MONTE CARLO METHODS FOR THE EVALUATION OF THE MEAN GLANDULAR DOSE: A PHANTOM STUDY

_______________________________________

Dipartimento di Fisica

Scuola di Specializzazione in Fisica Medica

Monte Carlo Methods for the Evaluation of the

Mean Glandular Dose: a Phantom Study

Relatore:

Prof.ssa Maria Evelina Fantacci

Candidato: Dott. Raffaele Maria Tucciariello Matr. 570304

C

ONTENTS

Introduction ... 1

1 Chapter 1 ... 3

1.1 Breast cancer and screening procedures ... 3

1.2 Formalism in Monte Carlo calculations ... 9

1.2.1 Dance et al. 1990-2016 ... 10

1.2.2 Wu el al. 1991-1994 ... 11

1.2.3 Boone et al. 1999-2002 ... 12

1.2.4 The introduction of DBT ... 12

1.3 The Monte Carlo model ... 14

1.3.1 Spectral model ... 16

1.3.2 Dose estimation ... 16

1.3.3 Uncertainties ... 18

1.3.4 Random Engine ... 19

1.3.5 The GEANT4-based MC code ... 20

1.4 MC code validation ... 23

1.4.1 AAPM TG195 validation ... 24

1.4.2 Literature validation ... 25

1.4.3 Experimental validation using XR-QA2 radiochromic films ... 26

2 Chapter 2 ... 32

2.1 DgN coefficients for commercial DBT systems using a homogeneous breast model ... 32

2.1.1 DgNDBT coefficients ... 32

2.1.2 Breast thickness interpolation ... 37

2.1.3 Beam quality dependence ... 37

2.1.4 Breast density dependence ... 38

2.1.6 Comparison with the actual reference dosimetry ... 39

2.2 Glandular dose estimates using heterogeneous digital phantoms ... 42

2.2.1 Literature reference ... 42

2.2.2 A proposal of a new model ... 45

2.2.3 Validation of the proposed digital phantom ... 47

2.2.4 Glandular dose estimates for DM with heterogeneous phantoms ... 49

2.2.5 Glandular dose estimates for DBT with heterogeneous phantoms ... 52

3 Chapter 3 ... 54

3.1 3D Printing Materials for Physical Breast Phantoms ... 54

3.1.1 3D-printing materials investigation ... 55

3.1.2 The physical breast phantom ... 60

Conclusions ... 64

Appendix A ... 66

Appendix B ... 75

References ... 84

L

IST OF EQUATIONS

(1) 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 = ( # 𝑜𝑓 𝑡𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒𝑠 # 𝑜𝑓 𝑡𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒𝑠 + # 𝑜𝑓 𝑓𝑎𝑙𝑠𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒𝑠) × 100 pag. 5 (2) 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 = ( # 𝑜𝑓 𝑡𝑟𝑢𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒𝑠 # 𝑜𝑓 𝑓𝑎𝑙𝑠𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒𝑠 + # 𝑜𝑓 𝑡𝑟𝑢𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒𝑠) × 100 pag. 5 (3) 𝑀𝐺𝐷 = 𝑐 ∙ 𝑔 ∙ 𝑠 ∙ 𝐾_𝑎𝑖𝑟 pag. 10 (4) 𝑀𝐺𝐷 = 𝐷𝑔𝑁 ∙ 𝐾𝑎𝑖𝑟 pag. 11 (5) 𝐷𝑔𝑁(𝐸) = ∑ 𝑓(𝐸) × 𝐸 × 𝛷(𝐸) × 𝐺 ×𝑎𝑟𝑒𝑎 𝑚𝑎𝑠𝑠 𝐸𝑚𝑎𝑥 𝐸=𝐸𝑚𝑖𝑛 pag. 12 (6) 𝐺 = 𝑓𝑔(𝜇_{𝜌 (𝐸))}𝑒𝑛 𝑔𝑙𝑎𝑛𝑑𝑢𝑙𝑎𝑟 𝑓𝑔(𝜇_{𝜌 (𝐸))}𝑒𝑛 𝑔𝑙𝑎𝑛𝑑𝑢𝑙𝑎𝑟 + (1 − 𝑓𝑔) (𝜇_{𝜌 (𝐸))}𝑒𝑛 𝑎𝑑𝑖𝑝𝑜𝑠𝑒 pag. 12 (7) 𝑝𝐷𝑔𝑁 = ∑𝐸𝑚𝑎𝑥𝛷(𝐸) ∙ 𝜗(𝐸) ∙ 𝐷𝑔𝑁(𝐸) 𝐸𝑚𝑖𝑛 ∑𝐸𝑚𝑎𝑥𝛷(𝐸) ∙ 𝜗(𝐸) 𝐸𝑚𝑖𝑛 pag. 12 (8) 𝑅𝐺𝐷(𝛼) =𝐷𝑔𝑁(𝛼) 𝐷𝑔𝑁0 pag. 13 (9) 𝐷𝑔𝑁 = 𝐷𝑔𝑁0× 1 𝑁∑ 𝑅𝐺𝐷(𝛼) 𝛼 pag. 13 (10) MGD = K ∙ c ∙ g ∙ s ∙ T with T = ∑ c_{i i}t(α_i) pag. 13 (11) 𝜑 = 𝜃 + 𝑠𝑖𝑛−1(𝑑 𝑠𝑖𝑛 𝜃 𝑟 ) pag. 13 (12) 𝑀𝐺𝐷𝜃 ≡ ∑ 𝐸_𝑗𝑑𝑒𝑝·𝐺(𝐸_𝑗) 𝑚_{𝑔𝑙𝑎𝑛𝑑} , 𝑗 pag. 17 (13) _𝐾 0 = ∑ 𝐸𝑖× (𝜇_{𝜌 )}𝑒𝑛 𝑎𝑖𝑟 𝑆 𝑐𝑜𝑠 𝜗𝑖 𝑛 𝑖=1 pag. 17 (14) 𝑀𝐺𝐷𝐷𝐵𝑇 = ∑(𝑤𝜃· 𝑀𝐺𝐷𝜃) 𝜃 pag. 18

(15) 𝐷𝑔𝑁_𝐷𝐵𝑇= 𝑀𝐺𝐷𝐷𝐵𝑇 𝑁 ∙ 𝐾₀ pag. 18 (16) 𝑞̅ =1 𝑛∑ 𝑞𝑖 𝑛 𝑖=1 pag. 18 (17) 𝑠2 ₌ 1 𝑛( ∑ 𝑞𝑖 _𝑖2 𝑛 − 𝑞̅ 2_{) pag. 19} (18) 𝐷𝑔𝑁𝐷𝐵𝑇 = ∑ (𝑤𝜃· 𝑀𝐺𝐷_𝑛 𝜃 𝜃 ) 𝑁 𝜃=1 𝑁 ∙_𝑛𝐾0 𝐾 pag. 19 (19) 𝑡(𝛼) = 𝑀𝐺𝐷(𝛼) 𝑀𝐺𝐷0 pag. 26 (20) 𝑅 = 1 216(𝑃𝑉𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑉𝑎𝑓𝑡𝑒𝑟) pag. 27 (21) 𝑅 = 1 216(𝑃𝑉𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑉𝑎𝑓𝑡𝑒𝑟) pag. 27 (22) 𝑛𝑒𝑡𝑅 = 𝑅 − 𝑅_{𝑐𝑜𝑛𝑡𝑟𝑜𝑙} pag. 28 (23) 𝜎𝑛𝑒𝑡𝑅 = 1 216√(𝜎𝑅)2+ (𝜎𝑅𝑐𝑜𝑛𝑡𝑟𝑜𝑙) 2 pag. 28 (24) 𝐾_𝑎𝑖𝑟𝑓𝑖𝑙𝑚= 𝑎 ∙ 𝑛𝑒𝑡𝑅 + 𝑏 ∙ 𝑛𝑒𝑡𝑅2 pag. 28 (25) 𝐷𝑚 𝑀𝐶_(𝑑) 𝐷_𝑖𝑛𝑐𝑀𝐶 ≅ 𝐾_{𝑎𝑖𝑟,𝑚}𝑓𝑖𝑙𝑚(𝑑) ⋅ 𝐵𝑃𝑀𝑀𝐴 ⋅ (µ_{𝜌 )}𝑒𝑛 𝑎𝑖𝑟 𝑃𝑀𝑀𝐴 𝐾_{𝑎𝑖𝑟,𝑖𝑛𝑐}𝑓𝑖𝑙𝑚 ⋅ 𝐵𝑃𝑀𝑀𝐴′ ⋅ (µ𝑒𝑛_𝜌 ′) 𝑎𝑖𝑟 𝑃𝑀𝑀𝐴 ≅ 𝐾_{𝑎𝑖𝑟,𝑚}𝑓𝑖𝑙𝑚(𝑑) 𝐾_{𝑎𝑖𝑟,𝑖𝑛𝑐}𝑓𝑖𝑙𝑚 pag. 30 (26) 𝐷𝑔𝑁_𝐷𝐵𝑇 = 𝑦₀+ 𝐴 ∙ 𝑒𝑥𝑝−𝑥 𝑎⁄ _{+ 𝐵 ∙ 𝑒𝑥𝑝−𝑥 𝑏}⁄ _{pag. 37} (27) 𝐷𝑔𝑁𝐷𝐵𝑇 = 𝑎2∙ 𝑓𝑔2+ 𝑎1∙ 𝑓𝑔 + 𝑎0 pag. 39 (28) 𝐺(𝑑, 𝜎_𝑑) = 1 √2𝜋𝜎_𝑑2𝑒 −(𝑑−𝜇𝑑) 2 2𝜎_𝑑2 _{, 𝜎} 𝑑 = 𝐹𝑊𝐻𝑀 2.35 ∙ 𝑙 pag. 46 (29) 𝑀𝐺𝐷𝐷𝑀 = 𝑏0+ 𝑏1∙ 𝑓𝑔+ 𝑏2 ∙ 𝑓𝑔2+ 𝑏3∙ 𝑓𝑔3+ 𝑏4∙ 𝑓𝑔4 pag. 50 (30) 𝐾𝑎𝑖𝑟,𝑚 𝑀𝐶 _(𝑑) 𝐾_{𝑎𝑖𝑟,𝑖𝑛𝑐}𝑀𝐶 ≅ 𝐾_{𝑎𝑖𝑟,𝑚}𝑓𝑖𝑙𝑚(𝑑) 𝐾_{𝑎𝑖𝑟,𝑖𝑛𝑐}𝑓𝑖𝑙𝑚 pag. 60

