredes-Gutiérrez and Reséndiz-González16 reported higher NTCP and TCP values for conventional treatment compared to the HypoRT regimen. Furthermore, the NTCP value in Astudillo-Velázquez et al.’s study Reference Astudillo-Velazquez, Paredes-Gutiérrez and Reséndiz-González16 was much higher than the values of our findings and Kazemzadeh et al.’s report. The discrepancies in the NTCP results among our study and also previous reports may be justified by the different radiobiological model parameters.
Kazemzadeh et al. Reference Kazemzadeh, Abedi, Amouheidari and Shirvany34 reported the TCP values for two regimens including conventional and hypofractionation (40 Gy in 15 sessions) using the EUD model as 99·16% and 95·96%, respectively. Additionally, Shanei et al. Reference Shanei, Amouheidari, Abedi, Kazemzadeh and Jaafari35 reported a TCP of 99·07% for the conventional method using the EUD model. In our study, EUD-based TCP values for conventional and hypofractionation (40 Gy in 15 fractions) regimens were 55·4% and 45·1%, respectively, showing significantly lower values compared to previous reports. Since the radiobiological model and parameters in these two mentioned studies were similar to our study, the lower values in our study can be related to different dose distributions resulting from different radiotherapy plans.
The heart NTCP values were consistently low and negligible across all treatment regimens. This aligns with findings from previous studies that reported similarly low or zero heart NTCP in various breast radiotherapy techniques. Reference Budach, Bölke and Matuschek30,Reference Zhou, Mei and Chen31,Reference Abi, Habibian, Salimi, Shakeri, Mojahed and Gharaati33 Despite the small magnitude of heart NTCP values, statistical analysis revealed no significant differences when comparing hypofractionation regimens. However, it is noteworthy that all three HypoRT methods consistently demonstrated significantly lower NTCP values compared to the conventional method.
Our study has inherent limitations that necessitate cautious interpretation of the results. The relatively small patient cohort limit the generalizability of our findings to larger populations. Additionally, our analysis did not account for individual variations in patient radiosensitivity, a factor that could potentially influence treatment outcomes. Furthermore, the absence of long-term follow-up data precludes us from making definitive conclusions about the long-term efficacy and safety of the evaluated fractionation regimens. Finally, relying on DVHs derived from a single CT scan may not fully capture potential anatomical changes during radiotherapy, potentially introducing inaccuracies in model predictions.
Future research efforts should address these limitations by employing larger and more diverse patient cohorts. Incorporation of radiosensitivity assessments into the analysis could provide valuable insights. Additionally, implementing robust long-term follow-up protocols would strengthen the conclusions regarding treatment effectiveness and safety. Exploring advanced treatment planning techniques that account for potential anatomical variations during therapy could enhance the accuracy of model predictions and potentially lead to more personalised treatment plans.
Conclusion
Our study employed radiobiological models (Poisson and EUD) to assess the potential trade-off between TCP and NTCP for different fractionation regimens in breast cancer radiotherapy. The findings suggest that HypoRT may offer advantages in terms of reduced NTCP compared to conventional regimens. However, the model predictions also indicate a potential decrease in TCP with HypoRT compared to conventional approaches. These results highlight the importance of further research to explore strategies that optimise the balance between minimising treatment-related toxicities and achieving effective tumour control. Future investigations could involve incorporating additional biological factors or utilising advanced treatment planning techniques that personalise fractionation schemes based on individual patient characteristics.
Acknowledgements
This work is based on the master’s thesis of Mrs. Bahareh Arjamand. We are grateful for the financial support provided by Jundishapur University of Medical Sciences of Ahvaz (code CRC 0003). We also extend our sincere thanks to the personnel of Radio-Oncology department in Golestan Hospital for their cooperation throughout this research project. Finally, we appreciate the assistance provided by Miss Shamsi and Miss Fadaee.
Financial support
This study was funded by the Ahvaz Jundishapur University of Medical Sciences with grant number CRC-0003.
Competing interests
The authors declare that they have no conflict of interest.
Compliance with ethical guidelines
This research work has ethical approval with code IR.AJUMS.MEDICINE.REC.1400.008 (2021-04-14).
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