Quantifying image quality

Linköping University Medical Dissertations No. 1050

Quantifying image quality in
diagnostic radiology using
simulation of the imaging
system and model observers

Gustaf Ullman

Radiation Physics, Department of Medicine and Health
Faculty of Health Sciences
Linköping University, Sweden

Linköping 2008

ii

©Gustaf Ullman, 2008

Cover picture/illustration: An oil painting by Gustaf Ullman representing a
chest radiograph

Published articles and figures have been reprinted with the permission of the
copyright holder.

Printed in Sweden by LiU‐Tryck, Linköping, Sweden, 2008

ISBN 978‐91‐7393‐952‐2
ISSN 0345‐0082

Don’t worry about saving these songs!
And if one of our instruments breaks,
it doesn’t matter

We have fallen into the place
where everything is Music.

The strumming and the flute notes
rise into the atmosphere,
and even if the whole world’s harp
should burn up, there would still be
hidden instruments playing.

So the candle flickers and goes out.
We have a piece of flint and a spark.

This singing art is sea foam.
The graceful movements come from a pearl
somewhere on the ocean floor.

Poems reach up like spindrift and the edge
of driftwood along the beach, wanting!

They derive
from a slow and powerful root
that we can’t see

Stop the words now.
Open the window in the center of your chest,
and let the spirits fly in and out.

Jalal al‐Din Rumi

iii

v
CONTENTS
1. INTRODUCTION................................................................................................ 1
1.1. Radiation protection in diagnostic radiology..................................... 1
1.2. Optimisation of diagnostic radiology .................................................. 2
1.3. Optimisation using a Monte Carlo based computational model ... 2
2. OBJECTIVE ........................................................................................................... 5
3. MONTE CARLO BASED COMPUTATIONAL MODEL OF THE
IMAGING SYSTEM................................................................................................... 7
3.1. Introduction............................................................................................... 7
3.2. Computational model of the x‐ray imaging systems ........................ 9
3.2.1. Model of the imaging system........................................................... 9
3.2.2. Monte Carlo simulation of photon transport............................... 14
3.2.3. Scoring quantities............................................................................. 18
3.2.4. Calculated quantities....................................................................... 19
3.3. Calculation of images from the high‐resolution phantom ............ 20
3.4. Uncertainties............................................................................................ 22
3.4.1. Stochastic uncertainties................................................................... 22
3.4.2. Systematic uncertainties.................................................................. 22
4. ASSESSMENT OF IMAGE QUALITY .......................................................... 25
4.1. Introduction............................................................................................. 25
4.2. Image quality assessment as developed in this work..................... 26
4.2.1. The task.............................................................................................. 26
4.2.2. Model of the imaging system and patient.................................... 27
4.2.3. Observers........................................................................................... 29
4.2.4. Figures of merit ................................................................................ 30
5. RESULTS AND DISCUSSION ....................................................................... 41
5.1. Ideal observer with a simplified patient‐model .............................. 41

Contents
5.2. Low resolution voxel phantom............................................................ 43
5.3. High resolution voxel phantom........................................................... 44
5.4. Ideal observer with simple anatomical background....................... 46
5.5. Correlation to human observers.......................................................... 49
5.6. Model observers with complex anatomical background ............... 52
6. SUMMARY AND CONCLUSIONS............................................................... 59
7. FUTURE WORK ................................................................................................. 61
8. ACKNOWLEDGEMENTS ............................................................................... 63
9. REFERENCES...................................................................................................... 65

vi

Abstract
vii
ABSTRACT
Accurate measures of both clinical image quality and patient radiation risk are
needed for successful optimisation of medical imaging with ionising radiation.
Optimisation in diagnostic radiology means finding the image acquisition
technique that maximises the perceived information content and minimises
the radiation risk or keeps it at a reasonably low level. The assessment of
image quality depends on the diagnostic task and may in addition to system
and quantum noise also be hampered by overlying projected anatomy.

The main objective of this thesis is to develop methods for assessment of
image quality in simulations of projection radiography. In this thesis, image
quality is quantified by modelling the whole x‐ray imaging system including
the x‐ray tube, patient, anti‐scatter device, image detector and the observer.
This is accomplished by using Monte Carlo (MC) simulation methods that
allow simultaneous estimates of measures of image quality and patient dose.
Measures of image quality include the signal‐to‐noise‐ratio, SNR, of pathologic
lesions and radiation risk is estimated by using organ doses to calculate the
effective dose. Based on high‐resolution anthropomorphic phantoms,
synthetic radiographs were calculated and used for assessing image quality
with model‐observers (Laguerre‐Gauss (LG) Hotelling observer) that mimic
real, human observers. Breast and particularly chest imaging were selected as
study cases as these are particularly challenging for the radiologists.

In chest imaging the optimal tube voltage in detecting lung lesions was
investigated in terms of their SNR and the contrast of the lesions relative to the
ribs. It was found that the choice of tube voltage depends on whether SNR of
the lesion or the interfering projected anatomy (i.e. the ribs) is most important
for detection. The Laguerre‐Gauss (LG) Hotelling observer is influenced by the
projected anatomical background and includes this into its figure‐of‐merit,
SNRhot,LG. The LG‐observer was found to be a better model of the radiologist
than the ideal observer that only includes the quantum noise in its analysis.
The measures of image quality derived from our model are found to correlate
relatively well with the radiologist’s assessment of image quality. Therefore
MC simulations can be a valuable and an efficient tool in the search for dose‐
efficient imaging systems and image acquisition schemes.

List of papers
ix
LIST OF PAPERS
This thesis is based on the following papers

I. Gustaf Ullman, Michael Sandborg, David R Dance, Martin Yaffe,
Gudrun Alm Carlsson. A search for optimal x‐ray spectra in iodine
contrast media mammography. Phys. Med. Biol. 50, 3143–3152 (2005)*
II. Gustaf Ullman, Michael Sandborg, David R Dance, Roger Hunt, and
Gudrun Alm Carlsson. Distributions of scatter to primary ratios and
signal to noise ratios per pixel in digital chest imaging. Radiat Prot
Dosim, 114, no 1‐3, 355‐358 (2005)*
III. Gustaf Ullman, Michael Sandborg, David R Dance, Roger A Hunt and
Gudrun Alm Carlsson. Towards optimization in digital chest
radiography using Monte Carlo modelling. Phys Med Biol 51, 2729‐
2743 (2006)*
IV. Michael Sandborg, Anders Tingberg, Gustaf Ullman, David R Dance
and Gudrun Alm Carlsson. Comparison of clinical and physical
measures of image quality in chest and pelvis computed radiography at
different tube voltages. Med. Phys. 33(11) 4169‐4175 (2006)*
V. Gustaf Ullman, Alexandr Malusek, Michael Sandborg, David R. Dance
and Gudrun Alm Carlsson. Calculation of images from an
anthropomorphic chest phantom using Monte Carlo methods. Proc of
SPIE 6142, (2006)*
VI. Gustaf Ullman, Magnus Båth, Gudrun Alm Carlsson, David R Dance,
Markku Tapiovaara, and Michael Sandborg. Development of a Monte
Carlo based model for optimization using the Laguerre‐Gauss
Hotelling observer. (To be submitted to Med Phys)