1

I

NTRODUCTION

Breast cancer is the leading cause of cancer deaths in female subjects. Screening Digital Mammography (DM) is the principal technique used to detect tumours even in an early stage, allowing greater possibilities for treatments. Since DM is performed by using ionizing radiation, Mean Glandular Dose (MGD, or Average Glandular Dose AGD) is adopted for cancer risk estimates and it must be assessed with an accurate dosimetry. Since dose to the gland can’t be measured directly, Monte Carlo (MC) simulations are performed to evaluate MGD, multiplying incident air kerma on the upper surface of the breast by suitable conversion factors computed by Monte Carlo codes. The same principle regards dose estimates for the Digital Breast Tomosynthesis (DBT) technique, which allows to reduce the tissue superimposition effect and making it easier for radiologists to distinguish normal from cancerous tissues. For dosimetry purposes, in both DM and DBT, geometric assumptions are followed, by involving a simple mathematical phantom for reproducing the breast geometry, and by using a homogeneous compound of adipose and glandular tissues surrounded by 5 mm thick adipose skin to reproduce the breast anatomy.

This thesis voluntarily deviates from the usual setting of scientific papers and a didactic description is followed; it is entirely inspired by works published in literature by the research group of which the author belongs. In paragraphs 1.1-1.2 a brief review of breast screening procedures and formalisms followed by international dosimetry protocols are described [1], [2].

Research in breast dosimetry leads to improve accuracy in MC calculations and the improvement on the models adopted, whether anatomical, geometric, or physical assumptions are routinely investigated for even better MC estimates. In this thesis a GEANT4-based MC code, developed by our research group is described and validated (par. 1.3-1.4). It has been developed for MGD estimates for commercial DBT units, taking into account specific operating and geometrical conditions for each one. GE SenoClaire, Hologic Selenia Dimensions, GE Senographe Pristina, Fujifilm Amulet Innovality, Siemens Mammomat Inspiration and IMS Giotto Class are reproduced in simulations and normalized glandular dose (DgN) coefficients are obtained. For gaining in MC accuracy, a new skin envelope is included in the phantom model, on the basis of new founding in literature regarding the breast anatomy (par. 2.1) [3].

In the paragraph 2.2, a new and innovative digital phantom model is proposed and evaluated, which overcomes the drastic assumption of the homogeneous mixture of adipose and glandular

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tissues, involving a voxelized breast phantom approach. Clinical results based on Breast Computed Tomography (bCT) investigation performed in the United States and published in literature suggested a new method for representing the gland, basically far from the current uniform distribution of gland within the breast; the proposed model here presented involves a gaussian distribution of glandular tissues, by means of glandular voxels distributed according to the position in the breast volume. MGD estimates are evaluated and compared with the current dosimetry method, and a proposal for involving the phantom model for dosimetry routines is presented [4].

This thesis is not limited in considering only digital breast phantoms, but discussions regarding physical breast phantoms are introduced with the support of the MC code. In the last years, thanks to the spread of 3D printers, the state of the art in different fields of medical physics, whether is radiology or radiotherapy, is the production of built-in-house phantoms presenting attenuation characteristics and/or digital images similar to those of the real tissues. For DM and DBT, test physical phantoms represent fundamental tools used to perform quality assurance (QA) procedures and allow the calculation of useful parameters for imaging and radiation dosimetry. QA procedures and research are usually performed using polymethyl-metacrilate phantoms (PMMA) blocks simulating the breast composition; in par. 3.1 low density 3D-printing materials are evaluated by using MC calculations for built-in-house phantoms for applications in breast dosimetry. A physical breast phantom is introduced, presenting dedicated homogeneous compounds for both the skin envelope and the inner part of the breast phantom, according to the actual reference dosimetry methodology [5].

3

1

C

HAPTER

1

This chapter briefly describes breast screening techniques, the main studies and formalisms adopted in international dosimetry protocols over the years. The GEANT4-based Monte Carlo code, which results derive from, is presented by describing the principal modules, aspects and action which it is characterized. Code validation among literature and experimental measurements is also presented.

1.1 Breast cancer and screening procedures

One of the tasks or the World Health Organization (WHO) is to monitor the public health situation, analyse the health trends and promote norms and standards related to health assistance. The understanding and interpretation of the trends plays a key role for sharing medical acknowledgments between the member states, in order to suggest best practices, prevention strategies and medical treatments for improving the quality and the duration of life. Through the World Health Statistics series, published annually since 2005, the WHO represents the state of the world’s health. In 2016, noncommunicable diseases, NCDs (also known as chronic diseases, may be long lasting and are the result of a combination of genetic, physiological, environmental and behaviours factors), caused 41 million deaths of the overall total of 57 million deaths in the world; the majority of such deaths were caused by the four main NCDs, which are cardiovascular disease (17.9 million deaths; accounting for 44% of all NCD deaths), cancer (9.0 million deaths; 22%), chronic respiratory disease (3.8 million deaths; 9%) and diabetes (1.6 million deaths; 4%) [6]. Worldwide, in female subjects, breast cancer is the most commonly diagnosed cancer, accounting about 2.1 million newly diagnosed breast cancer (1 in 4 cancer cases among women) and the leading cause of cancer death, followed by colorectal and lung cancer for incidence, and vice versa for mortality [7]. In 2018, among European females, breast cancer was by far the most frequently diagnosed neoplasm (522,500 , 28.2% of the total), followed by colorectal (228,000 , 12.3%), lung (158,000 , 8.5%) and corpus uteri (122,000 , 6.6%) cancers [8] (Fig. 1.1).

Due to its various morphological features, breast cancer is a highly heterogeneous disease which needs an in-depth classification, since this kind of neoplasm shows variable histopathological features, clinical outcome and systemic interventions. From an historical perspective, breast cancer can be classified in two main histopathological classes, namely invasive ductal carcinoma (IDCs)

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non otherwise specified (NOS) and invasive lobular carcinoma (ILC). Since tumours have very different biological and clinical profiles, the histopathological classification represents a fundamental task to identify together with the tumour grade and stage (TNM classification). Importantly, the accurate identification of “variant” or “special” subtypes has prognostic implications [9].

As suggested by the WHO, to improve breast cancer outcomes and survival, early detection is critical. There are two prerequisites for reducing the rate of death: early diagnosis and mass screening procedures. Screening consists in testing women to identify cancers before any symptom appears. This may lead to a tumour early detection, allowing greater possibilities for medical treatment and reducing the mortality rate. The increasingly earlier detection of cancer caused by screening procedures may produce an increase in both incidence rates and survival rates, as result of the introduction of a new procedure to screen subgroups of the population for a specific cancer (Fig. 1.2). It is important to emphasize that, in general, the improvements in screening procedures result in better patient survival rates because they are based on the survival time after diagnosis. Despite this clarification note, for breast cancer screening it has been demonstrated that the increased survival time is directly connected to the reducing of breast cancer mortality [10].

Fig. 1.1 - Estimated numbers of new cancer cases (1.85 million) and cancer deaths in Europe in 2018 for female subjects.

5 1980 1985 1990 1995 2000 2005 2010 2015 20 40 60 80 100 120 140 160 180 mortality ra tes pe r 1 00 ,00 0 year of diagnosis/death white females black females Cancer of the Female Breast (Invasive) in U.S.

incidence

Fig. 1.2 - Incidence and mortality rates due to invasive ductal carcinoma for female subjects in US. Data provided by the National Cancer Institute.

