Hybrid VMAT-3DCRT as Breast Treatment Improvement Tool

TL;DR

This paper proposes a hybrid radiotherapy technique combining 3DCRT and arctherapy to improve breast cancer treatment by optimizing tumor coverage and organ preservation, with tailored application based on patient characteristics.

Contribution

It introduces a hybrid approach that leverages the robustness of 3DCRT and the precision of arctherapy, offering a customizable treatment option for breast cancer patients.

Findings

Hybrid approach is effective for certain patient profiles.

Statistical analysis supports tailored application based on patient characteristics.

Potential to improve treatment outcomes and reduce side effects.

Abstract

Radiation therapy is an important tool in the treatment of breast cancer and can play a crucial role in improving patient outcomes. For breast cancer, if the technique has been for a long time the use of 3DCRT, clinicians have seen the management evolve greatly in recent years. Field-in-field and IMRT approaches and more recently dynamic arctherapy are increasingly present. All of these approaches are constantly trying to improve tumour coverage and to preserve organs at risk by minimising the doses delivered to them. If arctherapy allows a considerable reduction of high doses received by healthy tissues, no one can deny that it also leads to an increase of low doses in tissues that would not have received any with other techniques. It is with this in mind that we propose a hybrid approach combining the robustness of the 3DCRT approach and the high technicality and efficiency of arctherapy. Statistical tests allow us to draw conclusions about the possibility of using the hybrid approach in certain cases (right breast, BMI > 23, age > 48, target volume >350cc, etc.). Indeed, depending on the breast laterality and patients morphological characteristics, hybridization may prove to be a therapeutic tool of choice in the management of breast cancer in radiotherapy. a)

Tables

Table 1. Table 1 : Description of patients enrolled in the study concerning the age, volume of 50Gy target (cc; breast) and Body Mass Index (BMI)

	Breast R & L			Breast R			Breast L
	BMI	Age	Vol-PTV50	BMI	Age	Vol-PTV50	BMI	Age	Vol-PTV50
Mean	25.22	59.63	663.34	25.11	55.33	657.34	25.33	63.93	669.34
SD	4.82	17.24	426.49	5.20	18.33	470.72	4.58	15.48	393.86
Median	24.90	61.00	500.43	24.90	54.00	521.35	24.90	62.00	455.80
max	37.46	90.00	1910.00	37.46	90.00	1910.00	34.60	88.00	1541.00
min	16.30	25.00	151.90	16.30	25.00	151.90	19.00	42.00	257.60
Kurtosis	0.61	-0.71	1.25	1.85	-0.70	2.33	-0.49	-1.10	0.25
Skewness	0.60	0.03	1.26	0.85	0.14	1.44	0.33	0.25	1.14

Table 2. Table 2 : Volumes definition ( X C superscript 𝑋 𝐶 X^{C} for the complement of the set X 𝑋 X )

Volume	Definition	Remarks
PTV50	(CTV50+0.5cm) $\cap$  (LungIL)C	CBCT Reg/chest wall. Use for the Optimization
PTV50-Eval	PTV50 $\cap$  (Ext-0,5cm)	Use for the Validation
PTV47	CTV47+0.5cm	Use for the Optimization
PTV47-Eval	PTV47 $\cap$  (Ext-0.5cm)	Use for Validation
Bolus Breast Rossi, Boman, and Kapanen (2019b)	(PTV50+0.5cm) $\cap$  (LungIL)C	Density =0.9 during Optimization
Bolus Nodes	PTV47	Density =0.9 during Optimization

Table 3. Table 3 : Dosimetric parameters definition. Note that PTV50 and PTV47 must imperatively be replaced by PTV50-Eval and PTV47-Eval if we had not simplified the labels for the sake of readability