*Reprints have been included with the permission from the publisher

List of papers

Other peer reviewed papers by the author not included in the thesis

1. Gustaf Ullman, Michael Sandborg, David R Dance, Roger Hunt, and
Gudrun Alm Carlsson. The influence of patient thickness, tube voltage
and image detector on patient dose and detail signal to noise ratio in
digital chest imaging. Radiat Prot Dosim, 114, no 1‐3, 294‐297, 2005
2. Markus Håkansson, Magnus Båth, Sara Börjesson, Susanne Kheddache,
Gustaf Ullman, Lars Gunnar Månsson. Nodule detection in digital chest
radiography: effect of nodule location. Radiat Prot Dosim 114, no 1‐3,
92‐96, 2005
3. R A Hunt, D R Dance, P R Bakic, A D A Maidment, M Sandborg, G
Ullman and G Alm Carlsson. Calculation of the properties of digital
mammograms using a computer simulation. Radiat Prot Dosim 114, no
1‐3, 395‐398, 2005
4. D R Dance, R A Hunt, P R Bakic, A D A Maidment, M Sandborg, G
Ullman and G Alm Carlsson. Breast dosimetry using a high‐resolution
voxel phantom. Radiat Prot Dosim 114, no 1‐3, 359‐363, 2005
5. Roger A Hunt, David R Dance, Marc Pachoud, Gudrun Alm Carlsson,
Michael Sandborg, Gustaf Ullman and Francis R Verdun. Monte Carlo
simulation of a mammographic test phantom. Radiat Prot Dosim, 114,
no 1‐3, 432‐435, 2005.

Conference presentations

1. Ullman G, Sandborg M, Dance D R, Skarpathiotakis M, Yaffe MJ, Alm
Carlsson G. (2002) A search for optimal x‐ray energy spectra in digital
iodine subtraction mammography using Monte Carlo simulation of the
imaging chain. Digital Mammography IWDM 2002: Proceedings of the
Workshop, Bremen, Germany, June 2002. Ed. Peitgen H‐O (Springer‐
Verlag, Berlin) pp152‐154, 2002
2. M. Båth, M. Håkansson, S. Börjesson, S. Kheddache, C. Hoeschen, O.
Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, L. G. Månsson.
Investigation of components affecting the detection of lung nodules in
digital chest radiography. Accepted for presentation at Medical
Imaging, 12‐17 February 2005, San Diego, USA. Proc. SPIE 5749, 231‐242,
2005.
x

List of papers

Internal reports (not reviewed)

1. Gustaf Ullman, Michael Sandborg, Roger Hunt and David R Dance.
Implementation of simulation of pathologies in chest and breast
imaging Report no 94, ISRN ULI‐RAD‐R‐‐94—SE, 2003
2. Gustaf Ullman, Michael Sandborg and Gudrun Alm Carlsson.
Validation of a voxel‐phantom based Monte Carlo model and
calibration of digital systems. Report no 95, ISRN ULI‐RAD‐R‐‐95—SE,
2003
3. Gustaf Ullman, M Sandborg, D R Dance, R Hunt and G Alm Carlsson
Optimisation of chest radiology by computer modelling of image
quality measures and patient effective dose Report no 97, ISRN ULI‐
RAD‐R‐‐97—SE, 2004
4. Gustaf Ullman, M Sandborg, Anders Tingberg, D R Dance, Roger Hunt
and G Alm Carlsson Comparison of clinical and physical measures of
image quality in chest PA and pelvis AP views at varying tube voltages
Report no 98, ISRN ULI‐RAD‐R‐‐98—SE, 2004
5. Gustaf Ullman, M Sandborg, D R Dance, M Båth, M Håkansson, S
Börjesson, R Hunt and G Alm Carlsson On the extent of quantum noise
limitation in digital chest radiography Report no 99, ISRN ULI‐RAD‐R‐‐
99—SE, 2004
6. Gustaf Ullman, Michael Sandborg, David R Dance, Roger Hunt and
Gudrun Alm Carlsson Distributions of scatter‐to‐primary and signal‐to‐
noise ratios per pixel in digital chest imaging Report no 100, ISRN ULI‐
RAD‐R‐‐100—SE, 2004

xi

Abbreviations
xiii
ABBREVIATIONS

AGD Average glandular dose
ALARA As low as reasonable achievable
APR Apical pulmonary region
AUC   Area under the ROC curve
BKE Background known exactly
BV Background varying
C Contrast
CC   Cranio‐caudal
C/CB Nodule‐to‐bone contrast
Crel   Relative contrast
DQE Detective quantum efficiency
E Effective dose
FN   False negative
FOM Figure of merit
FP False positive
Ht Equivalent dose
HIL Hilar region
Kc, air Collision air kerma
LG   Laguerre‐Gauss
LAT Lateral pulmonary region
LME Lower mediastinal region
LNT Linear non‐threshold hypothesis
MC   Monte Carlo
MTF Modulation transfer function
NPS Noise power spectrum
PA   Posterior Anterior
RET Retrocardial region
ROC Receiver operating characteristics
SKE Signal known exactly
SNR   Signal‐to‐noise ratio
SNRhot, LG Laguerre‐Gauss Hotelling observer signal‐to‐noise ratio
SNRI Ideal observer signal‐to‐noise ratio
SNRp Signal‐to‐noise ratio per pixel
TN   True negative

List of papers
TP True positive
UME Upper mediastinal region
VGA Visual grading analysis
VGAS VGA score

Energy imparted per unit area from primary photons p
Aε
s
Aε
p
Energy imparted per unit area from scattered photons
Mean energy imparted per primary photon λ
Mean squared energy imparted per primary photon 2
pλ
s Mean energy imparted per scattered photon λ
Mean squared energy imparted per scattered photon 2
sλ
xiv

Introduction
1
1. INTRODUCTION
1.1. Radiation protection in diagnostic radiology
Diagnostic x‐ray examinations can support the radiologist with valuable
information that can be utilised to give a patient an accurate diagnosis, and
subsequently a successful treatment. However, imaging with ionising
radiation is also associated with a small risk for cancer induction or genetic
detriment. When x‐ray photons are scattered or absorbed inside the cells of the
human body, ionisations occur that can alter molecular structures and thus
make harm to the cell. The most important damage to the cell is damage in the
DNA since this may induce mutations. Ultimately, the damage may lead to
that the cell is killed, and if enough cells are killed, the function of the tissue or
organ will be deteriorated. This type of acute harm due to large radiation
exposures is referred to as a deterministic effect. However, at the relatively low
radiation exposures in diagnostic radiology, the damages caused by ionising
radiation are often rather easily repaired. Yet, sometimes the damage on the
DNA is more complex. This can cause mutations or chromosome aberrations,
which in turn may lead to a modified cell but with retained reproduction
capacity. In some cases, such modified cells can result in a cancer. In the case
where the harmful effects of ionising radiation are only known statistically, it
is referred to as a stochastic effect. The risk related to stochastic effects to a
human from exposure from ionising radiation is often quantified with the
effective dose, E (ICRP 1991, ICRP 2007).

