Università degli Studi di Napoli Federico II

Scuola Politecnica e delle Scienze di Base

Collegio di Scienze

Dipartimento di Fisica ”Ettore Pancini”

Corso di Laurea Magistrale in Fisica

TESI DI LAUREA SPERIMENTALE IN FISICA MEDICA

3D printed phantoms for X-ray breast imaging

Relatori Candidato

Prof. Paolo Russo Dott. Antonio Varallo

Prof. Giovanni Mettivier matr. N94/276

Anno Accademico 2018/2019

1

List of Contents

Introduction 1

Chapter 1 Digital phantoms: a valid aid for breast cancer research 4

1.1 Introduction 4

1.2 Full Field Digital Mammography 6

1.3 Digital Breast Tomosynthesis 8

1.4 Breast anatomy 11

1.5 Digital phantoms 15

1.5.1 Breast simulator 16

1.6 Virtual clinical trials: VCTs 20

Chapter 2 - Design and realization of 3D printed breast phantoms 23

2.1 Introduction 23

2.2 Additive manufacturing technology 22

2.2.1 Stereolithographic Laser Additive (SLA) 25

2.2.2 Sintering Laser Selective (SLS) 26

2.2.3 Fused Deposition Modelling (FDM) 27

2.3 U Varna, Univ. of Naples, Univ. of UC Davis: the VCT project 28

2.3.1 Simulation algorithm for soft tissue compression: SASTC 33

2.4 Breast physical phantoms used for 2D and 3D breast imaging 38

2.5 Phantoms printed in this work 39

Chapter 3 - Experimental validation of 3D printed breast phantoms 40

3.1 Introduction 48

3.2 PMMA stepwedge validations 50

3.3 Measurements: data and results 61

Appendix A 81

Appendix B 83

Appendix C 84

References 85

Acknowledgments 90

2

Introduction

Breast cancer is the first type of cancer by population and mortality female. The current

most popular method for early detection of breast cancer is x-ray mammography, a screen-

ing exam of breast tissue based on the contrast generated by differences in attenuation of x-

rays along their path through the tissue. This exam return two images projections (cranio-

caudal, CC, and mediolateral oblique, MLO) with a delivery of a low dose of x-rays in the

tissue (of the order of a few mGy). A major problem for an efficient detection of abnormal-

ities in the glandular tissue (where the cancer can develop) is the presence of a high glan-

dular fraction (ratio of glandular mass to glandular+adipose tissue masses). Such so-called

dense breasts generate high superposition of the tissues and the cancer mass may not be

visible with sufficient contrast. Hence, new techniques have been introduced in recent

years for aid breast cancer diagnosis, which return three-dimensional images, including

digital breast tomosynthesis (DBT) and computed tomography dedicated to the breast

(BCT). These new techniques have the advantage of producing dozens or hundreds of pro-

jections (instead of two as in CC+MLO views in mammography) from various angular

views around the compressed breast (in DBT) or the uncompressed breast (in BCT). With

appropriate algorithms and digital analysis, the anatomy of breast tissues can be recon-

structed in different planes transverse to the direction of the beam, so obtaining a three-

dimensional representation of the breast anatomy.

The new diagnostic techniques must be validated in clinical trials before entering

the clinical routine. Clinical trials are expensive and they can delay regulatory evaluation

of innovative technologies, affecting patient access to high-quality medical products. Alt-

hough computational modeling is increasingly used in product development, it is rarely at

the center of regulatory applications.

In the last years, with the increasing power of computers, virtual clinical trials

(VCTs) have been proposed in breast imaging. VCTs do not involve real patient but they

involve experiments using computer simulations and methods for validating new clinical

imaging systems or techniques. VCTs produce simulated images of the breast with or

without lesions. They may also provide glandular dose estimates. The medical physics re-

search team at Univ. Napoli Federico II have recently started a VCT project in breast im-

aging. For validating these virtual trials. 3D breast modelling, for 2D and 3D breast x-ray

imaging, would benefit from the availability of digital and physical phantoms that repro-

duce accurately the complexity in density and shape of the breast anatomy.

3

While a number of digital phantoms have been produced with increasing level of complex-

ity, physical phantoms reproducing the digital phantoms have been scarcely developed.

One possibility is offered by 3D printing technology, which, since a few years, is em-

ployed in many scientific and medical fields. For this reason, studies to investigate ther-

moplastic material have recently started for evaluating the x-ray attenuation property of

different thermoplastic materials in the diagnostic energy range 10-150 keV. The produc-

tion of anatomically realistic 3D printed breast phantoms with these plastic materials, used

in the 3D printing manufacturing, is the purpose of this my thesis; in particular this work

concerns the study of these phantoms tested for digital mammography and DBT.

The content of this work is divided in 3 chapters.

In the first chapter, after a description of the breast anatomy, we describe the importance

of the digitals phantoms and the use of one of the many software utilized in breast cancer

research, named “BreastSimulator” that permits to generate realistic digital phantoms and

to simulate a diagnostic exam as can be mammography, tomosynthesis or cone-beam

breast computed tomography to obtain synthetic breast images. Furthermore, a description

of the importance of virtual clinical trials is given.

The second chapter focuses on the various 3D additive printing techniques on the market

today in particular focusing on the melt filament printing used during this work. In addition

to the notions of 3D printing, we illustrate the VCT project and its potential in the field of

breast cancer research; we also describe the compression code for digital phantoms devel-

oped by the medical physics research team of the University of Varna. Finally, a brief de-

scription is given of the phantoms already on the market for imaging both in 2D (mam-

mography and DBT) and in 3D (BCT) with the description of the design used to print

them.

In the third chapter we give a description of the two radiological imaging techniques, en-

countered in this thesis work is provided, and are showed the results, of the measurement

about the absorbs of different materials used in this work, acquired at San Raffaele Hospi-

tal (Milan – Italy) and at the San Giovanni di Dio and Ruggi D'Aragona Hospital (Salerno

– Italy).

4

Chapter 1

Breast digital phantoms: a valuable aid for breast cancer

1.1 Introduction

Breast cancer is still the common form of cancer diagnosed in worldwide women today

and it contributes to over 4% of all European female deaths [1]. In the last tens years, the

detectable lesions, that the doctors diagnose, are grooving in numbers. The reason of this,

on the one hand should be sought like bad eating habits that we have in your life, for ex-

ample: bad diet, smoking, sedentary; on the other hand it depends from genetics factors,

age of the people and exposure to ionizing radiations. Not only the life style and the genet-

ics factors but above all the new technologies that have been discovered in the scientific

field in the last twenty years, have allowed professionals changes in the sector to diagnose

new pathologies that were ignored before. Better detectors for images acquisitions and vis-

ualizations was developed in the last years. For this reason is very important to follow rec-

ommended screening guidelines, which can help detect certain cancers early [1].

Fig.1.1: Number of new cases of cancer in 2018 (Italy), females, all ages[International Agency For Research

on Cancer].

As reported on web from The Global Cancer Observatory (GCO), an interactive web-

based platform presenting global cancer statistics to inform cancer control and research,

one of the most common cancers in the female is breast cancer [2]. The incidence of this

5

pathology increases in women over the forty. Instead about men is more common detect

prostate cancer, colon cancer, lung cancer [3]. There are many studies in literature that

confirm the importance of the early screening mammographic [4].

Fig.1.2: Number of new cases of cancer in 2018,both sex, all ages. [International Agency For Research On

Cancer]

Looking at the trends shown in the table in figures above, it is clear that the number of new

cancer cases in 2020 will increase therefore so the only modality to prevent and treat this

disease scrupulous and timely screening is recommended [3]. It is important to contrive a

new form of faster screening, that firstly protects the human tissue from radiation dose dur-

ing the radiographic exams, reduces waiting time, provides a targeted and rapid diagnosis

not on the physical patient but on the digital patient-based tissue and organs and at same

time it provides the synthetic acquisition of detailed images of the patients: we acts on the

digital breast phantoms or physical breast phantoms and not on the breast human tissue. As

we see in the section 1.2 of this work, there are many studies in the literature that confirm

the importance of digital phantoms for X-ray imaging study and for assurance quality dur-

ing the instrumental exams.

6

Digital phantoms that could be used in in-silico clinical trials should include a large

number of samples, so to have a large dataset containing different virtual patients, each

with its own characteristic on which to apply the different x-ray imaging techniques. The

digital phantoms features are closest to the human tissue or organs that they reproduced.

In the figure 1.3, is shown a table with the incidence, mortality and prevalence by cancer

site as reported from the International Agency for Research On Cancer.

Fig.1.3: The table showed in this figure report the incidence, mortality and prevalence by cancer site estimate

in Italy in 2018.[ http://gco.iarc.fr/today/data/factsheets/populations/380-italy-fact-sheets].

1.2 Full Field Digital Mammography (FFDM)

Digital Mammography is currently the most valid primary diagnostic tool for the detec-

tion of breast tissue anomalies in screening exam. It use x-ray radiations, in the range of

20-32 kV to obtain 2D projections of a 3D breasts. Over the years, the mammography sys-

tem has been optimized several times: the radiographic films previously in use have been

totally replaced by flat panel detectors (a-Se or CMOS) they are qualified an electrical con-

trol that is digitized and saved so that it can be processed later. The transition from the ana-

logic to digital images has brought enormous benefits in the breast cancer research. The

images are more in contrast than in the past and the radiation to obtain the same images is

7

reduced. Then from to digital 2D we are passed to 2D /3D digital scan and in the last years

totally 3D is coming out for breast cancer detect [43] [44].

Figure 1.2.1 : a) X-ray tube adopted in a conventional diagnostic screening imaging, b) Showed a tipical

mammographic exam. In this modality is acquired a CC view of the breast [www.cancer.gov].

The 2D images obtained are characterized by pixels with a side of 50-100 μm. In addition

to the aforementioned detector, the apparatus essentially consists of an X-ray tube and a

breast compression puddle, as shown in Figure 1.2.1. A metal foil (filter) is mounted in

front of the Beryllium window of the X-ray tube from which the X-ray beam comes out,

the purpose of which is to attenuate the spectral intensity of the low-energy photons, that is

harmful to the tissues because they are totally absorbed with respect to the high energy

photons which contribute to the transmission image [25]. In both 2D digital mammography

and tomosynthesis exams, the x-rays are transmitted to high-resolution computer monitors

with electronic tools that allow the images to be magnified or manipulated for more de-

tailed evaluation. Digital images are stored in a computer system called a PACS (picture

archive communication system) in DICOM format file. This allows the radiologist to re-

trieve previous exams for comparison from year to year and to manipulate the images for

complete viewing. The presence of the filter is generally worked with polyenergetic beams

and photons energy greater than about 10 keV. On the other hand, compression of the

breast is necessary because:

reduce the scattered radiation throughout the medium

reduce the dose of radiation absorbed

the contrast of the image is better

X-ray tube

8

The imaging detector has a typical size of 18 x 24 cm2 or [24 x 30] cm

2 (full field). Two

projections for each breast are acquired during the mammogram exam; a cranio caudal

view (CC) and a medio lateral oblique (MLO) view for a total of four 2D projec-

tions.(figure 1.2.1)

Figure 1.2.1: Standard Digital Mammogram Images: Cranio-Caudal (CC, left) and mediolateral oblique

(MLO, right) views of 48 year-old woman with palpable lump in upper outer left breast show heterogeneous-

ly dense tissue which may obscure small masses.[ https://eu.densebreast-info.org/breast-mammography-

tomosynthesis.aspx]

A limit in its diagnostic efficacy lies in the diagnosis of tumor mass in the particularly

dense breasts: in these, in fact, the high percentage of glandular tissue can "protect" a spe-

cific tumor lesion, or suggest the presence of a non-existent lesion. The problem can be re-

duced through new diagnostic tools, such as breast computed tomography (breast comput-

ed tomography, BCT), which we will analyze in follow sections.

1.3 Digital Breast Tomosynthesis (DBT)

Digital breast tomosynthesis (DBT) is a reduced scanning angle tomographic technique in

which the x-ray tube, rotating around its axis, it can cover an angle from 0° to 50°. In fig.

1.3.1 is showed a DBT scan modality. The set-up is formed by an x-ray tube rotating

around a horizontal axis (with an rotating Tungsten anode and an acceleration potential of

(23-49 kV) which, in a certain range of angles, acquires a series of low-dose projections of

9

the compressed breast and by an algorithm, are reconstructed in a slice of 1mm in thick-

ness.

Figure 1.3.1: a) Modality of images acquisition in digital breast tomosynthesis. If the breast present abnor-

mality: cyst (A), ductal cancer (B) or calcification (C) during a mammographic exam all anomalies in the

projection are superposed or missed. In DBT technique also, images of anomalies are acquired from different

angles, so the projections are polish from the superposition problem. b) Mammography unit for digital breast

tomosynthesis installed at San Raffaele Hospital in Milan(Italy).

During the examination, the three-dimensional nature of tomosynthesis, however, requires

less compression of the breast, which constitutes greater comfort for the patient than for

the mammography itself. The devices on the market acquire between 11 and 50 projec-

tions, in an interval of angles between 15° and 60° and in times that between 5 and 25 sec-

onds.

FFDM and DBT has flat panel digital detectors for imaging display. This device gives a

reduced reading time, minimum ghosting (due to residual images in subsequent acquisi-

tions), and minimal reduction of efficiency at low exposure; It principle at the base of im-

10

aging formation is the energy integrating type; the X-ray-energy of beam when reach the

pixels detectors is converted in an electric charge and then in a voltage signal.

Figure 1.3.2: A) Digital Mammography in cranio-caudal view in which calcificatios are visible, B) A slice of

the same breast in digital Tomosynthesis modality. [https://www.hologic.com/hologic-products/breast-

skeletal/selenia-dimensions-mammography-system#resources].

Figure 1.3.3: Scheme of a typical flat panel detector functioning for digital data acquisition.

The pixel size of the detector is in the order of 75-100 μm; approximately, the voxel size of

the image reconstructed depends from the n projections (with n variables between 9 and

25, in commercial apparatuses) turns out to be in the order of 100 μm × 100 μm × 1 mm.

The definition of the slice of reconstructed tissue, typically 1-2 mm in the z direction (i.e.

11

in the direction orthogonal to the detector), however, does not indicate the resolution in

that direction, which instead is a function of the angular interval at which the tomography

is defined The dose of radiation glandular is higher but comparable with that of a mammo-

gram (about 1.5 mGy).

1.4 Breast anatomy

The breasts are paired structures positioned on the anterior thoracic wall. It extends hori-

zontally from the lateral border of the sternum to the mid-axillary line, located between the

third and sixth intercostal spaces [5]. They are present in both males and females, yet are

more prominent in females following puberty. The breast is therefore an even organ, that

is, composed of two symmetrical organs whose components are the skin, the mammary

gland and the adipose connective tissue. The mammary gland rests on the pectoralis major

muscle, from which it is separated by a more or less adipose thick layer. A flap of mamma-

ry tissue extends to the axillary cavity. Each breast woman has very personal characteris-

tics in shape and in size, mainly due to the greater or lesser presence of fat and its distribu-

tion in it that determines the size of the breast (fig.1.4.1).