#	Structure	Parameter	Definition	Unit	Clinical Goal
1	Target 50Gy	PTV50-D98	Dose related to 98% of volume	Gy	45
2		PTV50-D2	Dose related to 2% of volume	Gy	53.5
3		PTV50-D50	Dose related to 50% of volume	Gy	50
4		PTV50-HI	Homogeneity Index Patel et al. (2020)	unitless	0.14
5		Vol-PTV50	Volume of PTV50	cc	n/a
6		Vol-iso95	Volume of isodose 95%	cc	n/a
7		Vol-intersec	Vol-PTV50 $\cap$  Vol-iso95	cc	n/a
8		PTV50-CI	Conformity Index Patel et al. (2020)	unitless	0.5
9		PTV50-V107	Volume of 107% of dose(53,5Gy)	%	1
10		PTV50-V95	Volume of 95% of dose(47,5Gy)	%	90
11		PTV50-V98	Volume of 98% of dose(49Gy)	%	80
12	Tagets 47Gy	PTV47-V95	Volume of 95% of dose(44,65Gy)	%	95
13		PTV47-V98	Volume of 98% of dose(46,06Gy)	%	80
14	Lung ipsolat	LungIL-Dmean	Mean Dose	Gy	15
15		LungIL-V20	Volume related to 20Gy	%	30
16		LungIL-V30	Volume related to 30Gy	%	20
17		LungIL-NTCP	NTCP related to Lyman model	%	5
18	Lung contralat	LungCL-Dmean	Mean Dose	Gy	5
19	Lungs (IL $\cup$ CL)	LungILCL-V5	Volume related to 5Gy	%	50
20	Heart	Heart-Dmean	Mean Dose	Gy	5
21		Heart-V25	Volume related to 25Gy	%	10
22		AIV-V30	Volume related to 30Gy (AIV)	%	30
23	Liver	Liver-V5	Volume related to 5Gy	cc	100
24	Breast contralat	BreastCL-Dmean	Mean Dose	Gy	5
25	Humeral head	HH-Dmean	Mean Dose	Gy	20
26	spinal cord (+3mm)	PRVSP-Dmax	Max Dose	Gy	20
27	Esophagus	Eso-V35	Volume related to 35Gy	cc	5
28	Trachea	Trachea-V35	Volume related to 35Gy	cc	5

Table 4. Table 4 : Beams definition

Method	Prescription	Beams	Nature	Angle (R)	Rotation	Angle (L)	Colli
3DCRT	Breast+IMN111internal mammary nodal region	TGint	FiF (X6/18)	55	n/a	305	0
		TGext	Wedged (X6/18)	233	n/a	127	90/270
	Other	3 beams	{Wed.+FiF} (X6/18)	250/275/30	n/a	110/85/330	0/90/270
VMAT	Breast+Nodes	Arc1-1	VMAT (X6)	200/250	CC	290/350	0
		Arc1-2	VMAT (X6)	10/70	CC	110/160	0
		Arc1-3	VMAT (X6)	70/200	CCW	160/290	90
Hybrid	Breast+IMN	TGint	Open (X6)	55	n/a	305	0
		TGext	Wedged (X6)	233	n/a	127	90/270
	Breast+Others	Arc	VMAT (X6)	200/70	CCW	160/290	0

Table 5. Table 5 : Arcs definition (Pinnacle 16.4)

Method	Beam	Max Deliv	Gant	Seg	Lea	Conv	Cont	MU	Dose fall	Targ	Targ Edge
		Time (s)	Spac	Area	Mot	Cycles	Mod	level	Off	Falloff	Weight
VMAT	Arc1-1	50	2°	15cc	0,4cm/°	6/2	Med	Med	25	40	2
	Arc1-2	50
	Arc1-3	100
Hybrid	Arc	100

Table 6. Table 6 : Optimization Initialyzing (run # 1)

Volume	Type	Target	Priority
PTV50	D95	47.5	Defaut
	Uniforme Dose	50.5	Defaut
PTV47	D95	44.65	Defaut
	Uniforme Dose	47.5	Defaut
PRVSP	Dmax	33	Very High
Lung ipso	Max EUD	12	Medium
Lung contra	Max EUD	5	Medium
Heart	Max EUD	5	Medium
AIV	Max EUD	30	Medium
Breast contra	Max EUD	5	Medium
HH	Max Dose	43	Medium
PRVmed 222Defined by (larynx $\cup$  esophagus $\cup$  thyroid)+0.3cm	Max EUD	30	Medium

Table 7. Table 7 : Mean Values (bold for best results and italic for worst)

