Voxelized Breast Phantoms for Dosimetry in Mammography

R. M. Tucciariello

1,2 a

, P. Barca

, D. Del Sarto

1,2 c

, R. Lamastra

1,2

, G. Mettivier

3,4 d

A. Retico

, P. Russo

3,4 f

, A. Sarno

, A. C. Traino

and M. E. Fantacci

1,2 i

Department of Physics, University of Pisa, Pisa, Italy

INFN, Pisa Section, Pisa, Italy

INFN, Napoli Section, Napoli, Italy

Università di Napoli Federico II, Dipartimento di Fisica “Ettore Pancini”, Napoli, Italy

Unit of Medical Physics, Pisa University Hospital “Azienda Ospedaliero-Universitaria Pisana”, Pisa, Italy

mettivier@na.infn.it, alessandra.retico@pi.infn.it, russo@na.infn.it,

c.traino@ao-pisa.toscana.it, maria.evelina.fantacci@unipi.it

Keywords: Monte Carlo Simulations, Digital Mammography, X-Ray Breast Dosimetry, Voxelized Phantoms,

Heterogeneous Breast Phantoms, GEANT4.

Abstract: X-ray breast imaging techniques are an essential part of breast cancer screening programs and their

improvements lead to gain in performance and accuracy. Radiation dose estimate and control play an

important role in digital mammography and digital breast tomosynthesis investigations, since the risk of

radioinduced cancer to the gland must be contained and dose delivered to the gland must be declared in the

medical report. The actual dosimetric protocols suggest the assessment of radiation dose by means of Monte

Carlo calculation on digital breast phantoms, providing the assumption of the homogeneous mixture of

glandular and adipose tissues within the breast organ, leading to a drastic approximation. In line with the trend

of other research groups, with the aim of improving the Monte Carlo model, in the current work a new

heterogeneous digital breast model is proposed, involving a voxelized approach and disengaging from the

concept of homogeneous phantom. The proposed model is based on new findings in the literature and after a

validation process, the model is adopted to evaluate mean glandular dose discrepancies with the traditional

model which is adopted in clinic for decades.

1 INTRODUCTION

Worldwide, breast cancer is the most commonly

diagnosed cancer in female subjects, accounting

about 2.1 million newly diagnosed breast cancer, with

1 in 4 cancer cases among women, and the leading

cause of cancer death, followed by colorectal and

lung cancer for incidence, and vice versa for mortality

(Yuuhaa et al., 2018). In 2018, among European

women, breast cancer was by far the most frequently

https://orcid.org/0000-0001-9600-4177

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https://orcid.org/0000-0001-6606-4304

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diagnosed neoplasm (522,500 , 28.2% of the total),

followed by colorectal (228,000 , 12.3%), lung

(158,000 , 8.5%) and corpus uteri (122,000 , 6.6%)

cancers (Ferlay et al., 2018).

As suggested by the World Health Organization,

early detection is critical to improve breast cancer

outcomes and survival, made possible with screening

procedures consisting in testing women to identify

cancers before any symptom appears. This may lead

to tumour early detection, allowing greater

154

Tucciariello, R., Barca, P., Sarto, D., Lamastra, R., Mettivier, G., Retico, A., Russo, P., Sarno, A., Traino, A. and Fantacci, M.

Voxelized Breast Phantoms for Dosimetry in Mammography.

DOI: 10.5220/0010322901540161

In Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2021) - Volume 3: BIOINFORMATICS, pages 154-161

ISBN: 978-989-758-490-9

possibilities for medical treatment and reducing the

mortality rate. Since last decades, the principal

technique adopted for breast cancer screening

programs is the Digital Mammography (DM), an X-

ray imaging technique consisting in acquiring two

digital images, a cranio-caudal and a medio-lateral

view; since 2011 when it was introduced in the

clinical routine, the new technique Digital Breast

Tomosynthesis (DBT) (Sechopoulos, 2013a, 2013b)

supports or might even replace DM, because it allows

to reduce the tissue superimposition effect, making it

easier for radiologists to distinguish normal from

cancerous tissues.

