Application of dose-gradient function in reducing radiation induced lung injury in breast cancer radiotherapy

1Introduction

Radiotherapy is the most important treatment for breast cancer after breast-conserving surgery, which has significant value in reducing the local recurrence rate and clinical mortality. Many studies have shown that volumetric modulated arc therapy (VMAT) is widely used in breast cancer after breast-conserving surgery, which can increase the target dose, improve the target dose distribution, significantly shorten the treatment time and reduce the dose of normal tissues [1–5].

Chest wall irradiation can affect the lung by exposing some of them to the radial and do harm to them, resulting various degrees of radiation-induced lung injury. In the era of three-dimensional radiotherapy, V₂₀, V₅ and mean dose of lung are commonly used to predict radiation-induced pneumonitis [6–9]. A prospective study [10] found that the volume of lung irradiated was closely related to the occurrence of radiation-induced lung injury, and was significantly related to the severity of radiation-induced lung injury. When V₂₀≤20%, no radiation-induced lung injury occurred. Only 8% of the patients had radiation-induced lung injury when V₂₀ is equal to 22% –31%, and no grade 3 radiation-induced lung injury occurred. Lind et al [11]. found that ipsilateral lung V₂₀ < 30% could significantly reduce the incidence of radiation pneumonitis in postoperative radiotherapy for breast cancer. Zeng Yuanyuan et al [12]. found that the incidence of radiation-induced lung injury after radical mastectomy was 9.78%, and most of them were grade 1 injury. The lung volume ratio receiving more than 20Gy (V₂₀) was an independent risk factor for radiation-induced lung injury after radical mastectomy. The V₂₀ value can be used to predict and recommend radiotherapy, which can effectively reduce the incidence of radiation injury. Therefore, the irradiated volume and dose of the lung should be carefully evaluated to minimize the irradiation to the normal lung tissue before radiotherapy.

Doctors and physicists still rely on dose volume histogram (DVH) and traditional layer-by-layer visualization of isodose lines to evaluate plans. It is difficult for doctors to choose different plans that can generate almost the same dose distribution. Physicists are puzzled by how to quantitatively determine whether a parameter in a plan has the space for decline. In order to fully evaluate the quality of the plan, in addition to the commonly used indicators of conformity such as conformity index (CI) and heterogeneity index (HI), it is also necessary to evaluate the dose gradient to ensure an optimal dose attenuation around the target. Some studies [13–16] have introduced different gradient indices to achieve the degree of dose attenuation near the target. Sung et al. [17] proposed a new dose gradient curve (DGC) suitable for clinical practice, and they believed that DGC was a reasonable method to visualize the dose gradient as the average distance between two isodose planes. The shorter the distance, the steeper the dose gradient. In this study, a dose gradient function (DGF) was defined and a dose gradient evaluation tool based on the relative spatial relationship between isodose lines was introduced, in order to provide a basis for physicists to evaluate and further optimize the plan.

2Materials and methods

2.4The definition of dose gradient function (DGF)

VMAT is a multi-field focused radiotherapy technique, which forms the distribution characteristics of isodose lines decreasing outward from the target area. The rate at which the radiation dose decreases outward from the target area determines the range of radiation dose received by the surrounding normal tissues. The faster decay rate, the less normal tissues are irradiated around the target area, and the higher the quality of the radiotherapy plan. In this study, dose gradient function (DGF) was defined and utilized to quantify the decay rate of dose and to guide the re-optimization of the plan, improving the quality of the radiotherapy plan. The DGF was defined as follows:

(1)

DGH=VDVp3

where V_D is the volume of isodose line generated structure, V_P is the volume of target (PTV). According to the above definition DGF, the thirty VMAT plans were analyzed. The volume of isodose line (from V₅₀Gy to V₁₅Gy, the step size is 0.25Gy) was generated for each case, and then the DGF was calculated. The Dose-DGF curve was plotted as shown in Fig. 1.

Fig. 1

The Dose-DGF curves of 30 patients.