With the aim of decreasing breast cancer mortality, several countries started breast cancer screening programs. Digital Mammography, highly recommended in women between 50 and 75, is the principal technique used to detect breast masses, even if the cancer is too small to be felt as a lump. Screening DM is a X-ray 2D-image examination performed by compressing the patient breast and acquiring two projections: a cranio-caudal and a medio-lateral (CC and MLO views); since mammography images are affected by the structure overlap, the use of a second view can help radiologists to distinguish normal areas of overlapping fibroglandular tissue from a cancer mass which can hide inside it. Different X-ray attenuation properties between normal and abnormal tissues are very slight and the adoption of optimized tools is critical to avoid false-negative results. Nevertheless, normal and cancerous tissues have even more small X-ray attenuation differences and, for women with dense breasts, sensitivity and specificity can be lower [11], where these two parameters reflect the ability of the screening equipment to identify who truly has a disease and who truly does not have a disease:

𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 = ( # 𝑜𝑓 𝑡𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒𝑠

# 𝑜𝑓 𝑡𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒𝑠 + # 𝑜𝑓 𝑓𝑎𝑙𝑠𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒𝑠) × 100 (1)

𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 = ( # 𝑜𝑓 𝑡𝑟𝑢𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒𝑠

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It has been shown on a study performed from 1985 to 1992 on 28271 mammographic examinations [11] that the sensitivity of screening mammography is higher on women aged 50 years and older with primarily fatty breast density, whereas is lower on women younger than 50 years and particularly low when the time between screenings is about 2 years or when women have a family history of breast cancer, possibly because of rapid tumour growth. Quantitatively speaking, sensitivity was 77.3% for women aged 30-39 years, 86.3% for women between 40-49 years, 93.6% for women between 50-59 years, 94.1% for women between 60-69 years, 91.2 for women >70 years. In support of more rapid tumour growth rates in younger women the decrease in sensitivity with increasing time for the detection of breast cancer (13 vs 25 months) appears to be more marked in younger than in older women, with a decrease of about 8-13% in sensitivity. Moreover, age influences sensitivity with fatty breasts in younger women (<50) who had a lower sensitivity for mammography than older women (81.8% vs 98.4%, respectively), while for women with dense breast aged both <50 and >50 sensitivities were similar (85.4% vs 83.7%).

Sensitivity is dependent not only from the density of the breast, but from the quality of the equipment too. Since the introduction on digital mammography, in literature is strongly suggested that digital mammography should replace screen-film mammography for both screening and diagnostic procedures [12]. Indeed, the accuracy of digital mammography is significantly higher respect film mammography among women aged <50 years, with dense and extremely dense breasts, and premenopausal or perimenopausal women [13].

As briefly introduced, the two-dimensional (2D) nature of mammography results in tissue superposition, which could reduce the visibility of a tumour mass due to the overlying and underlying glandular tissues surrounding it. The third dimension is thus flattened, partially contributing to reduce sensitivity and specificity of conventional mammography. In the last decades Digital Breast Tomosynthesis, a new pseudo 3D imaging technique, has been introduced in the clinic, making it possible to reduce the limitation of the superimposition of tissues and facilitating the discrimination between normal and cancerous tissues [9-10]. A DBT unit is similar to the DM except for the X-ray tube motion, which moves on an arc around the compressed breast (Fig. 1.4); a discrete number of projection images is acquired at different projections and then a set of fixed-thickness slices parallel to the detector plane is digitally reconstructed by applying a back-projection-filter or by using iterative algorithms. A comparison between breast cancer visibility in one-view breast tomosynthesis and in one- or two-views digital mammography was made by Andersson et al. (2008) [16], whose results indicate that cancer visibility on DBT is superior to DM, suggesting a higher sensitivity for breast cancer detection.

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Indeed, DBT significantly reduces the anatomical noise, which still remains a limiting factor in mammography for accurately classifying the breast density according to the BIRADS classification. Using a DBT procedure, signs of malignancy are generally better visible, like spiculated mass, asymmetries, irregular borders, architectural distortions or clusters of suspicious calcifications. Fig. 1.3 shows a comparison between MLO screening mammograms performed on a 68-year-old woman with fatty breast with both DM and DBT techniques, where the reduced masking textures in the in-plane tumour let the spiculations visible and the 8-mm tubular carcinoma [17].

Fig. 1.3 - Screening mammograms (MLO views) obtained with A digital mammography, and B digital breast tomosynthesis. Image from Østerås et al. (2019) [17].

Fig. 1.4 - Schematic drawing of the acquisition geometry for (a) mammography and (b) tomosynthesis setups. For mammography, two images are routinely acquired, while for tomosynthesis, projections are reconstructed forming slices referring to different positions along the vertical axis. Scan angle and number of projections differ depending on the commercial apparatus.

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In digital mammography and digital breast tomosynthesis, radiographic images of the breast are produced by using low energy photons, usually peak tube voltage between 24 to 38 kVp depending on breast thickness, since a thicker breast needs a harder spectrum, while for small breast sizes average energy has to be smaller (Tab. 1.1, Tab. 1.2). The anode/filter combination is at the discretion of the manufacturer. Nowadays, W anode material is used in DBT systems and the chosen filter can be Al, Rh, Ag, exception for GE SenoClaireTM and GE Senographe PristinaTM which use Mo/Mo, Mo/Rh, Rh/Rh and Rh/Ag anode/filter combinations. Compared to Mo and Rh targets, W target has better bremsstrahlung production efficiency and power loading. This permits higher milliamperage and shorter exposure times.

Tab. 1.1 Dose measurements for 2D images using Hologic Selenia Dimensions under AEC. mAs and MGD values include the pre-exposure pulse (5 mAs for breast thicknesses < 50 mm, 10 mAs otherwise), which do not contribute to the image. Data provided by the UK NHSBSP, Report 1307.

Tab. 1.2 Dose measurements for tomosynthesis procedures with Hologic Selenia Dimensions under AEC. mAs and MGD values include the pre-exposure pulse (5 mAs). Data provided by the UK NHSBSP, Report 1307.

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1.2 Formalism in Monte Carlo calculations

The goal of screening and diagnosing imaging techniques is to highlight any kind of malignancy formed within the breast. A simple differentiation regarding breast tissues considers the whole organ consisting of three major constituents: adipose tissue, glandular tissue and the skin which surrounds the organ. For the reasons described in the previous paragraph, the most important is the glandular tissue, considered the most radiosensitive tissue at risk, since ionizing radiation is involved. Thus, cancer risk estimates are performed by using the Mean Glandular Dose (MGD), or also referred as Average Glandular Dose (AGD) in UK and EU dosimetry protocol [18] and in the US protocol [19], that considers the glandular tissue as the tissue of interest on which accurate dosimetry have to be performed.

Nevertheless, it should be stressed that carcinogenic risk is considered small in relation to the potential beneficial effects of screening [20], inasmuch as both DM and DBT are low-dose radiation procedures.

Since MGD is not a physical quantity, dosimetry estimates are performed by using dedicated conversion coefficients applied to the incident Air Kerma (Kair) at the entrance surface of the

breast, without backscatter, for obtaining Mean Glandular Dose values (or Average Glandular Dose ones) for a given breast model due to a specific X-ray radiation beam. Conversion coefficients are computed with MC simulations where radiation glandular dose is derived from a representative simulation of the mammography exam. Glandular dose values depend on multiple factors; the breast size, the X-ray radiation beam and the breast glandularity, which is the main tissue parameter of interest. Under the assumption that breast tissue is composed by adipose and glandular tissues, glandularity expresses the percentage of glandular tissue with respect to the adipose tissue. The higher the glandularity, the higher the associated risk of cancer.

In Europe and countries following the IAEA protocol, dose to the breast is assessed by the AGD, estimated with MC-computed conversion factors (c, g and s) obtained by Dance and colleagues [21]–[25] applied to the Kair. In US old protocols, glandular dose was achieved with DgN

coefficients computed by Wu [26], [27], extended by Boone [28], [29], but the new manual utilises Dance’s method because it has been updated to include more breast thicknesses and all the X-ray spectra used in digital mammography [30], [31].

The Monte Carlo method refers to a set of computational methods based on the use of artificially generated random variables for solving mathematical problems that represent the phenomenon

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under investigation. The use of MC simulations has grown progressively with the spread of more and more performing computers. For a given incident X-ray spectrum, energy deposited to the breast phantom from all the simulated photons is scored and registered. This kind of approach is made possible thanks to certain geometry assumptions for digitally reproducing the breast phantom model. The approach followed until now considers the breast phantom made by a homogeneous mixture of adipose and glandular tissues, using weight fraction of elements and total tissue density of the main constituents of the breast tissue derived by Hammerstein [32] and shown in Tab. 1.3. Glandularities ranging from 0 to 100% are composed by mixing properly glandular and adipose tissues.