	Breast RL			Breast R			Breast L
Parameters	3DCRT	VMAT	Hybrid	3DCRT	VMAT	Hybrid	3DCRT	VMAT	Hybrid
PTV50-D98	45.02	45.38	45.4	45.21	45.93	46.03	44.82	44.82	44.76
PTV50-D2	52.3	52.68	52.88	52.48	52.64	52.78	52.11	52.72	52.98
PTV50-D50	50.01	50.29	51.04	49.95	50.29	51.26	50.07	50.29	50.81
PTV50-HI	0.145	0.145	0.146	0.1447	0.1327	0.13	0.1453	0.1573	0.1627
Vol-PTV50	663.3	663.3	663.3	657.3	657.3	657.3	669.3	669.3	669.3
Vol-iso95	980.1	804.9	891.5	1004	812.1	910.8	956.6	797.7	872.2
Vol-intersec	576.7	603	609.2	574	604.6	611.1	579.3	601.4	607.3
PTV50-CI	0.487	0.645	0.5917	0.471	0.629	0.578	0.504	0.661	0.6053
PTV50-V107	0	0.3923	0.612	0	0.2967	0.6867	0	0.488	0.5373
PTV50-V95	88.94	92.24	93.33	89.4	93.12	94.4	88.48	91.36	92.27
PTV50-V98	70.91	77.04	83.07	70.28	77.6	84.14	71.53	76.49	82
PTV47-V95	91.51	94.03	95.73	90.46	94.64	95.39	92.57	93.41	96.06
PTV47-V98	81.19	82.49	90.06	78.88	82.91	89.22	83.5	82.06	90.91
LungIL-Dmean	15.74	16.86	16.73	16.5	16.93	16.79	14.98	16.79	16.67
LungIL-V20	33.51	34.69	32.63	35.32	34.15	33.36	31.7	35.23	31.89
LungIL-V30	26.31	20.85	24.36	27.81	20.58	24.71	24.8	21.11	24.01
LungIL-NTCP	6.6	6.3	6.267	8.333	6.667	6.8	4.867	5.933	5.733
LungCL-Dmean	1.075	3.357	3.736	1.067	3.274	3.981	1.082	3.44	3.49
LungILCL-V5	26.94	50.02	45.99	30.67	53.97	50.51	23.21	46.08	41.47
Heart-Dmean	3.004	5.378	4.867	1.468	4.501	3.988	4.541	6.255	5.746
Heart-V25	2.502	1.428	2.049	0.009	0.052	0.019	4.995	2.803	4.079
AIV-V30	25.25	7.075	16.88	0	0	0	50.49	14.15	33.75
Liver-V5	43.16	172	178.8	85.74	310.9	317.5	0.576	33.14	40.15
BreastCL-Dmean	1.918	4.405	4.047	2.482	4.448	4.378	1.355	4.362	3.716
HH-Dmean	25.16	20.46	20.1	24.99	19.59	18.75	25.34	21.33	21.46
PRVSP-Dmax	19.21	24.01	27.62	24.14	28.62	30.45	14.28	19.41	24.79
Eso-V35	0.583	1.728	1.471	0.206	0.888	1.229	0.959	2.568	1.713
Trachea-V35	2.468	3.545	3.32	3.056	4.227	4.673	1.88	2.862	1.967

Table 8. Table 8 : Significant parameters and associated p-value related to Wilcoxon rank-sum nonparametric test