Since breast imaging techniques involve ionizing

radiation, radiation dosimetry must be accurately

assessed the glandular tissue is considered as the

target tissue for radiation damage. Radioinduced

cancer risk estimates are performed by using the

Average Glandular Dose (AGD) metric as defined in

UK and EU dosimetry protocol (Van Engen et al.,

2018) or also referred as Mean Glandular Dose

(MGD). It should be stressed that breast screening

procedures involve low-dose radiation and the

carcinogenic risk is small with a very favourable

trade-off of the potential beneficial effects of

screening with respect to the calculated risk of

induced cancer (Pauwels et al., 2016).

For both DM and DBT, dosimetry is performed

by using Monte Carlo simulations (Wu et al. 1994;

Dance and Sechopoulos 2016; Sarno et al. 2018;

Tucciariello et al. 2020) which involve models of the

anatomy of the breast (digital phantoms) with a

homogeneous mixture of glandular and adipose

tissues, surrounded by a skin envelope. This

methodology does not consider real heterogeneous

glandular distribution within the breast and the

assumption of the homogeneous compound is very

drastic (Sarno et al. 2018). Nevertheless, the advent

of the fully 3D quantitative technique of Breast

Computed Tomography (bCT) (Sarno, Mettivier, and

Russo 2015), helped to better characterize the breast

anatomy. On the basis of the results provided by

Huang and Hernandez (Hernandez et al. 2015; Huang

et al. 2011) which involved real bCT investigations

on patients, in this work a new voxelized phantom

model, which takes into account the heterogeneous

distribution of the gland, has been created to be

adopted for improving the accuracy of the Monte

Carlo (MC) simulations in dosimetry for DM and

DBT.

In view of the publication of the Task Group 282

of the AAPM in collaboration with EFOMP for the

development of a new universal breast dosimetry, the

purpose of this work is to propose a new

heterogeneous breast model which is more

representative of the real breast anatomies with

respect to the adoption of an homogeneous breast

model. Indeed, a simple glandular distribution model

is presented and the influence of this methodology on

dose estimates will be evaluated by comparing MGD

values with those of the homogeneous model. Sarno

et al. (2018) followed an alternative approach in

which a dataset of real investigations is involved for

dosimetry purposes and patient-specific dose

estimates are performed. It has to be said that this

represents a complex and time-consuming approach,

which takes in consideration one-by-one women

breast, while the proposed methodology in this work

adopts the average glandular distribution among

women.

2 MATERIALS AND METHODS

The radiation glandular dose cannot be assessed

experimentally and the use of Monte Carlo

simulations (MC) is required. MGD estimates are

performed by using dedicated conversion coefficients

from the incident Air Kerma (𝐾



, mGy) to MGD

values (mGy). In this work, the formalism provided

by Wu (Wu et al., 1994) and extended by Boone

(Boone, 1999) is adopted to estimate the MGD values

(eq. 1).

𝑀𝐺𝐷

[

𝑚𝐺𝑦

]

=𝐷𝑔𝑁∙𝐾



)

where DgN is the normalized glandular dose

coefficient (mGy/mGy).

In MC calculations, the rationale is to perform

simulations of the X-ray beam by tracing every

simulated photon over its track, from the radiation

source, towards the breast and to register energy

deposits in the volume (or mass) of interest. The MC

method produces the 𝐷𝑔𝑁 coefficients through the

calculation of the 𝑀𝐺𝐷 (which cannot be estimated

experimentally) and 𝐾



(measurable quantity). The

clinical practice uses 𝐷𝑔𝑁 numbers for converting

the measured 𝐾



at the entrance surface of the breast

to the estimated 𝑀𝐺𝐷 values (Sarno et al. 2019).

2.1 The Proposed Model

Using the GEANT4 simulation toolkit (Agostinelli et

al., 2003), following previous studies (Sarno et al.

