vdumetric of breast üensiityibr breast cancer risk · 2020. 4. 8. · cancer in women is caused by...
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Vdumetric Estirnafion of Breast üensiityibr Breast Cancer Risk Prediction
Olga Pawluczyk
A thesis submitted in conforrnity with the requirements for the degree of Master of Science
Graduate Department of Medical Biophysics University of Toronto
O Copyright by Olga Pawluczyk, 200 1.
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Volumetric Estimation of Breast Density for Breast Cancer Risk
Prediction
Olga Pawluczyk
Degree of Master of Science
Department of Medical Biophysics
University of Toronto
200 1
Abstract
Marnrnographic density has been shown to be a strong risk predictor for breast cancer.
Compared to an assessment by radiologists, cornputer-aided andysis of digitized mammograms
provides a quantitative and more reproducible rnethod for measuring amount of density in the 2D
projection of the breast. This thesis improves on existing computer-aided methods? by developuig
a tool for breast cancer risk assessment, which considers the whole 3D volume of the breast,
instead of 2D projected area.
The volumetric breast density (VBD) estimation requires an initial inhomogeneity
correction which reduces variations in the image of a uniform object fiom 15% to a%. Then,
VBD is estimated to within 2% of the actual value, using information about an aluminurn wedge
(imaged dong-side the breast), breast thickness and imaging technique. VBD can be used for
detemination of the appropriate fiequency of breast cancer screening, and might prove usefül in
predicting the effect of intervention measures such as drug therapy or dietary change.
Acknowledgments
This work would not have been possible without the help and support of several people to whom 1
wish to extend my thanks:
Forernost, I would like to thank my supervisor, Dr. Martin Yaffe, without whom 1 would not have
had a chance to work on this exciting project. Your support and guidance was indispensable for the
completion of this work.
To my cornmittee members, Dr. Norman Boyd, Dr. Don Plewes and Dr. Simon Graham for
providing me with new doors to open and paths to explore. The genuine interest you al1 showed in
diis project made your feedback and criticisms that much more important.
To the members of Dr. Yaffe's laboratory: thanks for your good sense of humor; it brightened
even the gloomiest of "1 can't" days! Your communal encyciopedic knowledge of Everything
helped to overcome even the most daunting dficulties.
To al1 other members of the Medical Biophysics: you al1 contribute to form an open, stimulating
and fnendly environment. 1 am privileged that 1 had a chance to be a member of your community.
Finally, to rny farnily: Thank you for your patience and support. 1 could not have done this
without the three of you!
Table of Contents
ABSTRACT ............. ,., ...,,, ......................................................................................................................... 11
ACKNOWLEDGMENTS ................... ..... ................................................................................................... III
TABLE OF CONTENTS ................................................................................................................................ IV
LIST O F FIGURES ....................................................................................................................................... VI1
....................................... LIST O F TABLES ............................................................................................ IX
GLOSSARY OF TERMS AND ABBREVTATIONS ......................... ,, .......................................................... X
CHAPTER 1: INTRODUCTION ..................................................................................................................... 1
3 1 - 1 BREAST CANCER RISK FACTORS ................................................................................................................. - 1.2 PARENCI-~YMAL APPEARANCE OF THE BREAST AS A RISK FACTOR .............................................................. 3
................................................................. 1.2. 1 Cztrrent Methods of Parenchymal Pattern Cfussrjkation 3
.............................................................................................................. (a) Rsdiologist cIassiI?cation - qualitative 5
............................................................................................................ (b) Radiologist classification - quantitative 6
(c) Cornputer-aided classification .......................................................................................................................... 7
(d) Fully-Automatic breast dcnsity estimation ....................................................................................................... 7
1-22 Disadvanrages of Czlrrent Methodri: Needfor a New Method ........................................................ ..a
1.3 VOLUMETRIC BREAST DMSITY ESTIMATION .......................................................................................... 10
1.4 THESIS OVERVIEW ................................................................................................................................... 11
.................................................................................. 1.4.1 Chpter 2: Field inhornogeneiry Correction 12
1.4.2 Chapter 2: Volzimetric Breast Density Estimation ......................................................................... 12
.......................................................................................... 1.4.3 Chaprer 3: Summary and Future Work 13
1.5 REFERENCES ....................................................................................................................................... 14
CHAPTER 2: FIELD INMOMOGENEITY CORRECTION ................... -. .......................................... 18
2-1 INTRODUC~ON ........................................................................................................................................ 18
2 2 THEORY ................... ., .......................................................................................................................... 19
2.3 MATERIALS AND METHODS .................................................................................................................... 2 4
2.3.1 Image AcqurSition ............................................................................................................................ 24
2.3.2 Image Pre- Processing ..................................................................................................................... 25
2.3.3 Sirnulution ........................................................................................................................................ 26
2.4 EMPIRICAL FIELD [NHOMOGENEITY CORRECTION .............................................................................. 1
2.4.1 Bowl Phanrom ................................................................................................................................. 31
2.42 Parh Obliquity Correction .............................................................................................................. -33
2.5 RESULTS ................................................................................................................................................. 34
2.5. 1 Non- Un form ity Correcr ion ............................................................................................................. 34
2.5.2 Validating Bowl Phanrom Correction ............................................................................................. 36
2.6 CONCLUS~ONS .......................................................................................................................................... 41
2.7 REFERENCES ............................................................................................................................................ 42
CHAPTER 3: VOLUMETRIC BREAST DENSITY ESTIMATION ........................... .. ........................... 44
3.1 INTRODUCTION ........................................................................................................................................ 44
3.1. I Volume densip measzïremenr ......................................................................................................... -45
3 -2 DEVELOPMENT OF METHODOLOGY .......................................................................................................... 46
............................................................................................................ 3.2.1 Design of the plasric wedge -50
3.2.2 Design of the alurninum wedge ..................................................................................................... - 3 3
3.3 MATERIALS AND METHODS ..................................................................................................................... 55
- - .................................................... 3.3.1 Plastic phanrom for testing ofbreasr density esrimation method 33
.................................................................................................. 3.3.2 Image acquisition and corrections 56
................................................................................................................... 3.3.3 Thickness measurement 56
3.3.4 Calibrarion ofaluminum wedge wirh breasr spivalent plastic ...................................................... 58
.......................................................... 3.3.5 Determinarion of volumetric densify o f the "hole" phantom 60
3.4 RESULTS AND DISCUSSION ....................................................................................................................... 61
.......................................................................................................................... 3.4.1 Calibrarion srudies 61
v
(a) Dependence on exposure time (mAs) ............................................................................................................. 6 1
(b) Dependence on peak voltage (kVp) ................................................................................................................ 64
.............................................................. 3.42 Determining volumetric breast density: phantorn stttdies 66
(a) Plastic wedge only .......................................................................................................................................... 66
(b) Aluminum wedge ........................................................................................................................................... 68
3.4.3 Preliminary clinical study- Conzparing alurninum to plastic wedge .............................................. 71
3 -5 CONCLUSION ............................................................................................................................................ 74
3.6 FEFERENCES ............................................................................................................................................ 76
CHAPTER 4: SUMMARY AND FUTURE WORK ............................... .... ....... 78 ................................................................................................................................................ 4.1 SUMMARY 78
4 . I . 1 Field fnhornogeneirv Correction ..................................................................................................... 78
4.1.2 Calculation of Volurnetric Breast Densiry ....................................................................................... 79
4.2 FUTURE WORK ......................................................................................................................................... 80
4-21 Breast Cancer Risk Prediction: Volzimerric Breasf Density in a Cfinical Stuc@ ............................ 80
.................................................................................................................... 42-2 Method Improvements -82
(a) Digital mammography .................................................................................................................................... 82
(b) Automation of breast and calibration wedge selrction ................................................................................... 83
(c) Compression paddle deflection: thickness error ............................................................................................. 84
4.2.3 Improving validation of volzrrnetric breast densiy estimation ......................................................... 85
.................................................................................................................................. 4.3 CLOSING REMARKS 86
4.4 REFERENCES ............................................................................................................................................ 88
List of Figures
Figure 1.1 . Anatomy of the brzast with a typical rnarnmograrn ........................................................ 5
............... Figure 1-2 . Example of the percent density calculation using projected area of the breast 9
Figure 1-3 . Density calculation using projected area as compared to the volume of the breast ...... 10
Figure 2-1 . Schematic of a typicd mamrnographic system ....................... .. .................................. 20
Figure 2-2 . Schematic diagram of the new calibration object (right) cornpared to flat object
imaghg ...................................................................................................................................... 22
Figure 2-3 . Comparison of field non-uniformity corrections, as affecthg Volumetric Breast
................................................................................................................ Density measurement 24
.............................................................................................. Figure 2 4 . Sample Sensitometry plot 2 6
Figure 2-5 . Mode1 geometry ............................................................................................................ 28
Figure 2 6 . Simulation results for heel effect ................................................................................... 30
............................. Figure 2-7 . Results of simulation of a 4crn 50/50 slab with a 28 kVp spectnun 31
Figure 2.8 . Photograph of the bowl phantom .............................................................................. 32
................. Figure 2.9 . Experimental results showing image profiles of 2cm and 4cm 50/50 slabs 35
Figure 3-1 . Plastic wedge used in estimation of volumetric breast density ..................................... 48
Figure 3.2 . X-ray attenuation is independent of object location within the path of the x-ray bearn .
................................................................................................................................................... 49
Figure 3.3 .
Figure 3.4 .
Figure 3.5 .
Figure 3.6 .
Figure 3.7 .
................................................................... Placement of the plastic calibration wedge 51
Sample three dimensional surface relating % density m, thickness and LRE ............... 52
...... Aluminum attenuation coefficient compared to fibroglandular and adipose tissue 54
......................................................... Aluminum wedge compared to the plastic wedge 55
.............................................. The "hole" phantom used in density estimation testing 56
vii
............................................................................................................. Figure 3.8. Thickness d e r - 57
............................................................................. . Figure 3-9 Calibration of aluminum step wedge 59
Figure 3-10 . Marnmogram of "hole" phantom ................................................................................. 60
........... Figure 3-1 1 . Cdibration of alurninum vs . plastic wedge (constant kVp, varying mAs) . ..... 63
Figure 3-12 . Calibration of aluminum vs . plastic wedge (constant mAs, varying kVp) ................. 65
Figure 3-1 3 . Calibration of aluminurn vs . plastic wedge (changing anode/filter combination) . . ,.. -66
Figure 3-14 . Breast Density Estimation using a plastic calibration wedge ...................................... 68
Figure 3-15 . Breast Density Estimation using alurninurn and plastic wedges ................................. 69
................................................ Figure 3-16 . Volurnetrk density estimation using a plastic wedge 70
. .. . Figure 3- 17 Volumetric density estimation using an aluminurn wedge .................................. 71
............ Figure 3-1 8. Comparing plastic and duminum estimations in a clinical setting ( by kVp) 73
..... Figure 3-19 . Cornparing plastic and durninum estimations in a clinical setting (by thickness) 73
.................. . Figure 4-1 Cornparison of Area density measurement to Volurnetric density measure 81
........................................... . Figure 4-2 Error in Volumetric Breast Density due to thickness error 85
................................. . Figure 4-3 Cornparison of Area Density to Volume Density measurements 87
... Vlll
List of Tables
3 Table 1.1 . Established Risk Factors for Breast Cancer in Women ......................... .... ...................... J
.............. TABLE 2-1 . Typical standard deviation and error in images of tissue-equivdent plastics 38
TABLE 2.11 . Effects of kVp changes on correction array ............................................................. 39
TABLE 2.111 . Effects of bowl phantom alignments on the correction array ..................... .... ..... -40
Glossary of Terms and Abbreviations
Risk Factor
Parenchyma
Stroma
Fibroglandular tissue
Adipose tissue
BD
VBD
LRE
Mo
Rh
Be
Al
PMMA
Cornmon characteristic that differentiates between patient with the
associated disease and those without
Ducts and lobules in the breast
Connective tissue in the breast
Radiographically absorbing breast tissue including parenchyma and
stroma
Fatty tissue, less absorbent to x-rays than fibroglandular tissue
Breast Density; Radiographically absorbing tissues in the breast
such as parenchpal and stroma1 tissues.
Percent Density; Percentage of the area of the breast occupied by
fibroglandular tissue
Volumetric Breast Density; Percentage of the volume of the breast
occupied by fibroglandular tissue
Peak kilovoltage; The energy of electrons hitting an anode to produce
x-rays. The maximum kilovoltage with which the x-rays can be
generated.
Log of Relative Exposure; Logarithm (base ten) of the relative
exposure of the radiographie film. The measurement is taken with
respect to a reference exposure.
Molybdenum
Rhodium
Beryllium
Aluminum
Polyrnethylmehacrylate, also known as trademark narne Lucite,
Plexiglass
Number of incident x-ray photons
Energy (kV) of incident photons
Linear attenuation coefficient (Um)
Thickness of an object (m)
Number of x-ray photons per pixel area
Shift correction used in inhornogeneity correction
Source to image distance
The proportion fibroglandular tissue in a colurnn of tissue above an
image pixel
Chapter 1 : Introduction
Breast cancer is the most commonly occurring cancer in women and, after lung cancer, is
the second highest cause of mortdity from al1 cancers. Lifetime breast cancer risk (up to the age of
85) for Canadian wornen is 1 in 9.5, and the risk of dying from breast cancer is 1 in 25.8'. This can
be compared to Iung cancer in women, which is less cornmon, but more lethai, with lifetirne cancer
risk is 1 in 19.9 and the risk of dying is 1 in 22.4'. Although the increased incidence of lung cancer
cases in women is worrisome, the causes of the disease are well known. Eighty percent of al1 lung
cancer in women is caused by cigarette smoking2. There is no such strong association for breast
cancer, as the causes for a large proportion of the incidence of this devastating disease are still
unknown. Although exact mechanisms causing breast cancer are not well known, it is possible to
predict the likelihood of breast cancer development, based on known risk factors. One of the
strongest known breast cancer risk factors, known today is the mammographic appearance of the
breast, where variations in the radiograph of a breast reflect the variations in tissue composition.
This thesis proposes a new, quantitative method of measuring breast density using the
information about the whole volume of the breast that improves on the current methods, which use
projected area of the breast. A review of known risk factors and an explanation of current
marnmographic appearance classification schemes are presented. The new technique is developed
showing that it is possible to determine the volumetric breast density of well-defmed, breast-like
phantoms. Furthermore, the method is compared to the existing computer-aided techniques,
showing that related, but different information is measured. As a part of a larger project, the
technique descnbed here will uhimately be used in the clinical setting with the expectation of
obtaining an even stronger risk factor than those obtained using current 2-dimensional algorithms.