Fig. 1.4.1: The breast anatomy in sagittal view.[4]

The function of women's breasts tissue is that to produce milk (glandular tissue) as well as

fatty tissue. The milk-producing part of the breast is organized into 15 to 20 sections,

called lobes. Within each lobe are smaller structures, called lobules, where milk is pro-

duced. The milk travels through a network of tiny tubes called ducts. The ducts connect

and come together into larger ducts, which transfer milk from the lobules to the nipple. The

12

dark area of skin surrounding the nipple is called the areola. Connective tissue and liga-

ments provide support to the breast and give it its shape. Nerves provide sensation to the

breast. The breast also contains blood vessels, lymph vessels, and lymph nodes. According

to cancer statistics, one over ten women during her life may could develop breast cancer

[5]. Breast cancer is an abnormal multiplication of cells in the breast and this phenomenon,

if not treated in time, can also spreading organs and tissues surrounding the area of the

outbreak. Breast cancer occurs almost exclusively in women, although men can be affect-

ed. The are many type of abnormality of which the breast is subject and it depends on the

area in which the disease is been generated; signs of breast cancer include a lump, bloody

nipple discharge, or skin changes. The most important cancer are:

Ductal carcinoma in situ: breast cancer bounded in the ducts cells (Figure.1.4.3).

Figure 1.4.2: Localization and evolution of a ductal carcinoma in situ.[https://www.cancer.org/cancer/breast-

cancer/understanding-a-breast-cancer-diagnosis/types-of-breast-cancer/dcis.html]

13

Figure 1.4.3: A) Progression of breast cancer and the histopathology of DCIS. B-E) Progressive stages of

high-grade breast cancer as defined by histopathology [7].

Lobular carcinoma in situ: breast cancer which occurs in the milk-producing lobule

cells (Figure.1.4.4).

Figure 1.4.4: A) Progression of breast cancer and the histopathology of DLIS.[ https://www.cancer.gov] B)

Progressive stages of high-grade breast cancer as defined by histopathology. [8]

Invasive ductal carcinoma: breast cancer that begins in the duct cells but then in-

vades deeper into the breast, Invasive ductal carcinoma is the most common type of

invasive breast cancer.

Invasive lobular carcinoma: breast cancer that begins in the milk-producing lobule

cells. Invasive lobular carcinoma is an uncommon form of breast cancer.

14

Breast calcifications: calcium deposits (CaCO3) in the breast are a common finding

on mammograms. This calcium deposits are clustered or isolated in the breast tis-

sue. The pattern of calcium might suggest cancer, leading to further tests or a biop-

sy (Figure.1.4.5) [9].

Simple breast cyst: a benign abnormality fluid-filled sac that commonly develops in

women in their 30s or 40s. Breast cysts may cause tenderness and may be drained.

Metastasis commonly occurs through the lymph nodes. It is most likely to be the axil-

lary lymph nodes that are involved because they become stony hard and fixed [3]. Fol-

lowing this, the cancer can spread to distant places such as the liver, lungs, bones and

ovary.

To assess a suspected breast cancer a triple assessment is carried out. This involves

clinical examination, diagnostic imaging using mammogram in 2D or 3D with or

without contrast, magnetic resonance and ultrasound, and finally a biopsy [10][11].

Figure 1.4.5: Mediolateral oblique (MLO) projection (on the left) and detail of the MLO view of the breast(

on the right). A small cluster of calcifications is seen in the circle ROI. [https://radiologykey.com/group-1-

one-or-two-clusters-of-crushed-stone-like-calcifications-of-the-mammogram-produced-by-malignant-

processes/]

The staging of breast cancer uses the I-IV stady or the Tumour Node Metastasis (TNM)

system as in detail showed in Appendix A. In figure 1.4.6 is illustrated the evolution in size

of the tumor.

15

Fig. 1.4.6: The tumor growth in female breast. [https://www.cancerresearchuk.org/about-cancer/breast-

cancer/stages-types-grades/tnm-staging]

Surgical treatment with adjuvant radiotherapy is the recommended treatment option.

The operation is local and aims to remove only the affected tissue area. Failing this it is

considered that a mastectomy is the best option. Adjuvant chemotherapy is also known to

improve survival rates [10].

1.5 Digital phantoms

Breast cancer, as we could see, is one of the most common cancers that affect women dur-

ing their life. The Achilles Heel of screening mammography is the detection of this male of

the century in females. These abnormalities of the breasts earlier are diagnosed, more like-

ly it is that people affected by this disease will come out unscathed. The goal of the re-

search in this field is to have more and more detailed and contrasted images during a diag-

nostic examination, minimizing the radiation dose supplied by the system scan that is given

to exposed tissues or organs, reducing the time of acquisition for each exam [11]. The first

level screening examination for breast cancer remains mammography [12]. This technique

return 2D images of a 3D object, but how we can see in the chapter 3 it has its limitation

respect to others new system x-ray scan where can be produced 3D projections acquired

from different angles, such as digital breast tomosynthesis (DBT) and breast computed to-

mography [13][14]. Such images are also useful in the development of new methods for

early detection and correct diagnosis of the breasts.

So, computational models for breast cancer research are important for the development of

new breast imaging techniques and dedicated computer-aided detection (CAD), including

machine learning systems that can assist in the detection and classification of the various

types of breasts [15][16][19]. Recently, there has been an acceleration in breast phantom

16

development for x-ray imaging systems, due to different motivations. The first reason as

mentioned above, include the advent of new 3D breast imaging modalities; the need to op-

timize these modalities including hardware design and acquisition geometry. The second

reason is concerned about the necessity to developing new approaches to constancy and

acceptance testing of the major x-ray imaging technique and finally the need of assessing

regulatory submissions to prove safety and effectiveness of these new breast imaging de-

vice [17].

The research during these years have created some platforms to create performed digital

phantoms and the focused set-up to investigate them [18]. In this work of thesis we will

give some information about one of the most important platform for generate breasts phan-

toms and synthetic images projections in silico of them: it is BreastSimulator. It is a soft-

ware that has been used by the team of the medical physics of Naples for some internation-

al studies [20][21][22]. In the section that follow we describe this platform and its potenti-

ality in medical physics research.

1.5.1 BreastSimulator

BreastSimulator is a software platform that permits to create digital breast phantoms and

pull out parameters correlates to the breast x-ray imaging quality and dosimetry. This soft-

ware is been developed by the team of Professor Kristina Bliznakova based at University

of Varna (Bulgaria) and at Department of Medical Physics of Varna also, and Professor

Nicolas Pallikarakis based at Department of Medical Physics, School of Medicine, Univer-

sity of Patras, (Greece). In the work of Bliznakova et al. (June, 2012) is been presented the

potentiality of this platform and its versatile characteristics [20].

BreastSimulator was created to allow the fidelity reproduction of the anatomy and

shape of the breast and for the digital simulation of the mammographic, tomosynthesis and

tomographic imaging system. The software returns a 3D representation of the simulated

anatomy and for example the mammographic projections (with monochromatic or poly-

chromatic X-ray beam) of the mammary simulacra ("phantoms") created by the user. It is

possible to model in detail normal or damaged breasts and to analyze the quality and fideli-

ty of the projections. This software is dedicated for breast x-ray imaging research, in par-

ticularly dedicated for breast cancer; it consists of four modules divide so:

17

Breast Modeling Module: for create three dimensional breast models with uncom-

pressed and compressed shape. In consist of others sub-modules that are utilized to

mimic the different breast components: glandular, fat and skin tissue, lesions, lym-

phatics (Fig.1.5.1.1).

Figure 1.5.1.1: A screenshots of the software application: a) design of breast components and setting the ex-

ternal dimensions; b) design of two clusters of ten calcifications each; c) a breast phantom without skin; d) a

composite model that contains the elemental compositions of the simulated breast tissues.

Compression Module: for simulate the mechanical compression of the breasts with

the Young’ modulus corresponding to each tissue (Table 1.5.1.1).

Table 1.5.1.1: Is reported the Young’s modulus for each tissue. *[Kellner et al.(2000)]

Image Generation Module for obtain mammographic projection images from the

visualization on the detector of x-ray photons, after that they across the phantom

breast.

The object that we imaged can be to contact to detector or distant to the detector so we

could have different quality images acquires. We define magnification (M) for the im-

age :

𝑀 =𝑆𝑜𝑢𝑟𝑐𝑒 𝑡𝑜 𝑑𝑒𝑡𝑒𝑐𝑡𝑜𝑟 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑆𝑜𝑢𝑟𝑐𝑒 𝑡𝑜 𝑜𝑏𝑗𝑒𝑐𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒=

𝑆𝐷𝐷

𝑆𝑂𝐷

Tissue Young’s modulus, (kPa)*

Adipose 1.0

Glandular Tissue 10.0

Skin 88.0

Calcification 43.0

Cyst 17.0

18

Figure 1.5.1.2: Simulations set up of x-ray mammography. SOD and SDD are source to object and source to

detector distances respectively.

This module contains information for the acquisition geometry, (e.g distances from the

source to the abject plane and detector), detector type, gantry angles and other imaging

parameters. It is possible to set both polychromatic and monocromatic beams for the

simulated acquisitions. Once the phantom has been created and the beam has been set up,

it is possible to perform mammography, tomosynthesis and tomography virtually [22]. It

possibile to choose the geometry of the beam that can be pencil, cone beam or parallel.The

dector module is a phosphors-based detectors (CsI, Gd2O2S) coupled with charge coupled

devices. The device is optimized for the Modulation Transfer Function of the detector also.

Main parameters of interest are the SOD and the SID, the acquisition angle, the number of

projections and the path of x-ray when they start from the source and arrive to the detector.

When phantoms are created, some foundamental parameters are finded so as: attenuation

coefficient of the breast, the mean glandular dose (MGD), it is the mean dose that the gland

acquired during the exam and the air Kerma [33][36]. The source emits a number No of x-

ray photons with energy sampled from the incident energy distribuition E0 towards each

pixel of the detector. The attenuation due to the presence of breast phantom along the

radiation direction, is calculated by adding the contributions of each voxel. The trasmitted

energy E reaching the detector pixels is calculeted using Lambert-Beer’s law:

𝐸 = ∑ 𝐸𝑗𝑁𝑗 ∗ 𝑒𝑥𝑝 (− ∑ 𝜇𝑖𝑑𝑖

𝑛

𝑖=1

)

𝐸𝑚𝑎𝑥

𝑗=𝐸𝑚𝑖𝑛

19

where [Emin - Emax] is the energy of the incident beam at the X-ray source, n is the

number of voxels in the breast phantom, μi and di are the attenuation coefficient and the

total path length that x-ray radiation cover when across a single voxel.

If we want to know the incident photon fluence, we exploit the relations between the

incident air kerma K, measured at the upper surface of the breast phantom and the photon

fluence [43][44].

𝐾𝑐,𝑎𝑖𝑟 = [𝜇𝑒𝑛

𝜌]

𝑎𝑖𝑟

∙ 𝐸 ∙ 𝜑

where Kc,air is the incident air kerma, E is the energy of the incident photons, φ is the

photon fluence and [𝜇𝑒𝑛

𝜌⁄ ]𝑎𝑖𝑟

is the mass energy absorption coefficients for air. Then the

air Kerma is derived from the relationship with the mean glandular dose (MGD):

MGD = K∙g∙c∙s

where g, c and s are the conversion factors depending on factors like breast thickness,

glandularity and incident spectra. The MGD values in mGy are defined according to the

European guidelines for quality assurance in breast cancer screening and diagnosis for a

standard unilateral mammography [33][36].

Visualization Module is finally the last part of the chain in software where it is pos-

sible to visualize the all simulation.

In figure 1.5.1.3 is shown a screenshot of the visualization module where it is possible to

watch the digital phantom and the synthetic mammogram in the figure 1.5.1.4 shown a

scheme of the entire chain of the Breastsimulator platform.

Figure 1.5.1.3: Visualization Module: a) mammography image display and b) 3D visualization of generated

breast models.

20

Figure1.5.1.4: A schematic chain of the main functionalities of the BreastSimulator software.

1.6 Virtual clinical trials (VCTs)

The number of tumors is growing more and more in the last years. Guidelines suggest early

screening to identify possible cancers as soon as possible. The main tools for the develop-

ment, optimization and evaluation of new techniques for imaging screening and diagnos-

tics are modeling and simulation. They reduce analysis times and waiting time as happen

in a real exam and reduce the dose effects produced by ionizing radiation on the biological

tissue of the patients; therefore virtual trial play a crucial role in the evolution of scientific

research. The possibility of having optimized devices for investigation and for scanning,

minimizing at the same time the dose rate to the patients, allows to the experts to have a

more precise diagnosis of the analyzed details or abnormalities that are inner the human

tissue. For this reason, the validation of any imaging system is challenging due to the

several number of system parameters that should be evaluated. In the other hand, the

long waiting times that patients have to endure for a diagnostic examination or for a clini-

cal trials and in parallel the rapid technological progress related to computing power in the

field of information technology, have led researchers, operating in this field, in the last

years to develop or consider a new way, or if we want, a preclinical alternative. For the

validation of clinical trials and optimization the various x-ray diagnostic techniques that

use x-ray radiation , for example: full field digital mammography (FFDM), digital breast

tomosynthesis (DBT), cone-beam breast CT (CBBCT) technique (these technique will dis-

cuss in the third Chapter) and Magnetic Resonance Imaging (MRI). The aim to have a vir-

tual clinical protocol and an reply of the setup used during the radiographic or diagnostic

exam, gives to the medical researches, the possibility to create in silico everything one

21

needs to conduct a real X-ray diagnostic exam; it is possible create digital breast phantoms

that reproduce or mimic the human pattern tissue in attenuation, in shape and in glandular

disposition inside the breast [25][30][33]. Not only digital phantoms with or without tu-

mors but it is possible create in silico digital detectors for the visualization of the images,

an X-ray beam source with appropriate geometry for to improve imaging quality in the

scan system and in this modality to reduce the dose to be given to the breast or other tis-

sues during the exam. It is also possible, but hardest to reproduce not only the primary ra-

diation path but the secondary radiation ( radiation scatter) also. The problem of scattered

radiation is been solved via MonteCarlo simulations code. [29] For the words mentioned

above virtual clinical trials are need. The term “virtual clinical trial” represent a clinical

trial in silico where there are no humans involved in it.

Thanks to the technological development in the many scientific fields of the last

decades, digital modeling and simulation techniques have been perfected to the point of

guaranteeing very realistic results. The main objective of breast x-ray simulations is to ob-

tain two-dimensional radiographic images. In particular, starting from two-dimensional

projections from various angles of view, it is possible to simulate tomographic images that

reproduce the attenuation of breast tissue in 3D [26][28].