According to the linear non‐threshold (LNT) hypothesis, there is a linear
relation between the effective dose and risk for cancer induction (ICRP 2005)
and means that the collective dose can be used as a measure of the harm to the
population. The collective dose from medical radiography is according to the
Swedish radiation protection authority (Andersson et al 2007) 8000 manSv per
year or 0.9 mSv on average per capita, and contributes the largest fraction of
the total dose to the population from man‐made sources.

Diagnostic radiology is invaluable for the health care but due to the radiation
risks, radiation protection of the patient becomes an important issue. Three
different principles are used for radiation protection (ICRP 2007). The first
principle is justification. Ionising radiation should only be used in those
situations where it brings more good than harm. The second principle is

Introduction
optimisation. It means that, in those cases where the use of ionising radiation is
justified, doses should be kept as low as reasonable achievable. This is often
referred to as the ALARA (As Low As Reasonably Achievable) principle. The
third principle is dose limits to the individual. However, this principle is more
applicable for personnel rather than for patients in diagnostic radiology.

1.2. Optimisation of diagnostic radiology
Optimisation means to balance the diagnostic information (image quality) and
patient dose so as to maximize the ratio between the two; either to keep the
information constant and minimize the dose or to increase information at
constant dose. The dose to the patient undergoing an x‐ray examination has, in
digital systems, a close relation to the quantum noise in the image. The
quantum noise depends on the number of photons incident on the image
detector and is approximately described with a compound poisson
distribution, which takes the energy absorption properties of the detector into
account. If we use too few photons, the image will be noisy and it will make it
difficult or even impossible for the radiologist to give a correct diagnosis. It
may also take longer time for the radiologist to give a diagnosis using a noisy
image. Yet, above a certain dose level, the quantum noise may become
negligible in comparison to the noise naturally present in the projected
anatomy (Hoeschen et al 2005). There will therefore be limited benefit to
increase the dose above this level.

How to make the trade off between the dose to the patient and the image
quality is a complex subject. A key aspect for the optimisation of diagnostic
radiology is to understand the relative importance of the quantum noise in the
image and the structures in the projected anatomy that act as noise. Several
authors including Kundel et al (1985), Samei et al (1999), Burgess et al (2001)
and Håkansson et al (2005b) have acknowledged the importance of projected
anatomy in relation to quantum noise. The consensus from these studies is
that at normal exposures, the projected anatomy is the most important factor
in hampering the detection of subtle nodules in chest radiographs and
mammograms.

1.3. Optimisation using a Monte Carlo based computational model
One method that has been utilised to search in a systematic way for the
optimal imaging parameters in diagnostic radiology is to use a model of the
imaging system, including the patient and observer, and to simulate the
photon transport through the imaging system using the Monte Carlo method.
2

Introduction
With this method it is possible to simultaneously calculate the dose to the
patient and measures of image quality.

However, the physical measures of image quality derived from simulations
must in some sense give us information on the usefulness of the image for a
radiologist to solve a specific clinical task. Our physical measures of image
quality must therefore correlate to clinical measures of image quality. Two
methods for assessment of clinical image quality are given attention in this
work, receiver operating characteristics (ROC) (Metz 1986) and visual grading
analysis (VGA) (Tingberg 2000). A challenge in this work has been to develop
a model, which includes realistic measures of image quality that takes the
projected anatomy into account.

3

Objective
5
2. OBJECTIVE
While patient doses are relatively straightforward to calculate, image quality
assessment is a more complex task and crucial for the optimisation process.
The main objective of this thesis is therefore to further develop methods for
assessment of image quality in x‐ray projection radiography. The main
method is Monte Carlo photon transport simulation (Monte Carlo model)
through the whole x‐ray imaging system including a model of the image
observer. As study cases, chest posterior‐anterior (PA) and mammography
cranio‐caudal (CC) projections are used as these are particularly challenging
for the radiologist.

The specific objectives are:

• To study how physical measures influencing image quality are
distributed over the image plane (paper II)

• To develop methods for calculating physical image quality measures
from simulated radiographs and search for correlations between these
measures and measures of clinical image quality (papers III and IV)

• To develop patient models of higher realism and finer anatomical
structures for calculation of synthetic x‐ray images to be used for image
quality analysis (papers V and VI)

• To complete our model of the imaging system by including a more
realistic model observer that can be used to directly make any task‐
related clinical image quality assessment from synthetic images
calculated by the model (papers V and VI)

• To use our model of the imaging system towards optimisation of image
quality and patient dose (paper I and III)

Monte Carlo model
7
3. MONTE CARLO BASED
COMPUTATIONAL MODEL OF THE
IMAGING SYSTEM
3.1. Introduction
The Monte Carlo method relies on taking random samples from known
distributions and is particularly useful for studying complex problems with
many degrees of freedom. One of the first applications of the method was in
Los Alamos, USA, during the Second World War where it was used to
simulate neutron diffusion. Today, Monte Carlo methods are employed in
widely diverse fields, from the evaluation of shares on the stock market
(Glasserman 2003) to the calculation of energy levels of molecules with
quantum Monte Carlo (Ceperley and Alder 1986).

In radiation physics, the Monte Carlo method is employed for simulating
radiation transport, mathematically described by the Bolzmann equation.
There are several general‐purpose computer codes available for the study of
radiation transport, for example, MCNP (Monte Carlo N‐Particle transport)
(Briesmeister 2000) developed in Los Alamos and designed to transport
neutrons, electrons and photons; EGSnrc (Electron Gamma Shower)
(Kawrakow and Rogers 2003, Nelson et al 1985), initially developed in
Stanford, which transports photons and electrons; PENELOPE (PENetration
and Energy Loss Of Positrons and Electrons) (Baro et al 1995) developed at
University of Barcelona, and used to transports electrons, positrons and
photons.

In diagnostic radiology, one of the most common applications of the Monte
Carlo method is in patient dosimetry. There are several Monte Carlo computer
codes that are used to estimate the effective dose. Jones and Wall (1985) used
the Monte Carlo method to compute organ doses using a mathematical
representation (Cristy 1980) of a human anatomy. Zankl and Wittman (2001)
have developed a family of more realistic, segmented anthropomorphic voxel
phantoms for organ dosimetry for external photon beams. Zankl and Petoussi‐
Henss (2002) calculated conversion factors based on the VIP man (Spitzer and
Whitlock 1998) anthropomorphic model. The user‐friendly Monte Carlo
computer program PCXMC by Servomaa and Tapiovaara (1998) calculates

Monte Carlo model
organ and effective doses based on either measured air kerma‐area product or
entrance air kerma values.