1.1 Breast cancer ris& fac tors
Currently there are several factors that put women at higher than normal risk of developing
breast cancer, the most cornmody used ones are mentioned in Table 1-1. Besides age, perhaps one
of the most widely recognized risk factors is the familial history of breast cancer, where women
whose fmt degree relative (either mother or sister) has had breast cancer are about two to four
times as likely to develop cancer as women without a family history of this disease. Another,
related but much stronger risk factor is the presence of BRCAl and BRCA.2 gene mutations. The
onset of breast cancer when these mutations are present occurs much earlier, so that by the age of
60, 54.2% of women with BRCAl and 61% of women with BRCA2 mutation develop breast
cancer'. 4. By the age of 70, it is 85% of women with either mutation develop breast cancer,
making the presence of these mutations the strongest known indicator for breast cancer. However,
the occurrence of these gene mutations is rare, and separately the BRCAl or BRCA2 mutations
affect between 0.05% to 1% of the populations* 6. With such low occurrence in the general
population, these two mutations can explain only 3.3% of al1 instances of breast cancer7.
Some additional often-used risk factors for breast cancer are listed in Table 1-1. As can be
seen, the familial history and age constitute high relative risk of cancer. Women in the high rkk
group are more than four times as IikeLy to develop breast cancer as the women in the low risk
categorïes. Such risk factors may be used to modiw women's medical decisions. For example, the
decision whether to use postrnenopausal hormone-replacement therapys, age of screening,
fiequency of screening, lifestyle changes, and even prophylactic mastectomy to prevent breast
cancer can al1 be influenced by these factors.
Breast Density High Low B4.0
Age ( ~ r s ) Old Young >4.0
Country of birth N. America, Asia, Africa B4.0
Europe
Socioeconomic status High Low 2.0-4.0
Age at first full term pregnancy - > 3 0 yrs -= 20 y r s 2.0-4.0
Previous breast cancer (1 breast) Yes No 2.0-4.0
Benign proliferative disease Yes No 2.0-4.0
Famiiy history first degree relative Yes No 2.0-4.0
Farnily history (mother and sister) Yes No >4.0
Mutations of BRCA-1 or BRCA-2 Yes No >10.0
Marital status Never married Married 1.1-1 -9
Place of Residence Urban Rural 1.1-1.9
Nulliparity Yes No 1-1-1.9
Age at menopause Late Earl y 1-1-1.9
Age at menarche Early Late 1-1-1.9
Weight, postrnenopausal Heavy Lean 1.1-1 -9
Previous cancer ovary or Yes No 1.1-1.9
endometrium
Table 1-I. Esîablished Risk Factors for Breasî Cancer in wornen. Y. l u
Wornen in the high-risk column have an increased risk of developing breast cancer when compared
to wornen in the low-risk column.
1.2 Parenchyrnal appeara nce of the breast as a risk factor
One of the factors mentioned in Table 1-1, is the parenchyrnal appearance of the breast. The
breast tissue in women undergoes many changes during life. Aging, monthly hormonal cycles,
child bearing and menopause al1 influence the hormonal content of the breast, as weI1 as the
amount of comective, glandular (fibroglandular) and adipose (fatty) tissues within the breast.
These structural changes can be seen in mamograms. A mammographie image is forrned when
x-ray photons travelling through the breast, are absorbed, or attenuated by different tissues. The
parenchyma (ducts and Iobules), as weII as the stroma (connective tissues) attenuate more photons
than the fatty tissue, so fewer photons pass through the breast in the regions where such structures
are present. An intensimg fluorescent screen that produces light photons upon interaction with x-
rays absorbs the photons that p a s through the breast. The resulting image is registered on film
which is placed emulsion down, on top of the screen. When the film is processed, a gray-scale
image of the x-ray absorption by the breast is fonned. The anatomy of the breast and a sarnple
marnmograrn are shown in Figure 1 - 1. Anatomy of the breast with a typical mammograrn.". The
bright structures in the mammogam correspond to areas of stroma and parenchyma in the breast,
also reffered to as "dense" areas of the breast, while the darker regions consist mainly of fatty
tissue which transmits more x-ray photons, thus exposing the film more (makes it darker).
Figure 1-1. Anatomy of the breast with a typical mamrnogram. "
1.2.1 Current Methods of Parenchymal Pattern Classification
Several methods of analyzing mamrnographic density for the purpose of breast cancer risk
prediction exist; however, each method has some tradeoffs and limitations, which motivated the
work described in this thesis.
(a) Radiologisf class~jication - qualitative
Classification of mammograms by a radiologist was the first method developed to
determine breast density. Depending on the protocol, the mammograms are divided into several
groups based on their parenchyrnal appearance. ~ o ~ e " introduced a system which classified
breast patterns into one of four types: N1, P 1, P2 and DY. The N1 pattern is typical of a "normal"
breast composed mainly of fat, while the DY pattern describes a breast, where density of the
parenchyrna is most pronounced, and occurs in nodular, or cloud-like patterns. The P t and PZ
categories are associated rnostly with progressive ductal prominence, or parenchymai patterns
radiating away f?om the nipple, and Iesser degree of parenchyrnal density. The studies conducted
by ~ o l f e l " ' ~ have s h o w that this qualitative classification of radiological appearance of
mamrnograms into the four density groups can yield very strong estirnates of breast cancer risk.
The initial studies showed that women in the DY group are 37 times more Iikely to develop breast
cancer than those women in the NI g r o ~ ~ ' ~ . Other studies which used the same classification
scheme did not reproduce such hi@ reIative risks, but instead reported a risk factor of 2-2-43 for
the most dense category as compared with the least dense 12. 15-17
The disadvantage of quaiitative density estimation as used in the above studies is that the
density classifications used are subjective, and depend on the training of the participating
radiologists. Discrepancies as high as 60% have been reported in density assessment by two
different radiologists.
(6) Radiologist classcjZcation - quantitative
Another different, quantitative classification scheme of mamrnograms was used in the work
by Wolfe and saftlas16, Boyd er al1', and Byrne er al2'. In these studies mammograrns were
classified not only by the structure and appearance of rnarnmographic paren~h~mal patterns, but
instead by the quantitative method of estimating the percent of the mammograrn occupied by
radiographically dense tissue. The quantitative measure provided a stronger risk factor than the
original Wolfe parenchymal categones, giving relative risks of 4.3-6.05. Furthemore, the Byrne
study determined that 28% of cancers were attributable to mammographic breast density above
50%~' . This shows that the mammographic breast density, as measured by the proportion of the
breast area composed of epithelial and stroma1 tissues can explain a large proportion of occuning
cancers and can possibly be used as a predictor Muencing medical decisions regarding patient
management.
Quantitative andysis of mammograms descnbed above was at first done by radiologists,
who classified the images into groups by the2 apparent densities. Such classification yields itself
well to computer analysis and many studies have been performed with either cornputer-aided
methods or completely automated analysis.
(c) Cornputer-aided classijkation
Cornputer-aided methods for breast density estimation have been developed to improve
repeatability of density estimation. The interactive method described by ~ ~ n ~ ' ~ provides a
quantitative calcdation of breast density based on limited operator input. The projected area
method requires the use of digitized marnmograms, which are subsequently displayed on a
computer monitor. Fîrst, the operator selects the overall area of the breast, and then selects a
threshold above which al1 the pixels of the breast are considered to be dense. The percent density
(PD) of the breast is calculated as a percentage of the "dense" pixels in the whole area of the breast,
so that no information about the pattern or distribution of parenchyma is used. A study by Boyd
and ~~n~~~ showed that computer-aided analysis of mammograms can give a relative risk of 4.04
for women classified in the highest 25% density when compared to the lowest density group.
(d) Fuiiy-Automatic breast density estimation
Several attempts have been made to estimate breast density automatically 60m digitized
mamrnograrns. Fractal d i rnen~ion~~, histogram analysisu and feature selection2', have ail been
used for this purpose. Although some of these measures provide a predictive value for breast cancer
risk, the risk estimates are much smaller (ranging between 2.5-3.5) than the predictive values
obtained by radiologists' reading or the cornputer-aided method descnbed above2*. Furthemore,
7
poor repeatability of the fkactal dimension measurements has been demons~ated if more than one
method are used".
1.2.2 Disadvantages of Current Methods: Need for a New Method
The interesting outcome of al1 of these studies is that quantitative breast density estimation
by the radiologists yields stronger risk factors than either the qualitative parenchyrnal pattern
classification based on Wolfe ~Iassification, or the computer-aided, purely quantitative method of
breast density estimation. The improvernent of the quantitative visud assessrnent of breast density
over the qualitative visual pattern classification can be explained by the reduction of observer
variability resulting from elimination of subjective classification, where the focus is on the amount
of density, not its appearanceZ7. The difference between the quantitative assessrnent by radiologist
as compared to the compter-aided method is more difficult to resolve. One plausible explanation
for this observation is that radiologists are able somehow to infer the volume of the breast when
estimating breast density. During mamrnography, an exposure technique will be chosen to provide
the best possible contrast and image quality of the breast, without unnecessarily increasing the dose
to the patient28. So for a thin, fatty breast, the same thickness of fat will appear brighter on the
mamrnograrn than if a thicker, denser breast is imaged. En the cornputer-aided method, since a
brightness threshold is selected to denote "dense7' tissue, a thin fatty breast wiII be classified as
denser than the thicker fatty breast. A radiologist, using such information as more prominent
features like arteries or veins in t h i ~ e r , less dense breasts can probably compensate for this effect
by being aware of the thickness of the breast.
The current computer aided method is limiteci, since percent density of the breast is
caiculated as an area measurement, without considering the 3D nature of the breast. Fuahermore,
an al1 or nodiing cutoff is implemented, so that al1 objects below some brightness are considered as
8
non-dense, and al1 objects above this threshold are considered as dense. This is illustrated in Figure
* Distance Along the image
Figure 1-2. Example of the percent densiîy calcularion using projected area of the breast.
OnZy objecrs which have a brightness above the "Densis" cutoff are considered fo be dense. AZZ
other objecrs are classz~ed as fat.
As illustrated in Figure 1-3, it is possible to obtain identical looking rnammograms for two
very different breasts. Using a projected area method, these two mammograms will yieid the same
PD value, although the actual breasts Vary considerably in their density content.
VBD 35% VBD 55%
Figure 1-3. Density calcuZation usingprojected area as compared to the volume of the breast.
For the same imaging conditions, the absorption of ench breast is identical, so that the projected
image is identical, giving an overall Percent Densiîy (PD) as calmlated using the area method, of
42%. However, the actual thichess and composition of the breast is dzferent, so thut in one the
dense tissue occupies 35% of the breast volume, and in the other 55%.
f.3 Volumetric Breast Den sity Estimation
There are several reasons why volumetric measurement of breast density might constitute
an hprovement over existing methods of parenchyrnal pattern classification. First, as seen in the
discussion above, the variability of classification of densities between radiologists and among
different studies is hi&; providing a technique that is completely automated and quantitative, will
reduce such variability. Second, the curent methods al1 use infornation exclusively fiom the
projected area of the breast, as it appears on a mammogram. The three dimensionality of the breast
is not taken into account, but although projected area of the breast might stay constant, the actual
compressed thickness varies arnong patients. Thus: sorne of the possible information about the size
of the breast is missed if only projected area is taken into account.
The last argument for measuring volumetric breast density as opposed to the area method, is
based on breast cancer etiology. Most breast cancers mise f?om the epithelial Iining of the ducts.
Although the link between breast density and the causes of breast cancer is still unknown, the
intuitive approach is that if the actual amount of dense or parenchyrnal tissue is measured in the
breast, then there are more ducts, and thus more epithelial cells, so that the arnount of tissue at risk
fiom breast cancer is deterrnined. Increased density means more tissue at risk, and therefore higher
breast cancer occurrence. Already an association has been reported between mammographie
density and histological factors such as epithelial proliferation and stromal fibrosis2? Furthemore,
severd studies show that increased breast volume and projected size are correlated with increased
risk of breast anc ce?^ 30 supporting the argument that larger breasts contain more tissue at rkk, and
therefore provide a higher Likelihood of breast cancer. If the volume of the breast is exarnined,
more information about the actuâl amount of tissue at nsk wilI be known, than in two-dimensional
methods,
The hypothesis of the thesis is that it is possible to determine the proportion of
radiographically dense, fibroglandular tissues within a well-characterized, breast-like phantom
material.
This thesis proposes a quantitative method of breast density determination using the volume
of the breast. The method overcomes the shortcomings of the curent computer-aided methods,
which use only information about the projected area of the breast. Lnstead, knowledge of the
compressed thickness and irnaging conditions allows for exact determination of breast density.
11
To develop methodology for volumetric breast density (VBD), the project was divided into
two parts. First, mamrnograms had to be pre-processed, so that computer analysis could be
performed. Second, once the breast images were prepared correctly, a method of extracting
voiumetric information £kom projected rnammograms had to be devised. A chapter of the thesis
has been devoted to each of these topics.
1 -4.1 Chapter 2: Field lnhom ogeneity Correction
When a uniform thickness and composition object is imaged in a typical mammographic
setting, its image does not appear uniform, but changes in intensity along the image. In
mammographic classifications by the radiologists such inhomogeneity does not constitute a
problem, but in quantitative computer analysis, each point along the image has to reflect the
thickness and composition of the irnaged object. Thus, the response of the imaging system should
be independent of the location along the imaging plane. To perforrn a computer anaiysis of the
mammogram, it is necessary to cornpensate for such inhomogeneities. This chapter develops
methodology used to correct rnammograms in such a way, that if a siab of uniform thickness and
composition is imaged, every point dong that object is represented by the same brightness as al1
other points,
1.4.2 Chapter 2: Volumetric B reast Density Estimation
In the Volumetric Breast Density Estimation chapter, a method of volumetric breast density
estimation is developed with the use of a breast tissue-like, well-defined calibration object shaped
like a step wedge. The methodology is then tested on well defined, breast-like plastic phantoms.
Finally, some preliminary clinical studies are presented in which the calibration objects are used
and tested. In addition, the results of the new volumetric breast density estimation technique are
compared with the standard method based on projected area.
1-4.3 Chapter 3: Summary a nd Future Work
The final chapter of the thesis surnmarizes the methodology and highlights some of the
most important results. Discussion of possible problems in the volumetric density estimation are
then given, dong with suggestions for possible solutions.
i. 5 References
National Cancer Institute Of Canada, Canadiun Cancer Statistics 2000. 2000, Toronto,
Canada,
Surgeon-General, Reducing the Health Consequences of Smoking: 25 Years of Progress.
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D.F. Easton, D. Ford and D.T. Bishop, Breast and Ovarian Cancer Incidence in Brcal-
Mutation Carriers. Breast Cancer Linkage Consortium. Am J Hum Genet, 1 995. S6(l) : p.
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D.F. Easton, L. Steele, P. Fields, W . Ormiston, D. Averill, P.A. Daly, R. Mcrnanus, S.L.
Neuhausen, D. Ford, R. Wooster, L.A- Cannon-Albright, M.R. Stratton, and D.E. Goldgar,
Cancer R i s h in Two Large Breast Cancer Families Linked to Brca2 on Chromosome
l3q12-13. Am J Hum Genet, 1997.61(1): p. 120-128.
C.I. Szabo and M.C. King, Population Genetics of Brcal and Brca2 [Editorial; Comment].
Am J Hum Genet, 1997.60(5): p. 1013-1020.
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49(1): p. 33-64, 32.
S.S. Coughlin, M.J. Khoury and K.K. Steinberg, Brcal and Brca2 Gene Mutarions and Risk
of Breast Cancer. Public Health Perspectives. Am J Prev Med, 1999. 16(2): p. 9 1-98.