Simulating an entire "imaging system" means creating a model of the individual

components of the system (detector, X-ray spectrum, sample to be analyzed) and of the

procedures: transport of radiation within the same, purchases of geometries and objects

same. Digital simulations are used by appropriate computer codes and using different algo-

rithms; described as output the generation of two-dimensional mammographic image pro-

jections. At the end of the simulation you will find the degree of evaluation of the radiation

dose absorbed by the radiographed object, the quality of the radiography and the validity of

the whole process. Among the different methods to simulate mammography, the most

common one simulates the transport of the beam through the sample using the exponential

implementation of the incident X-ray beam. This approach, based on ray-tracing algo-

rithms, provides to obtain images quickly but, unfortunately, simulates only the effects of

primary radiation and not the diffuse ones, and also does not allow to accurately stimulate

the radiation dose. An alternative method is applied by the use of simulation codes called

"Monte Carlo", which reproduces the stochastic interaction of the beam and the use of also

treating diffuse radiation. These codes are specific to each application and can be used to

generate very realistic artificial mammograms that facilitate the understanding of particular

aspects of imaging. Often these Monte Carlo codes derive from programs written for high

22

energy physics systems, such as the EGS5 code (developed at SLAC) and the GEANT4

code (developed at CERN). Today an integrated virtual clinical trial design program,

VCT designer, and a virtual clinical trial management program, VCT manager, are

freely available [27].

Validation of any imaging system is challenging due to the huge number of

system parameters that should be evaluated. The ultimate metric of system performance is

a clinical trial. However, the use of clinical trials is limited by cost and duration.

In addition, trials involving ionizing radiation require repeated irradiation of volunteers,

which may be impractical. In particular, breast-screening trials have a low incidence of

disease; therefore, radiation must be used judiciously. Therefore, strong proponents

of a preclinical alternative, in the form of VCTs, which model human anatomy,

image acquisition, display and processing, and image analysis and interpretation.

One of the most important virtual trial is VICTRE project. VCTRE is an acronym of

Virtual Imaging Clinical Trial for Regulatory Evaluation. This project born to attempted to

replicate a previously conducted imaging clinical trial using only computational models

and involved no human subjects and no clinicians [36][24]. All trials steps were conducted

in silico. The fundamental question the VICTRE trial addressed is whether in silico imag-

ing trials are at a mature development stage to play a significant role in the regulatory

evaluation of new medical imaging systems. The VICTRE trial consisted of in silico imag-

ing of 2986 virtual patients comparing digital mammography (DM) and digital breast

tomosynthesis (DBT) systems. The improved lesion, as calcifications cluster or a speculat-

ed mass detection performance favoring DBT is consistent with results from a comparative

trial using human patients and radiologists [24][25].

23

Chapter 2

Design and realization of 3D printed breast phantoms

2.1 Introduction

In this chapter we discuss the most popular types of 3D printing additive manufacturing

technologies, tracing from its origin and that are daily used by experts to create breast

physical phantoms for X-ray imaging. Realize a physical phantom, that can mimic the right

pattern of gland that is present inside the human breast is not easy; but most important it is

difficult to find the correct thermoplastic material that adsorbs X-ray radiation in the same

way or within limits like fat tissue, glandular tissue and skin. In recent years, the attention

of researches has been focused on the study of the absorbance properties in these materials

at in the typical energy used in diagnostic and radiotherapy imaging.

2.2 Additive manufacturing technology

Additive Manufacturing (AM) is a process that to describe the technologies that build 3D

objects by adding layer-by-layer of material, whether the material is plastic filament, metal

and ceramic powder, liquid resins or biocompatible materials. On the market there are to-

day a lot of models of 3D printers, but all model have in common the same principle: add

layer on layer to form the 3D object. The price of a 3D printer is variable and it depend to

the quality, speed, accuracy, built volume of printing and other parameters. Until a few

years ago the cost of a 3D printer was quite prohibitive since only industrial ones existed

and remained exclusive to a few people. Today, however, we can find on the market, 3D

printers of all types and all prices [44]. The additive manufacturing technology (AM) is in

opposite with the subtractive (SM) one by the fact that in the second one, instead of adding

material to obtain an object, it is removed it. (Figure 2.2.1)

In additive type printing, the piece takes shape as the layers are superimposed on

each other and the object is created when this process is finished. Common to AM tech-

nologies is the use of a computer, 3D modeling software (Computer Aided Design or

CAD), machine equipment and layering material. Once a CAD sketch is produced, the AM

equipment reads in data from the CAD file and lays downs or adds successive layers of

liquid, powder, sheet material or other, in a layer-upon-layer fashion to fabricate a 3D ob-

ject.

24

Figure 2.2.1: Two manufacturing modalities [https://www.advancedadditivemanufacturing.co.uk/blog/3d-

printing-vs-cnc-machining-key-differences/]

The term AM encompasses many technologies including subsets like 3D printing, rapid

prototyping (RP), layered manufacturing and additive fabrication. More recently, AM is

being used to fabricate end-use products in aircraft, dental restorations, medical implants,

automobiles, and even fashion products [35][36][37].

There are 3 main chemicals processes in additive manufacturing

Sintering process: it is a chemical process in which the particles of a solid material

in the form of dust, subjected to heating by UV radiations, approach and weld, orig-

inating a piece of compact material (figure 2.2.2).

Figure 2.2.2: Sintering process that occur in SLA technology.

Polymerization process: it is a chemical process that leads to the formation of a

polymeric chain, or a macro molecule made up of many equal parts that repeat in

sequence starting from simpler molecules, called monomers.(Figure 2.2.3)

Figure 2.2.3: A typical reaction of the acrylic monomer is the polymerization chemical process.

Initiator Activated monomer Oligomer Polymer

25

Extrusion process: it is a process that consists in bringing a plastic material to a flu-

id state and forcing it to pass continuously through the shaped profile of a mold

(extruder) where it takes the desired shape (figure 2.2.4).

Figure 2.2.4: a) How go on the filament material inside the nozzle. b) How the material is extruded starting

from the filament feed to the nozzle in the fused deposition technology [37].

2.2.1 Stereolithographic Laser Additive (SLA) technology

The first 3D printing patent dates back to 1984 and is in the name of Chuck Hull, the in-

ventor of stereolithography. The first 3D printed object dates back to 1986. This technique

involves sintering a photo-polymer by means of a laser. Chuck Hull formed the 3D Sys-

tem, one of the first SLS-type 3D printing companies in USA. Hull also developed the .stl

file format for CAD software since each machine needs the input project to function. A

tank contains a special liquid resin (photosensitive epoxy resins) capable of polymerizing if

exposed to light (photo-polymerization). The laser solidifies the resin according to the sec-

tion of the piece to be made, the platform on which the piece under construction is tied is

lowered, the doctor blade eliminates the excess resin and starts again with a subsequent

section to be solidified. This process is repeated until the piece is finished [35].

In stereolithography laser additive, laser cures photopolymer resin (figure 2.2.1.1). It

highly versatile material selection. Highest resolution and accuracy in 3d additive printing

technology, with fine details. It has the inconcenience because it can print only a material

in one time and not two or plus as coming in fused deposition modelling.

a) b)

26

Figure 2.2.1.1: a) 3D printing that use SLA technology. The beam laser is on the top of tank b) Inverted

SLA technology: the beam laser comes from below the tank. c) A view of the beam laser path that exit

from the base of the tank in a SLA technology produced from Formlab Industry (model Formlab 3).

[www.formlab.com]

2.2.2 Sintering Laser Selective (SLS) technology

Laser sintering is an additive technique, dating back to 1987 (Carl Deckard), which uses

thermoplastic, metallic or siliceous powders and uses a laser to sinter the materials used for

the construction of the prototype. Initially, a thin layer of powder is spread from a special

apparatus and the laser sinters where necessary. The table is lowered by the desired quanti-

ty, another layer of dust is spread and the whole is repeated (Figure 2.2.2.1).

Somewhat like SLA technology Selective Laser Sintering (SLS) utilizes a high

powered laser to fuse small particles of plastic, metal, ceramic or glass. During the build

cycle, the platform on which the build is repositioned, lowering by a single layer thickness.

The process repeats until the build or model is completed. Unlike SLA technology, support

material is not needed as the build is supported by unsintered material [36].

a) b)

c)

27

Figure 2.2.2.1: Sintering laser selective set-up technology.

2.2.3 Fused Deposition Modelling (FDM) technology

The fused deposition modeling technique (FDM) or also known as Fused Filament Manu-

facturing (FFF) was developed by S. Scott Crump in the late 1980s and marketed in the

1990s by Stratasys Inc. It uses an additive manufacturing process by extruding thermo-

plastic material. Process oriented involving use of thermoplastic (polymer that changes to a

liquid upon the application of heat and solidifies to a solid when cooled) materials injected

through indexing nozzles onto a platform. The nozzles trace the cross-section pattern for

each particular layer with the thermoplastic material hardening prior to the application of

the next layer. The process repeats until the build or model is completed and fascinating to

watch (figure 2.2.3.1). Specialized material may be need to add support to some model fea-

tures. Similar to SLA, the models can be machined or used as patterns. Very easy-to-use

and cool.

Figure 2.2.3.1: a) The extruder(1) lay layer by layer thermoplastic material on the built plate to create

3D object, b)operating principle of a FFF printer technology.

28

We must remember that in a 3D printing with a melted filament technique, the object will

not be completed full even we by setting filling factor at 100% but a piece will be empty. It

is estimated that around 2% is air and depends on the technique and printing accuracy (fig-

ure 2.2.3.2). This problem not occur in SLA manufacturing technique (figure 2.2.3.3).

Figure 2.2.3.2: a) Problems that arise when we print with double extruder or with only one. There is a

limitation in FDM printing technology.

Figure 2.2.3.3: a) No problems occurs about fill factor in printing with SLA technology,. There is not

vacuum between one layer and others surrounding.

2.3 Univ. of Varna, Univ. of Naples, Univ. of UC Davis: the VCT project

In a VCT for breast imaging, simulate both the breast (compressed or not, of date tissue

composition, given shape and size), and the irradiation apparatus (X-ray spectrum emitted

by the tube, irradiation geometry). The topic of this thesis is related to the VCT in the field

of breast imaging, which involves the evaluation of BCT, its possible optimization, and the

its comparison with DBT and DM. In particular, in the project in which I entered, construc-

tion is planned of a database of digital breast puppets, created in collaboration with the

University of California, Davis, starting from a dataset of about 100 pendulous breasts

scansed via cone-beam breast computed tomography technique (BCT). These pendulous

29

breast phantoms will then be compressed via software for the realization of mammographic

and tomosynthesis digital phantoms and then by 3D additive manufacturing it will be to re-

alize physical compressed and uncompressed breast phantoms. The Monte Carlo simula-

tions of the radiation (BCT, DBT and DM) will allow to determine the 3D distribution of

the glandular dose ( dose map) in the organ, and will allow the realization of a set of syn-

thetic images in the three imaging techniques, whose analysis will determine the results of

the VCT. The collaboration between the University of Naples Federico II(ITALY), the

University of California Davis(USA) and the Technical University of Varna(Bulgaria),

aims to create a database of realistic digital phantoms of uncompressed breast, in order to

perform virtual tests on BCT technology , and compare the DBT and DM techniques.

Since BCT is a relatively new technology, it must be both of a complete dosimetric charac-

terization and of appropriate optimizations for the spectrum, geometry and components of

the screening apparatus, used to improve imaging. The virtual phantoms, used on BCT

clinical scans on patients (then used in Monte Carlo simulations of BCT acquisitions with

spectra used in the clinic) will allow tests to be carried out both through 3D distribution

studies of the glandular dose, and for studies on image quality. For this purpose, a Monte

Carlo code has been set, which simulates the irradiation with: digital three-dimensional

noises of the uncompressed breast, belonging to a dataset which includes about 100; they

were obtained from healthy sinus scans performed with a BCT clinical scanner operating at

80 kV, used at the University of California Medical Center in Davis.

Figure: 2.3.1: A schematic set-up of cone-beam breast computed tomography where the position of patient is

supin on the bed of the scanner. This scanner type was used at UC Davis Medical Center for acquire all im-

ages which permitted to us to beginning this work.

30

These scans were subsequently processed with a semi-automatic algorithm, capable of

segmenting the image and classifying its voxels into four different categories, correspond-

ing to glandular tissue, fatty tissue, epithelial tissue and air; the dimensions of these voxels

are 0.25 × 0.25 × 0.35 mm3.

BCT scan parameters, such as X-ray spectrum, detector size, and scan geometry. On out-

put, the code returns the glandular dose distribution within the breast model and the breast

phantoms projection images not compressed. Figure 2.3.2 shows an example of the Monte

Carlo software output in question: starting from a phantom (obtained by segmenting the

image of a BCT) it is possible to simulate its radiation, and thus obtain a new completely

virtual BCT. Preliminary data deriving from the application of this Monte Carlo simulation

was presented, in June, at the 2nd International Conference on Monte Carlo Techniques for

Medical Application (MCMA), 2019 [11].

Figure 2.3.2: a) Clinical breast CT scan acquired at UC Davis Medical Center; b) Segmented via algorithm

CT phantom in four components: skin, adipose, glandular and air. c) Simulated CT phantom via MonteCarlo

simulations[ Sarno et al. (2019, Montreal Congress)].

In order to compare the BCT technique with digital mammography and digital

tomosynthesis, the breast model can be processed with additional software, which creates a

virtual compression of the digital phantom, keeping in mind the 28 properties of elasticity

of breast tissue. In this way it is possible to obtain, for each uncompressed puppet, a corre-

sponding puppet that describes the anatomy of the same virtual breast if compressed. The

software module, created by the University of Varna group, generates a specific compres-

sion for each puppet, based on the anatomy of the latter, obtaining different results, for ex-

ample, in the case of more or less dense breasts. Carlo described above allows virtual clini-

cal tests to be carried out on the phantoms, which consist in simulating their irradiation

even with units for BCT other than that used by the University of California, Davis.

31

Among these, the units designed respectively by Advanced BCT Imaging, in Germany,

and by the Koning Corporation, in Rochester (US), shown below. AB-CT Imaging, Ger-

many, designed and marketed an innovative scanner. The position of the patient during the

examination is the same as that of other BCT devices, but the image irradiation and image

acquisition system, is completely original (figure 2.3.3)

Figure 2.3.3: Breast CT scanner produced by AB-CT

First of all, it is characterized by a spiral orbit, and not circular, like all the other apparatus-

es: this means that, at a motion orbital around the isocenter (characteristic also of the other

apparatuses for BCT) for the detector and the X-ray tube, a translator and vertical motion is

combined; in a time interval of 10 seconds, about 2000 projections are made, which have a

resolution of the order of 0.1 mm. The X-ray tube operates at 60 kV. Another important

and innovative feature compared to the other devices is given by the geometry of the detec-

tor, which is not a flat panel, but a linear array CdTe detector. The x-ray beam is specially

shaped in such a way as not to cover the entire height of the breast, but only a fraction of

the order of 2-3 cm; this allows the use of a detector only a few cm high, but sufficiently

long to accommodate the image of the entire breast (i.e. about 20 cm). The detector nor-

mally used for this type of unit is a cadmium telluride (CdTe) detector. It is a semiconduc-

tor detector, which works in counting mode of single X-rays which, transmitted by the fab-

ric, arrive in each of the pixels of the detector (single photon counting SPC technology).

The images produced have a high signal-to-noise ratio, for the same dose, due to the SPC

type detector, and a high spatial resolution.