2017; 2018; 2019) the setup for simulations has been

replicated and reported in Figure 1. The scoring

volume for dose deposit is showed in pink colour and

the skin envelope is considered as a shielding layer of

1.45 mm thick (Huang et al., 2008) not involved for

Voxelized Breast Phantoms for Dosimetry in Mammography

155

the dose computation. Adipose and glandular tissues

was replicated in the simulation setup by using the

elemental composition (Hammerstein et al., 1979),

reported in Table 1. The methodology adopted in this

work employs a new phantom model which

disengages from the traditional method of estimating

the mean glandular dose; indeed, the well-known G-

factor is adopted for “correcting” the dose deposit in

the homogeneous phantom (Boone 1999, 2002;

Nosratieh et al. 2015; Sarno et al. 2018; Sarno,

Mettivier, and Russo 2017; Tucciariello et al. 2019).

The traditional methodology of estimating MGD

values for homogeneous phantoms has been deeply

investigated in literature and is not the intent of this

paper.

Table 1: Elemental composition and density for glandular

and adipose tissues as implemented in the MC code.

Tissue H C N O P density

(g/cm

)

glandular 0.102 0.184 0.032 0.677 0.005 1.04

adipose 0.112 0.619 0.017 0.251 0.001 0.93

skin

0.098 0.178 0.050 0.667 0.007 1.09

Figure 1: a) Schematic drawing of the cranio-caudal view

irradiation geometry; b) scheme of the adopted simulation

geometry.

To move towards a heterogeneous approach, the

volume inside the breast tissue has to be divided in

voxels by using a voxel grid, inside which either

adipose or glandular tissues can be included, with

voxel dimension of 1×1×1 mm

. Since cubic voxels

have to be fixed inside a non-cubic volume (semi-

cylindrical cross section), some space uninvolved by

glandular tissue occurs, mainly between the breast

tissue and the skin interface on the rounded side of the

phantom, while on the chest wall side the border of

the voxels grid perfectly overlaps with the border of

the breast tissue. Despite uninvolved space reduces

The term glandularity indicates the percentage of

glandular tissue respect to the adipose tissue, sometimes

referred as breast density.

while decreasing voxels dimensions, computational

times and memory required have to be considered and

optimized. For purely investigative purposes, in the

presented model a voxel dimension of 1×1×1 mm

used, leading to a grid generation time of few seconds

to generate the whole voxel grid and only about 100

MB of RAM are required for the digital phantom

initialization. Nevertheless, uninvolved volume is

occupied by adipose material, which surely surrounds

the breast gland on the interface with the skin layer

(Huang et al. 2011) and this geometrical

approximation can be negligible.

Huang and Hernandez (Hernandez et al. 2015;

Huang et al. 2011) characterized the glandular tissue

within the breast, providing a metric able to reproduce

it. bCT investigations performed over patients let to

explore different breast anatomies (various cup sizes

and glandularities

) and a representative model has

been chosen for simulations.

In order to create a representative phantom model,

comparable with the homogeneous one adopted

previously, for which dose estimates are available in

the literature, the semi-cylindrical cross section has

been maintained. The use of a single gaussian

distribution, with no right-left displacement (as

showed by Huang) is considered appropriate in order

to replace a representative phantom for both right and

left women breasts, and an average value of 0.34 for

the FWHM provided by Hernandez has been adopted.

Equation (2) shows the distribution for glandular

voxels within the breast over the directions y and z,

represented by d (see Figure 2), for a given

compressed breast thickness 𝑙, μ



the centers of the

distributions and 𝜎



the standard deviations in both

directions (eq. 3).

𝐺



𝑑,𝜎





2𝜋𝜎





𝑒



















(2)

𝜎



𝐹𝑊𝐻𝑀

2.35

∙𝑙

(3)

The choice of the material for each voxel is

performed by using a random approach, following the

distribution criteria adopted for the glandular tissue.

The assignment of glandular rather than adipose

material for each voxel is carried out by using



𝑑,σ





. The product G𝑦,σ



∙G



𝑧,σ





provides

the probability that a certain voxel in position (y,z) is

composed by glandular material depending of its

position in the breast volume. The randomness with

BIOINFORMATICS 2021 - 12th International Conference on Bioinformatics Models, Methods and Algorithms

156

which voxels are effectively fulfilled or not with

glandular material is provided by the uniform

probability distribution in the interval [0,1] produced

by the GEANT4 random number generator. The

amount of glandular voxels can be tuned in the MC

code to reproduce different breast densities.