K. Armstrong, A. Eisen and B. Weber, Primary Care: Assessing the Risk of Breast Cancer.
N Engl J Med, 2000.342(8): p. 564-572.
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Technical Aspects of Breast Imaging, mird Edition, A.G. Haus and M.J. Y a e , Editors.
1994, RSNA. p. 9-2 1.
14
[IO] D. Ford, D.F. Easton, M. Stratton, S. Narod, D. Goldgar, P. Devilee, D.T. Bishop, B.
Weber, G. Lenoir, J. Chang-Claude, H. Sobol, M-D- Teare, J- Struewing, A. Arason, S.
Scherneck, J. Peto, T.R. Rebbeck, P. Tonin, S. Neuhausen, R. Barkardottir, J. Eyfjord, H,
Lynch, B.A. Ponder, S.A. Gayther, M. Zelada-Hedman, and Et Al., Genetic Heterogeneity
and Penetrance AnaZysis of the h i and B r c a Genes in Breast Cancer Families. The
Breast Cancer Linkage Consortium. Am J Hum Genet, 1998.62(3): p. 676-689.
[ I l l Cardiothoracic haging: Normal Anatomy of the Breast. 2000, Yale University School of
Medicine.
[12] J.N. Wolfe, Risk for Breast Cancer Development Determined by Mammographic
Parenchyrnal Pa~ern. Cancer, l976.37(5): p. 2486-2492.
[13] J.N. Wolfe, Breast Patterns as an Index of Risk for Developing Breast Cancer. Am J
Roentgenof, 1976. 126(6): p. 1 130- 1 137.
[14] J.N. Wolfe, Risk of Developing Breast Cancer Determined by Mamrnography. Prog Clin
Bi01 Res, 1977.12: p. 223-238.
1153 A.F. Safilas, J.N. Wolfe, R.N. Hoover, L.A. Brinton, C. Schairer, M. Salane, and M. Szklo,
Marnmographic Parenchyrnal Patterns as Indicators of Breast Cancer Risk Am J
Epidemiol, 1989. 129(3): p. 5 18-526.
1 J.N. Wolfe, A.F. Saftlas and M. Salane, Marnmographic Parenchymal Patterns and
Quantitative Evaluation of Mammographie Densities: A Case-Control Study. Am J
Roentgenol, 1987. 148(6): p. 1087-1092.
[17] I.T. Gram, E. Funkhouser and L. Tabar, The Tabar CZasszjkation of Marnmographic
Parenchymal Patterns, Eur J Radioi, 1997.2412): p. 131-236.
[la] H- Lee-Han, G. Cooke and N.F. Boyd, Quantitative Evaluation of Mammographic
Densities: A Cornparison of Methods of Assessment- Eur J Cancer Prev, 1 995.4(4): p. 285-
292.
[19] N.F. Boyd, J.W. Byng, R.A. Jong, E.K. Fishell, L.E. Little, A.B. Miller, G.A. Lockwood,
D .L. Tritchler, and M. J. Yaffe, Quantirative Classification of Mammographic Densities and
Breast Cancer Risk Resulrs fi-orn the Canadian National Breast Screening Study. J Natl
Cancer Inst, 1995,87(9): p. 670-675.
[20] C. Byrne, C . Schairer, J. Wolfe, N. Parekh, M. Salane, L.A. Brinton, R. Hoover, and R.
Haile, Mamrnographic Features and Breast Cancer Risk: Effects with T h e , Age, and
Ménopause Status. J Natl Cancer Inst, 1995.87(2 1): p. 1622- 1629.
[21] J.W. Byng, N.F. Boyd, E. Fishell, R.A. Jong, and M.J. Yaffe, The Quantirative-AnaZysis of
Mammographic Densities. Phys Med Biol, 1994.39(10): p. 1629-1 638.
[22] C.B. Caldwell, S.J. Stapleton, D.W. Holdsworth, R.A. Jong, W.J. Weiser, G. Cooke, and
M.J. Yaffe, Characterisotion of Mammographic Parenchymal Pattern by Fractal
Dimension, Phys Med Biol, 1990.35(2).
[23] J.W. Byng, N.F. Boyd, E. Fishell, R.A. Jong, and M.J. Yaffe, Atrtomared Analysis of
Mamrnographic Densifies. Phys Med Biol, 1996.4 l(5): p. 909-923.
[24] P.G. Tahoces, J. Correa, M. Souto, L. Gomez, and J.J. Vidal, Cornputer-Assisted Diagnosis
- the Classifcation of Marnmographic Breasr Parenchymnl Patterns. Phys Med Biol, 1995.
40(1): p. 103-1 17.
[25] M.J. Yaffe, N.F. Boyd, J.W. Byng, R.A. Jong, E. Fishell, G.A. Lockwood, L.E. Little, and
D.L. Trïtchler, Breast Cancer Risk and Measured Mamrnographic Densis? Eur J Cancer
Prev, 2998. 7 Suppl 1: p. S47-55.
[26] N. Karssemeijer, Autornated Clossification of ParenchymaI Patterns in Mamrnograrns- Phys
Med Bio1, 1998.43(2): p. 365-378-
[27] 1. Kato, C. Beinart, A. Bleich, S. Su, M. Kim, and P.G. Toniolo, A Nested Case-Control
Sfudy of Mamrnographic Patterns, Breast Volume, and Breast Cancer (New York City? Ny,
United States). Cancer Causes and Control, L 995- 6(5): p. 43 1-43 8.
[28] L.W. Bassett, R.H. Gold and C. Kimme-Smith, History of the Technical Development of
Mammopaphy, in Syllabus: A Cafegorical Course in Physics Technical Aspects of Br-east
Irnaging, n i rd Edition. A.G. Haus and M.J. Yaffe, Editors. 1994, RSNA. p. 9-21.
[29] N.F.Boyd,G.A.Lockwood,J.W.Byng,D.L.T~tchler,andM.J.Y~e,Mammographic
Densities and Breast Cancer Risk. Cancer EpidemioIogy, B iomarkers and Prevention, 1 998.
7(12): p. 1133-1 144.
[30] D. Scutt, J.T. Manning, G.H. Whitehouse, S.I. Leinster, and C.P. Massey, The Relationship
between Breast Asymmetry. Breast Size and the Occlirrence of Breast Cancer. Br J Radiol,
1997.70(838): p. 1017-1021.
Chapter 2: Field ln homogeneity Correction
(Part of paper under the title "Field non-uniformity correction for quantitative analysis o f digitized marnrnograms", by
O. PawIuczyk and M Yaffe, submitted and accepted for pubIication in the journai Medical Physics)
2.1 Introduction
Recendy, several applications have been developed which require digitization and
quantitative analysis of marnmograms such as marnrnographic breast density measurement. Such
analysis is impaired, however, by several effects intrinsic to image acquisition, which introduce
non-uniform intensity and contrast changes throughout the images. The image formed is not only a
function of the thickness and composition of the imaged object, but also incorporates artifacts due
to the imaging system itself. These sarne effects generate errors when one attempts to determine
volumetric breast density fiom such uncorrected, digitized images. Correcting for these
inhomogeneities allows more meanin=@ quantitative measurements to be made.'.
This chapter describes a method that combines both empirical and analyticai models to
correct for field non-uniformity effects in screen-film marnrnography. This is very important in
determining of volumetric breast density, because to determine breast composition fiom a
mammograrn, the variations in the intensity of image should be due only to changes in either
diickness or the composition of the breast. However, uncorrected images have intensity variations
that are due to the imaging system and not the breast itself.
The objective of this chapter is to negate the effects of the imaging system, thus creating an
image in which spatial variations in the image signal are due only to variations in composition or
thickness of the breast. Thus, except for the effect of random processes such as quantum noise and
film granularity, the data from an image of an object of uniform composition and thickness should
be uniform. The process presented in this chapter builds upon the earlier work of Highnam et al
18
'and Smith et al.'. They both used an image of a "blank" film (exposure in air only) to correct for
field non-uniformity caused by the heel effect, inverse square law and path obliquity. However,
such an approach does not consider spectral beam hardening effects due to the breast. Furthemore,
it does not separate the effect of path obliquity in the imaging system from that occuning in the
breast.
Following a bnef discussion of the factors contributhg to field non-uniformity in
marnrnograms, a series of simulations which were performed to determine the magnitude of these
effects is described. h a g e pre-processing is performed to linearize the response of the screen-film
system. An empiricd correction utilizing an image of a spherical section, bowl-like phantom is
then used to remove the non-uniformities caused by the inverse square law, path obliquity through
components of the imaging system and the heel effects. Finally, a theoretical correction for path
obliquity in the breast is applied to the image to create a marnmogram where variations in gray-
levels correspond exclusively to the changes of either composition or thickness of the breast.
2.2 Theory
Mammograrns are generally analyzed under the assumption that variations in optical
density on the film are due solely to the changes in the composition of the breast. However, several
physical effects associated with image acquisition combine to cause field non-uniforrnity and thus
cause intensity variation across an image of an object of uniform composition.
An illustration of a typical marnmographic examination is shown in Figure 2-1. The insert
depicts the paths of electrons and x rays in the anode target in more detail.
Centrai ray i 1:
i '=:-Compression Plate
i . Breast
Focal Spot (0.0) Intensifying Screen
Fiwre 2-1. Schernatic of a typical nzamrnographic system.
The heel effecr (a vxa y, path obliquity (t vs. t 7 and inverse square lm @ vs. b ') are illustrated
Figure 2-1 addresses several effects, which contribute to field non-uniformity. In a typical
mamrnographic x-ray tube, the intrïnsic target angle on the rotating anode and the tilted mounting
of the x-ray tube combine to yield an angulation of the target with respect to the central ray of a r
22". The tube is mounted such that the focal spot is located at, or very close to the chest wali.
Assuming a uniformly cornpressed breast, the path length, t, of x-rays directly below the focal spot,
ie. the central ray, is shorter than t', the ray that passes throiigh the breast at some other angle. This
path length eEect occurs in d l objects in the x-ray beam, so that attenuation occurs non-unifomly
in the filter, compression plate, the breast, grid, image receptor and other components of the
20
mammographie system. Because lower-energy x rays in the spectnim are attenuated to a greater
degree than the higher energy quanta, both the angled anode and obliquity of the beam paths
contribute to "beam hardening." This means that the mean beam energy increases with increasing
angle a, thus stronger interaction with the film occurs. The effect occurs in both dimensions, so
that beam hardening increases with distance fi-om the central ray in the image.
The inverse square law effect occurs due to the divergence of the x-rays as they move
M e r away fiom the source, causing the fluence of x rays to reduce as distance in the image from
the cenîral ray increases. Finally, the tilted x-ray target is responsible for the heel effect. X-rays
generated in the anode undergo a non-uniform attenuation (self-filtration) as they travel along
different path lengths to escape the anode. As seen fiom the insert to Figure 2-1, the path Iength of
x-rays through the anode is dependent on a (a vs. a'). Furthemore, because the anode is tilted, the
effective focal spot size varies with the position along the imaging plane. The combined result of
al1 of the effects described above is that both the intensity and the energy spectrum of x-rays vary
along the irnaging plane. 5 -7
Previous field inhomogeneity corrections attempts, for example those by Highnam et al. as
well as Smith et al. both used an image of a "blank" film to correct for field non-uniformity caused
by the heel effect, inverse square law and path ~ b l i ~ u i t ~ . ~ . In this correction, a radiograph of a
completely empty setup (Le. no breast or compression paddle) is taken. The image is then
subtracted fi-orn each marnrnogram obtained on the same machine, with the hopes of removing
some of the non-unifomzity effects present in the system. However, such an approach cannot
separate the inverse square law phenornena fiom the path obliquity effect and the resulting
corrected images cannot be completely uniform. Furthemore, since there are no attenuators in the
path of x-rays, beam hardening does not occur in air, but is present when a breast is irnaged.
Finally, the scatter conditions in the imaging system are different when a breast is present, than
when there are no attenuators in the path of the x-rays.
This chapter deveiops an empirical correction, which uses a phantom made out of material
with similar x-ray attenuation to that of breast to obtain a correction image. The phantom is
designed in such a way, as to separate the inverse square Iaw and heel effects fiom path obliquity.
This allows for empirical correction for field non-uniformity stemming fiom the heel effect and
inverse square Iaw. A theoretical correction c m be implemented for the path obliquity effect.
Figure 3-2. Schematic diagram of the new calibration object (right) compared to jZat object
imaging.
As c m be seen in Figure 2-2, using a flat slab of material to correct the non-uniformity effects
would compound any effects occurring at the anode, path obliquity through the sIab itself. If a
spherical phantom is used instead, the path obliquity effect of the object is removed, and the
registered correction image is a result of the inverse square law and heel effect only.
Figure 2-3 shows the effects of field non-unifonnity on estimation of breast density. The
figure shows a calculation of breast density of a well-defined phantom with a correction similar to
the "blank" film approach, and with the correction developed in th is chapter. As can be seen, a
good correction scheme for field non-uniforrnity is essential for acceptable volurnetric breast
density estimation. The rest of this chapter will describe the effect of field non-uniformity
correction developed, its repeatability and application.
1 O 5 1 O 15 20
Distance from chest walI (cm)
Figure 2-3. Cornparison of field non-unifomity corrections, as affecfing Volume~ic Breasî
DensiSr measurernent.
Density of a well defined phantom (shown here as ac~uul) has been estimated afrer correction with
a correction using an image of a flat object (flot slab), and wifh rhe rnethod described here (bowl
phantom).
2.3 Materials and Methods
2.3.1 Image Acquisition
A Lorad M-II dedicated marnrnography unit (Lorad Medical Systerns Inc., Danbury,
Connecticut) was used for al1 data acquisition. The system is equipped with a high fiequency
generator, a molybdenum (Mo) target, berylliurn (Be) window and a Mo filter. The nominal focal
spot size of 0.3 mm was used for the experiments described here. Although the machine also has a
fully automatic exposure control, the peak kilovoltage (kVp) was set manually with auto-timer
enabled. Images were obtained on Kodak MR 2000 screen-film combination where both 18x24 cm
and 24x30 cm film cassettes were used. The films were then digitized with a Lurnisys 85 digital
scanner, atl2 bits and a resolution of 260 p. The scanner was calibrated each scanning day, to
ensure a linear, negative-siope relationship between its output and optical density on the film which
tends to Vary with humidity and the batch of film used.
2.3.2 Image Pre-Processing
The response of the screen-film combination is not Iinear with the nurnber of x-ray quanta
reaching it. The relationship between the optical density of the processed film and the logarithm of
the x-ray energy absorbed by the screen is a sigmoidal fimction. A very similar cuve is obtained
when instead of optical density, the brightness of the film is recorded at each step.
To correct for film non-linearity, an image of an optical, 2 1 step sensitometric strip (relative
exposure increased by a factor of with each step) was obtained for each set of experimental
images. To avoid flare and artifacts in the scanning process due to large gradients in optical
density, an optical mask was used to cover areas of large contrast between the background and
exposure steps of the sensitometnc sûip. The image was then digitized, and a sensitometric curve,
shown in Figure 2-4, was obtained. This curve was then used to convert the digitized image into an
image of logarithm (base ten) of relative exposure per pixel (LRE) that the film undenvent.
