Dose-Gradient Function-Guided Reduction of Radiation-Induced Heart Injury in Left-Sided Breast Cancer Treated With Helical Tomotherapy After Mastectomy.

Dose-Gradient Function–Guided Reduction of Radiation-Induced Heart Injury in Left-Sided Breast Cancer Treated With Helical Tomotherapy After Mastectomy - PMC Skip to main content An official website of the United States government Here's how you know Here's how you know Search Log in Primary site navigation Search Log in Search PMC Full-Text Archive Search in PMC Journal List User Guide As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsement of, or agreement with, the contents by NLM or the National Institutes of Health. Learn more: PMC Disclaimer | PMC Copyright Notice Technol Cancer Res Treat . 2026 Jun 1;25:15330338261454536. doi: 10.1177/15330338261454536 Dose-Gradient Function–Guided Reduction of Radiation-Induced Heart Injury in Left-Sided Breast Cancer Treated With Helical Tomotherapy After Mastectomy Yunyan Yang 1, * , Xiang Pan 1, * , Lingli Zhou 1 , Jinli Peng 1 , Tianwen Zhang 1 , Yan Xu 1 , Han Bai 1, ✉ , Ya Li 1, ✉ Author information Article notes Copyright and License information 1 The Third Affiliated Hospital of Kunming Medical University, Yunnan Cancer Hospital, Peking University Cancer Hospital Yunnan, Kunming, Yunnan, China ✉ Ya Li, The Third Affiliated Hospital of Kunming Medical University, Yunnan Cancer Hospital, Peking University Cancer Hospital Yunnan, No. 519, Kunzhou Road, Kunming, Yunnan 650118, China. Email: liya2@kmmu.edu.cn ✉ Han Bai, The Third Affiliated Hospital of Kunming Medical University, Yunnan Cancer Hospital, Peking University Cancer Hospital Yunnan, No. 519, Kunzhou Road, Kunming, Yunnan 650118, China. Email: cellbaihan@163.com * These authors contributed equally to this work. Received 2026 Jan 8; Revised 2026 Apr 19; Accepted 2026 May 5; Collection date 2026. © The Author(s) 2026 This article is distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 License ( https://creativecommons.org/licenses/by-nc/4.0/ ) which permits non-commercial use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages ( https://us.sagepub.com/en-us/nam/open-access-at-sage ). PMC Copyright notice PMCID: PMC13227034  PMID: 42223204 Abstract Introduction Radiation-induced heart injury (RIHI) remains an important concern in left-sided postmastectomy radiotherapy (PMRT), particularly when internal mammary lymph nodes (IMLNs) are included in the target volume. Helical tomotherapy (HT) provides excellent target conformity for complex targets, but cardiac sparing remains challenging. This study evaluated whether dose-gradient function (DGF)-guided optimization could further reduce cardiac exposure in left-sided breast cancer patients treated with HT after modified radical mastectomy. Methods Twenty-six female patients with left-sided breast cancer who underwent PMRT were retrospectively included. Initial HT plan was generated and evaluated using DGF, which quantifies dose falloff outside the target volume. The patient with the minimum DGF curve area ( S min ) was used as the internal benchmarking and was not re-optimized. The remaining 25 patients underwent DGF-guided re-optimization. Mean heart dose (MHD), cardiac dose-volume indices, left anterior descending coronary artery (LAD) dose, and the model-based relative risk increase (RRI) of major coronary events, were compared between the original and optimized plans. Results DGF-guided re-optimization significantly reduced cardiac dose parameters while maintaining target coverage and overall plan quality. MHD decreased from 6.190 ± 0.384 Gy to 5.322 ± 0.332 Gy (P < 0.001), and cardiac V 5 decreased from 43.084 ± 4.807% to 29.260 ± 4.453% (P < 0.001), with significant reductions in V 10 , V 20 , and V 30 (all P < 0.05). LAD V 5 decreased from 86.150 ± 8.152% to 81.240 ± 9.100% (P < 0.001), and LAD mean dose decreased from 18.786 ± 2.661 Gy to 18.230 ± 2.691 Gy (P < 0.001). Greater cardiac dose reduction was observed in the IMLNs irradiation group. The estimated relative risk increase decreased from 45.803 ± 2.839% to 39.383 ± 2.459% (P < 0.001). Conclusion DGF-guided optimization may improve HT plan quality for left-sided PMRT and achieve additional reductions in cardiac dose and model-based cardiac risk estimates, particularly in cases requiring IMLNs irradiation. Keywords: breast cancer, postmastectomy radiotherapy, helical tomotherapy, dose-gradient function, radiation-induced heart injury Introduction Breast cancer is the most prevalent cancer among women worldwide and a leading cause of female mortality. 1 Postoperative adjuvant radiotherapy is crucial to breast cancer management, reducing recurrence, metastasis, and death. Unlike radiotherapy after breast-conserving surgery (BCS) for left-sided cancer, postmastectomy radiotherapy (PMRT) positions the cardiac and left anterior descending coronary artery (LAD) within a steep dose gradient region, particularly when the internal mammary lymph nodes (IMLNs) are targeted. Consequently, the risk of radiation-induced heart injury (RIHI) rises substantially with increasing exposure. 2 , 3 Electing to irradiate the IMLNs creates a significant dosimetric challenge for radiotherapy planning. Even without deliberate targeting, incidental irradiation can deliver approximately 40-60% of the prescribed dose (e.g., 25-30 Gy mean dose from a 50 Gy prescription). However, deliberately including the IMLNs within the clinical target volume (CTV) inevitably raises radiation exposure for adjacent critical organs, especially the heart and lungs. 4 , 5 Clinical evidence consistently demonstrates that IMLNs irradiation increases cardiac dose. For left-sided breast cancer, the mean heart dose (MHD) rises from approximately 3.3 Gy without IMLNs irradiation, to 4.6 Gy with incidental exposure, and further to nearly 6.9 Gy when IMLNs are formally included in the planning target volume (PTV). 