Figure 2: a) perspective, b) top and c) front views of the

proposed voxelized breast phantom. Glandular

distributions evolve in y and z directions with gaussian

distributions, while in x direction with a constant

distribution. The voxel grid concerns the whole breast

tissue volume (white semi-cylinder) and for an easy display

purpose only glandular voxels are showed, while the

remaining part has to be considered filled with adipose

tissue.

2.2 Model Validation

A fundamental aspect of MC calculations is the

validation process. The MC code adopted derives

from a previously validated MC code for

homogeneous breast phantoms. The validation

process consisted in comparisons against literature

(Dance, Young, and Van Engen 2011; Sechopoulos

et al. 2014; AAPM TG 2015) and experimental

measurements by using radiochromic films.

Since in this work the code has been upgraded to

produce voxelized heterogeneous breast phantoms,

any consistent change in the model adopted should be

confirmed by some kind of verification. For

validation purposes of the voxelized methodology,

the phantom grid has been set using the uniform

probability distribution for assigning either glandular

or adipose tissues for each voxel. The rationale is to

compare MGD simulations results for the grid

phantom, with voxels randomly filled replicating a

uniform distribution of gland, with those of the

homogeneous phantom with the same breast density.

Three compression thicknesses of 3, 5 and 7 cm, and

five glandularities of 1%, 14.3%, 25%, 50% and 75%

have been replicated. For each model three spectra

have been involved for investigating different beam

qualities. In this case, MGD estimates do not involve

the usual relation provided by (Boone, 1999;

Nosratieh et al., 2015; A. Sarno, Mettivier, Di Lillo,

Tucciariello, et al., 2018), but is directly obtained by

scoring the energy deposited 𝐸



in all the n glandular

voxels with mass 𝑚



due to the X-ray beam (eq. 4)

𝑀𝐺𝐷 = 

𝐸



𝑛∙𝑚







(4)

2.3 Dose Estimates

Glandular dose estimates dependencies using

homogeneous phantoms have already been

investigated by many authors (Dance and

Sechopoulos 2016; Sarno et al. 2018, 2019;

Tucciariello et al. 2020; Tucciariello et al. 2019) and

are not within the intents of this work, but no

evidences have been published in literature about the

dependence of dose estimates with respect to the

breast density obtained with heterogeneous glandular

distribution within the breast. In order to quantify

discrepancies between the two methods, simulations

have been performed with both homogeneous and

heterogeneous models, for three compressed

thicknesses of 3, 5 and 7 cm, exposed respectively to

W/Rh 26 kV, W/Rh 31 kV and W/Ag 34 kV spectra.

For each breast thickness, 12 glandularities have been

replicated.

3 RESULTS

3.1 Voxelized Phantom Validation

The voxelized phantom validation process regarded

the comparison between MGD values obtained with

the homogeneous phantom (MGD

hom

) with those

obtained with the voxelized phantom (MGD

vox

) using

the constant distribution of gland among voxels. This

kind of verification, performed by choosing the same

Voxelized Breast Phantoms for Dosimetry in Mammography

157

breast density in both models, let to investigate the

discrepancy produced by the voxelized model,

regardless of the glandular distribution adopted.

MGD discrepancies are showed in Table 2, where a

maximum percentage difference of 2.3% and an

average value of 1.0% confirm the success of the

voxels grid phantom model. Figure 3 highlights the

goodness of the fit (R

≃ 0.9995) performed over the

data obtained from simulations.

