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

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 = \sqrt[3]{V_{D} / V_{P}}

(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.

Workflow of DGF-guided plan evaluation and re-optimization.

Figure 2.

(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

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 \times 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
left humeral head	$D_{Max}$ (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

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
Evaluation parameters		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
left humeral head	$D_{Max}$ (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

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).

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.

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.

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.

Figure 4.

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.

Figure 5.

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.

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

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, R² = 0.0118) or between $S$ and cardiac $V_{5}$ (r = -0.022, P = 0.916, R² = 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.

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.

Footnotes

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.

ORCID iDs

Yunyan Yang

Xiang Pan

Lingli Zhou

Jinli Peng

Tianwen Zhang

Yan Xu

Han Bai

Ethical Considerations

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.

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).

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of 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.*

Appendix

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