6 Given the established linear relationship between MHD and the risk of major coronary events, even a moderate increase in MHD may translate into a clinically significant rise in long-term cardiac morbidity and mortality. 7 , 8 Therefore, a central challenge in PMRT for left-sided breast cancer is achieving adequate target coverage of the chest wall and regional lymph nodes while minimizing radiation exposure to the heart. Helical Tomotherapy (HT) enables integrated irradiation of the chest wall and regional lymph nodes (including IMLNs) through its continuous helical irradiation and intensity-modulated capabilities, making it suitable for treating extensive and complex target volumes in PMRT. Due to frequent extension of the PMRT target volume into the supraclavicular region and IMLNs, conventional techniques often encounter difficulties with field matching and exhibit dose irregularities. HT, however, provides longitudinal continuous coverage through a single plan, improving dose uniformity within the target and reducing hot and cold spots. 9 Cardiac sparing is particularly challenging in left-sided PMRT, especially when irradiation of the IMLNs is required. Although HT can provide excellent target coverage for complex target volumes, it may also increase low-dose exposure to surrounding normal tissues. For patients with left-sided breast cancer, the IMLNs target volume is closely related to the anatomy of the heart and LAD, making cardiac dose control a core dosimetric objective in PMRT planning. Epidemiological evidence has demonstrated a linear association between MHD and the incidence of ischemic cardiac disease, further underscoring the importance of minimizing cardiac radiation exposure. 8 On this basis, HT combined with directional or complete blocking strategies can reduce moderate-to-high dose exposure to organs at risk (OARs), such as the heart (specifically the left anterior descending artery) and the lungs, while maintaining good target coverage and conformal quality for the chest wall and regional lymph nodes (including the IMLNs). 10 Traditional planning evaluation metrics, including dose-volume histogram (DVH), conformity index (CI), and homogeneity index (HI), are widely used to assess target volume coverage and dose uniformity, but do not directly quantify the three-dimensional spatial dose gradient. 11 , 12 In contemporary radiation therapy planning, parameters derived from DVH are not only used for post-planning evaluation but are also routinely used to guide iterative plan optimization and quality assurance, particularly in breast cancer radiotherapy. 13 , 14 Although various indices based on conformation and distance have been proposed to indirectly reflect dose distribution characteristics, their ability to describe the spatial rate of dose falloff around complex target regions remains limited. 15 , 16 To address this, gradient-based metrics have been introduced. Paddick et al proposed a dose gradient index (DGI) to complement conformity assessment. 17 More recently, Sung et al introduced the dose gradient curve (DGC), providing a quantitative description of dose decay as a function of distance from the target volume. 18 Building upon this concept, spatial dose gradients have been widely used to describe dose falloff outside the PTV and to evaluate plan quality in various radiotherapy techniques. 19 , 20 Specifically, the dose-gradient function (DGF) has been applied as a quantitative metric to guide plan optimization and reduce radiation-induced lung injury in breast cancer radiotherapy. 21 However, the clinical applicability of DGF-guided optimization in HT-based PMRT, particularly for patients requiring IMLNs irradiation, remains unclear. 22 Therefore, this study aimed to evaluate whether DGF-guided optimization could improve dosimetric plan quality and reduce cardiac exposure in HT-based PMRT for left-sided breast cancer after modified radical mastectomy, and to explore its potential impact on model-based cardiac risk estimates. Materials and Methods Patient Selection A total of 26 female patients with left-sided breast cancer who underwent PMRT at our institution between April 27, 2021, and July 17, 2023 were retrospectively screened according to predefined eligibility criteria. Patients who met the inclusion criteria and had complete clinical, target delineation, and dosimetric data available for analysis were included in the study. The mean patient age was 52 years (range 34-72 years). Seventeen patients received IMLNs irradiation, while nine did not. This retrospective study was approved by the Ethics Committee of Yunnan Cancer Hospital, The Third Affiliated Hospital of Kunming Medical University, Peking University Cancer Hospital Yunnan (approval No. KYLX2024-285; approved on November 20, 2024). Written informed consent was obtained from all participants. All patient information was de-identified prior to analysis. The study was conducted in accordance with the Helsinki Declaration of 1975, as revised in 2024. Target Volume Delineation The CTV was delineated by an experienced radiation oncologist according to the Radiation Therapy Oncology Group (RTOG) guidelines for modified radical mastectomy in breast cancer. The PTV was generated by adding 0.5 cm to the isotropic CTV, excluding any portions extending into the lung or beyond the skin surface. OARs included the heart, left lung, right lung, combined lungs, right breast, spinal cord, left humeral head and LAD. LAD delineation followed the method described by Memorial Sloan Kettering Cancer Centre, in which the anterior cardiac region was defined as the superficial 1 cm volume of the left anterior quadrant of the heart. 