Figure 2-4 Sample Sensitomeiry plût.
The pixel brightness is plotred against Zogarirhm base ten of relatfve exposure L E , as determined
by an optical sensitornetric strip. As can be seen the exherne ranges of LRE fa11 in the non-linear
region of this curve
2.3.3 Simulation
Simulations were performed to predict the magnitude of the effects of inverse square Iaw .
and path obliquity on inhomogeneity in the field intensity. The x-ray spectrurn of the Lorad
machine (Mo target and filter) was measured at 26 kVp (manual exposure control), using an
Amptek CZTlOO room temperature spectrometer aligned with a 50 p pinhole positioned in the
primary bearn. From this spectnim, the transmission of 2 cm and 4 cm uniform of 50%
fibroglandular and 50% fatty breast tissue (SOI50 material) was calculated. Energy dependent
attenuation coefficients for the tissue equivalent materials fiom were used for each 0.5 keV
step. The energy absorbed by the screen was then caiculated at each position of the imaging plane
(x,y), using the expression in Eqn 2.1 :
Eqn 2.1
Where No(x,y,E) is the number of photons with energy E that would be incident to the
pixel at position (x,y) in the absence of attenuators in the beam, p, and are the attenuation
coefficient and the thickness of the j" object respectively, and pst,,, t,,., are the correspondhg
parameters for the intensiwg screen. The energy dependent linear attenuation coefficient of the
GdtOtS screen denoted by pscr,,, has been calculated using the attenuation coefficients of
individual elements in the screen, combined according to methods provided by Johns and
~unnin~ham'. It was assumed that the light exposure to the film was linearly dependent on
Edepxited-
The simulation results were compared with experimental images, for which the effect of
film non-linearity was already removed; therefore, the simulation did not take into consideration
the characteristic cuve of the film. Furthemore, the effects of scatter and the grid were not
included. The transmission of the Be window and Mo filter of the x-ray source were included in the
experimentally-measured spectnun and so are not explicitly shown in Eqn 2.1. Figure 2-5 shows
the geometry considered in the simulation.
Figure 2-5. Mode2 geornew
An individual slab used in step-wise process is shown.
The breast was considered to be a set of uniform slabs of tissue. This allowed variation of
matenal composition through the breast. Step-wise calculation of the nurnber of photons going
through individual slabs was performed, with the quantum fluence transmitted by one slab being
the fluence entering the slab below it. First, the dispersion of x-rays due to the inverse square law
was considered.
Eqn 2-2
ro
where @ is the number of x-ray quanta per pixel area. Because
divergence was essentidly removed by Eqn 2.2: only the path obliquity
the dependence of beam
effect and the additional
effect of distance dong a ray had to be considered for each step. Ali the subsequent steps were
calculated using the relationship,
- 4' Eqn 2-3 ~ ( x Z I Y Y ~ J - -
ri
It is then possible to determine the number of x-ray quanta per pixel area at a point ( ~ ~ ~ , y ~ ~ ) ,
if no scatter term is included, for each energy in the spectrum:
The @ was interpolated for each new slab, for constant pixel
effects of path obliquity and the inverse square law to be considered
Eqn 2-4
area. The simulation allows the
individually or together.
Furtherrnore, each cornponent in the irnaging systern including the breast and compression
paddle c m be sirnulated, providing more in£orrnation about the effects that each has on image
For image receptors that are flat, it is necessary to consider an additional factor. As x-rays
diverge spherically from the source, the pixel at (x,y) will be exposed not only by x-rays that travel
a longer distance r', but its surface will be tilted with respect to the ray incident on the center of the
pixel. Including the correction for tilt, the final fluence at point (x,y) is:
Eqn 2.5
A second part of the simulation considered the heel effect. The stopping power of
electrons in molybdenum was used to calculate the point of x-ray emission within the target. The
geometry of the anode (insert to Figure 2-1) was then considered, and attenuation of x-rays through
the anode was calculated for each energy, thus also simdating a beam hardening effect. The
projection area of the anode, i.e. its effective size as seen at different locations in the imaging plane,
was also calculated. Combining these two calcuIations allowed for a prediction of relative number
of x-ray quanta of each energy incident on a given pixel of the imaging plane. Figure 2-6 is a
profile of the LRE along the center of the irnaging plane, caicuiated for 25 keV electrons incident
on a molybdenum
the intensity of the
anode with the total tilt of 22O. As the distance from the centrd ray increases,
bearn drops quickly.
-30 -20 -10 O 10 20 30 40 50 Distance along image plane (cm)
Figure 2-6. Simulation results for heel effect.
The relative intensity of photons along the imaging plane is plotted for a rnolybdenurn anode with
total tilt of 22", at 25 kVp. n e zero position indicates the focal spot at the chest waZ1.
The combined results of the simulation for a 4cm 50/50 slab imaged with a 28 kVp, Mo/Mo
spectnim are shown in Figure 2-7. Simulation data were adjusted so that the signal at chest wall is
the same for ail cases. As can be seen fiom the figure, the most significant image non-unifonnity
stems fiom the heel effect, however both path obliquity and inverse square law contribute as well.
Because the measured x-ray spectnun and the energy-dependent attenuation coefficients were
30
incorporated in the simulation, the graph of "all effects" includes the beam hardening associated
with the heel effect and with the path obliquity in the filter, compression plate and image receptor.
2'
inverse Square Law efh. I
-I compression paddle ath obliquity
AI1 effects
1.41 I O 2 4 6 8 I O 12 14 16 18 20
Distance from chest wall (cm)
Figure 2- 7. ResuIts of simulation @a 4crn 50/50 slab with a 28 kVp spectrum.
AU resuZts in LRE were shljied to pravide the same signal intensiîy at the chest wall,
2.4 Empirical Field lnhorn ogeneity Correction
2.4.1 Bowl Phantom
empirically obtained correction matrix was determined by imaging a specially-designed
calibration object. This was machined in the f o m of a sphencal shell, so that t = t' for al1 x and y.
Its image corresponds to the effects of the target angle, inverse square law and bearn obliquity
through al1 objects in the x-ray bearn except the breast. Two of these "bowl" phantoms were made
of polyrnethylmethacrylate (PMMA). Both phantoms have an outer radius of curvature of 20 cm,
but their shell thicknesses are 2.2 cm and 4.4 cm respectively. These sphencal shells are supported
by three legs, each 45 cm long; so that the phantom can be placed directly under the source with its
axis of symmetry aligned with the centml ray (Figure 2-8). To facilitate positioning, a set of lead
rnarkers has been embedded in the top and bottom surface of the phantom. Correct placement of
each phantom is indicated when the markers are superposed on the image. The phantoms were
made of PMMA, as this material has attenuation properties that are reasonably close to those of
breast tissue. Any beam hardening and scatter conditions present in the breast will be similar in
PMMA. l0-
Figure 2-8. Photograph of the bowlphantorn.
The phantom is positioned by radiographie alignment of markers a[ the centre of curvature.
Because each bowl phantom is a section of a sphere centered at the focal spot, the x-rays
travel through the same thickness of the material in each direction, so that there is no beam
obliquity effect in the phantom. Unlike in the "blank" film method, the registered image is
therefore a combination of only the heel effect, inverse square law and any other inhomogeneities
intrinsic to the marnmography system, completely removing the effects of beam divergence, or
padi obliquity. Thus, using this information obtained fiom imaging of the bowl phantom, it is
possible to correct al1 subsequent images for field inhomogeneities from the system, as well as
inverse square law and heel effect. For this purpose, a correction array is calculated.
Each of the bowl phantoms was imaged at multiple kilovoitage values. Each experiment
was performed three times to reduce the effects of noise. The images were then digitized, and,
using the sensitometry data, were converted into LM- Local variations were smoothed out using a
mean filter with a kernel of 5 mm since the digitization process can cause a slight misalignrnent (<
5 mm) in multiple scans of the same film. A 1 x 1 cm area around the central ray of the image
(containhg 1480 pixels) was then averaged, and a rnean L E value, LRE, was calculated for that
region. Using the LRE, for the central ray as a reference, the correction image C(x,y) was
detennined for ail x,y according to the expression,
C(X, = ZEq -'LRE(x,y) Eqn 2.6
Finally, to obtair? a fmal, more stable empirical correction array, al1 three sets of
measurements were averaged for each of the bowl phantoms. The final correction array was then
added to the LRE of uncorrected images to obtain field inhomogeneity corrected data sets.
2.4.2 Path Obliquity Correctio n
If the breast is compressed to a uniform thickness, t, the actual thickness of tissue through
which x-rays pas , r', will Vary with the position almg the imaging plane @,y) fiom its minimum
values at the central ray (0,O) as described by Eqn 2.3. and there will be increased beam attenuation
due to the greater thickness. If the average linear attenuation coefficient of the breast pbT at the
effective energy of the x-ray bearn zind r are both known, it is possible to determine a first order
correction for path obliquity.
When the digitized images are converted to LRE, the transmission equation for the breast
dong the centrai ray,
N, (0,O) = No (0,O) e-p*r*" Eqn 2.7
becornes:
'''1 (o,o) = log,, L h ( ~ 0 (O~O)) - p h t h , 1 Eqn 2.8
where No is the number of x-rays incident on the object .
Similady, at any position (x,y) in the image phne:
L R ~ ( ~ , Y ) = log,, e [~~NO(~~Y))-W', ,] Eqn 2.9
After the image has been corrected for field inhomogeneities using the bowl phantom, the
nurnber of photons f i (x,y) incident on the object is effectively equd to No (0,O) for al1 (x,y). From
Eqn 2.3, Eqn 2.8 and the source to image distance (SID), we obtain the log transmission, corrected
for path obliquity in the breast:
LRE,(~:Y)= LRE,(~,Y)+ log,, e
2.5 Results
2.5.1 Non-Uniforrnity Correction
Figure 2-9 shows the non-uniforrnity correction applied to the images of both 2 and 4cn1
uniform slabs of 50% fibroglandular and 50% adipose breast tissue equivalent plastic. Because the
attenuation coefficients and thickness are known for these two slabs, it was also possible to correct
for path length effects in the slabs. The linear attenuation coefficient was chosen for the 50/50
matenal close to the mean spectral energy of a 28kVp Mo/Mo spectnim (16.86 keV). The two
plots represent the mean LRE profile of each slab (each point corresponds to the mean of 200
pixels (20x 10) rectangle was sampled across the profile), at the center of the imaging plane (y = O),
fiom the chest wall to the opposite edge of the image. The images were obtained at 28 kVp, with
automatic exposure timing. The 2-cm slab was irnaged at 6.4 mAs, the 4-cm slab at 26.4 mAs. The
34
correction matrix described in tbe Methods section was used to correct for the intiinsic Geld
inhomogeneities. Results are shown both with and without correction for path obliquity in the
slabs. Performance of the correction was assessed by calculating the standard deviation, o, in LURE
for 90 points along the profile (every tenth 260 pn pixel was sampled) in the corrected image. The
standard deviation of the mean LRE of the profile shows the gross deflection of the profile f i o m its
mean. In a well-corrected image, o is reduced since most of the points along the profile lie alormg a
sîraight horizontal line. Application of the correction to the images brought the profile of the
uniform slab to be almost uniform, in both cases with O of the profile to be less than 0-05.
Furthemore, both of these two different data sets were corrected with a single correction matzrix,
obtained by irnaging the 4.4-cm bowl phantom at 27 kVp.
Profile of a 2 cm 50/50 unifomi breast equivalent slab
I Path obtiquity and bowi phantom. (1.84=0.03)
1.9 -
LU 5 1.7 - No correction (?.72=O-ZO)
1.6 -
1.5 .
1 -4 O 2 4 6 8 10 12 14 16 18 20
Distance from chest wall (cm)
Profile of a 4 cm SOI50 uniforni breast equivalent slab
2l
.. . O 2 4 6 8 10 12 14 16 18 2 a
Distance from chest wall (cm)
Figure 2-9. Experimental results showing image profiles of 2cm and ilcm 5060 slabs.
Correctedprofies together with the mean and standard deviation are also shown.
Comparing the empirically obtained results of Figure 2-9 to the previously discusësed
simulation shows that the simulation predicts some field inhomogeneity. However, it does not
sufEciently explain the non-uniformity around the chest wall area, where a maximum intensity
occurs at a position 6 cm away from the chest wall this is probably due to two factors. First, the
focal spot not located exactly above the edge of the imaging plane. Second, the scatter/primary
ratio for a breast is lower at the edge of the breast than in the middle" and will reduce the LRE of
the image in that region. The close agreement of the simulation with the actual experirnentd
results allowed us to explore the effects of other objects such as the polycarbonate compression
plate on field inhomogeneity. Simulations indicate that the presence of the compression plate
causes a minimal change in the system. In fact, in the simulation, the presence of the compression
plate appears to decrease the effect of path obliquity. This un-intuitive result can be explained by
the design of the simulation, where the LRE signal at the chest wall has been adjusted to have the
same value for dl factors under consideration. There is a progressive hardening of the beam with
distance away fiom the chest wall occurring in the x-ray target and filter. The increasing beam
quality appears to outweigh the increase in thickness of the compression plate caused by path
obliquity. Thus, the paddle appears to become more transmissive away f?om the chest wall.
2.5.2 Validating Bowl Phanto rn Correction
Although the bowl phantom correction provided satisfactory results in compensating for
field inhomogeneity, the practical use of such an ernpïricd correction depends on the repeatability
of the results. A set of experiments were performed to determine changes in the correction array
due to different kVp values and alignments.
First, blocks of different thickness, made of either 100% fibroglandular and 100% adipose
breast-equivalent materials were imaged directly underneath the focal spot at 26 kVp with
automatic control of exposure tirne. An area o f 1 x 1 cm was sampled (1 480 pixels) for each block,
and both the mean LRE, and standard deviation, o, of the LRE values were obtained for the region.
The standard error of the mean, O , . was then calculated, as s h o w in TABLE 2-1. As can be seen
fiom the table, the error of the mean is large for 7 cm gland. This is probabiy due to the scatter
created in a thick slab of higher attenuation material. The detected radiation will have a larger
component of scatter photons than in the other cases.
3 cm fat 2.554 0.0425 1.1E-3
5 cm fat 2.103 0.0 1 07 2.8E-4
7 cm fat 1.624 0.01 X3 2.9E-4
3 cm gland 2.209 0.0 169 4.4E-4
5 cm gland 1.524 0.0 140 3.6E-4
7 cm gland 1 .O29 0,0269 7-OE-4
TABLE 2 4 Typicai standard deviation and error in images ofrissue-equivalent plastics.
Vùryiing thickness blocks made of either fat or gZandtdar tissue-equivalent plastics were imaged.
Typical rnean LRE, values obtainedfiom averaging pkels fiom a square with dimensions of Ixl
cmZ (1480 pixels) close to the focal spot, 2 cm u w q from the cchst wall of each image. The
standard deviafion a, and the standard error of the mean, O,, are shown.