32

Unlike the new scanner, the Koning Corporation BCT unit, known as KBCT, has been on

the market since 2011. The Koning Corporation was founded by Professor Ruola Ning in

2002 as a spin-off from the University of Rochester (USA), with whom he had previously

collaborated on the making of BCT prototypes (the first prototype dates back to 1989).

(figure 2.3.4).

Figure 2.3.4: Koning Breast Computed Tomography scanner. [www.koning.it]

The scanner consists of a pulsed X-ray tube, ie characterized by "flash" X-ray emissions,

which operates at 49 kV, in step with an acquisition rate of 30 fps and a flat panel detec-

tor, equal to the one present in the first UC Davis prototype. This scanner produces 300

projections per second, from which images with voxel of about 0.25 mm side are recon-

structed, in the standard acquisition mode; however, there is the possibility of using the

unit also in High Resolution mode, which allows you to acquire an image with voxel of

about 0.17 mm in side. As anticipated, this apparatus is currently on the market, and scans

have been performed on about 100 patients (as illustrated in the literature), both with and

without injected contrast medium. The results obtained from the use of the unit made it

possible to affirm that, like the other BCT devices, the KBCT unit is characterized by a

high sensitivity to contrast (which further increases if a contrast medium is injected), and

effective localization of lesions. The resolution at which these results are observed is how-

ever worse than that which characterizes mammograms, since even if the high definition

acquisition mode is used, the size of the voxel will be greater than that of the pixels of a

mammogram. However, the technique has the advantage of 3D isotropic reconstruction .

The medical physics group of this department has been carrying out a project for a couple

of years together with the research group of the University of Varna in Bulgaria, whose

33

leader is Professor Kristina Bliznakova and the group of the University of Davis in Cali-

fornia which leader is Professor and Biomedical Engineer John Boone. The purpose of this

collaboration is to create a dataset of phantoms dedicated to the digital breast, which can be

used for validation in both 2D and 3D imaging. The platform to be created should offer

both digital phantoms of healthy breasts that have a variable percentage of glandular tissue

and digital phantoms with inclusions of tumors, fibers and calcifications. In addition to

providing the user with digital phantoms, the VCT project also aims to create puppets

through the use of 3D printing. These puppets can be used for quality checks in radiologi-

cal imaging, for image quality in the 2d (mammography) or 3 d technique (tomosynthesis

and computerized tomography dedicated to the breast). For the insertion of tumors, refer-

ence is made to the database of the already existing MAXIMA project carried out by the

University of Varna (Bulgaria) and which also group 5 of this department collaborates.

(Fig. 2.3.5)

Figure: 2.3.5: A screenshot of the web site of MAXIMA project.

2.3.1 Simulation algorithm for soft tissue compression: SASTC

Breast compression is an essential part of mammography and tomosynthesis and is an im-

portant component in producing high quality mammographic images. Breast compression

optimizes the image quality and hence the visualization of small lesions by reducing the

breast thickness. Compression also reduces the radiation dose to the breast, since the X-

rays pass through shortened breast thickness and therefore their attenuation decrease as

well. Finally compression minimizes the breast movement of the patient, which would

34

eventually cause blurring effects in the mammograms. Breast compression is a physical

process relevant to the processes of tissue shiftiness and deformation. For this reason a

code for compress digital breast phantoms is wrote by prof. Kristina Bliznakova and her

research’s group at Technical University of Varna (Bulgaria) [Bliznakova et al.(2007)].

This code as mentioned in Chapter 1, permit to create compressed digital phantom begin-

ning from a uncompressed digital phantoms for the result to print a physical compressed

phantom by 3D printing fused deposition technology. The phantom so realized could be

utilize for mammographic and tomosynthesis test for evaluation X-ray quality imaging pa-

rameters and for quality assurance but also to study different breast imaging techniques in-

volving compressed and uncompressed breasts. How this compression code act on the

breast or on the model? The compression solution in this code is reached using random

processes based on simple rules and boundary restrictions. The term SASTC is for simula-

tion algorithm for soft tissue compression. To understand how this code work and how it

pull out the result, in this code are introduced the following terms: model, elements, nodes,

spring between the nodes. The model is the volume of interest subjected to compression

simulation. This volume is divided into elements that are composed of a set of N*M*K

voxels. The term node represent the voxel. Each node is surrounded by other nodes. In fig-

ure 2.3.1.1a is shown model divide into elements. Elements consist of 27 nodes, as each

one (except the boundary nodes) is connected with 26 neighbor nodes. Each element has a

corresponding node at its center; thus the elements are as many as the nodes and the center

of each element overlaps with its central node. [Bliznakova et al. (2007)].

The nodes in the elements are connected with springs. A spring can be defined by two pa-

rameters: modulus of elasticity E and equilibrium length, Deq (fig.2.3.1.1b.).

Figure 2.3.1.1: Model components: a) element of the model, b) Equilibrium lengths of the springs between a

central and one of its surrounding nodes. Each sphere represent a voxel tissue.

35

If we suppose that a spring is deformed to a new length D. This action will result in a force

F that will appear at the spring edges in a direction parallel to the spring and of magnitude

given:

𝐹 = 𝐷𝑒𝑞 − 𝐷

𝐷𝑒𝑞∗ 𝐸 (1)

In this algorithm we assume the spring modulus of elasticity is to be linear and isotropic.

This means that E has a constant value for all the range of deformations that can be applied

on the spring. Each node represents a tissue sample and hence it inherits the modulus of

elasticity of that tissue. The spring between a central and one of its surrounding nodes in an

element has three components in the x, y, z directions. To simplify the model, the value of

the modulus of elasticity between two springs is assumed to be equal to the smaller one.

Each element is divided into eight sub-elements. A sub element is composed of eight

nodes, some of which are common with other sub-elements.(figure 2.3.1.2a). The mean

compression of a sub-element can be easily calculated as follows:

∆𝑧𝑚𝑒𝑎𝑛 =(𝑁001 − 𝑁000) + (𝑁101 − 𝑁100) + (𝑁011 − 𝑁010) + (𝑁111 − 𝑁110)

4 (2)

If we assume that the volume under compression is constant, we may introduce the concept

of spring variable equilibrium lengths that depend on the compression level. For this pur-

pose, the spring equilibrium lengths Deqx and Deqy are recalculated according to Eq 3. The

variable Nxyz shown in figure 2.3.1.2 and Eq.2, represent the z position of the node in the

volume under compression. The new x and y dimensions of the sub-element are defined by

means of expressions (3), (3.1), (3.2), assuming that the expansion along the axis x is equal

to the expansion along the axis y.

∆𝑧 ∗ ∆𝑦 ∗ ∆𝑥 = 1 ; ∆𝑦 = ∆𝑥 ; ∆𝑥 = ∆𝑦 = √1

∆𝑧 (3)

Where ∆x, ∆y and ∆z represent the x, y and z dimensions of the sub-element. The tissue

that correspond to the sub-elements can considered homogeneous and therefore the sub-

elements can expand symmetrically in the x-y plane during its compression. The forces

that arise between a central and its surrounding nodes are graphically depicted in figure

2.3.1.b.

36

Figure 2.3.1.2: A) The sub-element of an element; B) Forces exerted between a central and one surrounding

nodes.

According to the law of action-reaction, the forces that act on central node when it is driv-

en out of its equilibrium are equal in magnitude, and with an opposite sign, to the forces

that act on its surrounding nodes. In order that the central node is in equilibrium with its

neighbors, it is moved to a new position. This position can be defined as follows:

𝑋𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 =𝐹1𝑥 + 𝐹2𝑥 … + 𝐹26𝑥 + 𝐹𝑋𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙

𝐸1𝑥 + 𝐸2𝑥 + ⋯ + 𝐸26𝑥+ 𝑋0 (4)

𝑌𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 =𝐹1𝑦 + 𝐹2𝑦 … + 𝐹26𝑦 + 𝐹𝑌𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙

𝐸1𝑦 + 𝐸2𝑦 + ⋯ + 𝐸26𝑦+ 𝑌0 (4.1)

𝑍𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 =𝐹1𝑧 + 𝐹2𝑧 … + 𝐹26𝑧 + 𝐹𝑍𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙

𝐸1𝑧 + 𝐸2𝑧 + ⋯ + 𝐸26𝑧+ 𝑍0 (4.2)

Where Fix, Fiy, Fiz are the forces along x, y and z axis that are exerted on the central node

due to its surrounding nodes, and Fxexternal, Fyexternal, Fzexternal are the corresponding forces

that are exerted on the central node due to external factors (i.e gravity). If the central node

is translated from a point (X0, Y0, Z0) to a point (Xequilibrium, Yequilibrium, Zequilibrium), the net

forces that will act on it at this new position, according to expressions (4), (4.1), (4.2). For

each tissue, the modulus of elasticity is defined according to published data by Wellman et

al.(1999) [Wellman et al.]:

37

𝐸𝑓𝑎𝑡 = 4.5𝑘𝑁𝑚−2; 𝐸𝑔𝑙𝑎𝑛𝑑 = 15𝑘𝑁𝑚−2; 𝐸𝑠𝑘𝑖𝑛 = 17𝑘𝑁𝑚−2; 𝐸𝑎𝑏𝑛. = 45𝑘𝑁𝑚−2

For compress a digital phantom, we must set some parameters: breast matrix size, voxel

reconstruction size, number of iterations (more than 10000 iterations is a good value for

the convergence), positions of the compression puddle during the compression and position

of the compression puddle in front of the chest wall. In figure 2.3.1.3 is shown how the

code act on the digital model; it is stopping to run when accuracy was reached. In appendix

B we report a flowchart of the proposed method.

Figure 2.3.1.3: The breast is compressed in z direction. Breast slices taken laterally (a, b); frontally (c, d),

and craniocaudally (e, f). In the left of the column is shown the uncompressed digital breast. In the right of

the column is shown the compressed breast digital model.

38

2.4 Breast physical phantoms used for 2D and 3D breast imaging

In commerce there are pour phantoms tissue equivalent but not anthropomorphic phan-

toms that reproduce faithfully the pattern of the gland inside fatty tissue. Physical phan-

toms that researches commonly uses for imaging quality and quality assurance in radiolog-

ical techniques as 2D imaging (as mammography) and 3D imaging (as tomosynthesis and

breast cone-beam computed tomography) are create by the vendor CIRS Inc. CIRS is rec-

ognized as a leader in tissue simulation for medical imaging and radiation therapy. A

number of phantoms that are used for breast cancer research are made of epoxy resin. They

mimic glandular tissue or fatty tissue and inside of some of them there are abnormality

such as mass, fibers and calcifications. In the figures 2.4.1(A,B), 2.4.2(A,B), 2.4.3(A,B),

we show a number of physical phantoms that are used for imaging testing for clinical tri-

als and for research.

Figure 2.4.1: A) Breast tissue equivalent phantom used in mammography and in digital breast tomosynthe-

sis.(CIRS mod.011A); B) Breast tissue equivalent phantom used in mammography and in digital breast

tomosynthesis. This phantom is formed to 6 slabs of different thickness (Cirs mod.014A).

Figure 2.4.2: A) Breast tissue equivalent phantom used in mammography and in digital breast tomosynthe-

sis. This phantom is formed to 3 different slabs with different densities (Cirs mod.021A); B) Breast tissue

equivalent phantom used in mammography and in digital breast tomosynthesis. This phantom is formed to 4

different slabs with different densities and different thickness. Inside there are inclusions (Cirs mod.022).

A) B)

A) B)

39

Figure 2.4.3: A) Breast tissue equivalent phantom used in breast computed tomography and in digital breast

tomosynthesis. This phantom is formed to 6 slabs with different inclusions inside: mass, fibers and specks of

calcifications. It a phantom equivalent tissue that mimic 50/50 breast tissue; it is formed by 50% gland tissue

and 50% fat tissue. In figure, white color represent gland tissue and rose color is fatty tissue [Cirs BR3D

mod.020]; B) Insertions presents in a slab.

2.5 Phantoms printed in this work

The first step to creating an anthropomorphic physical phantom to be printed is to have a

stack of images to be segmented . Starting from these, by means of a segmentation code

(Matlab v.R2019), the starting motor in terms of pixel value is divided into 4 parts in

which air is associated to the zero value of the pixel , with the value 1 of the pixel is asso-

ciated to fat tissue, the value 2 associated to glandular tissue and the value 3 to the fat tis-

sue (Figure 2.5.2 (a,b,c,d)) [61].

Once this segmentation procedure is complete, we will find ourselves having 3 stacks of

images each containing a single type of tissue. With the aim of the imageJ software (figure

2.5.1) it is possible to load the various stacks and generate the corresponding .STL file

format through the 3D viewer plugin which will be used for generate the 3D printing. Once

that three CAD are generated in .STL file format, they are loaded onto the slicing soft-

ware Cura, offered free use by the Ultimaker Company (figure 2.5.4). It is possible, load

the CAD file relative to the digital phantom on to Blender software for apply some filters

as smoothing in external and internal surface of the 3D object [60].

A)

B)

40

Figure 2.5.1: ImageJ screenshot panel. This opens source software permit to opens and elaborate images

stack of the phantom and then return, by the plugin 3d Viewer, the CAD in .STL file format for each seg-

mented tissue so to be printed via 3D printer [57].

Figure 2.5.2: A) Compressed digital breast phantom produced by means of tissue classification and digital

compression. B) Segmentation for only skin tissue; C) Segmentation for only fat tissue; D) Segmentation for

only gland tissue. The process of segmentation was made via Matlab (vers. R2019a).[61]

After this routine finally we can load 3D object on Cura software. Cura is a free software

that allows us to see a preview of the layer by layer additive manufacturing as the 3D ob-

ject will be translated (in fact it slicing the model) from the print supplied. Through care it

is possible both in the material with which the object will be printed, and in the resolution

with which it wants to be made and in this case some parameters imported into 3D printing

come into play:

- height of layer: which defines the thickness in height of the extruded filament.

-the extrusion width: with which our material will be extruded

-the temperature with which we want to print the filament

41

- the temperature of the printing plate on is building the object

- the type of support between the object and the printing plate

- the fill factor relative to the infill material

- the robustness and surface patter with which to make the print

Figure 2.5.3: A screenshot of the panel of Blender software [61].

Figure 2.5.4: A screenshot of the panel of Cura software [59].

Beginning from CT data scan acquired at UC Davis in California, we create segmentation

for all three different tissue: gland tissue, adipose tissue and skin tissue. When we have the

stack of images segmented we can create the respectively CAD via ImageJ by 3D viewer.

Building plate

(20x20x18) cm

Setting print core size

and materials

Setting parameters

for the printing

42

Then for create the gcode file format that permit to print the 3D object or breast tissue we

use a free slicing software, in our case the software is Cura. On Cura software we can set-

ting all printing parameters. The 3D printer that we have used for create all phantoms is a

fused deposition modelling printer model Ultimaker 3. This 3D printer can extrude 2 dif-

ferent filaments at once in time.( figure 2.5.1) .

Figure 2.5.5: Digital 3D segmented tissues of the breast phantom. In the column on the left, there are seg-

mented tissues(skin(A), fat(B) and gland(C)) after smoothing (20 x) is applied on them by Blender software.