23 IMLNs irradiation was indicated based on the following criteria: (1) ≥4 positive axillary lymph nodes after dissection; (2) Inner-quadrant or central primary tumour with axillary lymph node metastases; (3) Age < 35 years with axillary lymph node metastases; (4) Radiologic evidence of IMLNs involvement at diagnosis or pathological confirmation in the absence of axillary lymph node dissection. Treatment Planning All treatment plans were generated using the Precision™ treatment planning system (TPS) on the Radixact® X system (Accuray Inc., Sunnyvale, CA, USA). Dose calculations utilized a convolution-superposition algorithm. All plans utilized a fixed beam width of 2.5 cm, a pitch of 0.4, and a modulation factor of 3.5. The initial plan was optimized using the institution’s standard planning template, without applying full-field or organ-based targeted blocking techniques. The optimization objectives prioritized PTV coverage, followed by cardiac and pulmonary protection. Relative weights were iteratively adjusted until all clinical requirements were met. Optimization was conducted using the iterative algorithm within the Precision™ TPS, running for approximately 3000 iterations. Prescription dose was 50Gy in 25 fractions (2Gy per fraction), with a requirement for ≥95% PTV coverage. Critical organ dose constraints followed our institutional criteria: cardiac ( D m e a n <8Gy, V 5 G y <40%), left lung ( V 5 G y <60%, V 20 G y <30%), right lung ( V 5 G y <50%), right breast ( D m e a n <6Gy), Spinal cord ( D max <40Gy), LAD ( V 40 G y <20%), left humeral head ( V 30 G y <20%). Dose-Gradient Function (DGF) A fast dose decay rate outside the target volume is a desirable plan feature, as it reduces radiation exposure to surrounding normal tissues. To quantify this rate, Li et al proposed the DGF, which enables the assessment of dose distribution characteristics for plan evaluation and re-optimization. 21 It is defined as follows: D G F = V D / V P 3 (1) where V D is the volume enclosed by a given isodose surface and V P is the volume of the PTV. Taking the cubic root of the volume ratio converts volumetric information into an equivalent linear distance metric under a spherical equivalence assumption, thereby enabling the DGF to reflect the relative separation between isodose surfaces and the target volume. The workflow of DGF-guided plan evaluation and re-optimization is illustrated in Figure 1 . For each patient, isodose volumes ranging from 50Gy to 2.5Gy (in 2.5Gy steps) were extracted from the original HT plans. Corresponding DGF values were calculated, and DGF curves were generated (Figure 2A ). DGF calculation in the present study was performed offline by extracting isodose volumes from the TPS and calculating the area under the DGF curve externally; this workflow has not yet been integrated into the TPS as an automated function. Figure 1. Open in a new tab Workflow of DGF-guided plan evaluation and re-optimization. Step 1: Extraction of isodose volumes from the original treatment plan; Step 2: Calculation of DGF values relative to the PTV; Step 3: Construction of the DGF curve and calculation of the area under the curve ( S ); Step 4: Iterative plan re-optimization when S exceeds the reference threshold ( S min ). S min represents the minimum area under the DGF curve observed in the reference patient Figure 2. Open in a new tab (A) DGF curves for all 26 patients; (B) Illustration of the area under the DGF curve ( S ) for two representative patients Mechanisms of DGF-Guided Radiotherapy Plan Optimization A shorter distance between isodose lines generally indicates a steeper DG, faster dose falloff, and a smaller irradiated heart volume. According to Equation ( 1 ), a lower V D value corresponds to a smaller DGF and a steeper spatial dose decay. As illustrated in Figure 2 , a smaller area under the DGF curve was hypothesized to reflect a more favorable dose falloff pattern and potentially lower irradiation doses to adjacent OARs. For illustrative purposes, assuming two hypothetical cases (A and B), a smaller area under the DGF curve ( S A < S B ) may reflect a more favorable dose falloff pattern and potentially lower doses to adjacent OARs ( D O A R ( A ) < D O A R ( B ) ). Here, S A and S B denote the areas under the DGF curves for hypothetical patients A and B, and D O A R ( A ) and D O A R ( B ) represent the corresponding OARs doses. The area under the DGF curve was calculated for all 26 patients using GraphPad Prism 10.1.2( Table 1 ). In this study, the minimum area under the DGF curve ( S min ) was used as an internal empirical benchmark derived from the best-performing plan and was not subjected to further re-optimization, rather than as a universal threshold applicable to all institutions or planning systems (Figure 2B ). Therefore, paired comparisons between the original and optimized plans were performed in the remaining 25 patients. As shown in Figure 2A , the plan for patient 4 was considered optimal ( S 4 = S min ). Patient 4 had IMLNs involvement, with a PTV coverage of 96.80% at 50 Gy, CI of 1.21, and HI of 0.09. The dosimetric parameters were as follows: cardiac V 5 41.80%, V 10 8.60%, V 20 3.60%, V 30 1.10%, and MHD 6.01 Gy; left lung V 5 54.50%, V 10 37.70%, V 20 26.00%, and MLD 13.90 Gy; right lung V 5 46.40%, V 10 21.70%, V 20 3.60%, and MLD 6.68 Gy; combined lungs V 5 49.80%, V 10 28.40%, V 20 13.00%, and MLD 9.71 Gy; right breast D M e a n 7.21 Gy, D Max 29.32Gy, and V 20 2.2%; LAD V 5 85.30%, V 10 60.60%, V 20 41.40%, V 30 15.20%, V 40 0.00%, D M e a n 16.85 Gy, and D Max 39.05 Gy; left humeral head V 30 47.30% and D Max 51.84 Gy; and spinal cord D Max 33.11 Gy. Notably, DGF-guided re-optimization was performed within the identical constraint framework as the original plans (cardiac D M e a n < 8 Gy, V 5 < 40%), with S min serving as an additional gradient objective rather than a replacement