There are also Monte Carlo codes developed for optimisation in diagnostic
radiology. Such codes rely on the fact that they are able to estimate both organ
or effective doses and measures of image quality. The main application of the
Monte Carlo method is for estimating the negative effect of scattered photons
reaching the image detector. Chan and Doi (1985) used the Monte Carlo
method to characterise scattered radiation in x‐ray imaging. Chan et al (1985)
also investigated the performance of anti‐scatter grids in screen‐film imaging
whereas Sandborg et al (1994a) did task‐dependent, anti‐scatter grid
optimisation for digital imaging. More recently McVey et al (2003) did an
optimisation study of lumbar spine radiography and Lazos et al (2003) have
developed a software package for mammography. The Lazos model also
includes a realistic model of the breast (Bliznakova et al 2003). Son et al (2006)
have developed software that calculates images from the visual human (VIP
man)(Xu et al 2000). They have used the EGSnrc code as a basis of the model,
used model observers and calculated effective dose.

In this work we have used an in‐house Monte Carlo code VOXMAN adapted
for conditions usually encountered in diagnostic radiology. It originates from
Dance and Day (1984) and Persliden (1986) who independently developed
computer programs to estimate scattered radiation in the image plane in
mammography and conventional radiography, respectively. A few years later,
Dance et al (1992) and Sandborg et al (1994b) merged the codes and did further
validation of the computer programs. McVey et al (2003) replaced the simple
homogeneous water or tissue phantoms, used in the earlier versions of the
code, by a voxelised anthropomorphic male phantom developed by Zubal et al
(1994). This step enabled more realistic organ dosimetry and made it possible
to describe how measures of physical image quality vary in the image plane
behind the patient.

The main focus of this thesis is on chest imaging. Therefore we have mainly
used the VOXMAN model, adapted to simulate chest radiography. In paper I
we used the version of the computer program dedicated for mammography.
This computer program was further developed by Hunt et al (2005) to
incorporate an anthropomorphic model of the breast developed by Bakic et al
(2002). A brief description of the VOXMAN model is presented below.

8

Monte Carlo model
3.2. Computational model of the x‐ray imaging systems
The Monte Carlo based computational method used in this thesis models the
x‐ray imaging system and simulates photon transport from the source through
patient, anti‐scatter grid and into the image detector. The computational
method consists of the following components:

A model of the imaging system. This comprises different sources of
input data and the imaging geometry. Input data includes x‐ray
spectrum, patient‐based voxel phantom, anti‐scatter grid, table or chest
support couch and image detector.

Monte Carlo simulation of photon transport through the imaging
system. The model uses different variance reduction techniques, briefly
described below, to increase the efficiency of the model.

Scoring variables such as organ and effective doses and calculation of
different measures of image quality such as contrast and signal‐to‐noise
ratio of nodule lesions or anatomical structures within the patient
model.

3.2.1. Model of the imaging system
The input data files are described below including geometry, x‐ray spectra,
voxel phantom, anti‐scatter grid and image detector.

3.2.1.1 Imaging geometry
The imaging geometries for the chest and mammography models are shown in
figures 3.1 and 3.2, respectively. Examples of specific imaging configurations
are listed in table 3.1. Substantial variations of the imaging system
configuration were employed particularly in papers I, III and IV and to some
extent also in papers II, V and VI.

9

Monte Carlo model

Figure 3.1. The simulated imaging geometry used in chest PA radiography
including an x‐ray source, voxel phantom, anti‐scatter grid and image
detector.

Figure 3.2. The simulated imaging geometry used in Cranio‐caudal (CC)
mammography. Notations are a) focus‐detector distance; thickness of b)
breast, c) compression plate, d) adipose layer, e) contrasting detail, f) breast
support, g) anti‐scatter grid and h) image detector.

10

Monte Carlo model
Table 3.1. Examples of imaging system configurations for chest and breast
imaging system component Chest PA Breast CC
imaging used in this work.

Typical
values
Focus‐detector distance (cm) 180   65
Tube voltage (kV) 90‐150
) Cu Cu
Patient PA or breast thickness (cm) 0‐28
es 10‐25 ocalcifications
Compression plate ‐ exiglas
erial arbon fibre / Al
/ grid ratio

(mg/cm2)
20‐55
Total filtration (mm 0.1‐0.5 mm

0.3 mm
25μm Rh
2 2‐8
Typical diagnostic tasks and size of
details
Nodul
mm
Micr
and soft tissue
masses
3 mm pl
Grid interspace mat C Carbon fibre
Lamella frequency (cm‐1) 40 / 12 60 / 5
Image detector material BaFCl, CsI CsI
Image detector thickness 100 100

.2.1.2 X‐ray spectra
was calculated with a computer program based on a
t

the VOXMAN model, the relative fractions of Bremsstrahlung and

3
The x‐ray spectrum
spectral model by Birch and Marshall (1979). The program calculates
Bremsstrahlung and characteristic x‐rays from a tungs en or molybdenum
anode target and allows the user to select appropriate thicknesses of added
filtration of aluminum, copper or molybdenum. In paper I, tungsten,
molybdenum and rhodium anode target spectra were instead calculated with
MCNP4C Monte Carlo code since the Birch and Marshall program did not
include a rhodium target or a rhodium filter.

In
characteristic x‐rays were computed and a random number selected from
which of the distributions the photon emerged. If a Bremsstrahlung photon
was selected, the photon energy was chosen using rejection sampling
(Sandborg et al 1994b).

11

Monte Carlo model
3.2.1.3
was
Low‐resolution chest phantom
anthropomorphic voxel phantoms were
Voxel phantoms
tom
a
A Mammography phan
In the mammography model, simple representation of the female breast
used (Ullman et al 2005). The breast was assumed to be a cylinder with
semicircular cross‐section and made of a homogeneous mixture of glandular
and adipose tissue in the central region surrounded by an adipose layer. The
tissue compositions were taken from Hammerstein et al (1979). The density of
glandular tissue was 1.04 g cm−3 and for adipose tissue 0.93 g cm−3. The
glandularity of the central part of the breast model was for the main part set to
50%, but was allowed to vary between 10‐90% to represent both dense and
fatty breasts.
B
In the chest model, three different
used as a model of the patient. The main phantom was the one developed by
Zubal et al (1994) and used in papers II, III and IV. The Zubal phantom
(displayed in figure 3.3) was segmented into organs such as lungs, heart and
bone marrow. It therefore allows for calculation of organ and effective doses.
The female‐specific organs: breast, ovaries and uterus were added manually to
the male body to enable effective dose to be calculated (McVey et al 2003).
However, the phantom has relatively large voxels (3x3x4 mm3) and is
therefore not suitable for calculating realistic images (see figure 3.4 below). In
addition, the lungs are comparably small since the phantom was based on a
CT scan where the male patient was imaged with non‐inflated lungs and in a
non‐upright position, contrary to the typical chest PA imaging situation.

igure 3.3. Volume‐rendered representation of the Zubal phantom (left) and F
the Kyoto Kaguku (PBU‐X‐21) phantom (right). An outline of the lungs,
trachea, heart and breast are shown in the left image.