In the right column (D-E-F) the same segmented tissues are reproduced without smoothing filter [61].

A) D)

B)

C)

E)

F)

43

It is possible to notice in the figure 2.5.5 that smoothing filter remove pixels in the seg-

mented images and so the external and internal surfaces don’t combine perfectly after this

process. For resolve this problem, smoothing filter may act only on the external surface .

This is possible by Meshmixer software that give to the user to remove the roughness

which is present on the external surface of the skin.

Figure 2.5.6 A) 3D printer used for create all phantoms(mod. Ultimaker3). The printing features are reported

in appendix C of this work; B) The view of two extruders from 0.4 mm that it possible to change for printing

[41].

During my thesis work, a number of breast phantoms that mimic the shape and glandular

pattern of a female breast are printed in the laboratory of medical physics at the University

of Naples Federico II. They are printed by the fused deposition modelling technology.

Thermoplastic filaments that are used for build these phantoms are: ABS (acrylonitrile-

butadiene-styrene), PET(polyethylene terephthalate ), PLA( polyvinyl alcohol).

The choice of these materials, used for the realization of these materials is necessary for

the studies done previously on these materials [51][52][53]. We wanted to evaluate the be-

havior of some of these materials for the attenuation property of fatty tissue, adipose tissue

and glandular tissue, in the range of energy between 15÷30 keV, energies that occur dur-

ing the diagnostic tests indicated in the breast imaging. Below in the next figures are a se-

ries of images of printed phantoms in order of printing time. All the phantoms present in

these works are composed only with two different material. The possibility of printing

phantoms with 3 or more materials is postponed to future studies. In this way it will also be

A)

B)

44

possible to print inclusions provided within them as calcifications and masses. In the figure

2.5.2 is shown filament of ABS, PLA and PET material before extrusion (with a diameter

of 2.85mm) and post extrusion (diameter is in the range 0.42 ÷ 0.47 mm).

Figure 2.5.7 Filaments used for printing all phantoms presented in this work. Filaments before the extrusion

and after the extrusion. The diameter size of the filament extruded represent the resolution in height.

Figure 2.5.8 Breast phantom with skin(white) separate from gland and fat tissue. Fat and gland are joint in

one object.

The printing for to produce all phantoms take a time variable from only 2 hours (step-

wedge thickness 5mm extruded with nozzle 0.25 mm in diameter) to more 9 days ( breast

phantom (DM1857) for print object with 65 mm in thickness compound with ABS and

PLA.

PLA orange

Ø= 2.85 mm

Ø= 0.47 mm

PLA white

Ø= 2.85 mm

Ø= 0.47 mm

ABS blue

Ø= 2.85 mm

Ø= 0.45 mm

PET trasparent

Ø= 2.85 mm

Ø= 0.42 mm

45

Figure 2.5.9: Phantoms in printing and printed. In the figure the white material is PET and the blue material

is ABS. On the left of the figure we printed in 2 different steps skin and glandular tissue separately.

Figure 2.5.10: A) Breast phantom Mammo2L2 printed all in one. In the figure the white material is PET and

the blue material is ABS. B) The same breast phantom during the printing.

Figure 2.5.11: A) Breast phantom DM57 after 9 day and 3 hours is printed. B) During the printing of

DM1857 breast. In the figure the white material is PLA and the blue material is ABS.

A)

B)

A) B)

46

Figure 2.5.12: A) Uncompressed breast phantom CT1857 positioned for testing, on the support of the gan-

try between the flat panel detector and the X-ray tube. B) During the printing of CT1857 breast phantom. In

the figure the white material is PET and the blue material is ABS. It has took more of 7days for printing this

phantoms.

Figure 2.5.13: Breast phantoms printed in three different step. A) View of half printed phantom with 20 mm

in thickness. B) View of the second half phantom with 14mm in thickness; C) View of the envelope of the

skin for the integer breast phantom and half breast phantom. D) Printing the only envelope skin tissue.

Breast phantom

“CT1857”

A) B)

A) B)

C) D)

47

A number of stepwedges are been printed during this work. Descriptions of the materials

that are used for the stepwedge 3D phantoms are the same used for building 3D breast

phantoms. The size of each stepwedge is reported in the third chapter.

Figure 2.5.14: A screenshot of the panel of Tinkercad, a free app that permitted to realize the 3D stepwedg-

es in three different sizes [58]. In blue color stepwedge with maximum height 60 mm and minimum height

equal to 30 mm. In grey color (in the middle of the work plane) is reported the stepwedge with maximum

height 20 mm and minimum height equal to 6mm and in white color is the stepwedge with maximum height

5mm and minimum height equal to 1mm.

Figure 2.5.15: Stepwedge phantoms printed in 3 different size and in 3 different materials to calculate atten-

uation property of materials: PET(trasparent), ABS(blue) and PLA(white). In this figure the third step-

wedge(size L) is missing because it was in printing when photo was acquired.

48

Chapter 3

Experimental validation of 3D printed breast phantoms

3.1 Introduction

The approach currently used in clinical practice is attenuation X-ray imaging. It is based

on the contrast generated by differences in the absorption of the X-rays along their path

through a biological tissue or plastic object used for testing (phantoms). In the case of the

tissues with weak absorption capacity, such as the soft tissue, the conventional attenuation

method leads to poor image quality . As showed in figure 3.1 when the normal and

tumor tissues have similar X-ray attenuation properties, becomes difficult to distinguish

them using the attenuation based method.

Figure 3.1.1: Linear attenuation coefficients for different breast tissues components as a function of the x-ray

energy. [Bravin et al. (2013)] b) Different interactio between X-ray and soft tissue at the energy of typical

diagnostic range (17-150 keV).[Hammerstein et al.]

This typically occurs, in clinical tests, such as mammography and angiography, in which it

is often necessary to resort to specific contrast agent, that alter the contrast of an organ, or

a of lesion respect to its surroundings, in order to make visible details that otherwise would

not be appreciable. In figure (1.1) is shown the dependence of the mass absorption co-

efficient, μ, of the adipose, breast, muscle and water in the X-ray energy. Using absorption

imaging method, soft tissue differences are only apparent at low energies (below 50 keV)

producing images with low contrast. In this work we focused the attention only about ab-

sorption imaging and not about phase contrast imaging that it is evident when we use as a

radiation beam a synchrotron radiation.

49

In precedent works of Ivanov et al. (2018) and Esposito G. et al. (2018) are discuss the ma-

terial attenuation property that are to be considered in 3D printed breast phantoms when

we use them for X-ray imaging studies testing or quality control. In the figure above is il-

lustrated the relative difference in attenuation coefficients μ (%) obtained by measurements

at the European Synchrotron Radiation Facility (ESRF) with respect to the breast tissue,

glandular tissue and skin at synchrotron radiation for 30 keV, 45 keV and 60 keV. In this

work we want to pull out the materials behave, in radiation attenuation, at energies below

30 keV, typical energy range used in breast imaging with the mammography and digital

tomosynthesis acquisition modality.

Figure 3.1.2: Relative difference in attenuation coefficients between gland and others plastic materi-

als/tissue obtained by measurements at ESRF with respect to the breast gland tissue for 30 keV, 45 keV, 60

keV.

Figure 3.1.3: Relative difference in attenuation coefficients between gland and others plastic materi-

als/tissue obtained by measurements at ESRF with respect to the breast adipose tissue for 30 keV, 45 keV, 60

keV.

50

Figure 3.1.4: Relative difference in attenuation coefficients between gland and others plastic materi-

als/tissue obtained by measurements at ESRF with respect to the breast skin tissue for 30 keV, 45 keV, 60

keV.

3.2 PMMA stepwedge validation procedure

The most popular phantoms (CIRS phantoms) that are in commerce, are been used by the

research in medical physics yesterday and today for testing the quality of images and for

dosimetry control in diagnostic imaging, are made in PMMA (Polymethylmethacrylate)

material. The X-ray absorption of PMMA material is known in literature [Hammerstein et

al.]. So for calibrate, your measurement, two PMMA stepwedge phantoms are used in our

procedure. In table 3.1.1 are reported the heights of the stepwedge. While in table 3.1.2 is

reported the X-ray spectra used for to acquire all projections of the PMMA stepwedge in

cranio-caudal modality at San Raffaele-Milan.

For the images acquisitions, it was used a Mammomat Inspiration Digital Breast Tomosyn-

thesis (Siemens Inc.) device, located at HS Hospital, while a Selenia Digital Breast Tomo-

synthesis devise (Hologic, Inc., Bedford, MA, USA) was used at San Giovanni Di Dio and

Ruggi D’Aragona Hospital (Salerno-Italy). The characteristics of these two devices are

shown in table 3.1. All projections were acquired in February 2020 thanks a strong collab-

oration between medical physics group of University of Naples to department of medical

physics of San Raffaele Hospital (Milan-Italy) and department of medical physics of San

Giovanni di Dio e Ruggi D’Aragona Hospital (Salerno-Italy).

51

Mammomat Inspiration

( Siemens)

Selenia Dimension

(Hologic)

Voltage 18-49 kV 18-49 kV

Anode Mo/W W

Filter Mo/Rh/ Rh/Ag/Al

Filter thickness 0.05 mm (Rh)

0.03 mm (Mo)

0.05 mm (Rh/Ag)

0.70 mm (Al)

Focal spot 0.3 mm 0.3 mm

Field of view 240 x 300 mm 240 mm x 290 mm

Image size (1996 x 2457) pixels

Pixel dector size 0.085 x 0.085 mm 0.070 x 0.070 (binning)

SID 650 mm 700 mm

Detector type

(energy integrating)

FPD+scintillator(CsI)

FDP + CCD(a-Se

FPD+scintillator(CsI)

FDP + CCD(a-Se)

Table 3.2.1: Technical characteristic of the two devices used for the radiographic projections acquisition

Figure 3.2.1: Hologic Selenia Dimensions mammography installed at Ruggi Hospital (Salerno); B)

Siemens Mammomat Inspiration mammography device installed at San Raffaele Hospital (Milan).

A) B)

52

Table 3.2.2: PMMA stepwedge thickness

Table 3.2.3: Spectra X-ray tube used for the imaged for PLA, ABS and PET stepwedge materials at San

Raffaele Hospital (Milan – Italy).

PMMA stepwedges size (mm)

L M

60 22.24

44.20 14.08

36.40 8.16

28.24 4.10

24.18 2.10

Spectra used for X-ray tube

Anode/Filter kV mAs (semi-auto)

Mo/Mo

26 27.6

28 20.5

30 16.0

32 13.1

Mo/Rh

26 25.6

28 19.4

30 15.6

32 13.0

W/Rh

26 28.8

28 22.7

30 18.9

32 16.1

Mo/Mo

26 76.1

28 50.8

30 36.0

32 26.7

Mo/Rh

26 63.4

28 44.6

30 33.4

32 26.0

W/Rh

26 65.4

28 49.3

30 38.9

32 31.2

53

When a monochromatic radiation beam crosses a medium with variable density the attenu-

ation that the beam undergoes can be calculated from the Lambert-Beer law:

𝐼 = 𝐼0𝑒−𝜇𝑥 (1)

where :

I represent the intensity of the beam that exit from the object and reach the detector,

I0 is the intensity of radiation beam, or background intensity.

μ represent the attenuation coefficient that in this case not depend from the beam

energy and the density of the material and from electronic density.

x is the thickness of the material that radiation beam across before to reach the de-

tector

When we have a heterogeneous medium that varies in same direction of the beam, the

Lambert-Beer law can be rewritten as :

𝐼 = 𝐼0𝑒− ∫ µ(𝑥)𝑑𝑥𝑏

𝑎 (2)

In this case (b-a) represent the thickness of material and the attenuation coefficient varies

along the direction x in the material.

When we have a polychromatic radiation the Lambert-Beer law become:

𝐼 = ∫ 𝐼0𝐸𝑒− ∫ µ(𝑥,𝐸)𝑑𝑥

𝑏

𝑎 𝑑𝐸 (3)

in this case attenuation coefficient and the intensity beam depend by energy also.

For the measurements reported in this work, we can use the relation (1), because we as-

sume of are in good geometry (scattered radiation is reduced) so we can invert the relation

(1) to obtain the linear relation between the logarithmic attenuation and the thickness of

material.

−𝑙𝑛 (𝐼

𝐼0) = 𝜇𝑥 (4)

54

In this relation µ represent the slope of the linear curve between logarithmic attenuation

and the thickness of material.

For the calculation of attenuation materials used in this work for printing breast phantoms

measure of I and Io are acquired by ImageJ. ImageJ is an open source image processing

program designed for scientific multidimensional images that contain many tools for the

elaborations of images. Initially, we load via ImageJ, the images acquired in cranio-caudal

projections (figure 3.2.5)

Then, for the measure of the attenuation coefficient we make a rectangular ROI inside the

stepwedge and we calculate by the tool Measure the value of I. We repeat the same pass

for the region of background and we measure the value of I0.

After this passages we can know the attenuation I/I0 of the stepwedge thickness phantom

and their value that are reported in figure 3.2.6.