To evaluate the effect of using correction matrices abtained at different kVp values, three
correction matrices were obtained by imaging the same alignment of the bowl phantom, at 25, 26
and 27 kVp. The mean correction values C(x,y), at a distance x from the chest wall dong the center
of the image were calculated according to Eqn 2.6, for each of the three images and are shown in
TABLE 2-11. For distances closer than 20 cm fiom the chest wall, the differences between the
three correction matrices are -0.01 L E , which corresponds to c 1% of the expected LRE, value
for 7 cm glandular material and < 0.4% for 3 cm of adipose.
C(x,y) for distance x fkom chest wall
~ V P 1 cm 5cm 10cm 15cm 20cm
TABLE 2-11 Effects of kVp changes on correction a r r q -
Mean correcfion values C(x,y) in LRE af a disrance x fiom chest wall, d o n g the centre of the
image, for three bowl phanforns obtained at d~flerent kVp seftings.
A thud experiment was perforrned to determine the effects of repositioning of the bowl
phantom on the correction matrix. Five images of the 4.4-cm bowl, al1 at 26 kVp and automatic
exposure control, were obtained over a period of three months. A correction matrix was obtained
for each image, as explained previously. The standard deviation, os, of the mean correction values
C(x?y) was then calculated for the f ive images. The variations between the images are represented
as a percent of os / L E , values for different thickness and composition blocks in TABLE 2-m.
As in the case of different exposure conditions, the variations at distances less than 20 cm fkom the
chest wall are small, approaching -2%.
0- Material - x 100%
3 cm fat 1.6 0.5 O. 1 O -3 O -4 O .9
5 cm fat 0.5 0.6 O. 1 O -4 0.5 1.1
7 cm fat 0.6 0.8 0.1 0.5 0.7 1 -4
5 cm gland 0.7 O -9 O. 1 O -5 0.7 1.5
7 cm gland 2.9 1.3 0.2 0.7 1.1 2 -2
TABLE 2-11% Effects of bowl phantom alignrnents on the correction array.
Percent variation in mean L E , values of uniform objects due to standard deviation os, between
five shifr matrices obfained for the same imaging conditions and dzrerent alignrnents.
2.6 Conclusions
In this chapter, a method of compensating for field inhomogeneities was described.
Although modeled field inhomogeneities and obtained results have been shown to be generally
similar in nature to the experünental results, they provide insuficient accuracy to correctly
compensate for al1 field inhomogeneities. Instead, a combination theoretical and experimental
approach was adopted, thus allowing for correction of field inhomogeneities in multiple
marnrnography systems. This method was found versatile and robust to variations in thickness of
the objects being imaged. Differences in the alignment of the bowl phantom and imaging energies
have only a small effect on the field non-unifomüty corrections.
A spherical PMMA bowl phantorn was used to correct for the heel effect, inverse square
law and for other intrinsic field inhomogeneities. Differences in the alignment of the bowl phantom
and imaging energies have only a small effect on the field non-uniformity corrections. A path
obliquiv correction c m also be applied if the geometry of the imaged object is weil known. Even
a "uniformly-compressed" breast will Vary in thickness fiorn center to periphery, although modem
marnmography machines provide a measure of the compression thickness. Under these conditions,
modification of the assumption of a slab to consider a more realistic mode1 of breast compression
will provide improved accuracy in the correction for attenuation effects due to path obliquity
through the breast.
2.7 References
J.W. Byng, N.F. Boyd, E. Fishell, R.A. Jong, and M.J. YafEe, The Quantitative-Analysis of
Mammographie Densities. Phys Med Biol, 1994.39(10): p. 1629-1 638.
LW. Byng, N.F. Boyd, E. Fishell, R.A. Jong, and M.J. YafEe, AutornatedAnalysis of
Mamrnographic Densities. Phys Med BioI, 1996.41(5): p. 909-923.
R. Highnam, M. Brady and B. Shepstone, A Representationfor Marnmographic Image
Processing. Medical Image Analysis, 1996. l(1): p. 1-1 8.
J.H. Smith, S.M. Astley, J. Graham and A.P. Hufion. The Calibration of Grey Levels in
Marnmograms. 1996: Elsevier Science B.V.
H.E. Johns and J.R. Cunningham, The Physics of RadioZom. 1983, Springfield, IL: Charles
C Thomas.
M. Bhat, J. Pattison, G. Bibbo and M. Caon, Off-Axis X-Ray Spectra: A Cornparison of
Monte Car20 Siw?ulared and Computed X-Ray Spectra with Measzired Spectra. Med Phys,
1999.26(2): p. 303-309.
J.A. Terry, R.G- Waggener and M.A.M. Blough, Half-Value Layer and Intensity Variations
as a Function of Position in the Radiation Fieldfor Film-Screen Marnmography. Med Phys,
1999.26(2): p. 259-266.
J.W. Byng, J.G. Mainprize and M.J. Yaffe, X-Ray Characterizution of Breast Phantom
Materials. Phys Med Biol, 1998.43: p. 1367-1377.
I. C. R. U Report 3 7, Stopping Powers for Electrons and Positirons. 1 984, International
Commission on Radiation Units and Measurements.
D.R. Dance, Monte Carlo Calculation of Conversion Factors for rhe Estimation ofMean
Glandular Breast Dose. Phys Med Biol, 1 990.35(9): p. 2 2 1 1 - 12 1 9.
42
[Il] D.R. Dance, J. Persliden and G.A. Carlsson, Calculation of Dose and Contrast for Two
Marnrnopraphic Grids. Phys Med Biol? 1992.37(1): p. 235-248.
Chapter 3: Volumetric Breast Density Estimation
3- f Introduction
Summarizing from Chapter 1, breast density and the parenchymal appearance of the breast
have been linked to the increased risk of breast cancer. Early studies by wolfei2, have shown that
dassification of radiologicd appearance of rnarnrnograms on the basis of the general distribution of
parenchyrna, stroma and fat, can yield very strong estimates of breast cancer risk. Since then,
many groups3", have also reported similar findings. More recent studies by Byng, Boyd et al7.'
show that a cornputer-aided classification system based on the mammographie density of the breast
can also provide a good indicator of breast cancer risk. In this cornputer-aided method, the area of
radiographically "dense" tissue is calculated as a percentage of the whoIe projected breast area.
However, the method does not consider the three dirnensionality of the breast, and does not
consider the exposure conditions. Shce breast exposure is controlled in an attempt to provide the
best possible film image, it is possible to obtain very similar appearing mammograrns for breasts of
very different size and composition. Thus, to correctly estimate the density of a breast, information
about the exposure conditions, as well as the thickness of the breast, should be used.
The method described here has been developed to overcome the current shortcornings of the
computer-aided method. Instead of considering only the projection of a breast, the use of a
calibration wedge, recording of the exposure conditions and compressed breast thickness
information allow for the calculation of the amount of radiographically dense tissue in the whole
volume of the breast.
Sorne technical difficulties with estimation of volumetric breast density (VBD) have been
descnbed in Chapter 2. The purpose of Chapter 3 is to describe the reasoning and methodology
used in determination of voiumetric breast density for the purpose of breast cancer risk prediction.
First, a discussion of the physics of mamniography as pertinent to the problem will be given. The
development and implementation of caiibration objects, as well as the methodology required for the
VBD estimation will be explored. Finally results, both on phantorns and some preliminary clinicd
data will be given and discussed dong with the underlying assumptions and problems inherent in
the methodology.
3.1 .i Volume density measurement
The curent density estimation techniques, as discussed in Chapter 1' have several
shortcomings. They either s s e r fkom large inter and k a observer variability, or are focused on
the measurement of density in a projected area of the breast. Furthermore, techniques such as
histogram analysis, fiactal dimension or texture analysis al1 attempt to rneasure variables that do
not have direct relevance with respect to the anatornical and physiological properties of the breast.
Instead they focus on local phenomena in areas of few pixels at a time,
Since breast density has already 8ieen shown to be an important factor in predicting the
likelihood of breast cancer development, a method of exactly measuring the proportion of dense
tissue: glandular and fibrous components, should be able to provide more information about the
risk of breast cancer developrnent. The hypothesis of this thesis is that it is possible to accurately
determine the volume of dense (fibroglandular) material in breast like phantoms. It is inferred that
eventually, breast density can be predicted using this method to provide a quantitative, user-
independent method for predicting tbe risk of breast cancer.
The objective of this project is ta develop a methodology for volumetric breast density
which can be used in the clhic- This introduces the following constraints:
Existing mammography machines have t o be used.
45
No sip;riificant modifications can be done in the clinical setting.
New objects introduced in the imaging field have to be unobtnisive, so that they do not change the
appearance of the mammogram for the purpose of diagnosis or screening, or otherwise impair the
examination.
Objects piaced within the imaging field must require only a minima3 maintenance fiom the
mamrnographic technologists.
The method has to be fairly simple to use, user-independent and should require no assistance fiom
the dinicians and radiologists.
3.2 Development of Metho dology
X-ray irnaging depends on attenuation, or absorption differences arnong different materials.
In the case of mammography, the energy of x-rays used, or the imaging spectrum is chosen in the
range of energies that wiil provide best differentiation of soft tissue, while delivering minimum
dose to the patient?
The rnarnmogram is a projection image of the composition of the breast, as defined by
differential attenuation of various tissues. The x-rays pass through the breast and are attenuated. as
shown in Eqn 3.1. The marnrnogram is forrned when x-ray quanta of different energies interact
with a fluorescent screen beneath the breast, and the light produced exposes a sheet of
photographie film which has been pressed tightly against the screen.
Eqn 3.1 describes the attenuation of x-rays in a medium. For one energy, E of the incident
quanta, N is the number of detected x-rays of this energy passed through the medium, is the
number of incident x-ray quanta, pi is the linear attenuation coefficient of the i" object in the path,
and fi is the thickness of the ilh object. In the monoenergetic case for x-rays passing through one
matenal (i=ï), if N, No are known dong with either the thickness or the attenuation coefficient, the
other variable c m be easily estimated. However, the expression becomes more complicated when
two materials (i=2) are considered, since the nurnber of independent variables increases from 3 to
5.
The composition of a breast can be approximated as consisting of two attenuating materïals.
The first is the radiographically dense, or fibroglandular component, which consists of both the
fibrous and glandular tissues, ( a h called the stroma and parenchyrna). The second distinct x-ray
attenuator in the breast is adipose or fatty tissue. To determine the VBD, the arnount of the
fibroglandular tissue has to be found with respect to the total volume. The attenuation coefficients
of both fibrous and adipose tissue have been either calculated from the tissue compositionL0, or
measured directly1'. A cornparison of the two methods shows good agreementi2; therefore, one
possibility is just to measure the linear attenuation coeKicient of tissue throughout the breast. This
approach causes problems, because determination of the exact imaging energy s p e c t m of the
incident beam is diEcult in a typical marnmographic setup, and attenuation coefficients Vary with
energy .
An approach which does not rely extensively on the a priori knowledge of the imaging
conditions, and does not require the exact determination of the attenuation coefficient of the breast
c m be more robust and easily implemented in a typical clinical marnmographic system. If a well
defined, two material step wedge made of breast-like materials is included in each radiograph,
knowing the thickness of the breast and of the object, it should be possible to deterrnine the
composition of the breast. Such a calibration wedge is illustrated in Figure 3-1.
cm
cm
cm
cm
Gland
4i 100% Fa t
Figure 3-1. Plastic wedge used in estimarion of voZumeîric breast density
One concem with the calibration wedge is that the breast tissue is layered in different
combinations through the breast. Breasts are not made of two distinct layers of adipose on the
bottom and glandular on top. However, as x-ray photons travel through objects, the nurnber of x-
rays detected afier the object is independent of how the attenuators are distributed with respect to
each other as illustrated by Figure 3-2. Several smdl experïments (data not shown) were
performed to determine the effects of scatter on superposition. Et was determined that image
brightness fiom radiograph of breast-like matenal in different arrangements does not Vary more
than typical bnghtness variation in a region of 1 cm2. This simplifies the makeup of the calibration
object, since not al1 permutations of materials have to be present, and the two breast-equivalent
materials could be layered one on top of each other.
Figure 3-2. X-ray attenuation is independent of object location wirhin the path of the x-ray beam.
The designed step wedge is made of steps of two separate materiais that are not layered on
top of each other. This simplification of the calibration object can be made, because if the fraction
rn occupied by fibroglandular tissue in a breast of thickness tris to be found, it is sufficient to have
only two steps for each thickness (t& one made completely of glandular-like material A, and the
other o f adipose-like material B.
In such a calibration wedge, for each step of thickness t ~ , the nurnber of detected photons
that passed through the wedge, is NA and NB for fibroglandular and fatty-like plastic respectively.
The expression for the calculation of the logarithm of the nurnber of detected photons (NA and NB)
is shown in Eqn 3.2.
l n ( ~ , ) = l n ( ~ 0 ) - P,& . I ~ ( N B ) = ln(% ) - pBtT Eqn 3.2
In a breast where a fraction rn of the total thickness is occupied by glandular material A,
such that the thickness of fibroglandular (ta) is a fraction of the total thickness of the breast ( t ~ ) :
t , = m t , and the thickness of fatty material B is t , = (1 - m) t , , the expression in Eqn 3.3 can be
used to estirnate the logarïthm of nurnber of photons N, going through.
ln (~ , )= rnln(~,)+(l- rn)ln(~,) Eqn 3.3
It follows that in a breast with unknown hct ion of dense tissue m, if the nurnber of
detected photons N, is known together with the information fiom the calibration wedge about NA
and NB, then the fraction rn c m be easily calculated.
To summarize, in order to determine the composition of a breast with unknown proportions
of fibroglandular and adipose tissues, it is sufficient to have a calibration wedge made of plastics
with the same attenuation properties as these two tissues. If the thickness of the breast (or, in this
case phantom) is known, and the same number of photons are incident on both the calibration and
breast, it is possible to determine the proportion rn, or the density of the breast.
It is not practical to make a calibration object from actual breast tissue. However, using the
knowledge about attenuation coefficients and the chemicd makeup of the breast, several mater&,
13 including plastics have been developed to mirnic x-ray attenuation properties of breast tissue .
With the use of such materials, it is possible to create a very weI1 descnbed calibration object
consisting of 100% glandular equivalent and 100% adipose equivalent steps, which d l allow the
detennination of the proportion of fibroglandular tissues in the breast.
3.2.1 Design of the plastic wedge
At the initial stages of the project, a plastic wedge, illustrated in Figure 3-1 was created for
breast density estimation. To preserve scatter conditions similar to those in a breast, the area of
each step was 1 cm2 and an additional 1 cm of cladding made fkom breast-like material was used to
surround the calibration steps. With this design, the area of each step of material was suffiiciently
large that the step produced an image with the same brightness values as a much larger slab of the
sarne matenal. Wedges with smaller step sizes, and no cladding suffered f?om scatter, and
provided a more highly exposed image than a larger slab. Further, the wedge was designed so that
at least two steps of each material (100% fibroglandular and 100% adipose) were visible and
differentiated under standard marnmographic imaging conditions.
Because the wedge was 7 cm thïck, it codd not be placed on the tabletop of the
mamrnography machine. Instead, it was placed at the edge of the compression paddle, as shown in
Figure 3-3. Furthemore, to accommodate x-ray divergence m e r away fiom the focal spot, the
wedge was tilted to centre it on the focal spot-
Plate
Figure 3-3. Placement of the plastic calibration wedge.