	Breast R&L		Breast R		Breast L
3D Vs VMAT	PTV50-CI	p=1.0e-05	PTV50-CI	p=0.004	PTV50-CI	p=0.001
	PTV50-V107	p=1.9e-10	PTV50-V107	p=2.7e-05	PTV50-V107	p=2.5e-06
	PTV50-V95	p=0.008	PTV50-V95	p=0.0114	LungIL-Dmean	p=0.018
	PTV50-V98	p=0.014	PTV50-V98	p=0.036	LungIL-V20	p=0.040
	PTV47-V95	p=0.001	PTV47-V95	p=0.001	LungCL-Dmean	p=4.5e-06
	LungIL-Dmean	p=0.039	LungIL-V30	p=0.001	LungILCL-V5	p=3.3e-06
	LungIL-V30	p=3.5e-05	LungCL-Dmean	p=5.0e-06	Heart-Dmean	p=0.003
	LungCL-Dmean	p=7.0e-11	LungILCL-V5	p=3.3e-06	AIV-V30	p=9.6e-05
	LungILCL-V5	p=1.4e-10	Heart-Dmean	p=3.3e-06	BreastCL-Dmean	p=4.1e-06
	Heart-Dmean	p=5.2e-06	Liver-V5	p=0.005
	Liver-V5	p=0.029	BreastCL-Dmean	p=0.001
	BreastCL-Dmean	p=1.5e-08	Eso-V35	p=0.013
	HH-Dmean	p=0.033
	Eso-V35	p=0.002
3D Vs Hyb	PTV50-D2	p=1.2e-05	PTV50-D2	p=0.011	PTV50-D2	p=0.001
	PTV50-D50	p=8.3e-07	PTV50-D50	p=0.001	PTV50-D50	p=0.001
	PTV50-CI	p=0.001	PTV50-CI	p=0.006	PTV50-CI	p=0.043
	PTV50-V107	p=1.6e-11	PTV50-V107	p=8.6e-06	PTV50-V107	p=6.8e-07
	PTV50-V95	p=0.001	PTV50-V95	p=0.001	PTV50-V95	p=0.027
	PTV50-V98	p=7.0e-07	PTV50-V98	p=3.3e-05	PTV50-V98	p=0.004
	PTV47-V95	p=2.3e-06	PTV47-V95	p=0.001	PTV47-V95	p=0.001
	PTV47-V98	p=4.6e-07	PTV47-V98	p=0.001	PTV47-V98	p=0.001
	LungCL-Dmean	p=3.0e-11	LungIL-V30	p=0.025	LungIL-Dmean	p=0.016
	LungILCL-V5	p=2.8e-10	LungCL-Dmean	p=3.3e-06	LungCL-Dmean	p=3.3e-06
	Heart-Dmean	p=0.001	LungILCL-V5	p=3.3e-06	LungILCL-V5	p=1.6e-05
	Liver-V5	p=0.015	Heart-Dmean	p=7.4e-06	Heart-Dmean	p=0.040
	BreastCL-Dmean	p=2.3e-06	Liver-V5	p=0.008	Liver-V5	p=0.048
	HH-Dmean	p=0.023	BreastCL-Dmean	p=0.001	BreastCL-Dmean	p=8.8e-05
	PRVSP-Dmax	p=0.000	PRVSP-Dmax	p=0.038	PRVSP-Dmax	p=0.001
	Eso-V35	p=0.001	Eso-V35	p=0.001
VMAT Vs Hyb	PTV50-D50	p=0.001	PTV50-D50	p=0.003	PTV50-D50	p=0.037
	PTV50-CI	p=0.040	PTV47-V98	p=0.007	PTV47-V95	p=0.021
	PTV50-V107	p=0.033	LungIL-V30	p=0.001	PTV47-V98	p=0.005
	PTV50-V98	p=0.019			LungIL-V20	p=0.005
	PTV47-V95	p=0.016			LungIL-V30	p=0.011
	PTV47-V98	p=0.001			AIV-V30	p=0.001
	LungIL-V20	p=0.014			PRVSP-Dmax	p=0.038
	LungIL-V30	p=2.9e-05

Full text

††preprint: AIP/123-QED

I Introduction

Improving the quality of breast cancer treatment is essential to reduce mortality and increase survival rates, as breast cancer is one of the most common cancers in women of all ages Waks and Winer (2019). The age of onset can vary, with a significant number of cases occurring in women over 50 but sometimes in younger women. Early detection and prompt treatment can lead to more positive outcomes, so continued efforts to improve breast cancer treatment and care are essential. Thanks to advances in technology, diagnosis and treatment methods, breast cancer survival rates have improved significantly. However, there is still much room for improvement, and ongoing research, clinical and dosimetric trials are essential to advancing the quality of care.

I.1 Radiation Therapy Role in Breast Cancer

Radiotherapy is an important tool in the treatment of breast cancer and can play a crucial role in improving patient outcomes Franco et al. (2023). One of the main advantages of radiotherapy is its ability to target and destroy cancer cells while minimising damage to healthy tissue Abdollahi et al. (2023). This makes it an effective option for treating breast cancer, particularly when used at an early stage Chung et al. (2013). Intensity modulated radiation therapy (IMRT), volumetric modulated arc therapy (VMAT) and three-dimensional conformal radiation therapy (3DCRT) are all forms of radiation therapy used in the treatment of breast cancer Gleeson (2022). IMRT is known for its ability to deliver high doses of radiation to the tumour while minimising high dose exposure to surrounding healthy tissue Kwa et al. (1998). This increases the accuracy and precision of cancer targeting and helps reduce side effectsWhite and Joiner (2006). VMAT also delivers high doses of radiation to the tumour while minimising exposure of surrounding healthy tissueCardona-Maya et al. (2023) and has the advantage of a faster treatment time Rossi et al. (2021). However, it is linked to a frequent increase in low doses in healthy tissues adjacent to the target volumes. 3DCRT is the reference and is a widely available and cost-effective form of radiotherapy, but it is less accurate and precise in targeting cancer than IMRT and VMAT, and results in greater exposure of surrounding healthy tissue Borger et al. (2007). It is important to note that exposure to high and low doses of radiationTaylor et al. (2017), can increase the risk of damage to the heart Chung et al. (2013) and lungs Roy, Salerno, and Citrin (2021).