2.5The mechanism of DGF guiding radiotherapy plan optimization

2.5.1A simple example describes the properties of DGF

Figure 2 A, B shows two typical DGF examples, indicating the area where the iso-dose line of 5000cGy-1500cGy intersects the left lung. The shorter the distance between the dose lines, the steeper the dose gradient and the faster the dose attenuation, the smaller the volume of the left lung that receives the radiation dose (Fig. 2A). Meanwhile, according to the formula (1), the lower the value of V_D, the less DGF, therefore, the faster the dose attenuation. As shown in Fig. 2C, the smaller the area under the D-DGF curve, the lower the irradiation dose received by organ at risk (OARs, when S_PA < S_PB, we have D_PA,OARs < D_PB,OARs, here S_PA, S_PB were indicated as area under the patient’s A and B D-DGF curve, D_PA; D_PA, D_PB were indicated as the dose of patient A and B). Thus, in this study, the area under the D-DGF curve was used as a trigger factor to guide the optimization of the plan, reducing radiation-induced lung injury in breast cancer postoperative radiotherapy.

Fig. 2

A, B) Two typical DGF examples; C) The area under the D-DGF curve of representative patient A and B.

2.5.2The mechanism of DGF guiding radiotherapy plan optimization

The area under the D-DGF curve of thirty patients were calculated by GraphPad Prism Software (Table 2). The volume of 2000cGy dose line (V₂₀) of left lung in original plan was statistical. As shown in Table 2, the plan of 9^th patient was considered to be the optimal plan, therefore, select and use the minimum area value (S_min) as the trigger operator to trigger the re-optimization of other patient plans respectively. The plans were triggered to optimize for area reduction.

Table 2

The area under the D-DGF curve and the V20 of left lung of thirty patients

No	Area (S, cm2)	V20 (%)	No	Area (S, cm2)	V20 (%)	No	Area (S, cm2)	V20 (%)
1	4413	15.6	11	4426	14.8	21	4533	12.26
2	4276	14.5	12	4538	18.4	22	4524	12.78
3	4532	13.4	13	4300	11.4	23	4496	9.76
4	4238	11.6	14	4390	11.9	24	4512	13.47
5	4287	11.9	15	4135	11.9	25	4461	15.48
6	4421	17.2	16	4198	11	26	4413	13.18
7	4355	16	17	4770	22.78	27	4432	20.31
8	4615	17.3	18	4681	20.21	28	4365	10.32
9	3981	10.5	19	4549	17.58	29	4412	5.65
10	4481	11.4	20	4567	15.44	30	4405	20.47

* NO is the number of 30 patients.

3Results

3.2Comparison of dose parameters of OARs

3.2.1Left lung

In the radiotherapy of breast cancer, the ipsilateral lung is one of the important OARs. Figure 3 compares of the V₂₀ of Left lung between the original plan and the DGF plan in 30 patients, the results showed that after optimization, the V₂₀ in the left lung is down (26 of 30 patients). All with statistical significance (P < 0.001) observed through paired comparisons (Table 4).

Fig. 3

The V₂₀ of Left lung between the original plan and the DGF plan in 30 patients.

Table 4

Comparison of OARs between the original plan and the DGF plan in 30 patients

Evaluation parameters		Original plan	DGF plan	P value
Lung-L	V5 (%)	43.01±12.67	35.82±7.54	0.005
	V10 (%)	25.00±5.74	19.74±4.87	< 0.001
	V20 (%)	14.28±3.81	10.96±3.30	< 0.001
	V30 (%)	9.22±3.25	6.45±2.46	< 0.001
	MLD (cGy)	920.61±151.73	763.63±143.65	< 0.001
Heart	D2cc (cGy)	3261.13±1040.46	2745.45±975.43	0.001
	MHD (cGy)	356.89±69.67	293.84±50.94	< 0.001
LAD	Mean (cGy)	1835.32±69.38	1453.06±57.22	< 0.01
Lung-R	V5 (%)	15.11±13.03	9.24±8.84	0.023
	V10 (%)	1.90±2.87	0.78±2.15	0.085
	V20 (%)	0.04±0.20	0.00±0.01	0.331
	MLD (%)	265.79±128.17	232.56±82.14	0.146
Breast-R	D1cc (cGy)	1782.05±824.25	2026.35±1110.95	0.183
	MBD (cGy)	369.99±159.63	323.19±119.36	0.121
Cord	DMax (cGy)	358.12±230.22	399.45±201.17	0.383