for dose-volume constraints. Table 1. Geometrical Parameters and DGF Curve Areas for 26 Patients NO V PTV ( cm 3 ) V Heart ( cm 3 ) S ( cm 2 ) NO V PTV ( cm 3 ) V Heart ( cm 3 ) S ( cm 2 ) 1 767.66 622.07 7509.00 14 719.73 615.27 7426.00 2 609.58 605.40 7484.00 15 477.85 431.23 7598.00 3 905.01 765.07 7396.00 16 739.55 501.06 7413.00 4 965.68 681.49 7271.00 17 796.86 616.04 7474.00 5 561.00 437.25 7798.00 18 598.04 545.70 7434.00 6 923.03 794.72 7519.00 19 762.75 665.53 7300.00 7 360.82 505.32 7961.00 20 949.27 747.20 7306.00 8 572.18 592.54 7900.00 21 717.65 552.75 7723.00 9 609.52 488.51 7769.00 22 755.29 579.73 7419.00 10 544.10 593.62 7803.00 23 817.77 595.05 7493.00 11 739.79 524.62 7366.00 24 734.07 730.86 7548.00 12 681.89 597.75 7609.00 25 746.89 502.52 7455.00 13 808.56 694.13 7465.00 26 730.75 499.84 7406.00 Open in a new tab Estimated Relative Risk Increase (RRI) RIHI was estimated using the linear dose-response relationship reported by Darby et al, which demonstrated a 7.4% increase in the relative risk of major coronary events per 1 Gy increase in MHD. 8 The RRI of major coronary events was estimated according to the Darby dose-response model based on MHD. Accordingly, the RRI was calculated as: R R I ( % ) = 7.4 × MHD ( Gy ) (2) This provides a model-based estimation and does not represent actual observed clinical outcomes. Evaluation Parameters To assess dosimetric differences between original and optimized plans, DVH parameters were extracted for all targets and OARs. Heart dosimetry parameters included MHD and V 5 , V 10 , V 20 , and V 30 . Lung parameters included mean lung dose (MLD), V 5 , V 10 , and V 20 for the left, right, and combined lungs. Additional parameters included right breast V 20 , mean dose and max dose; LAD V 5 , V 10 , V 20 , V 30 , V 40 , mean dose and max dose; left humeral head V 30 and max dose; and spinal cord maximum dose. V X represents the volume percentage receiving at least X Gy of radiation. Statistics Statistical analyses were performed using IBM SPSS Statistics (Version 27). Paired t-tests were used to compare dosimetric differences between the original and optimized plans. Pearson correlation and simple linear regression analyses were used to assess the associations between the DGF curve area ( S ) and cardiac dose metrics (MHD and cardiac V 5 ) in the original plans. Given the limited sample size, the correlation and regression analyses were considered exploratory. Results are presented as mean ± standard deviation. A two-sided P < 0.05 was considered statistically significant. Reporting Guideline The reporting of this study was prepared with reference to the STARD 2015 statement, where applicable, together with relevant EQUATOR reporting guidance for observational dosimetric studies. 24 Results Plan Quality and Target Coverage Dosimetric comparisons between the original and DGF-guided optimized plans were performed in the 25 patients who underwent re-optimization, excluding the reference case with the minimum DGF curve area. For 25 patients, DGF-guided optimization preserved adequate target coverage and plan quality. No significant differences were observed between the original and optimized plans in PTV coverage (D 95% ), HI or monitor units (MU) (all P > 0.05), indicating that cardiac dose reduction was achieved without compromising target dose homogeneity or treatment efficiency ( Table 2 ). CI exhibited a modest but statistically significant increase after optimization (1.225 ± 0.053 vs 1.245 ± 0.054, P = 0.002), which was deemed acceptable by experienced clinicians. Table 2. Comparison of Dosimetric Parameters Between the Original and DGF-Guided Optimized Plans in the 25 Patients Who Underwent Re-Optimization Evaluation parameters Original plan Optimized plan t P Cardiac V 5 (%) 43.084±4.807 29.260±4.453 13.514 <0.001 V 10 (%) 9.476±1.313 8.484±1.042 5.290 <0.001 V 20 (%) 4.216±0.718 3.822±0.640 3.171 0.004 V 30 (%) 1.628±0.471 1.520±0.471 2.571 0.017 MHD (Gy) 6.190±0.384 5.322±0.332 13.838 <0.001 LAD V 5 (%) 86.150±8.152 81.240±9.100 6.914 <0.001 V 10 (%) 62.235±8.701 61.195±8.844 5.180 <0.001 V 20 (%) 45.505±8.851 44.440±8.645 3.530 0.002 V 30 (%) 24.870±8.371 23.660±8.196 3.386 0.002 V 40 (Gy) 3.640±3.942 3.255±3.700 1.782 0.087 D M e a n (Gy) 18.786±2.661 18.230±2.691 6.920 <0.001 D Max (Gy) 44.201±2.868 43.803±3.247 2.124 0.044 left lung V 5 (%) 55.892±4.605 56.684±4.404 -1.682 0.106 V 10 (%) 37.548±1.336 37.920±1.698 -2.381 0.026 V 20 (%) 25.872±0.419 26.044±0.501 -3.320 0.003 MLD (Gy) 13.768±0.362 13.847±0.390 -4.120 <0.001 right lung V 5 (%) 42.284±4.984 41.756±5.310 0.875 0.39 V 10 (%) 19.716±2.850 19.988±2.837 -1.992 0.058 V 20 (%) 2.928±0.795 3.116±0.780 -3.204 0.004 MLD (Gy) 6.258±0.516 6.185±0.534 1.672 0.108 combined lungs V 5 (%) 48.048±4.014 48.408±4.047 -1.347 0.19 V 10 (%) 27.644±1.836 27.976±1.954 -3.990 0.001 V 20 (%) 13.132±0.672 13.316±0.669 -5.262 <0.001 MLD (Gy) 9.315±1.032 9.595±0.414 -1.426 0.167 right breast D M e a n (Gy) 7.071±0.338 7.102±0.372 -0.612 0.547 D Max (Gy) 26.194±5.032 26.416±4.813 -0.982 0.336 V 20 (%) 1.304±1.245 1.348±1.040 -0.314 0.756 left humeral head V 30 (%) 32.180±19.436 31.824±19.137 0.553 0.585 D Max (Gy) 44.112±5.775 44.431±5.726 -3.034 0.006 spinal cord D Max (Gy) 32.504±7.09 34.107±4.154 -1.425 0.167 CI 1.225±0.053 1.245±0.054 -3.573 0.002 HI 0.084±0.016 0.087±0.017 -1.398 0.175 PTV (D 95% ) 96.380±0.801 96.521±0.712 -1.458 0.158 MU 234327.027±23958.584 240272.348±17258.851 -1.493 0.148 Open in a new tab Dose parameters of OARs were compared between the original and optimized plans in each group. Data are presented as mean ± standard deviation. Statistical comparisons were performed using paired tests. P < 0.05 were considered statistically significant. Subgroup analyses demonstrated similar findings. In both the non-IMLNs irradiation