Since the creation of each heterogeneous digital

breast phantom involves a Monte Carlo approach, the

degree of reproducibility is questionable and one has

to wonders how much a certain model will differ with

the next one, with the same requested glandularity, in

terms of the amount of glandular voxels effectively

created and of mean glandular dose estimation. The

rationale is to create multiple models with same

glandularity and to verify the reproducibility

capabilities of the MC code. With the same

methodology, for each breast thickness of 3, 5 and 7

cm, five glandularities have been requested to be

reproduced by the MC code. In addition, for each

glandularity five models have been created, for a total

of 75 models, each of them irradiated with W/Al

spectra. In this case, between models with same

glandularity required, a maximum standard deviation

of 0.05% of glandularity is reached, which traduces

in very low MGD discrepancies, less than 0.5%.

Table 2: Data comparison between MGD values obtained

with homogeneous and voxelized phantoms for five breast

densities. Percentage differences refer to the ratio

(MGD

hom

- MGD

vox

)/ MGD

hom

× 100%.

MGD

vox

vs MGD

hom

1% 14.3% 25% 50% 75%

3 cm – W/Al 27kV 1.5% 1.4% 1.3% 0.9% 0.7%

3 cm – W/Rh 27kV 1.6% 1.1% 1.1% 0.9% 0.7%

3 cm – Mo/Mo 27kV 1.3% 2.0% 1.7% 1.3% 0.9%

5 cm – W/Al 30kV 0.1% 1.1% 1.1% 0.8% 0.7%

5 cm – W/Rh 30kV 2.3% 1.4% 0.7% 0.7% 0.6%

5 cm – Mo/Mo 30kV 0.9% 1.6% 1.5% 1.0% 0.9%

7 cm – W/Al 33kV -1.0% 1.0% 0.7% 0.8% 0.6%

7 cm – W/Rh 33kV -0.6% 0.9% 0.9% 0.9% 0.6%

7 cm – Mo/Mo 33kV 1.7% 2.0% 1.2% 1.1% 0.8%

Figure 3: Linear fit of MGD

vox

versus MGD

hom

in units of

mGy per incident photon. Concatenated data for 3, 5 and 7

cm compressed breast thicknesses. Origin 9.4 data analysis

software.

3.2 Dose Estimates in Mammography

Once the upgraded MC code which uses the proposed

phantom model has been validated, simulations over

the new model can be performed and new MGD

values could be investigated. As one can easily guess,

the adoption of the new model can lead to new MGD

values considering that the gland is mainly spread in

the central part of the volume. Di Franco and

colleagues (Di Franco et al., 2020) investigated the

glandular dose map within patient-derived digital

phantoms and highlighted a major dose distribution

towards the X-ray beam incident side (see Figure 1),

where however it should be mainly adipose voxels.

This kind of considerations led to treat the results

showed in Figure 4a more than reasonable, where

digital mammography investigations have been

performed for homogeneous and heterogeneous

breast models for various glandularities. Indeed, in

the homogeneous phantom a greater amount of

glandular tissue is in the upper layer of the breast with

the respect to the heterogeneous one, and glandular

dose deposit is higher, while in the heterogeneous

phantom the X-ray beam undergoes an X-ray

attenuation mainly due to the adipose tissues in the

upper layers and dose deposit is not scored by the MC

code. This effect also traduces in more discrepancies

for higher breast thicknesses and lower glandularities,

since glandular voxels are mainly disposed farther

from the upper surface.

BIOINFORMATICS 2021 - 12th International Conference on Bioinformatics Models, Methods and Algorithms

158

Figure 4: Mean glandular dose (mGy/photon) comparison

between the homogeneous breast model and the voxelized

one. Points in graphs refer to different glandularities.

Simulations have been performed by using the Hologic

Selenia Dimensions setup and typical irradiation settings in

DM modality for breast thicknesses of 3, 5 and 7 cm.

Discrepancies between MGD

het

and MGD

hom

are

reported in Table 3. Larger percentage variations

occur for breast densities less than 50% and decrease

with the increase of the breast density. It is a clear

evidence that for higher glandularities voxels marked

with gland tissue expand towards the border of the

phantom, approaching the 100% glandularity while

expanding and get closer to the homogeneous model.