I.2 VMAT and Low Doses (<10Gy)

What is known since the introduction of VMAT in breast cancer, is that it is a fabulous technique but that it induces a considerable increase in the volume of healthy tissue receiving low doses. Many teams are wondering about the possible deleterious radiobiological effects of these doses. This exposure can have long-term effects on the lungs Schröder et al. (2021), including a slight increase in the risk of lung cancer, fibrosis (scarring of the lung tissue) and impaired lung function. Studies have shown that exposure to low doses, can lead to changes in the DNA of lung cells that can result in mutations and an increased risk of lung cancer. It is important to note that the risk of lung damage from low-dose radiation exposure during radiotherapy depends on several factors, including the patient’s age, general health and the specifics of the radiotherapy such as dose, fractionation and irradiated volume. Several references support these conclusions, including the papers of Chhina et al. (2022) and Hurkmans et al. (2000). It should be noted that some papers suggest fatal lung disease as a function of low dose exposure after radiotherapy Keffer, Guy, and Weiss (2020), so it seems important to take these low doses into account and to propose new approaches accordingly. The same conclusions could be made by focusing on the effects on the heart as shown in Kang et al. (2021). Indeed, exposure of the heart to low-dose radiation can increase the risk of long-term cardiovascular effects, such as coronary heart disease and heart failure. The precise dose-response relationship for these effects is not well understood, but the risk is generally thought to increase with dose. It is likely that other organs are affected by low doses, but in the absence of literature it is best to apply the precautionary principle and try to minimise the use of techniques that induce low dose exposure to organs at risk. It is important to keep in mind that there is no direct evidence indicating that VMAT is not appropriate for breast cancer treatment, but it is important to use caution when using VMAT for large volumes of tissue that may receive low doses of radiation and to determine the best approach for each patient.

I.3 The Choice of Hybrid Approach (3DCRT & VMAT)

The advantage of models combination in engineering and physical sciences is that it allows the strengths of multiple models to be combined to overcome the limitations of a single model. Each model brings its own strengths and limitations, and their combination can provide a more complete view of the system and lead to more accurate and robust actions. It is in this perspective that it has been proposing for some years in radiotherapy, a hybridization of 3DCRT and VMAT modelsLiu et al. (2020). For breast cancer radiotherapy, a hybrid approach combining 3DCRT and VMAT may offer several advantages Doi et al. (2020). 3DCRT is a traditional and modulation-free technique inducing lower coverage of target nodes and may result in higher radiation doses to organs at risk with a volume of low doses in general, restricted. VMAT, on the other hand, uses intensity modulated arcs to deliver a radiation dose more consistent with target volumes (breast and nodes), reduces outside targets high doses but increases low doses. By combining these techniques, a hybrid approach can deliver a radiation dose more consistent with target volumes Marina Hennet et al. (2022), reduce doses to normal tissues Ashby and Bridge (2021) and reduce the risk of long-term toxicity Cilla et al. (2021). The decision to use a hybrid approach should be selective and reserved for certain patients Chen, Ramachandran, and Deb (2020) and treatments Veronesi et al. (2008) with nodes irradiation for example Rossi, Boman, and Kapanen (2019a). An effort must be made on the simplicity, speed van Duren-Koopman et al. (2018) and quality of proposed treatments related to the best PTV coverage and OAR saving compromise Xu et al. (2019). The structure of this paper is classic with the next section relating to the presentation of data and planning methods (Section II), then a part which will deal with all the results (Section III), before proposing a small paragraph dedicated to the technical feasibility of the hybrid method (Section IV) and concluding (Section V).

II Material and Methods

The patient sample used and the methodology followed throughout the simulations will be detailed in the Sections II.1 and II.2. Then we will expose the comparison metrics used to rank the three planning methods in Section II.3.

II.1 Patient Sample

To address the hybridization contribution concerning free breathing breast cancer treatments with nodal prophylactic irradiation (internal mammary chain, intrerpectoral, level 1-4 axillary, etc.), a cohort treated between 2021 and 2022, was used. This retrospective study includes 30 patients (50% right breasts and 50% left one). The descriptive statistics are given in the Table  1. For each patient, objective validation criteria had to be defined, as well as volumes related to dosimetric optimization. The modalities for generating these volumes were respected for all patients included in the study. In Table  2 are indicated the setup margins used for the target volumes. The exhaustive list of all parameters used during this study for set-up, optimisation and validation are listed in Table  3. As an example, the clinical objectives are given, but it should be kept in mind that they do not serve as a reference since other criteria could be used.