and IMLNs irradiation groups, PTV coverage and HI remained stable after optimization (all P > 0.05), confirming that the DGF-based optimization scheme maintains plan robustness even in the presence of IMLNs irradiation ( Table 3 ). Table 3. Comparison of Dosimetric Parameters Between the Original and Optimized Plans in the Non-irradiated and Irradiated IMLNs Groups Evaluation parameters Non-irradiated IMLNs group Irradiated IMLNs group Original plan Optimized plan t P Original plan Optimized plan t P cardiac V 5 (%) 41.278±4.682 29.189±4.807 13.997 <0.001 44.100±4.714 29.300±4.405 9.942 <0.001 V 10 (%) 9.056±1.519 8.144±1.455 2.623 0.031 9.712±1.168 8.675±0.708 4.580 <0.001 V 20 (%) 4.222±0.960 3.767±0.849 1.419 0.194 4.212±0.577 3.853±0.518 4.166 <0.001 V 30 (%) 1.633±0.490 1.567±0.500 1.265 0.242 1.625±0.477 1.494±0.468 2.226 0.042 MHD (Gy) 6.080±0.446 5.290±0.404 7.368 <0.001 6.251±0.344 5.340±0.298 11.740 <0.001 LAD V 5 (%) 79.750±7.165 74.975±5.781 5.967 <0.001 87.750±8.080 82.806±10.079 4.783 <0.001 V 10 (%) 55.375±3.883 54.100±3.585 5.473 0.001 63.950±9.870 62.969±10.075 3.399 0.004 V 20 (%) 40.575±4.608 41.000±4.253 -1.868 0.099 46.738±10.292 45.300±10.295 3.530 0.003 V 30 (%) 23.850±3.471 24.275±4.080 -1.676 0.132 25.125±10.264 23.506±9.924 3.275 0.005 V 40 (Gy) 3.725±1.372 4.250±2.247 -1.451 0.185 3.619±4.885 3.006±4.346 2.497 0.025 D M e a n (Gy) 17.442±1.467 17.270±1.509 4.528 0.002 19.122±3.095 18.469±3.172 5.799 <0.001 D Max (Gy) 44.628±1.264 44.465±2.103 0.554 0.595 44.095±3.499 43.637±3.790 1.852 0.084 left lung V 5 (%) 54.844±3.694 56.100±4.767 -2.040 0.076 56.481±5.063 57.012±4.312 -0.812 0.43 V 10 (%) 37.200±0.922 37.622±1.248 -2.098 0.069 37.744±1.513 38.088±1.923 -1.557 0.14 V 20 (%) 25.711±0.314 25.922±0.363 -3.744 0.006 25.962±0.451 26.112±0.563 -1.993 0.065 MLD (Gy) 13.620±0.405 13.722±0.447 -3.111 0.014 13.852±0.319 13.918±0.350 -2.777 0.014 right lung V 5 (%) 41.067±5.086 39.589±5.272 1.134 0.29 42.969±4.956 42.975±5.088 -0.011 0.992 V 10 (%) 18.411±3.500 18.456±3.371 -0.141 0.891 20.450±2.206 20.850±2.148 -3.391 0.004 V 20 (%) 2.744±0.803 2.900±0.834 -1.390 0.202 3.031±0.796 3.238±0.748 -2.980 0.009 MLD (Gy) 6.114±0.568 5.954±0.594 1.752 0.118 6.339±0.484 6.315±0.467 0.566 0.579 combined lungs V 5 (%) 46.511±3.782 47.067±4.404 -1.301 0.229 48.912±3.992 49.162±3.766 -0.717 0.484 V 10 (%) 26.878±2.102 27.089±2.171 -1.378 0.205 28.075±1.578 28.475±1.690 -4.122 0.001 V 20 (%) 13.078±0.604 13.211±0.609 -1.835 0.104 13.163±0.725 13.375±0.712 -5.842 <0.001 MLD(Gy) 9.444±0.430 9.449±0.453 -0.126 0.903 9.242±1.261 9.677±0.380 -1.438 0.171 right breast D M e a n ( Gy) 7.002±0.393 6.956±0.400 0.562 0.589 7.109±0.310 7.185±0.340 -1.160 0.264 D Max (Gy) 28.496±7.337 28.308±7.03 0.324 0.754 24.899±2.613 25.352±2.711 -3.367 0.004 V 20 (%) 1.500±1.584 1.278±0.854 0.585 0.575 1.194±1.052 1.388±1.156 -4.939 <0.001 left humeral head V 30 (%) 42.500±16.948 41.422±16.761 1.226 0.255 26.375±18.745 26.425±18.702 -0.057 0.955 D Max (Gy) 47.202±4.584 47.392±4.698 -1.544 0.161 42.374±5.762 42.766±5.699 -2.633 0.019 spinal cord D Max (Gy) 32.998±5.684 33.436±4.221 -0.414 0.69 32.226±7.936 34.485±4.204 -1.362 0.193 CI 1.208±0.020 1.221±0.032 -1.540 0.162 1.234±0.063 1.258±0.06 -3.255 0.005 HI 0.082±0.019 0.083±0.017 -0.229 0.824 0.085±0.015 0.089±0.017 -1.815 0.089 PTV (D 95% ) 96.300±0.992 96.544±0.776 -1.599 0.148 96.425±0.704 96.508±0.699 -0.661 0.518 MU 246305.356±11339.816 247520.467±11567.481 -3.068 0.015 226034.338±26535.865 236195.281±18867.257 -1.631 0.124 Open in a new tab Dose parameters of OARs were compared between the original and optimized plans in each group. Data are presented as mean ± standard deviation. Statistical comparisons were performed using paired tests. P < 0.05 were considered statistically significant. Heart and LAD Dose Parameters For all patients, DGF-guided optimization significantly reduced cardiac dose parameters ( Table 2 ). MHD decreased from 6.190 ± 0.384 Gy to 5.322 ± 0.332 Gy (P < 0.001). Significant reductions were also observed in cardiac V 5 (43.084 ± 4.807% vs 29.260 ± 4.453%, P < 0.001), V 10 (9.476 ± 1.313% vs 8.484 ± 1.042%, P < 0.001), V 20 (4.216 ± 0.718% vs 3.822 ± 0.640%, P = 0.004), and V 30 (1.628 ± 0.471% vs 1.520 ± 0.471%, P = 0.017). LAD dose parameters also improved. Significant decreases were observed in LAD V 5 , V 10 , V 20 , V 30 , mean dose and maximum dose (all P<0.05), indicating enhanced sparing of this critical coronary substructure. Subgroup analyses were summarized in Table 3 and illustrated in Figures 4 and 5 . In the non-irradiated IMLNs group, significant reductions were observed in cardiac V 5 , cardiac V 10 , and MHD (all P<0.05), whereas reductions in cardiac V 20 and V 30 did not reach statistical significance. LAD dose reductions in this group were primarily confined to low- and intermediate-dose regions ( V 5 and V 10 ) and mean dose. In contrast, the irradiated IMLNs group demonstrated significant reductions across a broader range of cardiac parameters, including cardiac V 5 - V 30 and MHD (all P<0.05). LAD dose reduction in this group extended to higher-dose regions, including V 30 and V 40 (all P<0.05). Figure 4. Open in a new tab Comparison of dosimetric parameters between the original and optimized plans in the non-irradiated IMLNs group. Dose parameters of the cardiac (A); LAD (B); left lung (C); right lung (D); combined lungs (E); right breast (F); left humeral head (G); and spinal cord (H) are shown. * P < 0.05, ** P < 0.01, *** P < 0.001, ns, not significant Figure 5. Open in a new tab Comparison of dosimetric parameters between the original and optimized plans in the irradiated IMLNs group. Dose parameters of the cardiac (A); LAD (B); left lung (C); right lung (D); combined lungs (E); right breast (F); left humeral head (G); and spinal cord (H) are shown. * P < 