Tab. 1.3 Elemental composition and density for glandular and adipose tissues.

Tissue H C N O P density

(g/cm3₎

glandular 0.102 0.184 0.032 0.677 0.005 1.04 adipose 0.112 0.619 0.017 0.251 0.001 0.93

1.2.1 Dance et al. 1990-2016

The method proposed by Dance and colleagues involves the use of a “standard breast” phantom, a cylinder of semi-circular cross section with a diameter of 16 cm, with central region composed by a uniform mixture of adipose and glandular tissues and an adipose surface layer 0.5 cm thick representing the skin (Fig. 1.5). The breast thickness was varied in the range 2–11 cm and the composition of the central region between 0.1% glandularity and 100% glandularity, with steps of 25% glandularity. The model also included the breast support plate.

Dosimetric formulation of indirect estimates of the absorbed dose starts really from incident Air Kerma 𝐾𝑎𝑖𝑟 at the upper surface of the breast and dedicated conversion coefficients are used to obtain a reference value of dose

𝑀𝐺𝐷 = 𝑐 ∙ 𝑔 ∙ 𝑠 ∙ 𝐾𝑎𝑖𝑟 (3)

where the g-factor is the conversion factor for a breast of 50% glandularity at the specified half-value-layer (HVL), the c-factor corrects for the glandularity of the breast and is less or more than 1 respectively for more or less glandular breasts. Both coefficients are tabulated against HVL. The s-factor corrects for spectral dependence of the g-factor and is assigned to each target/filter combination, independent of HVL and breast thickness. The ionization chamber is used in MC computations to obtain incident air kerma estimates and modelled as a cylindrical volume with

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diameter of 30 mm and thickness of 10 mm, placed on the top surface of the breast and with the compression paddle on it. The HVL values were calculated after the compression paddle. The X-ray spectra used were based on the work of Boone et al [33].

Fig. 1.5 - Homogeneous breast model adopted by Dance. The semi-cylinder radius is fixed to 8 cm, the thickness is varied and the skin is 5 mm thick composed by adipose tissue. Breast tissue glandularity is varied in the range 0.1% - 100% with 25% increments.

1.2.2 Wu el al. 1991-1994

In the United States, breast dosimetry was usually performed by using the Monte Carlo model of Wu and colleagues. In this model the breast shape has a semi-elliptical geometry with a long axis of 180 mm and a short axis of 160 mm. A 4 mm thick skin layer, made by adipose tissue, composes the outer layer of the breast, while the inner part is a homogeneous mixture of adipose and glandular tissues; the relative amounts of glandular tissue were 0%, 50% and 100%. The compositions of the three breast tissue types were based on the work of Hammerstein [32]. In this model, the Mean Glandular Dose in mGy is obtained by multiplying the incident air kerma 𝐾_𝑎𝑖𝑟 for the 𝐷𝑔𝑁 (mGy/mGy) number.

𝑀𝐺𝐷 = 𝐷𝑔𝑁 ∙ 𝐾𝑎𝑖𝑟 (4)

Wu tabulated DgN values for X-ray spectra derived from a Mo/Mo target/filter combination and, in a subsequent work, DgN coefficients have been extended for Mo/Rh and Rh/Rh spectra. Nevertheless, alternative tables for W anode systems were required.

As opposed to Dance method, Wu’s model incorporates in DgNs all the variables used for the calculation of MGD, and DgN estimates provide mean glandular dose normalized by the entrance surface air kerma.

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1.2.3 Boone et al. 1999-2002

Boone and colleagues used the Wu’s model and investigated other anode/filter combinations, including those with tungsten anode. They used for the digital breast phantom a semi-elliptical geometry with 8.5 and 10 cm radii, 4 mm thick adipose skin, variable breast thickness and glandularities of 0%, 50% and 100%. The formalism used for the calculation of DgNs coefficients involves MC runs with monoenergetic beams and the average energy deposited to the breast, per incident photon, was computed as follows:

𝐷𝑔𝑁(𝐸) = ∑ 𝑓(𝐸) × 𝐸 × 𝛷(𝐸) × 𝐺 × 𝑎𝑟𝑒𝑎

𝑚𝑎𝑠𝑠 𝐸𝑚𝑎𝑥

𝐸=𝐸𝑚𝑖𝑛

(5)

where 𝑓(𝐸) is the energy absorbed per incident photon divided by the photon energy, 𝛷(𝐸) is the photon fluence at a given energy bin E. By denoting 𝑓_𝑔 the glandular fraction, G is defined by

𝐺 = 𝑓_𝑔(𝜇_{𝜌 (𝐸))}𝑒𝑛 𝑔𝑙𝑎𝑛𝑑𝑢𝑙𝑎𝑟 𝑓_𝑔(𝜇_{𝜌 (𝐸))}𝑒𝑛 𝑔𝑙𝑎𝑛𝑑𝑢𝑙𝑎𝑟 + (1 − 𝑓_𝑔) (𝜇_{𝜌 (𝐸))}𝑒𝑛 𝑎𝑑𝑖𝑝𝑜𝑠𝑒 (6)

Polyenergetic DgN coefficients for a specified spectrum were obtained using the energy weighting method in equation 5 𝑝𝐷𝑔𝑁 = ∑ 𝛷(𝐸) ∙ 𝜗(𝐸) ∙ 𝐷𝑔𝑁(𝐸) 𝐸𝑚𝑎𝑥 𝐸𝑚𝑖𝑛 ∑𝐸𝑚𝑎𝑥𝛷(𝐸) ∙ 𝜗(𝐸) 𝐸𝑚𝑖𝑛 (7)

Spectral models have been implemented using algorithms for molybdenum, rhodium, and tungsten anodes, respectively dubbed MASMIPM, RASMIPM and TASMIPM [33], and based on experimental measurements of mammography-energy X-ray spectra.

1.2.4 The introduction of DBT

The introduction of DBT systems led to extend glandular dose assessment formalisms.

To simplify the MGD estimation for a complete DBT acquisition, the concept of relative glandular dose (RGD) has been proposed by Sechopoulos and colleagues [34] to be used in US protocols

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𝑅𝐺𝐷(𝛼) = 𝐷𝑔𝑁(𝛼)

𝐷𝑔𝑁₀ (8)

where the normalized glandular dose coefficients at a given projection angle 𝛼 are normalized by the coefficient referring to the straight projection at 0 degree. The total 𝐷𝑔𝑁 for a complete DBT acquisition with 𝑁 projections can be computed by

𝐷𝑔𝑁 = 𝐷𝑔𝑁₀× 1

𝑁∑ 𝑅𝐺𝐷(𝛼)

𝛼

(9)

Using the Dance’s method, the same formalism is followed by Dance and co-workers [24] who introduced the “tomo” factors, t and T, used to extend the MGD estimation respectively for a single projection and over the i-summation of the projections for a whole DBT examination

𝑀𝐺𝐷 = 𝐾 ∙ 𝑐 ∙ 𝑔 ∙ 𝑠 ∙ 𝑇 with 𝑇 = ∑ 𝑐𝑖 𝑖𝑡(𝛼𝑖) (10)

where 𝑐_𝑖 is the partition of the tube loading for each projection, 𝐾 is the incident air kerma in straight through position but referring to the total mAs of the examination, and 𝑡(𝛼_𝑖) = 𝑀𝐺𝐷(𝛼_𝑖)

𝑀𝐺𝐷0

⁄ .

In DBT geometry is important to define the tomosynthesis angle, measured using the source-to-detector distance or the source-to-center-of-rotation distance (Fig. 1.6). Denoting with d the distance from the center of rotation to the receptor, and r the distance from the X-ray source to the center of rotation, the relationship between the two angles 𝜑 and 𝜃 is

𝜑 = 𝜃 + 𝑠𝑖𝑛−1(𝑑 𝑠𝑖𝑛 𝜃

𝑟 ) (11)

Center of rotation can be, at discretion of the manufacturer, on the detector surface or few centimeters above on the vertical axis. Fig. 1.6Errore. L'origine riferimento non è stata trovata. shows the two geometries followed by manufacturers.

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Fig. 1.6 - Geometry used for commercial DBT units. a) refers to a geometry in which the horizontal rotation axis is placed on the detector surface; in b) otherwise, source-to-center-of-rotation distance is positioned some centimeters above the breast support (not to scale).

1.3 The Monte Carlo model

Various MC-based toolkits are available for dosimetry purposes. Among the most modern used toolkits there are GEANT4, MCNP, PENELOPE, EGSnrc. We propose in this paragraph the methodology used by our research group for dosimetry in mammography [2], [35] and breast tomosynthesis mainly based on Boone’s method. A GEANT4-based MC code is presented, version 10.5, but in principle the same methodology can be followed using other MC codes.