12

Monte Carlo model
C High‐resolution chest phantoms
s (voxel sizeTwo high‐resolution voxel phantom 0.97x0.97x0.6 mm) were
he manufacturer of the Kyoto Kagaku phantom claims that it is composed of
created from CT scans of two different anthropomorphic thorax phantoms: the
Alderson phantom and the Kyoto Kagaku PBU‐X‐21 phantom. The Alderson
phantom was used in paper V and did not include smaller vessels. The more
recent Kyoto Kagaku phantom was more realistic since it contained a more
human‐like distribution of small and medium‐sized vessels. Simulated x‐ray
images of the Zubal, Alderson and Kyoto Kagaku phantoms are shown in
figure 3.4 demonstrating an increasing realism from left to right.

T
materials with linear attenuation coefficients (μ values) resembling those of
human tissues. However, they failed to provide us with details of the atomic
compositions of the tissue substitute materials, which complicate a more
rigorous comparison with real x‐ray images of their chest phantom (see paper
VI). A more detailed description of the segmentation of the Kyoto Kagaku
phantom is given in Malusek (2008). The Alderson and Kyoto Kagaku
phantoms are used mainly for simulation of synthetic images with high
resolution but are not yet segmented into organs and tissue types and can
therefore not be used for direct calculation of effective dose.

Figure 3.4. Projection images of the three chest voxel‐phantoms used in this

.2.1.4 Anti‐scatter grid
as simulated by specifying the lamella thickness,
thesis. To the left the low‐resolution Zubal phantom, central the Alderson
phantom and to the right the Kyoto Kagaku phantom.
3
The anti‐scatter grid w
interspace material and thickness as well as cover thickness and grid ratio.
Typical grids are listed in table 3.1. In the Monte Carlo program the focused
grid was simulated by an analytical transmission formula developed by Day
13

Monte Carlo model
and Dance (1983). Scattered photons generated in the grid itself was simulated
by a separate Monte Carlo simulation in a parallel grid (Sandborg et al 1994b).

3.2.1.5 Image detector
ge detector was simulated in a separate Monte Carlo
he image detector thickness was specified in terms of a surface density in mg
.2.2. Monte Carlo simulation of photon transport
tion is described by
( )nnnnn wE ,,, Ωr=
The response of the ima
model of a semi‐infinite layer of the image detector material. This model is
included as a sub‐routine to the main VOXMAN program. Energy imparted
per unit area was assumed proportional to the image detector signal. The
image detector model does not include the transport of secondary electrons as
the kerma approximation was assumed. The transport of light photons was
also neglected. In papers V and VI, the detector response was calculated
separately with MCNP4C and was used for the calculation of primary
projections (Malusek 2008).

T
cm-2
(see table 3.1). In paper I, the detector material was needle crystals of CsI;
in paper II, III and IV an unstructured mixture of BaFCl grains simulating a
computed radiography (CR) fluorescent screen and finally in paper VI, a
Gd2O2S indirect flat panel (DR) fluorescent screen was employed.

3
The physical state of the photon after the n:th interac

α (3.1)

here rn is the position, En is the energy, Ωn is the solid angle and wn is the
.2.2.1 Photon interaction, cross‐sections and material compositions
w
statistical weight of the photon. Photon interaction types in the energy range
of diagnostic radiology (10‐150 keV) are: coherent scattering, incoherent
scattering and photoelectric effect. The photon interactions are described by
the differential cross sections for these events based on the atomic composition
of the materials and tissue types in the geometry. A flow chart of the main
steps in the Monte Carlo program is given in figure 3.6. A central part of the
Monte Carlo method is the utilisation of a random number generator. In this
work we have used the random number generators embedded in UNIX or
LINUX operating systems.

3
The differential cross‐section for coherent scattering is given by
14

Monte Carlo model
),()cos1(
2
22
2
ZxF
r
d
d ecoh
θ
σ
+=
Ω
(3.2)

where re is the classical electron radius, x is defined by )2/sin(θ
hc
E
x = where h
is Planck’s constant and c the speed of light. F is the atomic form factor, θ the
scattering angle and Z the atomic number.

For incoherent scattering the differential cross‐section is given by the Klein‐
Nishina relation times the incoherent scattering function S(x,Z):

),(sin
2
2
22
ZxS
E
E
E
E
E
Er
d
d eincoh
⎟
⎠
⎞
⎜
⎝
⎛
−
′
+
′
⎟
⎠
⎞
⎜
⎝
⎛ ′
=
Ω
θ
σ
(3.3)

Here, E is the incident photon energy and E´ is the scattered photon energy
given by the Compton relation

)cos1(1 θκ −+
=′
E
E
2
/ cmE e=κ
(3.4)

where , me is the electron rest mass.

For the photoelectric effect, it is assumed that the photon is locally absorbed in
interactions with atoms of low atomic number (such as carbon and oxygen).
Elements with high atomic numbers such as those in the grid (lead) and
detector materials (e.g. barium, gadolinium, cesium, iodine) may emit (high‐
energy) characteristic x‐rays if vacancies are created in the K‐ or L‐shells.

To describe these photon interactions we have used tabulated cross‐sections
from the XCOM library by Berger and Hubbell (1987). Cross‐sections for
compounds were computed based on the relative weight of individual
elements.   The atomic form factors, F(x,Z), were given by Hubbell and Överbö
(1979) and the incoherent scattering functions, S(x,Z), were given by Hubbell et
al (1975).

In the voxel phantom model of the patient, each organ is identified with one of
four tissue types, with different densities: average soft tissue (1.03 g cm−3),
healthy lung (0.26 g cm−3), cortical bone (1.49 g cm−3) and bone spongiosa (1.18
g cm−3). The tissue densities and compositions were taken from ICRU 46 (1992)
except for cortical bone, which was obtained from Kramer (1979).
15

Monte Carlo model
3.2.2.2 Primary photons
Primary transmission was calculated by first sampling the initial energy from
the pre‐calculated energy spectrum, and use Siddon’s algorithm (Siddon 1985)
to calculate the radiological path‐length from the focus to the detector

n
N
n
n dL ∑
=
=
1
μ (3.5)

The radiological path‐length can be used to calculate the contribution to the
energy imparted per unit area from primary photons as

dEEfeE
r
Es LEp
A ),(
)(
2
,
ξξε −Ω
∫=
Es ,Ω ),(
(3.6)

where is the source intensity, ξEf is the detector absorption efficiency
function depending on the photon energy E and cosine of incidence angle,
θcos=
),(
, at the detector surface; r is the focus detector distance. ξ

Equation 3.6 is calculated by two separate methods. In the original version of
the VOXMAN program, this calculation was embedded inside the Monte
Carlo code. It is then calculated by first sampling the photon energy E, from
the x‐ray spectrum, subsequently the optical path L from the source to a point
in the detector is calculated. Finally the photon is transported in a semi‐infinite
layer corresponding to the detector thickness in order to calculate ξEf
),(
.
However, this did not allow for the calculation of high‐resolution images,
since we were forced to run the Monte Carlo simulation for all these points. In
papers I, III and IV, the energy imparted to the image detector per unit area
from primary photons was therefore calculated to a very limited number of
points (1‐15) in the detector plane corresponding to those points where the
projection of the contrasting detail or lesion was located. In paper II, V and VI
the Monte Carlo simulations where performed for 40 x 40 points in the
detector. This is rather time‐consuming and is only feasible to perform with
high precision with a fast, modern computer.