0.05, ** P < 0.01, *** P < 0.001, ns, not significant Other OARs Changes in dose to other OARs were generally small after optimization ( Table 2 and Figure 3 ). For all patients, left lung V 10 , V 20 , and mean lung dose showed statistically significant increases after optimization. However, the absolute magnitude of these changes was limited, and all values remained within acceptable clinical planning constraints. Similar modest increases were observed for right lung V 20 and combined lung V 10 and V 20 , whereas right lung mean dose and right breast dose parameters remained unchanged. Notably, spinal cord maximum dose did not change significantly after optimization (32.504 ± 7.090 Gy vs 34.107 ± 4.154 Gy, P = 0.167), indicating that DGF-guided cardiac protection did not result in dose escalation to this critical structure. Figure 3. Open in a new tab Comparison of dosimetric parameters between the original and optimized plans in 25 patients who underwent re-optimization. Dose parameters of the cardiac (A); LAD (B); left lung (C); right lung (D); combined lungs (E); right breast (F); left humeral head (G); and spinal cord (H) are shown. * P < 0.05, ** P < 0.01, *** P < 0.001, ns, not significant Subgroup analyses showed similar trends ( Table 3 ), with minor yet statistically significant increases in some lung dose parameters, though clinically acceptable. Doses to the right breast and spinal cord remained stable. These trends are consistently illustrated in Figures 4 and 5 . Estimated RRI of Cardiac Events Based on the Darby dose-response model, the estimated RRI of major coronary events was significantly reduced after DGF-guided optimization for all patients (45.803 ± 2.839 vs 39.383 ± 2.459, P < 0.001) ( Table 4 ). Significant reductions in estimated RRI were also observed in both the non-irradiated IMLNs group (44.992 ± 3.298 vs 39.146 ± 2.987, P < 0.001) and the irradiated IMLNs group (46.259 ± 2.546 vs 39.516 ± 2.205, P < 0.001). Table 4. Estimated RRI of Major Coronary Events Before and After Optimization Group Original plan Optimized plan t P all patients 45.803±2.839 39.383±2.459 13.838 <0.001 non- irradiated IMLNs group 44.992±3.298 39.146±2.987 7.368 <0.001 irradiated IMLNs group 46.259±2.546 39.516±2.205 11.740 <0.001 Open in a new tab RRI was calculated based on the Darby dose–response model, assuming a 7.4% relative increase in cardiac event risk per 1 Gy increase in MHD. Association Between DGF Curve Area and Cardiac Dose Metrics No significant association was observed between S and MHD (r = 0.109, P = 0.597, R 2 = 0.0118) or between S and cardiac V 5 (r = -0.022, P = 0.916, R 2 = 0.0005), as S quantifies global spatial gradient characteristics distinct from local DVH parameters. Discussion HT integrates computed tomography (CT) and linear accelerator technology, enabling efficient 360° rotational thin-layer irradiation and facilitating conformal treatment of large or anatomically complex targets adjacent to critical organs. Compared with conventional intensity-modulated radiation therapy (IMRT), HT may provide improved dose distribution and target conformality in selected complex target settings. 25 , 26 For left-sided breast cancer, particularly following modified radical mastectomy, HT enables conformal dose delivery to the chest wall and regional lymph nodes, making it a useful technique for complex target coverage. With continued improvements in breast cancer survival, RIHI has emerged as a major long-term source of non-cancer morbidity and mortality, particularly after left-sided irradiation. 27 A systematic review indicated that the MHD in left-sided breast cancer patients receiving IMLNs irradiation was 8.4 Gy, approximately twice that of patients without IMLNs irradiation. 27 A retrospective study found that the cumulative incidence of ischemic cardiac disease in breast cancer patients irradiated to the IMLNs was 11.3% in those with cardiovascular risk factors and 6.4% in those without such risk factors. 28 A study of 55,000 breast cancer patients showed that left-sided patients had a 1.1-fold higher risk of cardiac death 10 years after radiotherapy than those with right-sided breast cancer. 29 Collectively, these findings underscore the critical need to minimize cardiac exposure, particularly when the IMLNs are included in the target volume. In the present study, DGF-guided re-optimization significantly reduced cardiac and LAD dose parameters compared with the original HT plans, with more pronounced reductions observed in the IMLNs irradiated subgroup. These results suggest that even within the inherently conformal framework of HT, DGF-guided optimization may achieve further cardiac sparing, thereby reducing model-based cardiac risk estimates without compromising target coverage. The significant cardiac dose reductions (IMLNs group: V 5 44.1% to 29.3%) demonstrate S min provides added value beyond routine constraint-based optimization. It should be emphasized that cardiac dose reductions reflect the combined effect of constraint-based and gradient-based optimization, with S min designed as a supplementary tool rather than a replacement for established dose constraints. While HT can provide favorable target conformity and normal tissue sparing, achieving a high-quality radiotherapy plan remains crucial for optimal therapeutic outcomes. Current plan evaluation methodologies have inherent limitations, because traditional metrics such as DVH parameters, CI, and HI provide valuable but incomplete information regarding the spatial characteristics of dose falloff. 13 , 14 The gradient index (GI) proposed by Paddick et al is widely used but remains dependent on target volume and geometry. 17 Sung et al introduced the DGI to estimate average distances between isodose surfaces, while DGC and related gradient-based methods further extended this concept for plan evaluation and quality enhancement. 