The use of Monte Carlo simulations in diagnostic medical imaging research is helpful thanks to the flexibility and ability to estimate quantities that are challenging to measure empirically. In order to perform mean glandular dose estimation in breast imaging techniques, the AAPM TG195 protocol geometry has been considered and implemented in our MC code, which includes all the geometry assumptions needed:

• The breast is represented by a semi-cylinder with a radius of 10 cm, composed by a homogeneous mixture of adipose and glandular tissues (Tab. 1.3) forming a certain glandularity, surrounded by a 1.45 mm thick skin layer with a dedicated composition, shown in Tab. 1.4 [28], in line with the experimental findings derived from clinical breast CT (bCT) scans [36].

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Tab. 1.4 - Elemental composition and density for the skin layer.

Tissue H C N O P density

(g/cm3₎

Skin tissue 0.098 0.178 0.050 0.667 0.007 1.09

• A water solid to represent the patient body having 303015 cm3 _dimensions.

• Simple solids representing the compression paddle and the breast support, and a scoring plane used to provide the beam collimation inside all the four edges of the detector have been included and can be modified in dimensions and composition in order to replicate all the commercial DM and DBT units available in clinics.

In the MC code, the ability to perform tomosynthesis investigation has been implemented, by moving the X-ray source on an arc over the breast phantom respect to the center-of-rotation; equation (11) regarding the relation between 𝜑 and 𝜃 angles is used.

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1.3.1 Spectral model

Spectral algorithms are needed for replicating a DBT polychromatic source. Polychromatic X-ray beams have been included using the external tools provided by Hernandez and colleagues [37] dubbed MASMICSM-T, RASMICSM-T, TASMICSM-T, developed for application to mammography and tomosynthesis, respectively for molybdenum, rhodium and tungsten anode materials. Every energy bin provided by algorithms are weighted in MC codes with their relative photon fluence, used in the computation as a statistical probability to produce an incidence photon in its energy bin. In DBT units, a major tube loading is needed because of the multiple projections, thus, the most common target material used is tungsten.

Since breast has to be compressed during the examination, polycarbonate is the most common material used by manufacturers for the upper compressing plate, involving an incident spectrum alteration. In Fig. 1.8b is represented a W/Al incident spectrum on a 2.8 mm thick polycarbonate compression paddle, normalized to 1 mGy air kerma (continuous line), and the transmitted spectrum through the paddle (dashed line). Lower energy photons are preferentially removed from incident beam, involving an increase of the average energy beam and consequently a 11% higher HVL value. Thus, spectrum alteration leads to consider incident air kerma below the compression paddle.

Fig. 1.8 - a) Example of Mo/Mo spectrum @ 25 kV used in mammography for small breast thicknesses. Incident W/Al spectrum @ 32 kVp, above a 2.8 mm thick polycarbonate compression paddle and below it. Spectra are normalized to 1 mGy air kerma.

1.3.2 Dose estimation

Starting from the X-ray source, all the photons and their interactions with matter are tracked and energy deposition is registered. Physics processes are modelled opportunely in MC codes mainly

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depending on particle energies involved. According to the prescriptions provided by the report of AAPM Task Group 195 [38], the “Option4” PhysicsList in GEANT4 should be used for energies ranging in mammography investigations, since constructors and instances that replicates physics processes are designed for any low-energy application. The production threshold (“range cut”) for the secondary particles, editable by the user, is expressed in GEANT4 in terms of the distance travelled by the particles in the medium1 and it must be carefully chosen. Rayleigh, photoelectric, Compton and bremsstrahlung processes are simulated.

The formalism adopted to estimate the glandular dose coefficients is the Wu’s method (par. 1.2.2), where the MGD values, for a certain projection angle θ, is obtained with

𝑀𝐺𝐷𝜃 ≡ ∑ 𝐸_𝑗𝑑𝑒𝑝·𝐺(𝐸𝑗) 𝑚𝑔𝑙𝑎𝑛𝑑 , 𝑗 (12)

where 𝐺_𝑗(𝐸) is the G-factor introduced by Boone, defined in eq. (6), evaluated for the energy of the j-th interacting photon, 𝐸_𝑗𝑑𝑒𝑝 the energy deposition of this photon and 𝑚_{𝑔𝑙𝑎𝑛𝑑} the glandular mass.

For providing conversion factors, air kerma estimation is required on the top surface of the breast. Geometry assumptions let the use of a scoring surface 22 cm2 _{placed on the top surface of the} breast, whose center is placed at 4 cm from the chest wall, in which air kerma scoring can be compute. Following Sarno et al. [39], let 𝑆 be the scoring surface through which 𝑛 photons cross, 𝜗_𝑖 angle between the i-th photon direction and the direction perpendicular to the surface,

(𝜇𝑒𝑛

𝜌 ) 𝑎𝑖𝑟

(𝐸_𝑖) the air mass energy absorption at a given photon energy 𝐸_𝑖 [40], air kerma at the

straight angle θ = 0 can be estimated using

𝐾0 = ∑ 𝐸𝑖 × (𝜇_{𝜌 )}𝑒𝑛 𝑎𝑖𝑟 𝑆 𝑐𝑜𝑠 𝜗𝑖 𝑛 𝑖=1 (13)

The factor 𝑐𝑜𝑠 𝜗𝑖 should be included because of the scattered photons deriving from the upper compressing plate; this may lead to a significant effect on air kerma estimation, traducing in an overestimation on the conversion factors.

1 _{The distance is expressed in GEANT4 in terms of energy; e.g. the range cuts of 1 mm for photons and 1 µm for} electrons correspond respectively to about 2.55 keV and 0.99 keV in 25% glandular breast tissue.

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For a tomosynthesis investigation having N projections, the total mean glandular dose 𝑀𝐺𝐷_𝐷𝐵𝑇 is computed with

𝑀𝐺𝐷_𝐷𝐵𝑇 = ∑(𝑤_𝜃· 𝑀𝐺𝐷_𝜃) 𝜃

(14)

where 𝑀𝐺𝐷𝜃 is the glandular dose portion deriving from the projection with angle 𝜃, 𝑤𝜃 is the weighting factor which takes into account a possible varying tube load at a certain angle 𝜃. The 𝐷𝑔𝑁_𝐷𝐵𝑇 coefficient is computed by

𝐷𝑔𝑁_𝐷𝐵𝑇 = 𝑀𝐺𝐷𝐷𝐵𝑇

𝑁 ∙ 𝐾₀ (15)

It has to be emphasized that in MC estimates, dose estimates must be normalized for the total events occurred i.e., in this case, incident photons launched in the simulation from the X-ray source. 𝑀GDθ and K0 estimates should be presented in terms of mGy/event even if photons coming from the X-ray source do not interact in the sensitive volume. Thus, the concept of dose deposit should be considered in terms of a normalized dose for event, as opposed to experimental exposures where the concept of dose is in terms of a “total” dose due to specific operational quantities (kVp, mAs). While in real exposures the major is the X-ray flux, the major is the dose deposit, in MC simulations the major the events, the better is the dose estimate precision (par. 1.3.3).

1.3.3 Uncertainties

Mean glandular dose and air kerma estimates should be provided by MC computations normalised for simulated photon (in mGy/event). The rationale is to run a high number of replications; the greater the number of the primary events (primary photons from the X-ray source), the greater the precision of the simulation. Uncertainties should be evaluated as follow Sempau et al. [41]. The expected value of a quantity of interest 𝑞 can be estimated by the average 𝑞̅ derived from the 𝑛 histories is 𝑞̅ =1 𝑛∑ 𝑞𝑖 𝑛 𝑖=1 (16)

19 𝑠2 = 1 𝑛( ∑ 𝑞_𝑖2 𝑖 𝑛 − 𝑞̅ 2_{) (17)}

In the MC simulations, the number of events was fixed at nk = 109 for the air kerma scoring in the

straight projection, due to the small ROI interested for air kerma computation, while for 𝑀𝐺𝐷𝐷𝐵𝑇 calculations, which concerns the whole breast tissue, a constant number of photon histories nθ =

108 was launched for each DBT projection. Then, the conversion factor estimate has been performed by simply using

𝐷𝑔𝑁𝐷𝐵𝑇 = ∑ (𝑤𝜃· 𝑀𝐺𝐷_𝑛 𝜃 𝜃 ) 𝑁 𝜃=1 𝑁 ∙_𝑛𝐾0 𝐾 (18)

The symmetry properties of the homogeneous phantom, let to adopt the strategy of performing simulations over the right side of the phantom only2, plus the straight angle θ= 0, and MGDDBT = MGDθ=0+ 2 ∙ MGD𝑟𝑖𝑔ℎ𝑡. Thanks to this strategy, that obviously aimed to reduce simulation times, nk and nθ have been chosen in order to reach an uncertainty of less than 0.2% for

the MGDDBT and less than 0.1% for K.