In papers V and VI, a different method was implemented for the calculation of
primary projections. The detector absorption efficiency function ξEf was
calculated separately with MCNP4C (Malusek 2008) and the projections were
calculated analytically averaged over the energy spectrum. This allowed for a
separate calculation of primary projections with high resolution.
16

Monte Carlo model
3.2.2.3 Scattered photons and variance reduction techniques
The simulation of scattered photons is time consuming. Therefore, different
variance reduction techniques, described briefly below, were used to increase
the efficiency. Monte Carlo methods that do not employ any variance reducing
techniques are often referred to as analogue Monte Carlo methods. An
algorithm for sampling the free path of the scattered photon, referred to as the
Coleman’s algorithm is also briefly described below.

A Coleman’s algorithm
The free path of the scattered photon is sampled using an algorithm described
by Coleman (1968). The sampling of the free path consists of several steps.
First, the distance to the first interaction point is sampled for a homogeneous
medium with the linear attenuation coefficient, μmax, corresponding to the
material with highest attenuation (e.g. bone). The sampling is performed by
testing whether a sampled random number from a uniform distribution in the
interval [0,1] is less than the quotient μ/μmax, where μ is the attenuation
coefficient of the material at the interaction point. If yes then the new point is
accepted and the algorithm ends. If no then the sampling of the distance to the
first interaction in the homogenous medium is repeated until the sampled
random number is less than μ/μmax.

B Collision density estimator
Analogue Monte Carlo methods are inefficient in estimating scattered photons
in the image plane due to the low probability that a scattered photon will pass
a given small target area in the image detector. Therefore in the VOXMAN
code, the collision density estimator (Persliden and Alm Carlsson 1986) is
used. The contribution to the energy imparted per unit area at a given point of
interest in the image detector is obtained from each interaction point in the
phantom. The contribution is derived through ∗
sε
sn
N
n
nns Tw ,
1
)( λαε ∑
=
∗
=

(3.7)

where λn,s is the contribution from the n:th interaction and T(α) is the
probability for the photon of state αn to be scattered to the point of interest; wn
is the photon weight. In the collision density estimator, incoherent and
coherent scattering are treated separately. The radiological path‐length from
the interaction point to the point of interest in the detector is calculated with
Siddon’s algorithm as in the case of primary photons.

17

Monte Carlo model
C Analytical averaging of survival and Russian roulette
The main purpose of the Monte Carlo model is to achieve an accurate estimate
of scattered photons generated in the patient and emerging towards the image
detector. If photons are absorbed in the patient they will not contribute to this
estimate. Therefore, a technique known as analytical averaging of survival is
used which does not allow photons to interact by the photoelectric effect. All
interactions in the phantom are therefore constrained to be either coherent or
incoherent scatterings. The new statistical weight, wn+1, for the photon after the
n:th interaction is calculated from the cross‐sections for photoelectric, τ(E) and
scattering processes, σ(E) to correct for the bias which this method would
otherwise introduce.

( )
( ) ( )EE
E
ww nn
τσ
σ
(3.8)
+
=+1

For high photon energies, E, the ratio wn+1/wn is less than, but close to 1 and the
statistical weight is only slightly reduced at each interaction. However, as the
photon energy is reduced the relative importance of photoelectric cross‐
sections increases, and the number of interactions before a scattered photon
escapes from the phantom geometry may be large. Hence, the statistical
weight of the photon may eventually be low and so its contribution to the
estimated image detector signal. Therefore, an unbiased procedure called
Russian roulette (Salvat et al 2003) is used. Once the weight is less than 0.05 a
random number is selected and in 95% of the cases the photon history is
terminated; in the other 5% of the cases the photon history continues with a
twenty times higher (100%/5%) statistical weight wn+1 compared to the original
weight. Photon histories are also terminated once the photon is scattered out
of the boundaries of the phantom.

3.2.3. Scoring quantities
3.2.3.1 Energy imparted to the image detector
Estimates of the mean energy imparted per unit surface area of the image
detector from scattered photons,
s
Aε and primary photons
p
Aε are computed.
The total energy imparted is calculated as the sum of primary and scatter
contributions sp
AA
t
A εεε +=
p
. In order to estimate the signal‐to‐noise ratio and
variance in the image detector signal, the first and second moments of energy
imparted per incident primary ( λ and ) and scattered (
2
pλ sλ and )
photon at the image detector was calculated (Dick and Motz 1981, Sandborg
and Alm Carlsson 1992).
2
sλ
18

Monte Carlo model
3.2.4. Calculated quantities
3.2.4.1. Contrast
A contrasting detail (e.g. corresponding to a lesion) is added to the model with
a thickness and location specified by the user. The contrasting detail is not
added directly into the voxel phantom but in an artificial way in a subroutine
inside the VOXMAN model. The contrast of this detail is calculated as
11
21
1
1
psp
pp
C
εεε
ε ε
+
⋅
−
= (3.9)

where εp1 is the mean energy imparted to the detector per unit area from
primary photons with the nodule present, εp2 the mean energy imparted per
unit area from primary photons with the nodule absent and εs is the mean
energy imparted per unit area from scattered photons.

3.2.4.2. Signal‐to‐noise ratios
The program calculates two types of signal‐to‐noise ratios. The signal‐to‐noise
ratio per pixel, SNRp is calculated as
22
sspp
p
A
p
NN
SNR
λλ
ε
⋅+⋅
=          (3.10)

where N is the number of photons incident on a pixel. The indices p and s
stands for contributions from primary and scattered photons, respectively. The
quantities λ and λ2 are mean and mean squared values of the energy imparted
to a specified pixel per incident photon.

Given the location and thickness of a specified lesion (detail), the computer
program calculates the signal‐to‐noise ratio for this detail with a projection
area corresponding to one pixel. It is here called the SNRMC and is given by
22
11
2211
sspp
pppp
MC
NN
NN
SNR
λλ
λλ
⋅+⋅
⋅−⋅
= (3.11)

where the index n=1 refers to a pixel in the image behind the nodule, and n=2
refers to the same pixel with the nodule absent.