II.2 Treatments Planning

The plan followed in this study is relatively simple, we had, for each patient established three dosimetries (field-in-field based 3DCRT, VMAT and Hybrid) and several dosimetric parameters (listed in Table 3) were collected. IMRT was not included in this study since the results are close to those obtained with the field-in-field technique. The sample (30 patients) will allow to use different statistical metrics (defined in the following subsection) to conclude whether model combination is useful. Some rules were followed throughout the simulations. All contours (CTV & OAR) were equitably distributed between three physicians and plannings between two physicists. The study guideline were :

• •

Isocentre positioned between supraclavicular nodes and the mammary gland in cranio-caudal direction and close to the center line in the internal-external one, so that realise CBCT is technically possible;

• •

Same isocentre for VMAT, 3DCRT and hybrid;

• •

Each trial (VMAT, Hybrid and 3DCRT) is done without comparison with the previous ones so as not to be tempted to enter into a logic of "fine-tuning" which would bias the study;

• •

Dynamic leaf gap of 1cm for all plans using arctherapy in order to improve plans quality control;

• •

VMAT plans made using the virtual bolus technique Tyran et al. (2018);

• •

3DCRT plans use different energies, wedge, fields-in-fields, etc. anything that allows to establish an acceptable output.

We insisted on proposing the most objective study possible by scrupulously respecting the rules set out above, as well as the definition of the beams that are identical for all patients and respects the characteristics set out in Table  4. The characteristics of arcs used during VMAT and hybrid planning are detailed in Table  5. Simulations concern the Treatment Planning System Pinnacle (V16.4), two Elekta linacs (Synergy with MLC Agility) and free Breathing slow-CT acquisitions (BigBore Philips). Concerning the run$\#$1 of arcs optimization, the same process (Table  6) was applied for all patients. During next runs, planners modified PTV and OAR optimization criteria as desired Mahé, Barillot, and Chauvet (2016). To eliminate hot spots, most of the time, several passes (between 2 and 4) were necessary according to Algorithm 1 where No Man’s Land (NML) is defined from the isodose 107% ($\lor$ and $\land$ are respectively logical OR and AND).

II.3 Comparison Metrics

Dosimetric comparison was made by the use of classical statistical tools. Knowledgeable reader will notice in the following that the normality of the distributions is not clearly established, imposing non-parametric hypothesis tests. Wilcoxon rank-sum and ANOVA tests will be proposed in order to test significant differences between distributions. The use of coefficients of determination and correlation will complete the analysis, by making it possible to estimate the statistical link between dosimetric quantities. In the last part of the results, analyzes through receiver operating characteristic (ROC) curves will be proposed, testing if “a priori” factors (age, volume of 50Gy target and BMI) could make it possible to highlight thresholds below which the clinical objectives (Table  3) are statistically achieved. The area of ROC curves (AROC) also referred to as area under curve (AUC) will be used to this task. It is important to notice that this test is closely related to the Wilcoxon one.

III Results

Several tools were used to compare the three planning methods presented above. We will start with probability distributions coupled with an ANOVA significance test (Part III.1), then means comparison non-parametric test (Part III.2), followed by coefficients of determination and a visual comparative approach (Part III.3) preceding a comparison based on the rank correlation coefficient (Part III.4). This is followed by a study of ROC curves (Part III.5). Findings will be discussed in each part and then the main ones will be included in the conclusion. All the data and codes related to this study are available in https://github.com/cyrilvoyant/Hybrid.

III.1 Probability Density Function

In Fig  1 are represented the probability distributions (according to violin plots built with 30 patients) of parameters previously presented in Table 3. The three studied methods (3DCRT, VMAT and Hybrid) are considered. Results of non parametric one-way ANOVA (pvalue) is shown in order to make easy the interpretation of the distributions comparison. The first important element that is visible is that the distributions are (mostly) not Gaussian, which leads to an inconsistent normal hypothesis. This is why we have favoured non-parametric statistical tools. Among the graphs that stand out, it is worth noting that for lungIL, only the V30 shows a significant difference between the three distribution types. The VMAT being the method showing the best results. For LungCL and LungILCL, there is also an extremely significant difference highlighting the quality of the 3DCRT dosimetry. For the other parameters, there is nothing really conclusive and even if it is clear that the distributions are not from the same population (pvalue < 0.5) the averages are relatively close and further studies are needed to conclude. In the following, we will separate three cases, all patients (n=30), those who had treatment on the right breast (n=15) and those on the left one (n=15).