1.3.4 Random Engine

Random number generators are fundamental tools used in MC toolkits, which provide to set the seeds for starting a given simulation. The purpose of the engine is to pull out random values (single or multiple values) to be used on shooting events. The rationale of MC calculations is to begin with a random number (or multiple random ones) with a repetition frequency3 as long as possible, making the process of the generating values more random as possible. Task groups work on random engines, performing increasingly accurate algorithms for generating random numbers. The random engine can be easily replaced by any other engine of user's choice, from 12 engines available in GEANT4.

The engine can be initialized with a particular seed. Fixed seeds guarantee the same simulation result from a given MC code, avoiding fluctuations, which can be helpful during research projects or equipment developments, to quantify the effect of a given change in the code. The rationale in

2 _{The left side would have been correct anyway.}

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MC codes is to obtain convergent results by using random numbers in the final accurate computations. In our simulations we used MixMaxRng engine provided by the CLHEP C++ library with random seeds.

1.3.5 The GEANT4-based MC code

GEANT4 (GEometry And Tracking) is a C++ based toolkit for simulating the interaction of particles through the matter. Its area of application includes experiments in high energy physics, nuclear physics, accelerators and medical applications. The toolkit is developed, and continuously updated, by a joint development project under the CERN Research and Development Programme; GEANT4 is based on the object-oriented programming C ++ informatic code. In the work presented here, GEANT4, version 10.5, has been installed in a Linux environment (Ubuntu 18.04 LTS operating system) using a virtual machine (VMware Workstation Player 14); the computer desktop used for developing the code and for the simulations is equipped with a Intel Core ™ i7-8700 @ 4.28 GHz processor (6 cores, 12 threads), 24GB of dedicated RAM. The code has been developed in order to take advantage of the GEANT4 multithreading capability. In this paragraph is briefly described the GEANT4-based MC-code using the UML language.

The main() method employs two G4 native classes4, G4MTRunManager and G4UImanager constituting the RunManager and the VisualizationManager respectively; the first sets the mandatory classes for running the program, the second is dedicated to the visualization options. The RunManager constitutes the kernel of the program and the user must provide his own classes derived from some abstract classes of GEANT4 and register them to the RunManager. The main() method that manages the source files calls is implemented in MyExecutable.cc which will be compiled when the code is ready to use.

Tree mandatory classes must be defined and initialized in the main program using the

RunManager5: DetectorConstruction (which defines the geometry setup),

PhysicsList (which includes all the physics list models and the constructors for the physics interactions) and ActionInitialization (which defines all the secondary classes calls to

4 _{Henceforward all classes or source files names with initial "G4" will be intended as part of the original toolkit, while} the others are to be considered as created by the user.

5_{G4MTRunManager* runManager = new G4MTRunManager;}

runManager->SetNumberOfThreads(12);

runManager->SetUserInitialization(new DetectorConstruction()); G4VUserPhysicsList* physicslist = new PhysicsListStdOpt4(); runManager -> SetUserInitialization(physicslist);

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the main program). The MC code has been developed in such a way that the user can interact with it using a macro file which is easy to use and avoids to re-compile the program when typical geometry or irradiation settings must be changed for performing the simulations (Fig. 1.9).

Fig. 1.9 – Class diagram in UML language for the mandatory classes.

The geometry setup, defined in DetectorConstruction, employs mathematical solids to replicate the setup depicted in Fig. 1.7. Each solid is represented by a solid class defining the absolute geometry (i.e. box or tub and its dimensions), its logical volume defining the materials which is composed, and a physical volume defining its position in the world volume.

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The PhysicsList used in this work is the Option4, whose constructors and instances are designed by the GEANT4 team for high accuracy in low-energy physics processes [38] (Fig. 1.11).

Fig. 1.11 – Basic class diagram for the PhysicsList class using the UML language.

All the secondary classes are instantiated by ActionInitialization, whose calls let to perform all the calculations and actions for finalizing the simulations (Fig. 1.12).

➢ PrimaryGeneratorAction class is dedicated to the radiation source, specifying the incident photon beam properties, including the energy spectrum and the beam collimation. All the simulated spectra are included in the PrimaryGeneratorAction with arrays, which represent the relative photon fluence for each photon energy bin of 0.5 keV (see par. 1.3.1). ➢ SteppingAction class is the core of the calculations. For MGD and Kerma estimates,

relations (4), (12) and (13) are performed for each photon interaction.

➢ RunAction class completes the calculations by calling methods specified in the Run class, dedicated to merge the small contributes deriving from all the interactions. RunAction provides the output of the simulations in terms of mGy/event for MGD and air kerma estimates (see par. 1.3.2) and, for the HVL estimation, the number of photons for each energy bin which pass through the upper compression paddle and reach the air kerma scoring surface.

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Fig. 1.12 – Class diagram for the secondary classes whose calls are performed by ActionInitialization class.

1.4 MC code validation

Any new Monte Carlo code needs to be validated before it can be used reliably. The MC code, described in the paragraph 1.3, from which this thesis takes the results, has been validated by comparing its results with protocols, literature references and experimental measurements. For each comparison the code has been edited in order to match the exact geometry with the reference one. The three-steps validation is described in the subsequent paragraphs.

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1.4.1 AAPM TG195 validation

The first validation concerned the AAPM TG 195 protocol, which is an appropriate benchmark protocol for validating a MC code in the field of medical imaging techniques, especially in dosimetry for mammography and breast tomosynthesis. In particular, cases I and III have been performed, respectively for the HVL determination and the MGD estimates, the last for 0 degree and 15 degrees projections, which guaranties a certain reliability of the MGD values for other projection angles in a DBT investigation. The setup adopted is represented in Fig. 1.7, where geometric values and specific materials are prescribed in the protocol. Seven ROIs have been implemented on the detector area for scoring primary and secondary photons which overcome the compression paddles and the breast tissue and reach the detector surface (Fig. 1.13). In addition, seven VOIs have been considered in the breast volume to compare energy deposit and MGD values due to monoenergetic (16.8 keV) and polychromatic (Mo/Mo @ 30 kV) beams. All these comparisons provide a test of reliability on the physics model adopted, accuracy and precision of the MC simulations, and the correctness of the calculations. In Fig. 1.14 are shown results concerning the MGD estimates for the whole breast for monoenergetic and polyenergetic beams, while in Tab. 1.5 the results for the absorbed energy (eV per event) due to the above mentioned beams.

Fig. 1.13 - Regions of interest on the detector surface (in white) and volumes of interest within the breast (coloured) involved for the comparisons with the AAPM TG 195 protocol.

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Fig. 1.14 - MGD per photon for the test in AAPM TG195 report, case III. a) comparison for a monoenergetic beam at 16.8 keV, with discrepancies of 0.03% and -0.28% respectively for 0° and 15° projections; b) comparison for a polyenergetic beam produced with a Mo/Mo spectrum at 30 kV, which led to discrepancies of 0.35% and 0.14%.

Tab. 1.5 - Absorbed energy (eV/photon) in the seven VOIs identified in the AAPM TG195 case 3 test within the irradiated breast model. Relative differences in percent [(this work – TG195 data)/TG195 data] between the results of this work and the ones in TG195 report are indicated.

View VOI

no.

Monoenergetic beam – 16.8 keV Polyenergetic beam – Mo/Mo 30 kV angle (°) _This work Uncertainty TG195 Difference (%) This work Uncertainty TG195 Difference (%) 0 1 17.6428 0.0023 17.7824 -0.785% 16.4603 0.0024 16.5281 -0.410% 2 17.8047 0.0023 17.9932 -1.048% 16.6721 0.0024 16.6716 0.003% 3 18.0252 0.0023 18.0736 -0.268% 16.8889 0.0025 16.8132 0.450% 4 17.5036 0.0023 17.5500 -0.264% 16.2661 0.0024 16.2645 0.010% 5 17.6797 0.0023 17.7868 -0.602% 16.5747 0.0024 16.5299 0.271% 6 5.53408 0.0007 5.5732 -0.703% 6.0038 0.0009 6.04892 -0.746% 7 56.2299 0.0074 56.2932 -0.112% 50.3133 0.0069 50.0746 0.477% 15 1 15.2275 0.0020 15.3298 -0.667% 14.5068 0.0021 14.4315 0.522% 2 16.8481 0.0022 16.9938 -0.857% 15.8663 0.0023 15.8749 -0.054% 3 16.9924 0.0023 17.0665 -0.434% 15.9603 0.0023 16.0065 -0.289% 4 16.5102 0.0022 16.5694 -0.357% 15.4349 0.0022 15.4895 -0.352% 5 18.3991 0.0024 18.4850 -0.465% 17.3104 0.0025 17.2192 0.530% 6 5.08142 0.0007 5.0863 -0.097% 5.59441 0.0009 5.62912 -0.617% 7 55.1348 0.0073 55.3379 -0.367% 49.1136 0.0068 49.1539 -0.082% 1.4.2 Literature validation

The accuracy of correctly replicating the tube motion is crucial on MGDDBT estimates. A comparison versus data provided by Dance et al. (2011) [24] has been performed by replicating 4 different spectra (Mo/Mo 25 kV, Rh/Rh 29 kV, W/Rh 34 kV and W/Ag 40 kV) and by scoring the MGD values projections from 0° to 30° with 5° increments for a fixed geometry. Comparison concerned the t-factors, shown in equation (19), i.e. an alternative definition of the relative glandular dose (RGD) described in equation (8).