16 , 18 However, these approaches still primarily rely on planar distance relationships and are insufficient for fully characterizing three-dimensional dose distributions. Building on this concept, Li et al proposed the DGF based on the overlapping volume histogram (OVH). 21 Unlike conventional DVH or conformity-based metrics, DGF provides additional spatial information on dose falloff outside the target volume, which is particularly relevant for cardiac sparing in left-sided PMRT. DGF quantifies the three-dimensional spatial relationship between the target and surrounding structures by reflecting the radius ratio of an “equivalent sphere.” Closer isodose surfaces to the target correspond to a steeper dose gradient and faster dose attenuation, and a smaller area under the DGF curve indicates a more favorable dose falloff. This provides the theoretical basis for using the area under the DGF curve as an empirical internal benchmark to guide plan optimization, particularly in cases involving IMLNs irradiation. Specifically, we hypothesized that these principles could also apply to the complex three-dimensional relationship between the heart, as a major OAR, and the target volume in left-sided PMRT. In this study, we constructed DGF curves for the heart and used the minimum area under the curve ( S min ) as an empirical internal benchmark to guide plan re-optimization. This approach was not intended to define a universal threshold for all PMRT settings. Rather, it was used to identify the steepest dose falloff achieved within this cohort under a consistent HT planning framework. The results suggest that DGF-guided optimization based on S min may provide additional cardiac sparing in left-sided PMRT. These findings are consistent with the concept that a steeper spatial dose gradient may be associated with lower dose to nearby critical structures. However, in the present cohort, correlation and linear regression analyses did not show significant associations between S and either MHD or cardiac V 5 . The absence of a significant linear correlation between S and individual DVH metrics does not necessarily diminish the utility of DGF, because DGF is intended to characterize the overall spatial dose-falloff pattern rather than serve as a direct surrogate for any single dosimetric endpoint. Because S min was derived from a single case, its generalizability should be interpreted with caution and requires further validation in larger cohorts. Previous studies have shown a linear relationship between MHD and the risk of major coronary events, and higher cardiac dose exposure has been associated with increased cardiac risk. 2 , 3 , 8 , 30 The spatial distribution of coronary artery stenosis has been shown to correlate with high-dose regions, especially those involving the LAD and IMLNs areas. 31 - 33 Clinically, cardiac dose constraints emphasize minimizing MHD; for example, the RTOG 1304 protocol recommends an MHD of <4 Gy to reduce cardiac exposure. Accordingly, MHD and cardiac V 5 were selected as the primary cardiac dose parameters in this study. As illustrated in Figure 6 , DGF-guided optimization yielded consistent reductions in both cardiac V 5 and MHD across most patients, with more pronounced improvements observed in those receiving IMLNs irradiation. Although some absolute reductions were numerically modest, small decreases in cardiac dose may still be relevant, particularly in breast cancer populations with long expected survival. However, because this was a dosimetric study, the present findings should not be interpreted as direct evidence of reduced clinical cardiac events. Application of the Darby dose-response model showed a statistically significant reduction in the estimated RRI of major coronary events after DGF-guided optimization, with the greatest absolute reduction observed in the IMLNs irradiation group. Overall, estimated RRI decreased by 6.420% (non-IMLNs: 5.846%, IMLNs: 6.743%), suggesting that patients with more complex target volumes may derive greater benefit. These findings support the potential value of DGF-guided optimization for mitigating cardiac exposure in left-sided PMRT. Figure 6. Open in a new tab Comparison of cardiac V 5 (A) and MHD (B) between the original and DGF-guided optimized plans in 25 patients who underwent re-optimization. Patient indices are shown in sequential order for visualization purposes and do not correspond to the original patient numbering Importantly, DGF is not intended to replace existing HT planning strategies (e.g., complete/organ-based directional blocks, constrained blocks, gantry angle restrictions) but rather to serve as a complementary quantitative tool for characterizing three-dimensional dose gradients. In this study, all original plans were generated according to standard HT practice, and DGF-guided re-optimization was subsequently performed under the same clinical constraints. DGF was then used as an empirical internal benchmark for re-optimization without altering beam geometry or clinical constraints, thereby enabling additional cardiac sparing through intensity redistribution within existing constraints. In this context, DGF should be viewed not as a competing replacement for established cardiac-sparing techniques, but as an additional quantitative planning aid that may complement existing optimization strategies. The observed reduction in cardiac dose, particularly in cases involving IMLNs irradiation, suggests that DGF may provide additional benefit even when established HT optimization techniques are already used. Additionally, several advanced techniques, including proton therapy, respiratory gating, and active breathing control, have been shown to mitigate cardiac exposure. 