19

Monte Carlo model
3.2.4.1 Air collision kerma
The air collision kerma, Kc,air is given by

( ) ( )( )∫ ⋅⋅= dE/ρEμEΦEK airenEc,air
airen )/(
, (3.12)
where ρμ is the mass energy absorption coefficient for air and is
the differential photon fluence with respect to energy.
)(EEΦ
tt HwE ∑=

3.2.4.2 Effective dose
The effective dose is the tissue‐weighted sum of the equivalent doses in all
specified tissues or organs of the body calculated according to ICRP 60 (ICRP
1991).

(3.13)

where wt is the tissue or organ weighting factor and Ht the equivalent dose for
that tissue or organ. It is recognized that a new ICRP publication 103 (ICRP
2007) has recently been adopted and uses slightly different values of the tissue
weighting factors in the calculation of effective dose. A detailed analysis of the
effect on the figures of merit due to this change, for example signal‐to‐noise
ratio per effective dose, SNR2
/E, has not been performed here. The absolute
values of SNR2
/E may change, but the main conclusions on for example the
appropriate tube voltage for chest PA radiography is unlikely to be affected by
the change of weighting factors, particularly since the weighting factors for the
lungs are the same in ICRP 60 as in ICRP 103.

3.3. Calculation of images from the high‐resolution phantom
The scatter projection, SNRp and other quantities calculated with the MC
method are rescaled (i.e. from 40 x 40 points) to fit the number of pixels in the
primary image. In paper V this number is 1760 x 1760, and in paper VI the
number of pixels is 2688 x 2688. The rescaling is performed using a bilinear
interpolation function in MATLAB. The interpolated scatter projections are
added to the primary image to give the estimate of the mean energy imparted
per unit area of the detector for the i:th pixel, s
,
p
,
t
, iAiAiA εεε += . Noise is
subsequently added to the image. In paper V, white gaussian noise is added
with the standard deviation
20

Monte Carlo model
ip,
p
,
SNR
iA
i
ε
σ = .
The white noise is generated by adding sampled random numbers for each
pixel i from the appropriate distribution to the calculated image. In paper VI,
correlated noise is added with a method similar to the one used in Båth et al
(2005c). In order to add correlated noise, knowledge of the noise power
spectrum (NPS) for the clinical system is needed. The NPS is then normalized
to correspond to unit variance. A random phase is added to the square root of
the normalized NPS with the constraint that the random phase image ),( vuφ
should have the symmetry ),(),( vuvu = −φ − −φ . By taking an inverse Fourier
transform of this spectrum a real and correlated noise image is created. The
vector δ is a multivariate random variable with mean corresponding to a null
vector and covariance matrix corresponding to the measured NPS. The noise
fluctuation for each pixel is rescaled with the relation
εˆδ
εˆ
iAiiA σ ,,
ˆδε εδ⋅= . It is
assumed that the NPS was invariant under a logarithmic transformation. The
total energy imparted to the detector per unit area including noise fluctuations
becomes iA
t
iAiA ,,
t
, δεεε +=
t
,iAε
cbag iAi += )ln( t
,ε
. The pixel value in the i:th pixel is calculated by taking
a logarithmic transformation of using the relation

(3.14)

where the parameters a, b and c are calculated with non‐linear regression to
make the best fit to the real phantom images. The method to add primary,
scattered and noise images is illustrated in figure 3.5.

+ =+

Figure 3.5. The method for calculating images illustrated in a cutout in the
retrocardial region (see further figure 4.1.). From the left: primary projection,
scatter projection, noise image and total image (to the right).

21

Monte Carlo model
3.4. Uncertainties
3.4.1. Stochastic uncertainties
The choice of the number of photon histories used in the simulation is a trade
off between computer time and statistical precision. If the statistical precision
of the simulation is doubled, the computer time is increased by a factor of 4.
For instance, the computer time for a typical simulation (for calculating the
scatter contribution to a synthetic image) on the computer Alpha (AMD
Opteron processor 250, 2.4 GHz; 6.26 GB RAM) in 40 x 40 points of interest, at
the tube voltage 141 kV, with a precision of 1% (one standard deviation) takes
approximately 17 hours. The statistical uncertainty has to be kept low when
we are calculating images, since if the statistical uncertainty is too high, the
scatter projection often contains artifacts when it is interpolated to a higher
resolution.

3.4.2. Systematic uncertainties
There are several sources of uncertainty that affect the results. These include
uncertainties in the cross sections, but also uncertainties in estimation of the
different parameters in the input files. In an internal report, Ullman et al (2003)
studied the effects of uncertainties in x‐ray spectrum half value layer (HVL),
field size, grid lamella thickness and detector thickness. The conclusion from
this study is that the systematic uncertainty due to these factors in the
estimated εs/εp behind the grid is approximately 11%. Later, analysis of
variance (ANOVA) and regression analysis was used to analyse similar
uncertainties and the systematic uncertainty in εs/εp behind the grid was
estimated to be approximately 9%. However, these relatively large
uncertainties only apply in those cases where we attempt to mimic a real x‐ray
imaging system and compare measured quantities from that system with our
calculated quantities. In the cases where we only use simulations to study
relative differences between alternative acquisition schemes for an imaging
system, the stochastic uncertainty is more relevant.
22

Monte Carlo model

23

Figure 3.6. Flow chart describing the most important steps in the Monte Carlo
program
Yes
Set-up geometry, voxel phantom, cross-
sections, image detector and grid
Select photon energy
Calculate contributions from primary
photons analytically to point of interest
(Siddon’s algorithm)
Start calculating contributions
from scattered photons
Select direction of motion
of incident photon
Calculate free path with Coleman’s
algorithm.
Calculate the contribution to collision density
estimator from scattered photons.
Select type of interaction
and assign weight
Store energy imparted to the
phantom
Sample new direction of motion and
continue photon history
Terminate
by Russian
roulette?
Select new path length
(Coleman’s algorithm)
YesIs the next
interaction within
the phantom?
No
Was this the
last history?
Calculate scoring
quantities

Monte Carlo model

24

Assessment of image quality
25
4. ASSESSMENT OF IMAGE QUALITY
4.1. Introduction
Image quality assessment means quantifying the usefulness of an image to
solve a specific diagnostic task. It is preferred if this image quality assessment
is objective. There are, according to Barrett (1990), four criteria that are
essential for objective assessment of image quality.

A. The task
Image quality can only be described in relation to a well‐defined task. This
often means detection of an object in a structured or homogeneous
background. A summary of different tasks to be solved in chest radiography is
given in ICRU 70 (ICRU 2003). Among those, the search for malignant nodules
at different positions in the lung is a common case treated in the literature
(Samei et al 1999). In mammography it is common to search for calcifications
or masses (Burgess et al 2001). Several different types of tasks are discussed in
the literature (Barrett and Myers 2004).