Once the wedge was placed on the compression paddle, an image of both the breast and the
calibration wedge was obtained during one exposure. The image was then digitized, converted to
log(Re1ative Exposure) (LRE) and corrected for field inhomogeneity, as described in Chapter 2.
The correction was perfonned so that at each point of the image, the number of incident photons
No(x,y) was the sarne. Eqn 3.2 and Eqn 3.3 could then be used for each pixel of the image, to
determine the fraction of dense tissue rn in the column of tissue above the pixel. To simplifjr
process hg, instead of performing the calculation for eac h pixel, a three dimensional surface
relating volurnetric breast density, or rn, with thickness, and was obtained nom the Mage of the
calibration wedge. If the thickness of the breast was noted, for each point of the breast, knowing its
LRE, the fraction rn could be obtained by a lookup on the three dimensional surface. A sample
surface is shown in Figure 3-4.
% density step (cm)
Figure 3-4. Sample three dimensional surface relating % densiry rn, thickness and LRE.
To accommodate the large size of the calibration wedge, rnammograms were taken using
only the large (24x30 cm) film size, so that no images were obtained for 18x24 cm film. This
becarne curnbersome to the radiologists reading the films, because it is easier to compare
rnammograms taken at different times if they are the same size. Therefore, to facilitate the use of
calibration objects for VBD estimation in a typical clinical setup, the size of the calibration object
had to be reduced. To reduce both the projected area, as well as thickness of the calibration object,
aluminum was used.
As the project progressed, it was found that the plastic wedge comprornised the quality of
mamrnograms obtained in clinicai setting. B was unwieldy in use, since it required carefül placing
and tilt. Furthemore, the large size of the projected image of the wedge created extremely bright
area in the mammograrn, thus comprornising the radiologist's ability to distinguish low-contrast
variations in the image. To overcome these shortcomings, an aluminurn wedge was designed.
3.2.2 Design of the aluminum wedge
The idea to use an aluminum wedge began with work reported by Johns and Y&e ". The
authors descnbed a method of modeling x-ray aitenuation coefficient of any materiai 5 over a
diagnostic range of x-ray energies, by using a combination of two other, well defined matenals
such as aluminum (UT) and polymethyimethacrylate (PMMA), also known as Lucite (lu). This
relationship can be described by Eqn 3.4.
Pg (E) = alu (5 )Ph (E)+ a, (5 )pu[ (E) Eqn 3.4
The relationship described above holds tme for energies fiom 20 to 1 10 keV. However, in
marnmography the peak voltages Vary between 25-32 kvpi4, with the mean energy of the beam
varying between 20-25 keV. This means, that a much smaller range of energies has to be included
in the estimation of the attenuation coefficient. Since neither the fibroglandular and adipose tissue
have a photoelectric absorption edge at these energies, the linear attenuation coefficient p(E) is a
srnooth, monotonically decreasing function'', which approaches a linear function in the range of
20-25keV. For this range, the relationship of Eqn 3.4 c m be simplified by Eqn 3.5, especially if
some energy dependent calibration of the Gr can be performed.
Eqn 3.5
FiC3we 3-5 shows that in the mammographie range of mean beam energies (22 to 25 kVp),
the values of ad for both fibroglandular and adipose tissues are almost constant. Thus, it should be
possible to use an alurninum wedge to approximate the two types of tissues.
Values of a=, for adipose and glandular tissues
Figure 3-5- A Zum irzurn attenuation coeficient cornpared to fibroglandular and adipose tissue.
Because alurninum has a higher density than breast tissue, much smaller thickness could be
used to obtain the sarne x-ray attenuation. The wedge consists of 7 steps, increasing in thickness
by 2.0 mm, each with area of O.5xl.Ocm . Cornparison to the plastic wedge is shown in Figure 3-6.
Since the wedge is only 14 mm thick, it could be attached to the tabletop, and did not have to be
tilted towards the focal spot. The area through which the x-rays pass is large enough compared to
the thickness of the wedge and the divergent rays pass mostly through individual steps, so that as
opposed to the untilted plastic wedge, each step of alurninum is clearly visible and is easily
separable into thickness regions..
Figure 3-6. Alurninurn wedge cornparad ro the plastic wedge.
3.3 Materials and Methods
3.3.1 Plastic phantom for testing of breast density estimation method
To test the accuracy of the developed methodology, a breast equivalent "hole" phantom,
shown in Figure 3-7 was created. The phantom consisted of 1 cm layers of breast equivalent
material representing a combination of 50% by thickness of fibroglandular-Ilike and 50% adipose-
Iike plastics. Each layer had 5 cutouts of 2 cm diameter each. The layers were filIed with vax-ious
composition "plugs," thus dlowing for a rigorous control over both the thickness and composition
of the phantom. The plastic breast-like phantom was used in al1 subsequent experiments to test the
accuracy of density estimation techniques.
Figure 3-7. The "hole" phantom used in density estimation testing.
3.3.2 Image acquisition and corrections
Al1 images were obtained on film using Lorad clinicai mamrnographic machines, and were
subsequently digitized using a Lumisys 85 digital laser film scanner, at 12 bits and a resolution of
260 p.
The use of the calibration wedge to estirnate VBD is lirnited by the assurnption that the
number of incident photons, MJ is the sarne for both the breast and the calibration object. This bas
been achieved by applying field non-uniformity correction as described in Chapter 2. Thus, al1
subsequent discussion of density estimation assumes that the images have been corrected and have
already been converted to LRE.
3.3.3 Thickness rneasuremen t
A ruler based on x-ray magnification was developed to measure the compressed breast
thickness in older models of mamrnographic machines. A schematic diagram in Figure 3-8 shows
that the position of the marker pIaced on top of the compression paddle changes against a ruler
placed on the imaging plane, due to divergence of the x-ray beam. As the distance between the
paddle and the tabletop change, the x-rays incident on the marker have a greater incidence angle,
and thus project M e r on the scale. The d e r was calibrated using plastic blocks of known
thickness. Newer rnodels of rnammographic machines have built-in compressed thickness
measurements, so that there is no need for an external thickness measuring systern.
FQpre 3-8. Thickness ruler.
Unfortmately, both methods of thickness measurement are prone to the same errors. The
compression paddle is made of thin PMMA plastic. The paddle does not stay parallel to the
tabletop, but depending on the size and compliance of the breast and the force of compression, the
paddle deflects and bends around the breast. This problem has not been addressed in this work;
however, measurement of the thickness error (data not shown) indicates that the thickness
estimation error at the chest wall does not seem to exceed 2 mm.
3.3.4 Calibration of aluminurn wedge with breast equivarent plastic
Although the introduction of an aluminum wedge made clinical use of VBD estimation
more feasible, several problems arose. In the dual energy method, any material such as tissue, can
be represented by a combination of two materials like aluminum and PMMA. This allows for
matching tissue over a wide range of x-ray beam energies. However, PMMA has density similar to
that of tissue, so in order to create a calibration wedge for dual energy decomposition, it would
have to be almost as Iarge as the initial plastic wedge. Instead, aluminum only was used, thus
reducing the effective range over which it could be treated as a scalable basis describing properties
of tissue. Therefore, alurninum was calibrated over a range of several exposure conditions
occurring during normal mamrnographic examinations. For each exposure, scaling constants were
detennined so that the signal detected fiom the aluminurn wedge could be scaled to match the
signal obtained fiom tissue-like plastic phantoms. Calibration of aluminum involved matching
each step of the aluminum to a correspondhg thicker step o f the plastic wedge. The calibration
was done separately for both large and srnaII film formats, since the film sensitometric
characteristics, location of the aIurninum wedge and non-uniformities due to the cassette were
different for the two formats. It should be emphasized that the calibration was performed only
once, not on actual mamrnograms, but on specially prepared caiibration images.
A plastic wedge was imaged in a standard mamrnographic position, while an aluminurn step
wedge was placed in the corner of the imaging plane. A plot of step number versus the LRE was
piotted for both 100% dense and 100% adipose-like plastics- The curve obtained for aluminum
was then either stretched or shnink to fa11 on top of both of the curves obtained for the plastic. This
is illustrated in Figure 3-9. The plastic "hole" phantom was included in each setup, and density
estimation was perfonned. Calibration was deemed successful when the measured density differed
by less than 5 percent density from the actual value. This had to hold for both low and high-density
cases. That is, if the true density was 50%, values of >45% and (55% wouid be accepted-
gbnd fat aluminium
a l i n g of Aluminium step wedge at 25 kVp. 161 mAs. breasj = 4.1
- gland - fat -- al gland - - a1 fat .
Figure 3-9. Calibraiion of aluminum step wedge.
A plastic wedge with steps of adipose and glandular-like plastic is imaged along wirh an aluminum
wedge. 72s mean intensity values in LRE for a sqzrare are of 5x5 mm of each step of the wedges
are shown in (a) and (b), the error bars represent a standmd deviation of pixel values in each
square (3 60 pixels). A scaling operation is performed to scale the nlurninum cuwe of (a) to match
both the glandzdlar and adipose step intensities, as shown in (6). m e error bars represent a
standard deviation ca
Since the a,[ value of Eqn 3.5 was not exactly constant over marnrnographic energy ranges,
it was necessary to determine how this affects the aluminurn calibration over a range of energies.
Two variations of the experiment were performed to determine calibrations required. First, the
irnaging energy was kept constant, and the exposure time was varied. Then the calibration was
performed for each kVp value used in typical clinical settings for the machine (25 - 32 kVp). The
machine was set to auto-timer, in order to obtain the best possible exposure of the film for a given
experirnental phantom configuration and energy setting. These experiments are described in more
detail in the Results and Discussion section.
3.3.5 Determination of volurn etric density of the "hoien phantom
After calibration was performed, the density of eight conf7gurations of the plastic "hole"
phantom was deterrnined. Five thicknesses of the phantom were configured, such that the densities
of the piugs varied fiom al1 adipose (O % density) to a11 glandular tissue (100 % density), in regular
intervals. The phantom was placed in the sarne position as a normal breast would be imaged,
shown in Figure 3-10. The aluminum wedge was attached in the corner of the imaging plane, as it
is now used in clinical setting. The phantom was then imaged at an auto setting of the machine to
ensure the best possible exposure conditions.
Figure 3-1 0. Mamrnogram of "hole" phantom.
This was used for volumetric density estimation.
The obtained mammogram was then converted to LRE and field non-uniformity corrections
were applied as descnbed in the previous chapter. A surface sirnilar to that of Figure 3-4 was then
created fiom either the plastic "L" shaped wedge, or the aluminum wedge. Since the thickness of
the phantom was known fiom the d e r reading, for each pixel of the marnrnograrn, a calcutation of
the % fibroglandular content was performed. Finally, a single number? the actual Volumetric
Breast Density VBD, was obtained using Eqn 3.6. A,,/ is the area of each individual pixel within
the breast (or phantom), rn(x,y) is the proportion of that pixel occupied by fibroglandular tissue and
t(x,y) is the thickness of the breast above that pixel.
Eqn 3.6
Volume Density = bmaf
bmavr
3.4 Resulfs and Discussio n
3.4-1 Calibration studies
The calibration procedure required stretching and rotating of the alurninum curve to fa11 on
top of either the curves for 100% adipose breast-like plastic or 100% dense tissue like plastic.
(a) Dependence on exposure tirne ( 4 s )
The first set of experiments was performed to determine the dependence of the calibration
on exposure time. The images were obtained at 25 kVp, and 123, 161 and 233 mAs. One set of
scaling numbers was used to match the alurninum curve to the plastic breast-equivalent curve.
Figure 3-1 1 shows that the exposure time had almost no impact on the calibration. The fines
(a1Urninu.m and plastic) overlap for the three cases, especially at the thickness ranges where the
breasts were imaged.
The tirne of the exposure should not affect the calibration constants, since the average
number of photons at a given energy per unit of time is always the same. Thus, scatter, and x-ray
attenuation is the same at dl time intervals. The cdibration can be expected to change oniy if
different scatter and absorption properties occur.
0.5 0.5 O 2 4 5 8 10 O 2 4 6 8 10
Step (cm) S I ~ P (ml
Scaiïng of Aluminium çtep wedge at 25 kVp. 123 W. breasr, = 4.2 Scaling of Aluminium step wedge at 25 kVp. 161 mAs. bre- = 4.1
Scaling of Aluminium step wedge at 25 kVp. 233 mAs. breast, = 5.4
3.5r
3
2 5
- 2 -0 2- 8' -
1.5
1
Figure 3-1 1. Calibration of aluminurn vs. pZustic wedge (constant kVp, varying A s ) .
3.5- - gland - gland - fat - fat - - algbnd - - al gbnd - - - alfat 3 - - - al fat .
- 2 5 -
-
y
The sume culibration consfanCs were used in all three cases. The aluminum wedge was pIaced in
normal corner position on the tabletop, while the plastic '2" wedge was tilted at the edge of the
compression plate. The peak voltage was set to 25 k Vp, and auto timer was engaged to provide the
best exposure for a given composition/rhickness breast figures show images obtained ut 123, 161,
233 mAs. The thickness of each of the imaged breasts, breast, is indicated above individualplots.
I
Mean LRE value of 5x5 mm square of each step is shown in each line. The error bars indicate a
standard devia tion of values in each square.
The divergence of the calibration lines at the extreme thickness values in Figure 3-1 1 can be
explained by large errors in LRE calcuIation due to the film non-linearity. If auto-timer is engaged
to assure a good image contrast for a specific breast thickness and composition, the objects that are
much less attenuating or much more attenuating will fa11 in the non-Iinear regions of the film
sensitometric curve. As explained in Chapter 2, in such cases even very small variations of
brightness will correspond to very large LRE changes, and thus will cause calibration lines to
become inconsistent.
(6) Dependence on peak voltage (k Vp)
The change of energy of the x-ray photons shouid produce a change in the matchhg of the
aluminum and plastic wedge. This occurs because as discussed earlier, a,! of Eqn 3 -5 is not exactly
independent of energy E in the mammographie range of energies. Thus, if the mean energy of the
x-ray beam is changed, the attenuation of plastic changes differently than that of alurninurn. Figure
3-12 shows calibration curves for four different kVp values, when the mAs was kept constant. Al1
f o u curves have been obtained with the sarne scaling constants, which were deterrnined for the 26
kVp case. As can be seen, the calibrations of alurninurn versus the fibroglandular and adipose
tissues become more diverging for higher kVp values; however, at the imaged breast thickness
(breast, ), the agreement is still hi&. When the anode and filter combination was changed for an
exposure at 31 kVp from MoMo to Rh/Rh, as shown in Figure 3-13, the alurninurn calibration
changed significantly. This occurs because the shape of the x-ray spechum changed, and thus the
energy dependance of a,, is more pronounced. The experiments discussed here show that
calibration of aluminum has to be done for several energies. However, to detemine the optimal
number of calibrations, M e r study detennining errors in VBD estimation due to few calibrations
had to be performed. These experiments are descnbed in the next section.
Scaling of Aluminium step wgdge at 26 kVp. 192 mk. breas$ = 5.1 Scaling of Aluminium step wedge at 27 kVp. 175 mAs. breast, = 5.8
Scaling of Aluminium step wedge at 28 kVp. 196 mAs. breasi,= 6
- gbnd - fat
- gland - fat . - - al gland - - al fat
. *.