The studies have shown that radiation-induced lung injury after volume-modulated radiotherapy (VMAT) for left breast cancer is correlated with the different dose volumes and mean dose of the ipsilateral lung, and the low dose volume of the ipsilateral lung has a certain degree of influence on the occurrence of radiation-induced lung injury as well as the high dose volume of the ipsilateral lung. In breast cancer radiotherapy, in addition to paying attention to the traditional predictors of radiation-induced lung injury such as V₂₀, the evaluation of V₅, V₁₀, V₃₀ and MLD should be further strengthened. In this study, we found that when V₂₀ decreased, V₅, V₁₀, V₃₀ and MLD also decreased, all with statistical significance (P < 0.01) observed through paired comparisons (Table 4). It was concluded that the introduction of DGF could affect the whole dose curve of the left lung.

3.2.2Other OARs

Comparison of OARs between the original plan and the DGF plan in 30 patients. As shown in Table 4, compared with the original plan, the D_2cc and D_mean of heart and V₅ of right lung were significantly decreased in the DGF plan guided by dose gradient function, all with statistical significance (P < 0.05). In addition, although the V₁₀, V₂₀, D_mean of the right lung, D_1CC, D_mean of the breast-R and D_Max were not statistically significant (P > 0.05), all met the clinical requirements.

3.3The DVH and dose distribution of the typical patients

The DVH curves between the original plan and the DGF plan of the typical patient are shown in Fig. 4. The DVH curves illustrate that there was no significant change in the target dose after optimization, however, the doses to OARs were significantly reduced. Figure 5 shows the position relationship between 5000cGy, 2000cGy and the left lung on the patient’s transverse section. After optimization (Fig. 5B), the overlap area between 2000cGy and the left lung was smaller, reduces damage to normal left lung tissue.

Fig. 4

The DVH curves between the original plan and the DGF plan of the typical patient.

Fig. 5

The dose distribution between the original plan (A) and the DGF plan (B) of the typical patient.

4Discussions

Breast radiotherapy is challenging and complicated, as the target being located on one side of the body and surrounding organs make this an inherently difficult site to achieve a homogeneous dose distribution. Plane 2D resulted in dose inhomogeneities, particularly in women with larger breasts. An inhomogenous dose may lead to increased normal tissue side effects and poor cosmetic results, which can cause significant psychological morbidity for patients. The introduction and wide application of CT and computer technology in radiotherapy were the beginning of precise radiotherapy. Three-dimensional conformal radiation therapy (3D-CRT) was the beginning technology of the precise radiotherapy. 3D-CRT followed by Intensity modulated radiation therapy (IMRT), and then many sub-technologies were developed based on IMRT. The study of Selvaraj, et al. showed that the reductions of V₁₀₅ and V₁₁₀ for the IMRT compared to 3DCRT were 44.7% and 66.3%, respectively (P < 0.01). The mean dose and V₃₀ for heart with IMRT were 2.3 (SD: 1.1) and 1.05 (SD: 1.5) respectively, which was a reduction by 6.8% and 7.9%, respectively, in comparison with 3D. Similarly, the mean dose and V₂₀ for the ipsilateral lung and the percentage of volume of contralateral volume lung receiving > 5% of prescribed dose with IMRT were reduced by 9.9%, 2.2%, and 35%, respectively [20]. A dosimetric study on radiotherapy for left side breast cancer showed that both VMAT and IMRT led to improved PTV_95 % coverage (95.63±1.82% in VMAT; 93.70±2.16 % in IMRT; 81.40±6.27% in 3D-CRT) and improved CI (0.96±0.02 in VMAT; 0.91±0.06 in IMRT) as compared to 3D-CRT (0.66±0.11) [21]. It can be seen that the dose of peripheral organs at risk can be reduced effectively by selecting better radiotherapy techniques. But when the technique is not optional, how to judge plans can be improved is remaining a problem.