III.2 Mean Comparison and Nonparametric Test

The means of all parameters for all treatment techniques used are available in the Table  7. Both bold and italic values allow rank the three planning methods for each dosimetric variables (13 concerning the target volumes and 15 considering the organes at risk). At first sight, a trend seems to be emerging, if hybrid appears to be the method of choice for target volumes, 3DCRT is for organs at risk. On closer inspection, the differences are often not large, which encourages the use of hypothesis testing in the future. For ease but above all in order to make the comparison objective, we have decided to propose a non-parametric test on pairwise comparisons. This corresponds to three scenarios observed in Table  8. First, considering 3DCRT and VMAT, this last is the best way considering PTV50 and PTV47 for all the three samples. Mean dose related to LungIL and V5 of LungILCL are undeniably minimised by the 3DCRT method as shown in Figure 2.

III.3 Determination Coefficient Study

We have seen previously that VMAT and hybrid share common qualities and shortcomings regarding certain dosimetric parameters. This section will focus on separating these two types of approach proposing a graphical estimation using simple $y=x$ plots (Figure  3). In addition, we suggest the use of coefficient of determination to refine the interpretation. Points (related to right or left breasts) above the diagonal line ($y=x$) signify a higher value for Hybrid than for VMAT, and vice versa. For points located in the colored band, no conclusion can be drawn as to its significance. For left breasts, V20 of LungIL are often in favour of hybrid, which is not necessarily true for right breasts. However, for V30 and AIV, the result is clear: VMAT puts everyone in agreement offering best results. For the mean dose of heart or dose related to PTV, Hybrid is preferable. If it was chosen to show in this figure only results with an $R^{2}<0.8$ (cases where a majority of points are outside the non-significance area), one parameter seems somewhat disturbing because its distribution of points seems random: LungCL. With an $R^{2}<0.01$ and a trend (especially for right breasts) in favour of VMAT (although below the clinical goal) few conclusions are possible.

III.4 Spearman Coefficient Study

A cross correlation estimation is proposed concerning all available parameters. Figure  4 summarizes all the results related to the Hybrid, 3DCRT and VMAT plannings. The explanation related to the overall colored line observed with 3DCRT is because le PTV50-V107 is null for all patients. All significant correlations observed close to the diagonal are not surprising (no wonder the V95 and V98 of the target volumes are correlated), what will interest one, are the statistical dependencies outside the diagonals. Thus it is clearly seen that the AIV dose is strongly correlated with HI (for VMAT and Hybrid). This is important because it means to properly preserve the AIV, it is necessary to discover the target volumes. Even more true for the VMAT where HI low values are related to spared liver, heart, HH, etc.. This phenomenon is also observed for the V95 of PTV50. For hybrid, it will mainly be the lungIL dose which will be correlated to the PTV50 coverage. There are fewer orange boxes for Hybrid than for VMAT outside the diagonal, suggesting that the Hybrid method is more robust and requires less compromise to use it.

III.5 ROC Study

As defined in the Section  II.3, this part is dedicated to the use of ROC curves. Only curves relating to AUC $>0.7$ will be presented so as not to make the reading of this paper cumbersome. This threshold, taken purely arbitrarily, corresponds in some way to a criterion of significance at 70%. In Figure  5 are shown the results concerning both R &  L breasts while the Figure  6 is dedicated to the R breasts. Note that there is not significant ROC curves concerning the L breast. In the first one, we see that age is very little represented. Let’s not forget that both sides are considered (right and left), so we will neglect Heart-V25 which is clinically irrelevant for right breasts. This leaves only an interaction between age and esophagus concerning VMAT which is surprising and probably not worth considering. The BMI and Vol-PTV50 are more relevant because for VMAT, BMI > 22.6 or Vol-PTV50 > 440cc induce a loss of chance to respect the LungIL-Dmean clinical goal (exposed in Table 3). No such result is obtained for hybrid but it is essential to compare this result with the average obtained in the Table 7 and which confirms this conclusion. If we focus on R breasts, the results are just as interesting. Indeed, VMAT induces a decrease in the success rate of clinical objectives concerning LungILCL-V5 when BMI > 23.4, age > 48 and Vol-PTV50 > 354. Again, 3DCRT and Hybrid outperform VMAT with a slight advantage for the latter, as it offers much better target volume coverage and therefore allegedly better tumour control. The thresholds established in this study should not be considered as absolute values. Any statistician will recognise statistical instability due to the small number of patients included in the study (15 R and 15 L). This is sufficient to draw conclusions on the trends observed but not to objectify thresholds or create dosimetric references.