The attenuation coefficients, as the energies vary, of the materials used in this thesis work

are reported in the table 3.2.4 below:

𝝁 (cm-1

)

FAT GLAND SKIN PLA PET ABS PMMA

Energy

(keV)

0,93

(g/cm3)

1,04

(g/cm3)

1,09

(g/cm3)

1,217

(g/cm3)

2,167

(g/cm3)

1,04

(g/cm3)

1,19

(g/cm3)

15 0,9663 1,5943 1,6950 1,5346 1,3760 0,8415 1,314

15,1 0,9505 1,5673 1,6655 1,5091 1,3532 0,8288 1,292

15,2 0,9356 1,5402 1,6372 1,4835 1,3316 0,8164 1,271

15,3 0,9204 1,5132 1,6088 1,4592 1,3101 0,8042 1,251

15,4 0,9058 1,4872 1,5816 1,4336 1,2885 0,7924 1,230

15,5 0,8913 1,4612 1,5533 1,4093 1,2670 0,7807 1,210

15,6 0,8772 1,4352 1,5260 1,3862 1,2470 0,7693 1,190

15,7 0,8631 1,4102 1,4998 1,3618 1,2267 0,7580 1,171

15,8 0,8493 1,3863 1,4737 1,3387 1,2066 0,7464 1,151

15,9 0,8356 1,3624 1,4475 1,3168 1,1869 0,7351 1,133

16 0,8223 1,3385 1,4225 1,2949 1,1675 0,7240 1,114

16,1 0,8109 1,3177 1,4007 1,2754 1,1509 0,7148 1,098

16,2 0,7996 1,2979 1,3789 1,2559 1,1347 0,7057 1,083

16,3 0,7886 1,2782 1,3581 1,2377 1,1188 0,6968 1,067

16,4 0,7779 1,2584 1,3374 1,2194 1,1032 0,6881 1,052

16,5 0,7673 1,2397 1,3178 1,2022 1,0878 0,6794 1,038

16,6 0,7570 1,2210 1,2982 1,1847 1,0729 0,6710 1,023

16,7 0,7469 1,2033 1,2786 1,1678 1,0582 0,6628 1,009

16,8 0,7370 1,1856 1,2600 1,1513 1,0439 0,6547 0,995

16,9 0,7273 1,1679 1,2415 1,1350 1,0298 0,6468 0,982

17 0,7178 1,1513 1,2230 1,1190 1,0160 0,6390 0,969

55

17,1 0,7084 1,1346 1,2055 1,1035 1,0025 0,6313 0,956

17,2 0,6993 1,1180 1,1881 1,0881 0,9893 0,6238 0,943

17,3 0,6902 1,1024 1,1718 1,0732 0,9762 0,6164 0,931

17,4 0,6815 1,0868 1,1543 1,0584 0,9634 0,6091 0,918

17,5 0,6729 1,0712 1,1380 1,0441 0,9510 0,6021 0,906

17,6 0,6642 1,0566 1,1216 1,0295 0,9383 0,5950 0,894

17,7 0,6556 1,0410 1,1053 1,0150 0,9258 0,5879 0,882

17,8 0,6470 1,0256 1,0893 1,0009 0,9135 0,5809 0,871

17,9 0,6387 1,0109 1,0735 0,9870 0,9015 0,5741 0,859

18 0,6305 0,9963 1,0581 0,9734 0,8897 0,5674 0,848

18,1 0,6235 0,9836 1,0444 0,9614 0,8793 0,5616 0,838

18,2 0,6165 0,9710 1,0311 0,9497 0,8692 0,5560 0,828

18,3 0,6096 0,9588 1,0181 0,9382 0,8593 0,5504 0,819

18,4 0,6028 0,9467 1,0052 0,9269 0,8495 0,5449 0,809

18,5 0,5962 0,9349 0,9926 0,9158 0,8399 0,5394 0,800

18,6 0,5897 0,9232 0,9801 0,9048 0,8304 0,5341 0,791

18,7 0,5833 0,9119 0,9680 0,8941 0,8211 0,5288 0,782

18,8 0,5770 0,9006 0,9560 0,8835 0,8120 0,5237 0,773

18,9 0,5707 0,8896 0,9444 0,8732 0,8030 0,5186 0,765

19 0,5647 0,8788 0,9328 0,8631 0,7942 0,5137 0,756

19,1 0,5587 0,8682 0,9214 0,8531 0,7855 0,5087 0,748

19,2 0,5528 0,8577 0,9103 0,8433 0,7769 0,5038 0,740

19,3 0,5470 0,8474 0,8993 0,8335 0,7686 0,4990 0,732

19,4 0,5413 0,8373 0,8885 0,8240 0,7602 0,4943 0,724

19,5 0,5357 0,8274 0,8779 0,8148 0,7521 0,4896 0,716

19,6 0,5302 0,8176 0,8675 0,8055 0,7441 0,4851 0,708

19,7 0,5247 0,8081 0,8573 0,7965 0,7363 0,4806 0,701

19,8 0,5194 0,7986 0,8473 0,7876 0,7285 0,4761 0,694

19,9 0,5141 0,7894 0,8373 0,7789 0,7209 0,4717 0,686

20 0,5086 0,7796 0,8269 0,7698 0,7129 0,4673 0,679

20,1 0,5041 0,7712 0,8179 0,7620 0,7062 0,4636 0,672

20,2 0,4995 0,7630 0,8092 0,7544 0,6996 0,4600 0,666

20,3 0,4950 0,7549 0,8006 0,7469 0,6932 0,4564 0,660

20,4 0,4907 0,7470 0,7922 0,7394 0,6868 0,4528 0,654

20,5 0,4864 0,7392 0,7838 0,7323 0,6806 0,4493 0,648

20,6 0,4821 0,7315 0,7756 0,7251 0,6744 0,4458 0,642

20,7 0,4778 0,7239 0,7676 0,7180 0,6683 0,4425 0,636

20,8 0,4737 0,7166 0,7596 0,7111 0,6623 0,4391 0,630

20,9 0,4697 0,7092 0,7518 0,7043 0,6563 0,4358 0,625

21 0,4657 0,7020 0,7441 0,6975 0,6505 0,4325 0,619

21,1 0,4617 0,6948 0,7365 0,6909 0,6448 0,4293 0,613

21,2 0,4577 0,6879 0,7291 0,6843 0,6391 0,4261 0,608

21,3 0,4539 0,6810 0,7218 0,6779 0,6335 0,4230 0,603

21,4 0,4501 0,6742 0,7145 0,6715 0,6281 0,4198 0,597

21,5 0,4463 0,6676 0,7074 0,6652 0,6226 0,4167 0,592

56

21,6 0,4427 0,6610 0,7004 0,6591 0,6172 0,4137 0,587

21,7 0,4390 0,6545 0,6935 0,6530 0,6120 0,4107 0,582

21,8 0,4352 0,6480 0,6866 0,6468 0,6064 0,4075 0,577

21,9 0,4314 0,6417 0,6798 0,6406 0,6011 0,4041 0,572

22 0,4278 0,6354 0,6732 0,6345 0,5956 0,4010 0,566

22,1 0,4246 0,6298 0,6672 0,6294 0,5912 0,3985 0,562

22,2 0,4217 0,6244 0,6614 0,6243 0,5867 0,3960 0,558

22,3 0,4186 0,6190 0,6556 0,6192 0,5824 0,3936 0,554

22,4 0,4157 0,6136 0,6499 0,6142 0,5781 0,3912 0,550

22,5 0,4127 0,6084 0,6443 0,6094 0,5740 0,3889 0,546

22,6 0,4099 0,6032 0,6387 0,6045 0,5696 0,3866 0,542

22,7 0,4070 0,5980 0,6333 0,5997 0,5656 0,3842 0,538

22,8 0,4042 0,5930 0,6278 0,5950 0,5615 0,3819 0,534

22,9 0,4014 0,5880 0,6226 0,5904 0,5575 0,3796 0,530

23 0,3987 0,5831 0,6173 0,5857 0,5534 0,3774 0,526

23,1 0,3959 0,5782 0,6121 0,5812 0,5495 0,3751 0,522

23,2 0,3932 0,5735 0,6070 0,5767 0,5456 0,3729 0,519

23,3 0,3906 0,5687 0,6020 0,5722 0,5418 0,3708 0,515

23,4 0,3880 0,5640 0,5970 0,5679 0,5380 0,3687 0,511

23,5 0,3854 0,5594 0,5921 0,5636 0,5342 0,3665 0,508

23,6 0,3828 0,5549 0,5873 0,5593 0,5305 0,3644 0,504

23,7 0,3803 0,5504 0,5825 0,5551 0,5268 0,3623 0,501

23,8 0,3778 0,5460 0,5778 0,5509 0,5233 0,3603 0,497

23,9 0,3753 0,5416 0,5731 0,5468 0,5196 0,3583 0,494

24 0,3728 0,5373 0,5685 0,5428 0,5162 0,3562 0,490

24,1 0,3705 0,5330 0,5640 0,5388 0,5126 0,3542 0,487

24,2 0,3681 0,5288 0,5595 0,5347 0,5092 0,3522 0,484

24,3 0,3658 0,5247 0,5550 0,5309 0,5058 0,3503 0,480

24,4 0,3634 0,5206 0,5507 0,5270 0,5025 0,3484 0,477

24,5 0,3611 0,5166 0,5464 0,5232 0,4992 0,3465 0,474

24,6 0,3590 0,5127 0,5423 0,5195 0,4959 0,3447 0,471

24,7 0,3567 0,5089 0,5381 0,5159 0,4927 0,3429 0,468

24,8 0,3546 0,5050 0,5341 0,5124 0,4897 0,3410 0,465

24,9 0,3525 0,5014 0,5302 0,5088 0,4865 0,3392 0,462

25 0,3503 0,4976 0,5263 0,5053 0,4835 0,3375 0,459

25,1 0,3485 0,4943 0,5227 0,5021 0,4808 0,3360 0,457

25,2 0,3466 0,4910 0,5191 0,4990 0,4780 0,3345 0,454

25,3 0,3448 0,4877 0,5156 0,4959 0,4754 0,3330 0,451

25,4 0,3430 0,4844 0,5121 0,4929 0,4728 0,3316 0,449

25,5 0,3412 0,4812 0,5086 0,4898 0,4702 0,3301 0,446

25,6 0,3394 0,4780 0,5052 0,4869 0,4676 0,3286 0,444

25,7 0,3376 0,4749 0,5018 0,4839 0,4650 0,3272 0,441

25,8 0,3359 0,4717 0,4986 0,4811 0,4626 0,3257 0,439

25,9 0,3341 0,4686 0,4953 0,4782 0,4600 0,3244 0,437

26 0,3325 0,4656 0,4920 0,4752 0,4575 0,3229 0,434

57

26,1 0,3308 0,4626 0,4889 0,4724 0,4551 0,3216 0,432

26,2 0,3291 0,4596 0,4856 0,4696 0,4527 0,3202 0,430

26,3 0,3275 0,4567 0,4825 0,4668 0,4503 0,3188 0,427

26,4 0,3258 0,4538 0,4794 0,4642 0,4479 0,3174 0,425

26,5 0,3242 0,4508 0,4763 0,4614 0,4455 0,3162 0,423

26,6 0,3225 0,4480 0,4733 0,4587 0,4432 0,3148 0,421

26,7 0,3209 0,4452 0,4702 0,4561 0,4409 0,3135 0,418

26,8 0,3194 0,4424 0,4673 0,4535 0,4386 0,3122 0,416

26,9 0,3178 0,4396 0,4643 0,4509 0,4364 0,3109 0,414

27 0,3163 0,4369 0,4614 0,4482 0,4341 0,3096 0,412

27,1 0,3147 0,4342 0,4586 0,4458 0,4319 0,3084 0,410

27,2 0,3132 0,4316 0,4557 0,4432 0,4296 0,3070 0,408

27,3 0,3117 0,4290 0,4530 0,4407 0,4275 0,3058 0,406

27,4 0,3102 0,4264 0,4502 0,4382 0,4253 0,3046 0,404

27,5 0,3088 0,4238 0,4474 0,4359 0,4233 0,3034 0,402

27,6 0,3074 0,4213 0,4448 0,4335 0,4212 0,3022 0,400

27,7 0,3060 0,4188 0,4421 0,4312 0,4191 0,3010 0,398

27,8 0,3045 0,4163 0,4395 0,4287 0,4171 0,2998 0,396

27,9 0,3031 0,4138 0,4369 0,4264 0,4151 0,2987 0,394

28 0,3018 0,4114 0,4343 0,4241 0,4130 0,2975 0,392

28,1 0,3006 0,4092 0,4320 0,4222 0,4114 0,2966 0,390

28,2 0,2994 0,4071 0,4297 0,4202 0,4096 0,2957 0,389

28,3 0,2982 0,4050 0,4274 0,4182 0,4080 0,2947 0,387

28,4 0,2970 0,4029 0,4252 0,4162 0,4063 0,2938 0,385

28,5 0,2958 0,4008 0,4229 0,4143 0,4046 0,2929 0,384

28,6 0,2947 0,3987 0,4207 0,4124 0,4029 0,2919 0,382

28,7 0,2936 0,3967 0,4186 0,4105 0,4013 0,2910 0,381

28,8 0,2925 0,3947 0,4164 0,4085 0,3996 0,2901 0,379

28,9 0,2914 0,3926 0,4142 0,4067 0,3981 0,2892 0,377

29 0,2903 0,3906 0,4121 0,4049 0,3964 0,2883 0,376

29,1 0,2891 0,3886 0,4101 0,4031 0,3949 0,2875 0,374

29,2 0,2880 0,3867 0,4080 0,4012 0,3933 0,2865 0,373

29,3 0,2870 0,3848 0,4059 0,3994 0,3918 0,2857 0,371

29,4 0,2859 0,3828 0,4038 0,3976 0,3902 0,2848 0,370

29,5 0,2849 0,3810 0,4018 0,3959 0,3886 0,2839 0,368

29,6 0,2837 0,3791 0,3998 0,3941 0,3871 0,2831 0,367

29,7 0,2827 0,3772 0,3979 0,3924 0,3855 0,2823 0,365

29,8 0,2817 0,3753 0,3959 0,3907 0,3842 0,2813 0,364

29,9 0,2807 0,3736 0,3939 0,3890 0,3826 0,2805 0,363

30 0,2797 0,3719 0,3922 0,3872 0,3812 0,2797 0,361

Table 3.2.4: Attenuation coefficients values for all materials in the range of energy 15-30 keV

58

Figure 3.2.2: a) Projection view of the PMMA stepwedge phantom in X-ray mammography, b) A zoom of

the image where we measure the value of I and Io with a rectangular ROI (yellow color), c) The pluging of

ImageJ that permit to measure the values of I and I0.

In the figure 3.2.3 we report the position of PMMA stepwedges before the acquisition.

In table 3.2.5 are reported the values obtained for PMMA that to be graphed:

a)

b)

c)

I0 I

I0 (AIR)

59

Figure 3.2.3: PMMA stepwedges on the compression paddle of the mammography unit.

PMMA stepwedge size M _ 26 kV_ Mo/Mo

Step (mm) I/I0 -Ln(I/I0) Δln(I/I0)

22.24 0.032 3.440 0.187

14.08 0.047 3.050 0.129

8.16 0.070 2.649 0.086

4.10 0.114 2.164 0.054

2.10 0.152 1.883 0.042

Table 3.2.5: Attenuation and logarithm attenuation values respect to the thickness of the material.

Figure 3.2.4: Logarithmic attenuation at increasing thickness of the PMMA material.

y = 0,0753x + 1,8745

0

0,5

1

1,5

2

2,5

3

3,5

4

0 5 10 15 20 25

-Ln

(I/I

0)

PMMA material thickness (mm)

26 kV - 28mAS - Mo/Mo

300 𝜇𝑚 𝑓𝑜𝑐𝑎𝑙 𝑠𝑝𝑜𝑡 𝑠𝑖𝑧𝑒

60

From the slope of the linear curve we obtain a value in attenuation equal to 0.753 cm-1

and

if we divide this value by the PMMA density (1.19 g/cm3) we obtain, the attenuation

mass coefficient equal to 0.6327 cm2/gr. We find this value tabulated on Xmudat

[https://www-nds.iaea.org/publications/iaea-nds/iaea-nds-0195.htm] and we seek that this

value correspond to a radiation of 19 KeV (0.6426 gr/cm2) in accordance to a typical ener-

gy of polychromatic spectra Mo/Mo. We obtain :

𝝁𝒆𝒇𝒇(𝑷𝑴𝑴𝑨) = (0.753 ± 0.003)𝑐𝑚−1 ; 𝑬𝒆𝒇𝒇 = 19 𝑘𝑒𝑉

PMMA stepwedge size: L _ 28 kV_ W/Ag

Step (mm) I/I0 -Ln(I/I0) Δln(I/I0)

44.2 0.104 2.262 0.02

36.4 0.146 1.920 0.01

28.24 0.212 1.548 0.01

24.18 0.259 1.348 0.01

Table 3.2.6: Attenuation and logarithm attenuation values respect to the thickness of the material.