Scaling of Aluminium Sep wedge at 30 kVp. 194 mA.. breaq= 6.2
3-5r - gland
Figure 3-1 2. Calibration of aluminum vs. plastic wedge (constant mAs, var ying kVp).
The same calibralion constants were zrsed in all four cases. The aluminum wedge was placed in
normal corner position on the tabletop, while the plastic "Lu wedge was tilted at the edge of the
compression plate. The auto timer was engaged during the marnmographic procedure, however all
of the four presented cases have been selected to have similar rnAs values (- 190 mAs) and peak
spectral energy of 26, 27, 28 and 30 kVp.
Scaling of Aluminium step wedge at 31 kVp. 191 &. breast, = 6.3
- gland - at -- al giand - - al fat
Figure 3-13. Calibration of aluminum vs. plastic wedge (changing anode/fiIter combination).
As in the previousfigure, the exposure wns kept -190 d s . The calibration constants used here
are the same as for the previous 4 cases in F m r e 3-12; however, instead of Molybdenum (Mo)
anode andflter, Rhodium (Rh) was used-
As can be seen from Figure 3-9 as well as Figure 3-1 1 to Figure 3-13, the calibration of
aluminum to plastic wedge works for a range of kVp values . However, the calibration will fail if
an exposure not suited to the imaged breast is used. For example, if a calibration used successfully
for a 6.2 cm breast of Figure 3-12 is used to estimate the density of a thin, 2 cm breast, it will fail,
as shown by the divergence of the plastic glandular line with the aluminurn estimation.
3.4.2 Determining volumetric breast density: phantom studies
(a) Plastic wedge only
In the initial stages of the project, a set of experïments was performed as a proof of
principle that VBD can be cdculated to within a few percent in phantom materials. A plastic
wedge was placed on top of a compression paddle and breast-like phantoms of known
fibroglandular and adipose type plastics were imaged. This was performed for both unifomiity
corrected and uncorrected images. As can be seen from Figure 3-14, density estimation is
66
acceptable only when appropriate non-uniformity corrections are made. The plot represents mean
signal fkorn squares of 5 mm2 along the centre of the image. The error bars show the standard
deviation of the signal in these squares. When carefiil pre-calibration of the system is empIoyed, so
that field non-unifonnity is corrected for, the estimation of W D varies <2 % density fiom the
actual value, as c m be seen fiorn the figure the uncorrected image varies by more than 20% density
in the areas of the phantom further fkom the focal spot. This shows that it is possible to measure
breast density in a marnmogram. However, the use of a plastic wedge in a clinical setup will be
impossible, as noted above. Instead, the ability of VBD estimation with calibrated aluminum was
tested in phantoms.
Profile of the breast phantom
O 5 1 O 15 20 Distance from chest wall (cm)
Figure 3-1 1. Breast Density Estimation using a plasiic calibration wedge.
The estimation was performed for both corrected and non-uniforrn images. The Zines represent the
mean signalfrom squares 5x.j mm (360 pixeis) along the centre o f the image. Emor bars show the
standard deviation in these squares.
(b) Alurninum wedge
The calibrated alurninum wedge was used to calculate the VBD of the "hole" phantom,
which was then compared to the same calculation ~ising the plastic wedge. Figure 3-15 shows that
well calibrated aluminum can be used to determine VBD as accurately as that calculated using the
plastic wedge. It should be noted that the drop-off En the region 7.5 cm away from the chest wall is
due to an air-gap between two slabs of material. Furdierrnore, the roll-off at 18 cm is due to scatter
around the edge of the phantom.
Profile of the breast phantom
O 5 10 7 5 20 Distance from chest wall (cm)
Figure 3-1 5. Breast D e n s e Estimation using aluminum and plastic wedges.
The ewor bars have been removed to show how closely the two curves match.
Figure 3-14 and Figure 3-15 show the votumetric breast density performed on the same
image. The radiograph was obtained for a "hole" phantom 3 cm thick, at 26 kVp and 57 mAs. The
calibration of aluminum versus plastic was performed on a calibration image taken at 26 kVp and
192 mAs. This calibration c m be seen in the top left corner of Figure 3-12. Eight more images of
the plastic phantom were analyzed to determine how well yBD c m be estimated for a wide range
of densities. A radiograph of the piastic phantom was obtained at each value between 25 and 32
kVp with automatically selected exposure where the autotimer was placed under a block of 50%
density. Measurements were made for 3, 4, 5, 5, 5, 6, 6, and 7 cm starting at 25 kVp on. Both the
plastic and aluminum wedges were positioned in the image. Cdibration of alurninum versus
plastic was performed at 4 energies: 25, 26, 30 and 3 1 kVp. These calibrations were then used for
the following kVp intervals: [25, 26), [26, 28), [28, 31), [31, 321. Figure 3-16 shows VBD
estimation using plastic wedge information. Figure 3-17 shows the sarne information for the
aluminun wedge estimation- The error bars on both figures represent the standard deviation of %
density values in a 1 cm2 region of each composition.
The two figures show that KBD estimation is possible for the whole range of densities
varying from O% to 200% fibroglandular content within one, well-exposed marnmogram. With an
appropriate calibration, an alurninum wedge c m be used to estimate the VBD with a degree of
accuracy very similar to the estimation done with pIastic. As can be seen, both figures show Iarger
than normal errors in coiumns at 30 % density. This is due to under-exposure of the low-density
areas at 25 kVp, so that 30% looks very sirnilar to higher densities. The opposite was true for the
estimation of density at 3 1 kVp, where the 30% area was over-exposed, and looked very simiiar to
lower density. In these ranges, due to the non-linearity of film response, small differences in pixel
brightness translate to large changes in % density, thus increasing the standard deviation of density
values,
Density Estimation using Plastic Wedge
Figrire 3-1 6. Volumerric density estimation using a plastic wedge.
Density Estimation using Aluminium Wedge
110 1
-10 1 1
O 33 50 70 100
Expected Density (%)
Figure 3- 1 7. Volumetric density estimation using an ahminum wedge.
Aluminum calibration was pevorrned at 25, 26, 30 and 31 kVp. T?iese calibrations were used
respectiveZy for the following intervals: [25, 26). [26, 28), [28, 31), [31, 32J The error bars
represent the standard deviation of density estimation in n I cm2 region Most of the error bars do
not extend more than 3% densi@
3.4.3 Prelirninary clinical stud y: Cornparïng aluminurn to plastic wedge
The previous sections show results from well-controlled experirnents. However, the
purpose of VBD estimation is to be used in the clinic. To this end, a small clinical study was
performed to determine how the duminum calibration and plastic wedge density estimation
compare when obtained from actual mammograms. The aluminurn wedge was calibrated for [25,
27), 127, 29), [29, 321 kVp intervals. Both the alurninum and plastic wedges were provided to the
Sunnybrook mamrnography clinic and were installed on one of four local mammography machines.
The technologists were trained how to place the wedges within the mamrnography setup. The
alurninum wedge was attached to the upper corner of the tabletop, as shown earlier. A support
stand was made for the plastic wedge which was placed on top of the compression paddle. To
ensure that the screening accuracy was not compromised by image qudity, both the plastic and
aluminum wedges were used only during examinations which required a large film (24x30 cm).
This biased the study to Iarge and mostly thick breasts, with the average projected breast area of 25
cm2. Al1 mammograms obtained on the large film fiom this mamrnography machine over a period
of two months were digitized, In total, 159 mammograms were obtained. Ody 1 12 of these had
both wedges present. Furtherrnore, another 14 mammograms had the plastic wedge positioned in
such a way, that it was not compIeteIy visible in the mammogram, or that the steps were
overlapping. Finally, 4 mammograms were rejected due to digitization artifacts, such as streaks
over the area where the wedges were placed- This decreased the usefid sample to 94
mammograrns.
The Lorad M4 machine on which the study was performed records the imaging technique
and the compressed thickness of the breast on each mammogram. The thickness measure was
tested using known thickness plastic phantoms, giving a maximum error of S mm.
M e r the digitization was done, the images were corrected for non-uniforrnity. The area of
the breast was selected using an edge detection program and both the plastic and aluminurn wedges
were used to estimate the volumetric breast density. Finally, Eqn 3.6 was used to calculate the fmal
VBD value of each marnmogram. Figure 3-18 and Figure 3-19 show the cornparison of the VBD
values as obtained by using the alurninurn and plastic wedges. The figures have been sorted by the
kVp of the image (Figure 3-1 8) or by the thickness of the imaged breast (Figure 3-1 9).
Aluminium vs Plastic Volume Density (by kVp) correlation coeff.= 0.959 100r. .................................... -. ................. -. ......................................
--0-
Figure 3-1 8. Comparing plastic and aluminurn estimations in a clinical setting ( by k Vp)
me Pearson correlation, bestfir and the identity line are indicated
Aluminium vs Plastic Volume Density (by thickness) correlation coeff.= 0.959
1 ..y 00' r 20 40 60 80 1 O0
9% Density (Plastic)
Figure 3- 19. Comparing plastic and ahminurn estimations in a clinical setting @y thickness)
Although it is impossible to determine the actual density of the breasts imaged in this study
and therefore it is unknown how well both methods estimate the density, several interesting
conclusions can be drawn fiom the above plots. First, it seems that most of the outliers are in the
73
relatively thin breast categories, suggesting that breasts imaged at low kVp and mAs settings might
be not estimated as well as somewhat thicker, more dense breasts. Second, it seems that that three
calibrations will suffice in providing VBD estimation comparable to that of plastic when using the
aluminum wedge. The Pearson correlation between the two methods was hi&, at 0.96. This shows
that P73D can be estimated in the clinic by using a calibrated alurninum wedge and a priori
knowledge about the compressed breast thickness and imaging technique.
3.5 Conclusion
This chapter described a method for calculating volumetric breast density by using a well-
d e h e d calibration object. Plastic calibration wedge composed of two materials can be used to
determine phantom density, and the only a priori knowledge required is the thickness of the
phantom. However, the plastic breast-equivalent wedge is too large to be used easily in a clinicd
setup. The wedge can be replaced by a much thinner alurninum wedge, which must be calibrated
versus the plastic wedge. To ensure good VBD estimation, this calibration procedure has to be
performed for three mammographie energy values. Thus, to use an aluminum wedge, both the
thickness of the irnaged breast, and the imaging conditions must be known a priori. This should
not be a problem in a modem marnmography clinic, where most of the machines record the
imaging technique and breast compression on the rnamrnogrm. Results show that although it is
impossible to determine how weIl VBD was estimated in the smail clinical study, the correlation
between plastic and alurninum wedge estimations was excellent at 0.96. Phantom studies show that
using the aluminurn wedge, VBD can be estirnated to within 3% density of the actual value.
Volumetric breast density should improve over the existing rnethods of determining breast density,
since it is a user-independent, quantitative method, and thus does not sufYer fiom observer bias.
Also, VBD will provide information about the whole volume of the breast, as opposed to just the
projected area, fike the current methods.
3.6 References
J.N- Wolfe, Breast Patterns as an Index of Risk for- Developing Breast Cancer, Am J
Roentgenol, 1976.126(6): p. 1 230-1 137-
J.N. Wolfe, Risk for Breast Cancer Development Determined by Marnmographic
Parenchymal Pattern, Cancer, 1976.37(5): p. 2486-2492.
P .M. Kroo k. Marnmographic Parenchymal Patterns as R isk Indicators for Incident Cancer
in a Screening Program: An Extended Andysis. Am J Roentgenol, 197 8,131(6): p. 103 1 -
1035.
A.F. Safilas, J.N. Wolfe, R.N. Hoover, L.A. Brinton, C. Schairer, M. Salane, and M. Szklo,
Marnmographic Parenchymal Patterns as Indicators of Breast Cancer Risk Am J
Epidemiol, 1989.129(3): p. 5 18-526.
L. Tabar and P.B. Dean, Marnmographic Parenchyrnal Patterns. Risk Indicator for Breast
Cancer? JAMA, l982.247(2): p. 185- 1 89.
I.T. Gram, E. Funkhouser and L. Tabar, me Tabar ClassiJcation of Marnmographic
Parenchymal Patterns. Eur J Radiol, 1997.24(2): p. 13 1 - 13 6.
J.W. Byng, N.F- Boyd, E. Fishell, R.A. Jong, and M.J. Yaffe, The Quantitative-AnaZysis of
Marnrnogmphic Densities. Phys Med Biol, 1994.39(10): p. 1629-1638.
N.F. Boyd, J. W. Byng, R.A. Jong, E.K. Fishell, L.E. Little, A.B. Miller, G.A. Lockwood,
D.L. Tritchler, and M.J. Y&e, Quantitative Classification of Marnmographic Densities and
Breusf Cancer Risk: ResuZts fiom the Canadian National Breast Screening Study. J Natl
Cancer Inst, 1995.87(9): p. 670-675.
191 L.W. Bassett? R.H. Gold and C . Kimme-Smith, History of the Technical Developrnent of
Mammography, in Syllabus: A Categorical Course in Physics Technical Aspects of Breasr
Imaging, Third Edirion, A.G. Haus and M.J. YafTe, Editors. 1994, RSNA. p. 9-2 1.
[l O] G.R. Harnmerstein, D. W. Miller, D.R. White, M.E. Masterson, H.Q. Woodard, and J.S.
Laughlin, Absorbed Radiation Dose in Mammography. Radiology, 1 979(l3 0): p. 485-49 1.
[ I l ] P.C. Johns and M.J. Yaffe, X-Ray Characterisation of Normal and NeopZasitc Breast
Tissues. Phys Med Biol, 1987.32(6): p. 675-695.
[12] J.W. Byng, J.G. Mainprïze and M.J. Yaffe, X-Ray Characteriration of Breast Phantom
Materials. Phys Med Biol, 1998.43: p. 1367-1 377.
[13] CIRS Technical Paper: Tissue EquivaZent Photo timer Consistency Testing Slabs. 1993,
Computerized Imaging Reference Systems Inc.: Norfolk, VA.
[14] G.T. Barns, History of the Technical Development of Mamrnography, in 1999 Syllabus.
Cat egorical Course in Diagnostic Radiology Physics: Physical Aspects of Breast Imaging
- Current and Future Considerations, A.G. Haus and M.J. Yaffe, Editors. 1999, RSNA
Radiological Society of North America. p. 41 -59.
Chapter 4: Summary and Future Work
4.1 Summary
In the previous chapters, a method of estkating volumeûic breast density was developed
and described. This rnethod should provide a user-independent, quantitative measure of breast
density. Furthemore, it wiII consider the whole volume of the breast, instead of just the projected
area, currently in clinical use '".