26

𝑡(𝛼) =𝑀𝐺𝐷(𝛼)

𝑀𝐺𝐷₀ (19)

Tab. 1.6 – t-factors percentage differences versus data of Dance et al. (2011).

Proj. angle (deg) Mo/Mo 25 kV Rh/Rh 25 kV W/Rh 34 kV W/Ag 40 kV

0 0.00% 0.00% 0.00% 0.00% 5 0.25% 0.03% -0.02% -0.07% 10 -0.02% 0.04% 0.10% -0.28% 15 -0.06% -0.23% 0.07% -0.13% 20 -0.34% -0.49% -0.04% 0.21% 25 -0.22% -0.11% 0.05% 0.06% 30 -0.54% -0.39% -0.28% -0.07%

Fig. 1.15 - Validation vs data in Dance et al (2011). Point data are those produced via the code developed in this work and line/dot curve are data in Dance et al (2011). b) Ratio between t-factors produced via the code used in this work and those in Dance et al (2011).

1.4.3 Experimental validation using XR-QA2 radiochromic films

Among the dosimeters involved in medical physics, radiochromic films represent one of the most easily used solutions for both clinical and research dosimetry applications. Radiochromic films are well suited for many different activities thanks to the self-developing of the response after the irradiation process without the need of chemical development, the relatively low cost and the ease-of-use. Films are routinely used in clinics for performing QC tests or research in both radiology and radiotherapy as alternative to the more expensive active digital detectors. Applications relate phantom measurements for QA procedures in stereotactic radiotherapy, skin dose assessments as well as research in-vivo. In these contexts, radiochromic films can measure an accurate absolute dose on condition that a calibration process is performed and a calibration curve is established.

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Experimental validation of the MC code has been performed by using GAFchromicTM _XR-QA2 films6 (lot #04111901), which are sensitive in the dose range 1-200 mGy for radiology energies with anode tube potentials ranging from 20 to 200 kVp. An increasing change in optical reflectance occurs at increasing doses.

Using the Hologic Selenia Dimensions DBT unit supplied by the Senology Department of the University Hospital “Santa Chiara”, Pisa, Italy, the radiochromic films have been exposed for calibration and in-phantom measurements, following the formalism defined by Tomic et al, Devic et al, Di Lillo et al [42]–[44] and discussed above.

From original XR-QA2 1012'' sheets, samples of 33 cm2 _{have been cut to be used for} calibrations and measurements. Using a flatbed scanner (Epson Expression 10000XL), samples were scanned before and after7 the exposition, in 48-bit RGB mode, at 150 dpi, in the same position of the scanner surface and saved as TIFF image file format. Multiple scans for each sample were executed. Raw images have been analysed with the open software ImageJ8. Formalism provides the film response in terms of reflectance change R ± 𝜎_R using the 16-bit red channel in a ROI of 11 cm2 in the center of each sample (Fig. 1.16). We proceeded to realize three in air calibration curves for 30, 35 and 40 kVp using W/Al spectra, by placing the radiochromic sample below the compression paddle and minimizing the potential backscatter radiation. For each calibration curve 12 points were used, each of them deriving from the average value of 3 different radiochromic samples. Since X-ray mammography units permits low-doses irradiations, in order to observe the XR-QA2 dose range, a Radcal 20X6-60E ionisation chamber coupled with the 2026C dosimeter9 was used to choose correct mAs tube loading values and air kerma exposures, chosen in an optimal range from about 1 mGy to a maximum value depending on the kilovoltage applied. The reflectance R ± 𝜎_R has been evaluated by using

𝑅 = 1 216(𝑃𝑉𝑏𝑒𝑓𝑜𝑟𝑒− 𝑃𝑉𝑎𝑓𝑡𝑒𝑟) (20) 𝜎𝑅 = 1 216√(𝜎𝑃𝑉𝑏𝑒𝑓𝑜𝑟𝑒) 2 + (𝜎𝑃𝑉𝑎𝑓𝑡𝑒𝑟) 2 + (𝜎𝑠𝑐𝑎𝑛𝑛𝑒𝑟)2 (21) 6 _{http://www.gafchromic.com/}

7 _{Scans for irradiated samples have been executed 24h after the exposition.} 8 _{https://imagej.nih.gov/ij/}

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where 𝑃𝑉_{𝑏𝑒𝑓𝑜𝑟𝑒} and 𝑃𝑉_{𝑎𝑓𝑡𝑒𝑟} are the mean pixel value of samples respectively before and after the X-ray exposition, 𝜎_{𝑃𝑉𝑏𝑒𝑓𝑜𝑟𝑒} and 𝜎_{𝑃𝑉𝑏𝑒𝑓𝑜𝑟𝑒} the standard deviations and 𝜎_{𝑠𝑐𝑎𝑛𝑛𝑒𝑟} is the statistical uncertainty due to scanner response in multiple scans. For calibration and measurements, 5 samples have been used to quantify background radiation. The final value is considered the net reflectance 𝑛𝑒𝑡𝑅 with the relative uncertainty 𝜎netR

𝑛𝑒𝑡𝑅 = 𝑅 − 𝑅_{𝑐𝑜𝑛𝑡𝑟𝑜𝑙} (22) 𝜎𝑛𝑒𝑡𝑅 = 1 216√(𝜎𝑅)2+ (𝜎𝑅𝑐𝑜𝑛𝑡𝑟𝑜𝑙) 2 (23)

Fig. 1.16 – Schematic drawing of 33 cm2 _{radiochromic samples where the 11 cm}2 _{ROI used for the pixel}

values estimation is highlighted. Samples undergo a darkening when exposed to radiation doses. For control samples, which are not exposed directly, darkening have to be assessed too.

The free-in-air calibration curves for the XR-QA2 radiochromic films involved a zero-intercept second order polynomial (eq. 19) as suggested by Di Lillo et al [44] by using the software Origin 9.4 (OriginLab Corporation, Northampton, MA)10 which provides the Orthogonal Distance Regression algorithm). In Fig. 1.17a are reported the fitting curves for in-air calibration and in Fig. 1.17b the relative dose uncertainty versus air kerma, evaluated by adding in quadrature the fitting error and experimental uncertainty.

𝐾_𝑎𝑖𝑟𝑓𝑖𝑙𝑚 = 𝑎 ∙ 𝑛𝑒𝑡𝑅 + 𝑏 ∙ 𝑛𝑒𝑡𝑅2 (24)

29 0.00 0.05 0.10 0.15 0.20 0.25 0 4 8 12 16 20 24 W/Al 700 m 30 kV 35 kV 40 kV 30 kV 2nd order fit 35 kV 2nd order fit 40 kV 2nd order fit Air Ker ma ( mGy) net R XR-QA2 lot #04111901 a) fit R2 _{> 0.999} 0 5 10 15 20 25 30 5 10 15 20 25 30 35 XR-QA2 lot #04111901 b) Tota l r el ati ve un ce rta in ty (%)

Air kerma (mGy)

30 kV 35 kV 40 kV

W/Al 700 m

Fig. 1.17 - a) Calibration curves of radiochromic films for 30, 35 and 40 kV tube voltage (W/Al 700 µm), and b) corresponding relative dose uncertainties.

The validation was performed by comparing results from experimental measurements against those obtained in the replicated setup in the MC code. Dose measurements were performed in a polymethyl-metacrilate (PMMA) phantom having 240  300  50 mm3 _{dimensions by inserting} five radiochromic samples below the upper layer at 10 mm depth from the phantom surface (Fig. 1.18) and irradiating them with the same kilovoltages used in calibration procedure in DBT modality. The air kerma derived from the film response in DBT irradiation was normalized to the incident air kerma, measured with a calibrated radiochromic film piece placed on the surface of the phantom (in air), below the compression paddle and exposed with the tube angle fixed at 0° (Fig. 1.19).

Fig. 1.18 - Scheme of the setup adopted for the experimental validation using radiochromic films. For the in-depth dose assessment five samples have been placed at 10 mm depth inside the PMMA phantom with the compression paddle in place. a) top view and b) perspective view of the geometry adopted.