Standard error about the step is 0.01 mm.

Figure 3.2.5 : Attenuation and logarithm attenuation values respect to the thickness of the material.

From the slope of the graph, we obtain that the value of attenuation coefficient is equal to

0.516 cm-1

and this value on Xmudat is obtained to the energy of the beam equal to 23.3

keV.

y = 0,0455x + 0,2559 R² = 0,9996

0

1

2

3

0 10 20 30 40 50

-Ln

(I/I

o)

PMMA thickness (mm)

28 kV_ 40mAs_W/Ag

PMM…

61

3.3 Measurements: data and results

During this thesis work we 3D printed a number of stepwedge phantoms for investigate the

attenuation property of some thermoplastic materials at the energy less than 30 keV that

usually is used for digital mammography and for digital tomosynthesis imaging technique.

Materials that we are used: polyethylene terephthalate transparent (PET), acrylonitrile-

butadiene-styrene(ABS), and polylactic acid(PLA). In the figure 3.2.3 are showed all

stepwedge phantoms that are been used for the mammography acquisition while in table

3.2.1 we report stepwedges size. For the generate the CAD for the stepwedges, we used

Tinkercad is an easy-to-use 3D CAD design tool. Quickly turn ours idea into a CAD model

for a 3D printer [58].

Size

H1

(mm)

H2

(mm)

H3

(mm)

H4

(mm)

W

(mm)

L

(mm)

L1 = L2 = L3= L4

(mm)

Material:

-ABS

-PET

-PLA

S 1 2 4 5 20 160 40

M 6 10 15 20 20 160 40

L 30 40 50 60 20 160 40

L1 = L2 = L3= L4 = 40 mm

Table 3.3.1: Stepwedges size.

The stepwedges size S and size M are created with a nozzle of 0.25 mm in diameter . The

stepwedges size L are created with a nozzle of 0.4 mm in diameter.

The elemental composition of the materials used to create stepwedge phantoms and breast

phantoms is summarized in table 3.2.2.

Figure 3.3.1 : Stepwedges phantoms dimensions

62

Figure 3.3.2: Some stepwedges phantoms printed in this work; A) stepwedges size S, B) stepwedges size

M, C) stepwedges size L;

Data were token from National Institute of Standard and Technology (NIST) database [36].

The density reported in the table 3.1 for thermoplastic material it isn’t the nominal density

that give us Ultimaker but it is the density calculated in laboratory, weighing the phantom

and calculating its volume. We know that:

𝐷𝑒𝑛𝑠𝑖𝑡𝑦 = 𝑀𝑎𝑠𝑠

𝑉𝑜𝑙𝑢𝑚𝑒

Tissue/

Material H C N O S P K

Density

(gr*cm-3

)

GLANDa 0.102 0.184 0.032 0.677 0.005 1.040

SKINa 0.098 0.178 0.050 0.667 0.007 1.090

FATa 0.112 0.619 0.017 0.251 0.001 0.930

PETb 0.075 0.652 0.271 0.002 1.267

ABSb 0.075 0.855 0.053 0.016 0.001 1.040

PLAb 0.053 0.519 0.426 0.001 0.001 1.217

PMMAc 0.080 0.600 0.320 1.19

Table 3.3.2: Elemental composition as percentage weights and density of used breast material substitutes in

this work. a:[Hammerstein]; b: [Ahllabash].

For evaluate the attenuation coefficient of the stepwedge material, the same procedure

adopted whith the PMMA stepwedge phantoms are been used for white PLA, blue ABS

and transparent PET material. In the figure 3.4.1 are shown two stepwedge phantoms of 60

A)

B) C)

63

mm (maximum thickness), put on the plate of the Mammomat Inspire device for the acqui-

sition of projections at the mammography unit. Phantoms are been placed near the side of

the table of the mammography for unit for minimize the scattered radiation (good geome-

try) that get worse in imaging quality and to have a X-ray radiation as perpendicular as

possible at the surface of the stepwedges phantoms.

In figure 3.2.2 are shown two stepwedge built in PLA material and ABS material before

radiographic exposure.

Figure3.3.3: PLA (a) and ABS (b) stepwedge phantoms between the compression paddles of the mammog-

raphy unit before the acquisition. (San Raffaele Hospital-Milan).

Figure3.3.4: PLA (a) stepwedge phantoms between the compression paddles of the mammography unit be-

fore the acquisition. b) Monitor of Hologic Selenia for tomosynthesis and mammography images acquisi-

tions. (Ruggi D’Aragona Hospital-Salerno).

Xray beam

direction

a) b)

a) b)

64

PLA stepwedge _ 28 kV_ 40mAs_W/Ag

Step (mm) I/I0 -Ln(I/I0) Δln(I/I0)

20 0,2175 1,5253 0,0006

15 0,30565 1,1853 0,0003

10 0,43936 0,8224 0,0003

8 0,6010 0,5092 0,0003

5 0,6630 0,4109 0,0002

4 0,7132 0,3380 0,0002

2 0,8362 0,17878 0,0002

1 0,9055 0,0992 0,0002

Table: 3.3.3: Attenuation and logarithm attenuation values respect to the thickness of the material.

Standard error about the step is 0.01 mm

Figure 3.3.5: Attenuation and logarithm attenuation values respect to the thickness of the PLA material.

The slope of the graph return a value for attenuation coefficient for PLA material equal to

0.673 cm-1

and this value correspond to 21.4 keV in energy on Xmudat tabulated value . A

tipycal spectrum W/Ag at 28 Kv with filter thickness of 0.05 mm (Ag) return an effective

energy of 20 keV (Tasmics code). The attenuation coefficient value of gland tissue at 21.4

keV is 0.6742 cm-1

. So the pencentual relative difference of PLA attenuation respect to

gland, fat and skin tissue is so reported:

∆𝜇

𝜇%(𝐺𝑙𝑎𝑛𝑑 − 𝑃𝐿𝐴) =

𝜇𝑔𝑙𝑎𝑛𝑑 − 𝜇𝑒𝑓𝑓(𝑃𝐿𝐴)

𝜇𝑔𝑙𝑎𝑛𝑑= 0.8%

∆𝜇

𝜇%(𝐹𝑎𝑡 − 𝑃𝐿𝐴) =

𝜇𝑓𝑎𝑡 − 𝜇𝑒𝑓𝑓(𝑃𝐿𝐴)

𝜇𝑓𝑎𝑡= 51%

∆𝜇

𝜇%(𝑆𝑘𝑖𝑛 − 𝑃𝐿𝐴) =

𝜇𝑠𝑘𝑖𝑛 − 𝜇𝑒𝑓𝑓(𝑃𝐿𝐴)

𝜇𝑠𝑘𝑖𝑛= 6%

y = 0,0758x + 0,0178 R² = 0,9904

0

2

4

0 5 10 15 20 25

-Ln

(I/I

0)

PLA material thickness(mm)

PLA white Focal spot: 300 μm

65

It is only minus of 1% the difference between PLA material and gland tissue; The differ-

ence between PLA material and fat tissue is equal to -51%, while the difference between

PLA material and the skin tissue is equal to 6 % so if we watch also the graphs in figure

3.2.6/.7 we can notice that PLA is a good candidate to mimic glandular tissue in the range

of diagnostic energies used in 2D and 3D X-ray imaging modality.

ABS stepwedge_ 28 kV_ 40mAs_W/Ag

Step (mm) I/I0 -Ln(I/I0) Δln(I/I0)

60 0,0532 2,9341 0,0006

50 0,0741 2,6017 0,0006

40 0,1110 2,1977 0,0005

30 0,1772 1,7302 0,0003

20 0,3084 1,1764 0,0002

15 0,4071 0,8987 0,0003

10 0,5374 0,6208 0,0002

8 0,6815 0,3834 0,0004

5 0,7225 0,3250 0,0002

4 0,7667 0,2655 0,0002

2 0,8665 0,1432 0,0003

1 0,9271 0,0756 0,0003

Table: 3.3.4: Attenuation and logarithm attenuation values respect to the thickness of the ABS material.

Standard error about the step is 0.01 mm.

Figure 3.3.5: Attenuation and logarithm attenuation values respect to the thickness of the ABS material.

y = 0,0499x + 0,1049 R² = 0,9933

0

0,5

1

1,5

2

2,5

3

3,5

0 10 20 30 40 50 60 70

-Ln

(I/I

0)

ABS material thickness (mm)

ABS_Blue Focal spot: 300 μm

66

In this case the slope of the graph return a value for attenuation coefficient for ABS mate-

rial equal to 0.499 cm-1

and this value correspond to 19.3 keV in energy on Xmudat tabu-

lated values. A polychromatic spectrum W/Ag with filter thickness of 0.05 mm (Ag) re-

turn an effective energy of 20 keV (Tasmics Code). So the percentage relative difference

of ABS attenuation material respect to gland, fat and skin tissue is so reported:

∆𝜇

𝜇%(𝐺𝑙𝑎𝑛𝑑 − 𝐴𝐵𝑆) =

𝜇𝑔𝑙𝑎𝑛𝑑 − 𝜇𝑒𝑓𝑓(𝐴𝐵𝑆)

𝜇𝑔𝑙𝑎𝑛𝑑= 41 %

∆𝜇

𝜇%(𝐹𝑎𝑡 − 𝐴𝐵𝑆) =

𝜇𝑓𝑎𝑡 − 𝜇𝑒𝑓𝑓(𝐴𝐵𝑆)

𝜇𝑓𝑎𝑡= 8 %

∆𝜇

𝜇%(𝑆𝑘𝑖𝑛 − 𝐴𝐵𝑆) =

𝜇𝑠𝑘𝑖𝑛 − 𝜇𝑒𝑓𝑓(𝐴𝐵𝑆)

𝜇𝑠𝑘𝑖𝑛= 44 %

It is 8 % the difference so if we watch also the graphs in figures 3.2.6/ and3.2.7 we can no-

tice that ABS is a good candidate to mimic fat tissue in the range of diagnostic energies

used in 2D and 3D modality.

PET stepwedge _ 28 kV_ 40 mAs_W/Ag

Step (mm) I/I0 -Ln(I/I0) Δln(I/I0)

40 0,0908 2,3996 0,0195

30 0,1542 1,8694 0,0165

20 0,2840 1,2587 0,0219

15 0,3834 0,9586 0,0175

10 0,5167 0,6604 0,0168

8 0,6652 0,4076 0,0218

5 0,7087 0,3443 0,0142

4 0,7537 0,2828 0,0145

2 0,8580 0,1532 0,0147

1 0,9223 0,0809 0,0149

Table: 3.3.5: Attenuation and logarithm attenuation values respect to the thickness of the PET material.

Standard error about the step is 0.01 mm

67

Figure 3.3.6: Attenuation and logarithm attenuation values respect to the thickness of the PET material.

In this case the slope of the graph return a value for attenuation coefficient for PET materi-

al equal to 0.605 cm-1

and this value correspond to 21.8 keV in energy on Xmudat tabulat-

ed values . A polychromatic spectrum W/Ag with filter thickness of 0.05 mm (Ag) return

an effective energy of 20 keV (Tasmics Code). So the percentage relative difference of

PLA attenuation respect to gland, fat and skin tissue is so reported:

∆𝜇

𝜇%(𝐺𝑙𝑎𝑛𝑑 − 𝑃𝐸𝑇) =

𝜇𝑔𝑙𝑎𝑛𝑑 − 𝜇𝑒𝑓𝑓(𝑃𝐸𝑇)

𝜇𝑔𝑙𝑎𝑛𝑑= 6 %

∆𝜇

𝜇%(𝐹𝑎𝑡 − 𝑃𝐸𝑇) =

𝜇𝑓𝑎𝑡 − 𝜇𝑒𝑓𝑓(𝑃𝐸𝑇)

𝜇𝑓𝑎𝑡= −37 %

∆𝜇

𝜇%(𝑆𝑘𝑖𝑛 − 𝑃𝐸𝑇) =

𝜇𝑠𝑘𝑖𝑛 − 𝜇𝑒𝑓𝑓(𝑃𝐸𝑇)

𝜇𝑠𝑘𝑖𝑛= 12 %

It is only 6% in difference so if we watch also the graphs in figures 3.2.6/ and3.2.7 we can

notice that also PET is a good candidate to mimic glandular tissue in the range of diagnos-

tic energies used in 2D and 3D modality.

Figure: 3.3.7: Attenuation coefficients expected at increasing of the beam energy (1÷50 keV) for PLA mate-

rial, PET material and gland tissue.

y = 0,0605x + 0,0251 R² = 0,9982

-1,00

7,00

15,00

0 10 20 30 40 50

μ(c

m-1

)

PET material thickness (mm)

PET trasparent

0,01

0,1

1

10

100

1000

10000

0 10 20 30 40 50 60

μ (

cm-1

)

Energy (KeV)

PLA GLAND PET

68

Figure: 3.3.8: Attenuation coefficient expected at increasing of the beam energy (1÷50 keV) for PLA mate-

rial, PET material and skin tissue.

Figure 3.3.9: Attenuation coefficient expected at increasing of the beam energy for ABS material and fat tis-

sue

We define glandular fraction in mass and in volume as:

0,1

1

10

100

1000

10000

0 10 20 30 40 50 60

μ(c

m-1

)

Energy (keV)

SKIN PET PLA

0,1

1

10

100

1000

10000

0 10 20 30 40 50 60

μ(c

m-1

)

Energy (keV)

FAT ABS

69

𝑔𝑙𝑎𝑛𝑑𝑢𝑙𝑎𝑟 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 = 𝑔𝑙𝑎𝑛𝑑 𝑡𝑖𝑠𝑠𝑢𝑒

𝑔𝑙𝑎𝑛𝑑 𝑡𝑖𝑠𝑠𝑢𝑒 + 𝑓𝑎𝑡 𝑡𝑖𝑠𝑠𝑢𝑒

𝑉𝑜𝑙𝑢𝑚𝑒 𝑔𝑙𝑎𝑛𝑑𝑢𝑙𝑎𝑟 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 = 𝑉𝑜𝑙𝑢𝑚𝑒 𝑔𝑙𝑎𝑛𝑑 𝑡𝑖𝑠𝑠𝑢𝑒

𝑉𝑜𝑙𝑢𝑚𝑒 𝑔𝑙𝑎𝑛𝑑 𝑡𝑖𝑠𝑠𝑢𝑒 + 𝑉𝑜𝑙𝑢𝑚𝑒 𝑓𝑎𝑡 𝑡𝑖𝑠𝑠𝑢𝑒

The mass of glandular tissue in a stack of images will be:

𝑚𝑔 = 𝑛. 𝑣𝑜𝑥𝑒𝑙𝑠𝑔𝑙𝑎𝑛𝑑 ∗ 𝜌𝑔𝑙𝑎𝑛𝑑 ∗ 𝑉𝑣𝑜𝑥𝑒𝑙

”Histogram” plugins, offered by ImageJ permit to evaluate the number of pixels for each

tissue consisting the phantom. Glandular fraction and Volume glandular fraction are two

parameters most important in X-ray imaging quality and in quality assurance [13].