IV Feasibility

In this section, it is about how the treatments quality control (Delta4) make it possible to validate Hybrid approach generated during this study. It is important to propose a complete study which is not limited to a dosimetric one. The measurement aspect is important because the best theoretical technique could not be considered from a practical point of view, if it does not correspond to technical requirements. In our case, we use the local gamma passing rate criterion which must be $>95\%$ (concerning the 3%/3mm criterion and the threshold of 10%) as well as an average gamma lower than 0.4. In order to verify the dosimetric overlap between the two modes of dose delivery (static and arctherapy), we decided to test both arcs and tangentials (with a 9cm cranial offset to test as many points as possible). Results do not take into account the combined results (accumulation of several beams) but only results related to each beam in order to be objective and to limit the compensation effects. The gamma passing rate was equal for the first linac to 97.2% (std=1.23%) while for the second one it was 96.4% (std=1.67%). The mean gamma was respectively 0.33 and 0.35 and the dose deviation 0.11Gy and 0.16Gy. This is in fact the same order of magnitude of what is observed during VMAT checks. Less than 5% of dosimetries fail to meet the previously mentioned technical goals and (sometimes) require re-planning.

V Conclusion

The methodologies and conclusions of this study support and improve those established in different studies dealing with hybridization in locoregional breast cancer treatmentLin et al. (2015); Xie et al. (2020); Lang et al. (2020). This study deals with the comparison between 3 types of ballistics used for the treatment of breast cancer. Among them, a hybrid approach mixing the robustness of 3DCRT and the high conformation of VMAT is examined. The idea that has been pointed out for some years concerning the use of arctherapy for such a pathology, lies in the fact of decreasing the low doses deposited in distant healthy tissues. Indeed, in this study, we realize that the doses to the contralateral breast and lung are indeed low (Dmean < 10Gy) but much higher than those observed with 3DCRT. The same is true for the average dose to the heart, which frequently exceeds 5Gy. The strong points of VMAT are the reduction of high doses in organs at risk, so that ipsolateral lung V30, IVA V30 and heart V25 are low with this type of treatment. Concerning D5 of the union of the two lungs or isolateral lung V20, everything suggests that VMAT is less efficient. It has been shown that patients classified as BMI > 23-23.5 or age > 48 or Vol-PTV50 > 350-450cc do not perceive a direct benefit from the use of VMAT due to increased lung doses and failure to achieve certain clinical goals (Tables 3 & 7). As a result, the hybrid method is positioned (and this was proven in this study) as a robust alternative to VMAT and 3DCRT. For right breasts, it seems clear that this method is preferable, both in terms of lungs, contralateral breast and heart doses. This study reveals, however, that vigilance must be paid to spinal cord, trachea, esophagus and liver. Although the doses are low, it will be appropriate in the context of optimization to add a constraint concerning these organs (without necessarily a large weighting). For the left breast, if the question is more delicate, the answer is just as much so! We would tend to favour the hybrid method, in particular because of the coverage of PTV that it induces, however, VMAT and the reduction of high doses to the heart do not allow us to make a clear decision. In any case, we must not forget that these three methods are more complementary than rivals. Therefore, if the material and human resources allow it, proposing three treatment plans to the physician seems the best solution so that he/she can decide according to what he/she prioritizes. The calculation tools allow to set up these ballistics and associated calculations quickly (< 2h), so it is not a real obstacle. VMAT and hybrid QC show equivalent results in terms of gamma passing rate and mean gamma. If during this study, we have favored parsimony and proposed a hybrid approach with a single arc (in order to minimize the duration of the treatment), it is quite possible (and the dosimetric results are even better while the machine controls are equivalent) to propose a double arc approach (collimator angles set to 0° and 90°) by keeping the limits of arm rotation identical to those presented here. It is likely that the hybrid approach will play an important role in the future of breast cancers treatment, even more so with deep inspiration breath hold technique that move the heart (for left-sided breasts cancer) away from the irradiated area.

Acknowledgements.

We would like to thank M. Brian Baron for his suggestions and for allowing us to benefit from his knowledge and experience in hybrid planning with Pinnacle TPS.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Author Contributions

CV: Methodology, Investigation, Formal analysis, Writing – original draft, Project administration. MP: Investigation, Conceptualization, Formal analysis, Writing – review & editing, Project administration. DL: Investigation,Writing – review & editing. SP: Investigation. FS: Investigation, data. MAA: Investigation, Writing – review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper: no conflicts to disclose.