As opposed to MGD coefficients for

homogeneous phantoms, which trend follows a 2

order polynomial fit respect to the breast density

(Sarno et al. 2018), dose estimates for the voxelized

phantom show a 4

order polynomial fit dependence

against glandularity, for both low and high

compressed breast thicknesses, where, moreover, for

7 cm thickness a non-monotone trend is presented and

a concave curve is highlighted (Figure 4).

Discrepancies highlighted in Table 3 are in line

with literature (Dance et al. 2005; Hernandez et al.

2015) and these results should be emphasized,

because major variations occur for the most popular

breast densities among female subjects.

Table 3: Percentage variation of dose estimates between

heterogeneous and homogeneous models.

(MGD

hom

- MGD

het

)/ MGD

hom

× 100%.

3 cm 5 cm 7 cm

Model

Glandularity

(normalized)

variation

(%)

gland. var.

(%)

gland. var.

(%)

1 0.03 -8.3% 0.02 -18.0% 0.03 -28.0%

2 0.08 -9.2% 0.06 -19.7% 0.06 -31.9%

3 0.16 -11.9% 0.13 -24.1% 0.16 -37.3%

4 0.28 -14.6% 0.18 -26.8% 0.28 -41.1%

5 0.40 -13.8% 0.24 -28.8% 0.35 -39.5%

6 0.49 -12.3% 0.39 -27.4% 0.50 -32.7%

7 0.65 -8.9% 0.56 -21.3% 0.60 -27.0%

8 0.74 -6.7% 0.65 -17.0% 0.69 -20.9%

9 0.80 -5.2% 0.74 -12.6% 0.79 -14.0%

10 0.90 -2.6% 0.84 -8.1% 0.86 -9.4%

11 0.93 -1.8% 0.89 -5.3% 0.94 -3.7%

12 0.97 -0.8% 0.97 -1.5% 0.98 -1.0%

4 CONCLUSIONS

Since the 90’s, X-ray breast dosimetry has been

performed with Monte Carlo calculations by adopting

the assumption of the homogenous compound of the

breast tissue. Studies in literature showed a non-

uniform distribution of the glandular tissue and

quantitative data are available. This work was aimed

to overcome the drastic approximation of the current

digital breast phantom and therefore to improve

Monte Carlo accuracy for dosimetry in DM and DBT.

Based on findings in the literature, involving results

from real bCT scans on patients, a new methodology

for creating digital breast phantoms is proposed, in

order to provide a more representative phantom to

adopt for dose estimates; the proposed model

involves a voxelized phantom with glandular voxels

which follow a gaussian distribution among vertical

and lateral axis. The validation phase has been

conducted by comparing the current dosimetry

methodology with the proposed one, showing good

reliability and reproducibility of the voxelized

method. Finally, MC calculations have been

performed for both homogeneous and heterogeneous

models in typical DM investigations, in order to

quantify the discrepancy between the two phantom

models; wide variations have been confirmed, mostly

for low breast densities, the most common

characteristic among women and a new trend curve

has been found regarding the MGD values versus the

glandularity. The underestimates of MGD values with

the adoption of the voxelized phantom are in line with

literature results.

Voxelized Breast Phantoms for Dosimetry in Mammography

159

Nevertheless, a justification for today's adoption

of the old protocols based on homogeneous phantoms

can be given by confirming a conservative approach

of the actual method related to glandular dose. More

alarming would have been if the comparison would

lead to exactly opposite results. However, it must be

said that the MC approach is aimed to reproduce

experimental configuration with a certain degree of

accuracy, and the better the methodology used, the

greater the reliability. Moreover, MC calculations are

particularly useful for optimizing support equipment

for experimental measurements, like physical breast

phantoms for quality assurance or research activities

in the field of imaging (Ivanov et al. 2018;

Tucciariello et al. 2020; Barca et al. 2019; Lamastra

et al. 2020) and efforts in Monte Carlo calculations

represent one of the right ways to go through.

ACKNOWLEDGEMENTS

The presented work is part of the RADIOMA project

which is partially funded by "Fondazione Pisa",

Technological and Scientific Research Sector, Via

Pietro Toselli 29, Pisa (Italy). The authors would like

to thank Fondazione Pisa for giving the opportunity

to start this study.

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