Before acquiring tomosynthesis and mammography projections to the phantoms, we asked

ourselves which could be the hypothetical material, between PLA and PET that could best

mimic in attenuation the glandular tissue at energy less of 30 keV.

To solve this problem, for testing, we took, by the X-ray tube present in the laboratory of

medical physics at University of Naples (X-ray microfocus tube of Hammamatsu Compa-

ny) X-rays impressions of a slab with thickness of 6mm. As shown in figure 3.3.10, one

slab is made in ABS(mimic fat) and PLA(mimic gland) while the other one is made in

ABS(mimic fat) and PET(mimic gland). In the figure 3.3.10(c-f) we show the projection of

this testing measure. In figures 3.3.10(a-d) are shown the experimental set-up for the con-

trast testing quality for X-ray imaging. The distance between source to image was set to

67.5 cm( fore reproduce the same distance used for acquire CT images at UC Davis (Cali-

fornia-Usa). From the mammograms acquired, it saw that the PLA material contrast better

than PET material; so we used PLA for mimic gland in the last printed breast phantom.

70

Figure 3.3.10: a) A slab(b) of 6 mm of ABS+PET material is attached to the detector for to be imaged. A

view of the experimental set-up. b) A thin slab of phantom(ABS+PET), 6mm thickness is shown in the fig-

ure. c) Mammogram. (d-e-f) The same procedure is replicate for the slab of 6 mm thickness ABS+ PLA ma-

terial.

a) c)

71

Phantom ”Mammo2_L2” small

Chest wall–nipple distance: 46.45 mm

Lateral direction: 129.39 mm

Head-to direction: (compressed): 36.68 mm

Skin tissue: PET material (CPE for Ultimaker material)

Gland tissue: PET material (CPE for Ultimaker material)

Fat tissue: ABS material (Ultimaker material)

Double Extrusion: 0.4 mm

Diameter filament: 2.85 mm

Height of layer : 0.1 mm

Temperature of extusion: 230° for ABS and 240° for PET

Temperature of the plate: 60° C

Time for build the phantom: 3days - 6 h

Fill Factor: 100%

Printing all in one

Density (ultimaker): 1.10 g/cm3 (ABS) – 1.27 g/cm

3 (PET)

Density measured: 1.267 g/cm3

Glandular fracion: 26%

Table 3.3.4: Breast phantom dimensions, printing characterists and glandular fraction value.

72

Figure 3.3.11: Mammo2_L2 breast phantom. ABS material mimic fat tissue. PET material mimic skin tissue

and gland tissue

Figure 3.3.12: Tree projections in mammography modality for the breast phantom “Mammo2_L2_small”;

A) Mammogram at 28 kV, 40mAs and combination anode/filter: Tugsten/Silver with filter thickness:0.05

mm (Ag); B) Mammogram at 28 kV, 40mAs and combination anode/filter: Tugsten/Rhodium with filter

thickness:0.05 mm (Rh); C) Mammogram at 25 kV, 40mAs and combination anode/filter: Tugsten/Silver

with filter thickness: 0.05 mm (Ag). These images are acquired at Ruggi D’Aragona Hospital (Salerno-Italy).

ABS (FAT)

PET(GLAND)

PET(SKIN)

28 kV_ 40 mAs

W/Ag

28 kV_ 40 mAs

W/Rh

25 kV_ 40 mAs

W/Ag

73

Figure 3.3.13: A-B) Tomosynthesis slices acquired by Selenia Mammomat device installed at San Raffaele

Hospital.(Milan-Italy). C) A tomosynthesis reconstruction acquired by Hologic Selenia device at Ruggi

D’Aragona( Salerno-Italy).

Figure 3.3.14: A mammographic projection acquired by Mammmomat device. Entrance dose is 1.435mGy.

28 kV_ 118 mAs

W/Al

29 kV_ 120 mAs

W/Al

27 kV_ 57 mAs

W/Rh

28 kV_ 40 mAs

W/Al

A) B) C)

29 kV_39 mAs

W/Al

74

Phantom ”Mammo2_L2”

Chest wall – nipple distance: 46.45 mm

Lateral direction: 89.50 mm

Head-to direction: 36.68 mm

Skin tissue: PET material (CPE for Ultimaker material)

Gland tissue: PET material (CPE for Ultimaker material)

Fat tissue: ABS material (Ultimaker material)

Double Extrusion: 0.4 mm

Diameter filament: 2.85 mm

Height of layer: 0.1 mm

Temperature of extusion: 230° for ABS and 240 for PET

Temperature of the plate: 60° C

Time for build the phantom: 3days - 6 h

Fill Factor: 100%

Printing half a time

Density (ultimaker): 1.10 g/cm3 (ABS) – 1.27 g/cm

3 (PET)

Densiy measured: 1.267 g/cm3

Glandular fracion: 26%

Table 3.3.10: Breast phantom dimensions, printing characterists and glandular fraction value

75

In figure 3.3.15 (A) is shown half 3D compressed phantom without its skin envelope. In

figure 3.3.15 (B) is shown the same phantom on the compression puddle of the

mammography unit (San Raffaele-Milan) before of the exposuring.

In figure 3.3.16(A) is shown a slice of the compressed breast phantom MammoL2_2 in

Tomosynthesis modality acquired with a Voltage of the X-ray tube of 29 kV, a product

current-time of 101 mAs and a Tungsten/Aluminium like anode/filter combination.

Figure 3.3.15: A) Half of 3D printed breast phantom made in PET and in ABS. B) The same integer

phantom MammoL2_2 put on the compression puddle of the mammography unit before to be imaged.

29 kV_ 101 mAs

W/Al

27 kV_ 60 mAs

W/Rh

A)

B)

A)

B)

76

Figure 3.3.16: A) Slice of a tomosynthesis of the phantom acquired by Siemens Mammomat device; B) A

mammogram. Entrance dose is equal to 1.603 mGy.

Phantom “ DM1857”

Chest wall–nipple distance: 109 mm

Lateral direction : 160 mm

Head-to direction: 660 mm

Skin tissue: PLA material

Gland tissue: PLA material

Fat tissue: ABS material (Ultimaker material)

Double Extrusion: 0.4 mm

Diameter filament: 2.85 mm

Height of layer : 0.1 mm

Temperature of extusion: 230° for ABS and 210° for PLA

Build plate temperature: 60° C

Time for manufacturing the phantom: 3days - 6 h

Infill density: 100%

Infill line distance: 0.3 mm

Infill pattern: linear

Printing all in one: Skin+Fat+Gland

density (ultimaker): 1.24 g/cm3(PLA) / 1.10 g/cm

3(ABS)

Glandular fracion: 33%

Volume glandular fraction:

77

Table 3.3.10: Breast phantom dimensions, printing characterists and glandular fraction value.

Figure 3.3.17: A) DM1857 breast phantom where it is possible to notice the pattern of gland in the fatty tis-

sue ; B) Another view of DM1857 breast phantom where it is possible to see the external surface of the skin.

Figure 3.3.18: DM1857 breast phantom under the mammography unit for to be exposed. Images acquired at

San Raffaele Hospital (Milan – Italy).

A)

B)

B)

30 kV_ 507 mAs

W/Rh

78

Figure 3.3.19: A) Mammogram of the phantom with thickness 65 mm printed in PLA+ABS material. En-

trance dose is equal to 19.4578 mGy. Virtual projection via ImageJ of the same phantom at 30 keV.

Figure 3.3.20: A) Mammography, B) A slice in tomosynthesis technique at the same phantom “ DM1857”.

Images acquired at San Raffaele Hospital (OSR Milan, Italy).

34 kV_ 100 mAs

W/Al

34 kV_ 50 mAs

W/Al

A) B)

79

Figure 3.3.21: Two synthetic mammograms acquired in tomosynthesis modality at San Raffaele Hospital

(Milan-Italy).

34 kV_ 3.2 mAs

W/Al

34 kV_ 6.7 mAs

W/Al

80

Conclusions

Digital phantoms reproducing the anatomy of the female breast both in the compressed

condition (as in Digital mammography and digital breast tomosynthesis clinical exams)

and in the uncompressed condition (as in computed tomography dedicated to the breast)

have been devised within the Virtual Clinical Trial project of UNINA, UC Davis, U Varna.

These digital phantoms are anatomically realistic since they are derived from clinical scans

of breast-healthy patients undergoing dedicated breast computed tomography. In this thesis

we have developed physical reproductions of those digital phantoms, using the technology

of 3D printing with the Fused Deposition Modelling technique. Using plastic materials like

ABS, PLA, PET, we 3D printed a number of compressed and uncompressed breast phan-

toms, reproducing the three tissues: adipose, glandular, skin. Images of these physical

phantoms have been obtained with mammography and digital breast tomosynthesis units in

a clinical environment, for different radiographic techniques. The suitability of these mate-

rials in reproducing the X-ray attenuation of the breast tissues has been verified by printing

and then imaging stepwedge phantoms of known thickness, for derivation of the effective

linear attenuation coefficient via the Lambert-Beer law.

A number of issues have been faced and solved in the realization of those phantoms, relat-

ed to the printing manufacturing details, the compatibility of filament materials in dual

printing. The result of this work is satisfactory, from this point of view. The 3D printed

phantoms appear as reasonably accurate reproduction of the breast anatomy as seen in

breast computed tomography scans, and the radiographic contrast they generate when im-

aged in a clinical setup are comparable to the one seen in real breasts. Future work will be

dedicated to triple-extruder 3D printing (with three filament materials reproducing sepa-

rately the attenuation of skin, adipose and glandular tissue, respectively) and to printing

phantom containing lesions. These phantoms will be useful for validation of Monte Carlo

simulations of virtual clinical exams as ongoing in the medical physics lab of the Federico

II University.

81

Appendix A

The breast cancer TNM staging system is reported in table 1. It is the most common way

that doctors stage breast cancer.

[https://www.cancerresearchuk.org/about-cancer/breast-cancer/stages-types-grades/tnm-staging].

Tumour (T)

Tumour describes the size of the tumour (area of cancer). This is a simplified description of

the T stage.

TX means that the tumour size can't be assessed.

Tis means ductal carcinoma in situ (DCIS).

T1 means that the tumour is 2 centimetres (cm) across or less.

T1 is further divided into 4 groups:

T1mi means the tumour is 0.1cm across or less

T1a means the tumour is more than 0.1 cm but not more than 0.5 cm

T1b means the tumour is more than 0.5 cm but not more than 1 cm

T1c means the tumour is more than 1 cm but not more than 2 cm

T2 means that the tumour is more than 2 centimetres but no more than 5 centimetres

across.

Metastasis(M)

Metastasis (M) describes whether the cancer has spread to a different part of the

body.

M0 means that there is no sign that the cancer has spread.

cMo(i+) means there is no sign of the cancer on physical examination, scans or x-

rays. But cancer cells are present in blood, bone marrow, or lymph nodes far away

from the breast cancer – the cells are found by laboratory tests

M1 means the cancer has spread to another part of the body.

82

Node (N)

Node (N) describes whether the cancer has spread to the lymph nodes.

NX means that the lymph nodes can't be assessed (for example, if they were previously re-

moved).

N0 means there are no cancer cells in any nearby nodes.

Isolated tumor cells (ITCs) are small clusters of cancer cells less than 0.2 mm across, or a

single tumor cell, or a cluster of fewer than 200 cells in one area of a lymph node. Lymph

nodes containing only isolated tumor cells are not counted as positive lymph nodes.

N1 means cancer cells are in the lymph nodes in the armpit but the nodes are not stuck to

surrounding tissues.

pN1mi means one or more lymph nodes contain areas of cancer cells called micrometasta-

ses that are larger than 0.2mm. Or the nodes contain more than 200 cancer cells but are

less than 2mm.

pN1a means that cancer cells have spread (metastasized) into 1 to 3 lymph nodes and at

least one is larger than 2mm.

pN1b means there are cancer cells in the lymph nodes behind the breastbone (the internal

mammary nodes) found with a sentinel node biopsy but the areas are too small to feel.

pN1c means there are cancer cells in 1 to 3 lymph nodes in the armpit and in the lymph

nodes behind the breastbone, but they are too small to feel.

N2 is divided into 2 groups:

N2a means there are cancer cells in the lymph nodes in the armpit, which are stuck to each

other and to other structures.

N2b means there are cancer cells in the lymph nodes behind the breast bone (the internal

mammary nodes), which have been seen on a scan or felt by the doctor. There is no evi-

dence of cancer in lymph nodes in the armpit.

N3 is divided into 3 groups:

N3a means there are cancer cells in lymph nodes below the collarbone.

N3b means there are cancer cells in lymph nodes in the armpit and behind the breastbone.

N3c means there are cancer cells in lymph nodes above the collarbone.

83

Appendix B

The below scheme represent a workflow for the digital breast compression code used

in this work.

84

Appendix C

In the table below are reported the Ultimaker 3 technical specifications

[https://ultimaker.com/3d-printers/ultimaker-3]

Single extrusion build volume 215 x 215 x 200 mm

Dual extrusion build volume 197 x 215 x 200 mm

Assembled dimensions 342 x 505 x 588 mm

Print techlogy Fused filament fabrication

Compatible filament diameter 2.85 mm

Weight 10.6 kg

Maximum power output 221 W

Layer resolution

0.25 mm nozzle: 150 – 60 micron

0.4 mm nozzle: 200 - 20 micron

0.8 mm nozzle: 600 - 20 micron

XYZ resolution 12.5, 12.5, 2.5 micron

Feeder type Dual-geared feader

Display Dot-matrix display with click wheel

Print core replacement Swappable print cores

Print head Dual extrusion print head with an auto-nozzle

Nozzle diameters 0.25 mm, 0.4 mm, 0.8 mm

Build speed < 24 mm2/s

Nozzle temperature 180-280°

Nozzle heat-up time < 2 minutes

Operating sound 50 dBA

Build plate levelling Active levelling

Build plate 20 - 100 °C heated glass build plate

Operating ambient temperature 15 - 32 °C

Supplied free software Ultimaker Cura – print preparation software

Ultimaker Connect – printer management software

Supported file types

Ultimaker Cura: STL, OBJ, X3D, 3MF, BMP, GIF,

JPG, PNG

Printable formats: G, GCODE, GCODE.gz, UFP

85

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Acknowledgments

Prof. J. Boone (University California Davis Medical Center) provided the dataset of clini-

cal breast CT scans.

Prof. Kristina Bliznakova (Medical University of Varna, Bulgaria) provided the software

code for compression of the digital phantoms.

Dott. Sarno Antonio (University of Naple – FedericoII- Medical Physics Research) provid-

ed the segmentation codes for the images.

Dr. Roberta Castriconi – Dr. Aldo Mazzilli ( San Raffaele Scientific Institute, Medical

Physics Department- Milan –Italy) for the acquisitions of the images in 2D and 3D X-ray

imaging technique that are shown in this work.

Dr. Antonio Orientale – Dr. Pierluigi D’Andria - Dr. Immacolata Pilotti ( San Giovanni Di

Dio e Ruggi D’Aragona Hospital, Medical Physics Department, Salerno, Italy) for the

permission to the acquisitions of the images in 2D and 3D X-ray imaging technique shown

in this work.