34 - 39 Combining DGF-guided optimization with motion management or geometric displacement techniques may further enhance cardiac protection by increasing the effective distance between the heart and the target volume. Such integrated strategies warrant further investigation. In the present workflow, DGF calculation required extraction of isodose volumes and external computation of the curve area, which added workload to the planning process. Although this process was not fully automated in the current study, future TPS scripting or other automated data-processing tools may improve clinical efficiency and reduce the additional workload associated with DGF-guided optimization. This study has several limitations. First, it was a retrospective single-center study with a relatively small sample size, particularly in subgroup analyses. Second, S min was derived from a single internal reference case, and its generalizability therefore requires further validation in larger cohorts. Third, the estimated reduction in cardiac risk was based on a published dose–response model using MHD rather than directly observed long-term clinical cardiac outcomes. Lastly, this study cannot isolate the independent contribution of S min from constraint-based optimization.Therefore, the present findings remain limited to dosimetric analysis and model-based risk estimation. Overall, the present findings should be interpreted with caution, and prospective studies with larger cohorts, automated workflows, and long-term follow-up are needed to further clarify the clinical value and independent effect of DGF-guided optimization. Conclusion This study suggests that DGF-guided optimization complementing standard constraint-based approaches may improve HT plan quality for PMRT in left-sided breast cancer and achieve additional reductions in cardiac dose and model-based cardiac risk estimates. Particularly for complex target volumes requiring IMLNs irradiation, DGF-guided optimization in HT may offer further dosimetric advantages beyond conventional optimization. Acknowledgments The authors used generative artificial intelligence only for English language editing and readability improvement. All scientific content, data analysis, interpretation, and conclusions were developed and verified by the authors. Appendix. Abbreviations RIHI radiation-induced heart injury HT helical tomotherapy DGF dose-gradient function IMLNs internal mammary lymph nodes OARs organs at risk BCS breast-conserving surgery PMRT postmastectomy radiotherapy MHD mean heart dose LAD left anterior descending coronary artery DVH dose-volume histogram CI conformity index HI homogeneity index GI gradient index DGI dose gradient index DGC dose gradient curve CTV clinical target volume RTOG Radiation Therapy Oncology Group PTV planning target volume RRI relative risk increase MU monitor units TPS treatment planning system CT computed tomography IMRT intensity-modulated radiation therapy OVH overlapping volume histogram. Footnotes Author Contributions: Conception and design: Yunyan Yang and Xiang Pan. Development of methodology and model: Han Bai and Ya Li. Acquisition of data: Yunyan Yang; Jinli Peng and Tianwen Zhang. Analysis and interpretation of data: Yunyan Yang and Yan Xu. Writing, review, and revision of the manuscript: Yunyan Yang; Xiang Pan and Lingli Zhou. Administrative, technical, or material support: Xiang Pan; Lingli Zhou; Han Bai and Ya Li. All authors read and approved the final manuscript. Funding: The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was funded by the Yunnan Provincial Department of Science and Technology-Kunming Medical University Joint Special Project for Applied Basic Research (No. 202201AY070001-161) and the Kunming Medical University Graduate Education Innovation Project (No. 2025S273). The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. ORCID iDs Yunyan Yang https://orcid.org/0009-0008-4313-2536 Xiang Pan https://orcid.org/0000-0001-7322-7765 Lingli Zhou https://orcid.org/0009-0002-8223-2210 Jinli Peng https://orcid.org/0009-0005-3896-7908 Tianwen Zhang https://orcid.org/0009-0005-7631-0384 Yan Xu https://orcid.org/0009-0007-3695-3195 Han Bai https://orcid.org/0000-0003-3593-1262 Ethical Considerations This retrospective study was approved by the Ethics Committee of Yunnan Cancer Hospital, The Third Affiliated Hospital of Kunming Medical University, Peking University Cancer Hospital Yunnan (approval No. KYLX2024-285; approved on November 20, 2024). Consent to Participate Written informed consent to participate was obtained from all participants. Consent for Publication Not applicable, as no identifiable personal data are included in this study. 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[ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] Associated Data This section collects any data citations, data availability statements, or supplementary materials included in this article. Data Availability Statement The data that support the findings of this study are not publicly available due to patient privacy and institutional restrictions, but are available from the corresponding author upon reasonable request and with permission from the institution. * Articles from Technology in Cancer Research & Treatment are provided here courtesy of SAGE Publications ACTIONS View on publisher site PDF (4.5 MB) Cite Collections Permalink RESOURCES Similar articles Cited by other articles Links to NCBI Databases Follow NCBI NCBI on X (formerly known as Twitter) NCBI on Facebook NCBI on LinkedIn NCBI on GitHub NCBI RSS feed Connect with NLM NLM on X (formerly known as Twitter) NLM on Facebook NLM on YouTube National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894 Web Policies FOIA HHS Vulnerability Disclosure Help Accessibility Careers NLM NIH HHS USA.gov Back to Top

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