4.1 -1 Field Inhomogeneity Co rrection
In the Field Non-uniformity- chapter, a method of pre-processing and correcting of
marnrnograms was developed where field non-uniformities due to the inverse square law, heel
effect, path obliquity and other inherent uihomogeneities of the mammographie system were
corrected. This allows for quantitative analysis of mammograms, since most of the non-uniformity
is removed and thus al1 regions of the mammogram appear as if the same spectrum of x-rays, al1
perpendicular to the imaging plane was used to obtain the image. The marmnogram is first
converted using a sensitometric curve, to an image of logarithrn of relative exposure (LRE). This
removes most of the film non-linearity effects. Once this is done, a correction obtained fiom
imaging a sphencal section PMMA phantom is applied to the image. The PMMA phantom is
designed to have absorption similar to that of breast tissue. Since it is centred on the focal spot, x-
rays pass through a uniform thickness of the phantom. Thus, beam obliquity effects are removed
from the image obtained in this way. The correction image contains non-unifonnïty due to the heel
effect and to the inverse square law. Once the actual mamrnogram is corrected for these
inhomogeneities, it is possible to d e t e d e the exact thkkness of matenal through which x-ray
photons pass due to path obliquity effect. A simple algebraic correction can be then applied to each
rnammogram to determine the exact path length of x-ray photons passing through the attenuating
material above each point dong the Unaging plane.
The experiments discussed in this chapter show that using the developed method, it is
possible to reduce the field non-unifomity fiom >10 % LRE to (2%. To obtain a good non-
unifonnity correction, only one thickness of bowl phantom has to be imaged, at one energy.
4.1 -2 Calculation of Volumetric Breast Density
The Volurnetric Breast Density (VBD) chapter developed a methodology of measuring the
percentage of the whole volume of a breast occupied with radiographically dense fibroglanddar
matenal in the inhomogeneity corrected images. A small durninum wedge placed in each
mamrnogram cm be used to determine the volurnetric breast density. This is done by first
calibrating the aluminum, at three mammographic energies, with breast-equivalent plastic, to
detemine what thickness of aluminum corresponds to the sarne registered LRE signal from 100%
fibroglandular or 100% adipose tissues. Once the thickness of the compressed breast is known
dong with the irnaging technique, an appropriate calibration is used to create a three dimensional
surface which reIates percent density, breast thickness, and LRE of the image. For each point of the
breast, knowing its LRE and the exact thickness through which x-rays traveled, the percent of
radiographicaily dense fibroglandular tissue is detemined. This estimation has been shown to be
within 3 percent density of actuai value in phantoms, thereby validatirig the hypothesis that it is
possible to determine the density of well defmed phantoms by using the Vohmeûic Breast Density
rnethod. Furthemore, the aluminum calibration has been cornpared to a much larger plastic wedge
in its effectiveness to determine VBD. The correlation between the two methods is high, at 0.96.
4.2 Future Work
4.2.1 Breast Cancer Risk Prediction: Vdumetric Breast Density in a Clinical Study
This work proposes a method of measuring Volurnetric Breast Density. The results show
that it is possible to measure VBD to within acceptable error ranges of about 3% in well defined,
breast-like plastic phantoms. However, the present work is a part of a larger Volume Density
project as descnbed in the Introduction chapter, which has a goal to estimate the volumetric breast
density for the purposes of breast cancer risk prediction. The hypothesis of the overail project is
that since the volurnetric method wil1 give a more representative measure of breast density, the
breast cancer risk estimation using this method will be greater than the values reported with
existing rnammogam classification methods. To test the overall hypothesis, it is necessary to
conduct a large ch ica l study, which wil1 provide breast density measures using the existing area
rnethod and using the volumetrk method. The predictive vdue for breast cancer of each method
will be calculated and only then wiI1 it be possible to determine how well VBD estimation
compares to ex i shg methods- Currently, a three-year study matching 800 cases to 800 controls is
underway in the Ontario Cancer Institute, under the direction of Dr. Norman Boyd in association
with Dr. Martin Y a e . Although this study has yet not been completed, a small clinicd study was
perfonned with a use of aluminum wedge in the Sunnybrook mammography clinic. The objective
was to find whether the volumetric density estimation measures features of the breast comparable
to those of the existing, area density measurements. The results shown in Figure 4-1 indicate that
the correlation between the two methods is hi&. However, there is enough discrepancy to show
that volumetric density measures mammographie features slightly different than those measured in
the area method. The breast cancer risk factor of the volumetric method is still unknown, but since
this method is correlated to the area method, there should be a relationship between increased
80
volumetric density and the likeiiood of developing of breast cancer. The extensive clinical study
will provide evidence whether volumetric density estimation is a strong predictor of breast cancer
risk. This can iead to the introduction of VBD measurement as a standard screening procedure.
Camparing Area v~. Volume Density. (4 cafibrations) Condation CO&.= 0.755 Cornpanhg Area vs. Volume Oensity. (8 calibrations) Codalion cwff.= 0.764 100 0 1 0 0 0
0 0 0 0
0 .. 0 * 0
V V O O r O ..--.. O .*& .-..--'
BO 80 v . -.*
I o 25kVp F 26 kVp v 27kVp + 28 kVp 0 29 kVp 4 30 kVp V 31 kVp 1
- - riniiv line
O 29 kvp
O 31- A 32kvp ......
uni Iine
OF< +, 20 : A o r - a 1
40 60 80 100 20 40 60 80 100 % Density (Area MeViod) % Density (Area Melhod)
(4 (b>
Figure 4-1. Comparison of Area density measurement to Volumetric density measure.
The two methods of density measurement were performed on 97 mammograrns. Four aluminum
calibrafions used to obtain a correlation of 0.755 (a). When each imaging energy had a dzrerent
aluminzun calibration, for a total of eight calibrations, the correlation between the volzrmetric and
area methods increased to 0.764 (b).
Perhaps one of the most interesting aspects of Figure 4-1 is the outlier in the upper left
corner. That point corresponds to 80% density by volume area, and 15% density by the area
method. Although at this point, it is impossibte to actually know which of these two methods
performed better in density estimation, two possibilities arise. First is that the volume method is
completely wrong in this case (taking the area method as Cctnith''). The second, much more
interesting possibility is that the volume method is actually giving the right reading. Upon
checking, the thickness of this particular breast was only 3 cm. However, the auto-exposure
mechanism imaged the breast at 27kVp, which is a very high value for such a thin breast. This
seems to indicate that the breast in question was quîte dense and that is why the higher exposure
was used. It is possible that the overall breast looked quite uniform, and thus the area density
estimation was much tower.
If the volumetric method is taken as being the absolute '?rue" way of measurïng breast
density, and the correlation bettveen area and volume methods is considered to be the error of -
measurernent of the area method, then the relative risk range of 4-6 gven by the area method for
the most dense breasts can be modified by Eqn 4.14. Ra,, is the risk associated with the area
method, R,,, is the risk associated with the volume method, and r is the Pearson's correlation
between the volume and area measurements. Assuming a correlation of 0.75, as obtained in Figure
4-1, the possible relative risk predicted using the volumetric technique could be as high as 7 or 11.
This will make the volumetric technique one of the strongest risk indicators for breast cancer.
Eqn 4. I
4.2.2 Method lmprovements
Although the VBD method has been shown to work well in phantoms and some promising
results have been obtained with actual mammograms, the method still has several possibilities for
improvement.
(a) Digital mammograplry
Introduction of the methodology into digital mammography can overcome many problems
which are encountered in the fiLm/screen marnmography. First, much of the image pre-processing
needed for proper KBD caiculation in film systems would be unnecessary. The response of a
digital machine is linear, not sigrnoidal like the film used in conventional mammography5, so that
the conversion to LRE using the films sensitometric curve does not have to be performed. The
digitization step of the process could be removed, and al1 field inhomogeneity corrections can be
performed directly on each rnamrnogram in the digital forrn
Properties of the detector do not change very much over time, unlike those of film;
therefore, the digital mammography machine could be calibrated with large breast equivalent
wedges positioned in the centre of the irnaging field, creating a typical three dimensional surface
relating breast density, thickness and image brightness. The patients can be then imaged separately
without any wedges, and only the imagïng technique needs to be recorded. If both the clinicai
mamrnogram and the calibration are performed using the same technique, an equal brightness pixel
on both wiU correspond to the same x-ray absorption of rnaterial above that pixel. This would open
a possibility for perfonning prospective as weIl as retrospective volumetric studies of
mammograrns.
(6) Automation of breast and calibration wedge selection
Currently, to analyze a mammogarn, an operator has to manually select each step of the
alurninum wedge. The area of the breast is then segmented out of the mamrnogram by a simple
region growing algorithm6. The data are then passed to a compter program, which calculated the
breast density. The wedge selection is a very mundane task, and although it requires almost no
special training, if many mammograms are to be analyzed, it will be necessary to automate this
step.
At this point, al1 of the breast is considered to be compressed to a uniform thickness.
However, the edges of the breast "roll-off', such that the breast periphery must be thinner than its
centre. A srnall experiment was performed to determine to what degree the periphery changes the
volumetric density estimation. The average volurnetnc breast density of 112 rnamrnograms was
33.4% when the periphery was considered to be as the sarne thickness as the rest of the breast.
When the periphery was ignored, the average volumetric breast density was 34.3%. Aithough this
suggests that the periphery does not greatly influence the overall VBD reading, by being able to
determine the exact thickness of the roll-off of the breast would reduce one source of error.
(c) Compression paddIe deflection: titickness error
One of the rnost pronounced sources of error that affects VBD calculation, is the breast
thickness estimation. The thickness is measured only in one region of the rnammogram, using
either a d e r (discussed in Chapter 3), or a buiit-in compression gauge of the mammography
machines. The thin compression paddles are cornpliant, and deflect under applied force. Zn the
calibration of thickness measurements, the paddle was measured to deflect as much as 2 mm. As
seen in Figure 4-2, an error of 2 mm in estimation of thickness can lead to 10% density error. For
thin breasts of 2 cm, if 5 mm thickness error is recorded, the data becorne unusable, with errors of
about 30% density. Thus, the cornpressed thickness must be measured with minimal errors. For
this, the deflection of the compression paddle should be investigated in more detail.
2 3 4 5 6 7 0 1 2 3 1 5 6 7 O: 2 3 4 5 6 7 n c k m s ~ (an) -t-kkws(m) an au (ml
(a) (b> (cl Figure 4-2. Error in Volurnetric Breast Densi& due tu thickness error.
VBD was calculated for simulated slabs of 2, 3, 4, 5, 6, 7 cm of 50% fibrogZanduZar and 50%
adipose-like plastic. A thickness errors of lmm (a), 2 mm fi), and 5 mm (c) w e r e introduced. The
error bars show the change in density r-eading due fo such errors ut each thickness.
4.2-3 lrnproving validation of volumetric breast density estimation
At this point, VBD methods can be tested on well-defmed plastic phamtoms, or can be
compared to current methods of density estimation such as the area method. However, no way of
validating the actual voIumetric density rneasure of a breast has been devised. For this, several
possibilities arise. First, a rough volume of the dense tissues could be calculated f i o m stereoscopic
marnmograrns. By placing several points defining the periphery of "dense" regions in three
dimensions, a rough estimate of volume occupied by these regions should be possiible.
Another possibility is to use ultrasound to determine îhe arnount of density withim a breast. Study
by Blend et al, shows that there is a high correlation between rnammographic density and
echogeneic structures in the breast7. Since ultrasound does not introduce harrnflll radiation,
multiple scans dong several planes should allow for volumetric estimation of breast density.
Finally, an inherentiy three-dimensional breast imaging technique, such as MRrl can be used to
determine the amount of fibroglandular tissue in the volume of a breast. A study by Graham et al8
shows that a high correlation to marnmographic density c m be obtaining by measuring the relative
water content of the breast. Using this imaging technique, it would be possible to determine how
well the volurnetnc breast density estimation compares to a tnrly three dimensional density
estimation.
4.3 Closing Remarks
The appearance and classification of parenchymal patterns on mamrnograms has been
shown to be one of the strongest nsk factors for breast cancer. The currently used methods of
classification are ofien susceptible to inter and intra observer variability. Also, most measures used
today utilize only the projected area of the breast, without any regard to the imaging technique.
Figure 4-3 illustrates why a volumetric technique might become an even more powerfül tool in
breast cancer risk prediction. The mammograrns illustrated in the figure appear very similar, and
have been obtained using the sarne imaging technique. Only when the thickness of the breast is
considered, c m the difference in composition of these two breasts be noticed- At this point in time,
no techniques exist to integrate such information into a breast density measure. The rnethodology
proposed in this work attempts to correct these shortcomings, and might provide a tool which
greatly improves breast cancer risk prediction.
(a) 26 kVp, 1 85 mAs
Area Density = 4.3%
Volume Density = 4.6%
Compressed thickness = 5.9 cm
@) 26 kVp, 194 rnAs
Area Density = 1.7%
Volume Density = 38%
Compressed thickness = 5.2 cm
Figure 1-3. Cornparison of Area Density to Volume Density measurernents.
Both breasts were irnaged at very sirnilar technique, and both have been classifed as very low
density using the area density method. However, the vo Iumetric technique iakes into account the
thickness of the breasts, providing very dzfferent density measzrres.
Perhaps one of the most exciting implications of this work is that if the volumetnc breast
density does prove to be a strong indicator of breast cancer, rnammography will serve not only as a
breast cancer fmding modality, but also will be used preventatively. Women who are found to be
in the high risk group for breast cancer will be able to modie their lifestyle, undergo more rïgorous
screening, or even take medications which slow the development of cancers, before onset of
detectable disease.
4.4 References
J.W. Byng, N.F. Boyd, E. Fishell, R.A. Jong, and M.J. Yaffe, The Quantitative-Anabsis of
Mammographie Densifies. Phys Med Biol, 1994.39(10): p. 1629- 1638.
2. Huo, M.L. Giger, 0.1. Olopade and S.A. Cummings, Computerized A d y s i s of
Parenchymal Patterns for the Assessment of Breast Cancer Risk. Radiology, 1 998.209P: p.
943.
C.B. Caldwell, S.J. Stapleton, D.W. Holdsworth, R.A. Jong, W.J. Weiser, G. Cooke, and
M.J. Yaffe, Characterisarion of Mamrnugraphic Parenchymal Pattern by Fraetal
Dimension- Phys Med Biol, 1990.35(2).
B.G. Armstrong, The Effects of Measurernent Errors on Relative Risk Regressions. Am J
Epiderniol, 199Cb. 132(6): p. 1 176-1 184.
M .J. Yaffe, Digi-taï Marnmography, in 1 999 Syllabus. Categorical Coz(rse in Diagnostic
Radiology Phys Fcs: Physical Aspects of Breast Imas-ng - Current and Future
Considerations, AG. Haus and M.J. Yaffe, Editors. 1999, RSNA Radiological Society of
North Amerka. y. 229-247.
R.C. Gonzales aznd R.E. Woods, Digital Image Processing. 1992, New York: Addison-
Wesley Publishing Company.
R. Blend, D.F. Rideout, L. Kaizer, P. Shannon, B. Tudor-Roberts, and N.F. Boyd,
Parenchymal Patterns of the Breast Defined by Real T h e (ntrasound Eur J Cancer Prev,
1995.4(4): p. 393-298.
S.J. Graham, M J. Bronskill, J.W. Byng, M.J. YafZe, and N.F. Boyd, Quantifative
Correlat ion of Breast Tissue Parameters Using Magne tic Resonance and X-Ray
Marnmography. Br J Cancer, 1996.73(2): p. 162-168.
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