Therefore, many methods have been raised, which can be used to improve the quality of plans. An earlier model for predicting the dose of OARs in radiotherapy for breast cancer was proposed by Oxford and researchers assessed the value of maximum heart distance (MHD) in predicting the dose and biologically effective dose (BED) to the heart and the left anterior descending (LAD) coronary artery for left-tangential breast or chest wall irradiation [22]. With our proposed DGF optimization, the dose gradient at the edge of the target is improved, the dose “diffused” to the LAD is reduced. And then OVH was proposed, and the OVH achieves a new patient’s DVH by comparing the distance of the OARs and targets of the new patient with those of prior patients, whose plans were maintained in a database. The basis for this calculation was r _ v, 1 ⩾ r _ v, 2 ⇒ D_v,1 ⩽ D_v,2. For v > OVH(0), we have r_v,2 > r_v,1; then D_v,2 > D_v,1 was expected. For v < OVH(0), we have r_v,1 > r_v,2; then D_v,1 < D_v,2 was expected. For v = OVH(0), we have r_v,1 = r_v,2; then D_v,1 = D_v,2 was expected. This method is effective in predicting the dose of parotid gland in NPC radiotherapy [23]. Several subsequent studies based on OVH expanded the connotation and application scope of OVH [24–26]. However, one shortcoming of these method is that the distance r exists between two points, but the edge of the target is three-dimensional-space curved surface, besides the dose variation occurs in a three-dimensional space. So, only considering the distance in one plane is not enough for optimizing plans.

In the paper, the research team obtained DGF based on the continuance of the dose gradient (DF) concept in SBRT [27–29]. DF’s formula is DGF=V50%PDVP3 , and the dose “50% PD” is 50% of the prescribed dose. Because every three-dimensional volume has a sphere that has the same volume. It can be seen that DG reflects the ratio of the radius of the “equivalent sphere” formed by 50% prescription dose in three-dimensional space to the radius of the “equivalent sphere” formed by PTV. In a similar way, DGF’s formula is DGH=VDVp3 , which reflects the ratio of the radius of the “equivalent sphere” formed by the dose “D” in three-dimensional space to the radius of the “equivalent sphere” formed by PTV. The larger the value of DGF, the larger the ratio and the slower the rate of dose decline. In addition, since the value of DGF varies with D in each physical plan, this study uses the area obtained by integrating DGF to perform its function instead of DGF. When integrating in the same domain ([1500, 5000], as shown in Fig. 2), the smaller the DGF, the smaller the area. The smaller the DGF, the faster the dose decline, i.e., the smaller the dose “diffused” into the ipsilateral lung and heart adjacent to the PTV. This is the reason that when the minimum area triggers plans reoptimize for area reduction, the dose of lung and heart will be reduced, and these results are shown in Table 5 and Fig. 3. Reading Fig. 3 carefully, it is not difficult to find that most plans (26/30) were triggered and re-optimized to achieve lower V₂₀ of ipsilateral lung, but some plans (4/30) failed to achieve lower V₂₀. The reason may be that DGH=VDVp3 only contains the volume information, but does not contain the shape information of PTV. Experience tells us that the shape of breast cancer PTV, such as the degree of curvature of the PTV, also has some effect on the dose.

The pursuit of lower doses of OARs is essentially an expectation of lower NTCP. So, this study also investigated the change of NTCP caused by the decrease of physical dose, and the results showed that the decrease of physical dose actually resulted in the decrease of NTCP, as shown in Table 6. With the method proposed in this study, the NTCP of the ipsilateral lung can be reduced by about 4.5% and the heart by about 0.5%.

Through the method proposed in this paper, we can review the team’s previous breast-conserving radiotherapy plans to obtain a DGF-curve to guide the design of new plans, or extract a DGF-curve from the plans designed by experienced physicists (dosimetrists) to guide the plan design of entry-level physicists (dosimetrists). Can guarantee continuously improving the quality of plans and keeping the quality level of plans from declining due to the different experiences of the physicist (dosimetrist). In the clinical workflow, the proposed method provides guidance for optimization and, in theory, reduces the number of trial and error in planning. Another potential implication is to programmatically build the recommended methods into TPS to evaluate plans or drive automatic optimization of plans, and our research team will address it in future studies.

5Conclusion

The dose-gradient function is valid in reducing radiation induced lung injury in breast cancer radiotherapy.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Author contributions

HB, QL, and XP conceived and designed the study. HS, QL, JB, RW, XL and FC retrieved and analyzed the documents. QL and HS collected the Figures. HB wrote the paper. XP supervised the study, reviewed, and edited the manuscript. All authors approved the final manuscript.

Funding

This work was financially supported by the Science, Technology Department of Yunnan Province (202101AY070001-164).