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Fig. 1.19 - Scheme of the setup adopted for the dose measurements at the reference position at the top side of the PMMA phantom with the compression paddle in place, where a radiochromic film piece was positioned to provide the normalization incident air kerma value. a) top view and b) perspective view. The setup reported in Fig. 1.19 and Fig. 1.19 has been implemented in the MC code and absorbed dose to 10  10  1 mm3 VOIs in the same position of the radiochromic samples has been registered11. Since the linear relation between dose and air kerma in the phantom (Tomic et al. [42]), the relative simulated dose values and the simulated air kerma values were comparable by using the backscatter factor 𝐵𝑃𝑀𝑀𝐴 and the ratio of the energy-absorption coefficients between

PMMA and air, weighted on the spectrum (µen

ρ )_air PMMA

. In equation (25), 𝐾_{𝑎𝑖𝑟,𝑚}𝑓𝑖𝑙𝑚(𝑑) is the air kerma

evaluated with the film inside the medium at the given depth 𝑑, 𝐾_{𝑎𝑖𝑟,𝑖𝑛𝑐}𝑓𝑖𝑙𝑚 is the incident air kerma on the upper surface of the phantom, 𝐷_𝑚𝑀𝐶(𝑑) and 𝐷_𝑖𝑛𝑐𝑀𝐶 are respectively the absorbed dose in the medium at the depth 𝑑 and the absorbed dose at the entrance phantom surface.

𝐷𝑚𝑀𝐶(𝑑) 𝐷_𝑖𝑛𝑐𝑀𝐶 ≅ 𝐾_{𝑎𝑖𝑟,𝑚}𝑓𝑖𝑙𝑚(𝑑) ⋅ 𝐵𝑃𝑀𝑀𝐴 ⋅ (µ_{𝜌 )}𝑒𝑛 𝑎𝑖𝑟 𝑃𝑀𝑀𝐴 𝐾_{𝑎𝑖𝑟,𝑖𝑛𝑐}𝑓𝑖𝑙𝑚 ⋅ 𝐵_{𝑃𝑀𝑀𝐴}′ ⋅ (µ𝑒𝑛_𝜌′) 𝑎𝑖𝑟 𝑃𝑀𝑀𝐴 ≅ 𝐾_{𝑎𝑖𝑟,𝑚}𝑓𝑖𝑙𝑚(𝑑) 𝐾_{𝑎𝑖𝑟,𝑖𝑛𝑐}𝑓𝑖𝑙𝑚 (25)

The prime symbol indicates the slight differences that values can present within the phantom i.e. a slight change in the energy spectrum and the different amount of PMMA below the film samples (50 mm for the upper one, 40 mm for the in-depth radiochromic samples). Tab. 1.7 shows percentage differences obtained with the experimental validation for the kilovoltages involved, proving absolute differences less than 4% between simulated data and measurements.

11 _{Due to the small VOIs 10}9 _{incident photons have been simulated for each projection angle in order to provide a} good statistics (see par. 1.3.3), leading to uncertainty associated to MC calculations be less than 0.1%.

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Tab. 1.7 - Experimental and MC-simulated data for the five samples positioned in depth normalized for the incident one. Percentage differences are reported in terms of [(Kexp-KMC)/Kexp].

X-ray tube voltage

Position 30 kV 35 kV 40 kV (𝐾 𝐾⁄ 𝑖𝑛𝑐) 𝑒𝑥𝑝 (𝐷 𝐷⁄ 𝑖𝑛𝑐) 𝑀𝐶 _Diff. (%) (𝐾 𝐾⁄ 𝑖𝑛𝑐) 𝑒𝑥𝑝 (𝐷 𝐷⁄ 𝑖𝑛𝑐) 𝑀𝐶 _Diff. (%) (𝐾 𝐾⁄ 𝑖𝑛𝑐) 𝑒𝑥𝑝 (𝐷 𝐷⁄ 𝑖𝑛𝑐) 𝑀𝐶 _Diff. (%) 1 0.499 ± 0.057 0.491 ± 0.001 +1.6 0.576 ± 0.061 0.557 ± 0.001 +3.3 0.618 ± 0.065 0.634 ± 0.001 -2.7 2 0.540 ± 0.059 0.550 ± 0.001 -1.8 0.605 ± 0.068 0.58 7 ± 0.001 +2.8 0.638 ± 0.066 0.637 ± 0.001 +0.1 3 0.575 ± 0.060 0.561 ± 0.001 +2.4 0.661 ± 0.066 0.648 ± 0.001 +1.9 0.690 ± 0.069 0.667 ± 0.001 +3.3 4 0.522 ± 0.058 0.537 ± 0.001 -2.9 0.610 ± 0.066 0.606 ± 0.001 +0.6 0.643 ± 0.064 0.630 ± 0.001 +1.9 5 0.549 ± 0.062 0.544 ± 0.001 +1.0 0.623 ± 0.065 0.606 ± 0.001 +2.8 0.655 ± 0.069 0.639 ± 0.001 +2.5

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2

C

HAPTER

2

This chapter describes the main innovative results in dosimetry for DM and DBT obtained with previously described and validated MC code. The first paragraph regards the DBT-specific dosimetry for the most used commercial DBT units, by using a homogeneous breast phantom with the adoption of a new skin model. The characterization of DgNDBT numbers versus breast density, compressed breast thickness and beam quality is presented, and interpolation conditions are explored. Complete results regarding DgNDBT values are reported in Appendix A and Appendix B. The second paragraph investigates the adoption of a new digital breast phantom which disengages from the homogeneous mixture of glandular and adipose tissues within the breast, by involving a heterogeneous glandular distribution. Differences in terms of glandular dose are explored and a proposal of its adoption in dosimetry is reported. The adopted GEANT4-based MC code (v. 10.5) has been developed with a collaboration with the Medical Physics group of the University of Naples. It represents a substantial improvement of an old MC code [2], completely reviewed and upgraded.

2.1 DgN coefficients for commercial DBT systems using a

homogeneous breast model

2.1.1 DgNDBT coefficients

Formalisms described in par. 1.2 demonstrate the continuous renewal, over the time, of MC models and dose coefficients for converting the air dose in mean glandular dose (or average glandular dose), in sight of both new technical updates (new anode/filter combinations involved in actual DM units) and new founding in literature regarding more accurate models. Any new update found over a clinical dataset of patients can certainly refine the state of the art of MC calculations and consequently the accuracy of dose estimates. Two publications, Huang et al. (2008) [36] and Yaffe et al. (2009) [45], led to revalue the need of recalculation of dose coefficients for digital mammography. The first study was aimed to quantitatively characterize the breast skin thickness by using a dedicated breast CT scanner, founding a mean breast skin thickness value of 1.45 ± 0.30 mm, with a dedicated composition not ascribable to the adipose tissue, bringing down the assumption of considering the adipose skin of 4-5 mm of thickness. The study of Yaffe brought to

33

light a mean glandular fraction far from what was assumed to be the standard breast of 50% glandularity, by deriving a mean glandular fraction by volume of 14.3% over a study involving 2831 women. In sight of these evidences, obtained with a quantitative 3D technique, Sarno et al. [35] derived new DgN conversion coefficients for almost all digital mammography units, by considering seven anode/filter combinations, and for a wide range of anatomical breast characteristics, by simulating compressed breast thicknesses ranging from 2 to 9 cm and glandularities of 0.1, 12.5, 14.3, 25, 50, 75 and 100%, giving the chance to interpolate coefficients due to the potential anatomic variability. Multiple MC calculations were performed to cover the wide range kV that could be used, each of them with two HVL values, for interpolating for the beam quality too.

While in digital mammography dose estimates are not influenced by slight differences in geometrical setup, like source to image detector or FOV, on the other hand, DBT procedures require a suitable protocol for glandular dose estimates dedicated for the specific DBT unit. Currently, clinics can rely on multiple commercial tomosynthesis devices, each one having specific geometries; Dance et al. [24] showed a consistent dependence of conversion coefficients from the DBT scan angle, suggesting appropriate T-factors (see par. 1.2.1 and Fig. 1.15a) for each commercial apparatus.

In line with previous works on MC simulations regarding dosimetry in mammography, in which the author of this thesis was engaged [1], [2], [35], [46], [47], a collaboration between the Medical Physics group of the University of Pisa and that of the University of Naples has been carried on, in order to perform DBT-specific MC calculations, helpful for various breast models with thickness ranging from 2 to 9 cm and glandularities of 1, 25, 50, 75, 100%. The MC code and the methodology involved are described in par. 1.3 and 1.4.

In this work, six DBT systems commercially and clinically available have been subject of simulations: GE SenoClaire, GE Senographe Pristina, Hologic Selenia Dimensions, Fujifilm Amulet Innovality, IMS Giotto Class, Siemens Mammomat Inspiration. For the GE apparatuses a double target/filter choice is used; Senographe Pristina commonly uses for breasts below 30 mm thick the Mo/Mo combination and Rh/Ag otherwise, while SenoClaire uses Mo/Mo for 20-mm thick breast and Rh/Rh target/filter combination for the other cases; Fujifilm Amulet Innovality provide a double DBT scan modality: standard modality (ST mode) with a 15 degrees scan angle and high definition modality (HD mode) with a 40 degrees scan angle.

Tab. 2.1 summarizes the main characteristics of the DBT systems as implemented in the simulations. The purpose of this work was aimed to provide DgNDBT coefficients data capable of