B. Image and object properties
We need to understand the physical and statistical properties of the imaging
system as well as the object being imaged. For example, the radiologist has an
internal model of both the human anatomy as well as a large “data bank” of
common pathologies in order be able to distinguish a malignant nodule from
normal anatomy. The radiologist also needs to understand some of the physics
behind the imaging technology in order to recognize some of the artefacts that
may be present in the image.

C. Observer
An observer that can perform the task is needed. This can be a human or a
model observer. It is the human observer (radiologist) that is the final decision
maker. Therefore, measures of image quality should always take the human
observer into account. Yet, clinical trials involving human observers are costly
and time demanding. Model observers may then be used to give insights into
how image quality depends on the physical and technical image acquisition
parameters.

D. Figure of merit
The figure of merit (FOM) is a number that tells us how well the observer
performs the task. The FOM depends on the detection task; a commonly used
FOM is the signal to noise ratio (SNR) or AUC, the area under the receiver
operating characteristic curve (ROC). In some cases, image quality is described
by physical properties derived from the image rather than by the performance
of an observer on a specific task, for example, the modulation transfer function
(MTF) or the noise power spectrum (NPS). We will refer to this as physical
image quality.

4.2. Image quality assessment as developed in this work
In this work, different tasks and figures of merit have been used, changing
along with an improved modeling of the imaging system including the patient
and improved model observers. In some cases, figures of merit based on pure
physical measures of image quality were used and correlated to measures of
the performance of human observers in clinical trials. A summary of the
development is given below.

4.2.1. The task
Two main types of tasks are used in this work. The first task is to search for a
known signal (e.g. a nodule) in a known background, referred to as the
SKE/BKE (signal known exactly/background known exactly) task. The second
task is to search for a known signal (e.g. a nodule) in a varying background,
referred to as the SKE/BV (signal known exactly/background varying) task.

The SKE/BKE task was addressed in paper I, which was devoted to the
optimization of tube voltage and filtration in iodine subtraction
mammography. The task was to detect a blood vessel filled with iodine
contrast of thickness 6 mg cm‐2 against a homogeneous background.

In paper IV the task was to compare two images from an x‐ray chest phantom
and see in which image the structures corresponding to the image criteria
were most clearly visible (the VGA study). In some sense, the background can
be considered as known in this study since the same anthropomorphic
phantom (the Alderson chest phantom) is used for all comparisons. Thus, the
observer may be able to remember the background. In addition, the phantom
used in this study does not contain as fine and complex structural details as
are present in real phantoms (see further figure 5.4).

26

The SKE/BV task was addressed in papers III and VI were the task was
detection of nodules at various positions in the lungs. In paper III, the size and
shape of the nodules corresponded to those used in the trial by Håkansson et
al (2005b). The anatomical structures vary at different positions in a chest
image and differ from patient to patient. When the background is unknown
for the observer it hampers the detection of subtle details (Samei et al 2000).

The two papers II and V were dedicated to describe the physical
characteristics of the simulated image rather than to solve a specific detection
task. Paper II was dedicated to calculate the variation of the scatter‐to‐primary
ratio εs/εp in the image plane in a chest examination as well the variation in the
signal‐to‐noise ratio per pixel (SNRp). These quantities influence contrast and
noise and thus detectability of lesions varies with position in the imaged
anatomy.

4.2.2. Model of the imaging system and patient
Knowledge of the imaging system is in this work translated into a model of
the system including the patient. This model is used together with Monte
Carlo techniques to calculate dosimetric and image quality parameters,
needed for optimising the imaging system. The realism of the system, in
particular the model of the patient, has been increased during the work.
Details of the model and Monte Carlo calculations are given in Chapter 3. The
development of the model of the patient can be summarised as follows.

In paper I the breast was modeled using a slab phantom with homogeneous
materials and the detail (blood vessel) was modeled as a layer of iodine, see
Figure 3.2.

To allow for more realistic calculations of how the scatter‐to‐primary ratios
varies at various positions in the anatomy behind large anatomical structures
like the spine, heart and lungs, a low‐resolution anthropomorphic phantom,
the Zubal phantom, was used in papers II‐IV. In paper III the anatomy was
divided into several regions corresponding to different anatomical properties,
see figure 4.1. This approach was also used in paper VI.

In order to simulate images with realistic anatomical background variations,
(see section 3.3) a high‐resolution anthropomorphic phantom was created
from CT images of an anthropomorphic (Alderson) phantom in paper V. This
is an important step in the model development, since it has been shown in
27

clinical trials that the fine details (such as small and medium sized vessels) of
the projected anatomical background strongly influence detectability (Kundel
et al 1985, Samei et al 1999, Håkansson et al 2005b) and thus act as noise besides
system (quantum) noise. In Paper VI a new and still more realistic high‐
resolution anthropomorphic phantom (Kyoto Kagaku) was implemented in
the model. A mathematical model of a lesion, referred to as a designer nodule
(Burgess et al 1997) was inserted in the projection radiographs for studies of
detectability using model observers. Figure 4.2 shows cut outs of a chest image
from the hilar region without lesion (4.2a) and with an added designer nodule
(4.2b). Figures 4.2c and 4.2d show corresponding images against a background
of quantum/system noise only. The figures clearly demonstrate the large
difference in difficulty between detecting a nodule in an image containing
anatomical structures and in a pure quantum noise image, respectively.

Figure 4.1. The six anatomical regions of the chest PA image used in papers III
and VI: APR: Apical pulmonary region, LAT: Lateral pulmonary region, RET:
Retrocardial region, LME: Lower mediastinal region, HIL: Hilar region and
UME: Upper mediastinal region.

28


a                                                    b


c                                                      d


Figure 4.2. Cut outs of a simulated chest image from the hilar region without
lesion (4.2a) and with an added designer nodule (4.2b). Figures 4.2c and 4.2d
show corresponding images against a background of quantum noise only. The
contrast (C=0.10) and size (D=10 mm) of the nodule are the same in images
4.2b and 4.2d. The amount of quantum noise (corresponding to a collision air
kerma Kc,air=0.3 μGy central in the image) is the same in all four images. The
dose level is kept unrealistically low for illustration purposes.

4.2.3. Observers
Two model observers have been used, the ideal observer and the Laguerre‐
Gauss Hotelling observer. The method for calculating the ideal observer SNRI
was developed in the previous work by Sandborg et al (1994b) using an
expression from ICRU 1996. This observer is one who can make use of all the
information in the image and is often used to describe the ultimate
29

performance of an imaging system. Also, this observer is able to perform non‐
linear operations on the data. It works most easily under the condition of
SKE/BKE when the detection only is disturbed by system noise. The Laguerre‐
Gauss Hotelling observer was applied in Paper VI utilizing the method to
simulate high‐resolution images developed in paper V. This observer can also
be used for the SKE/BV task. The Hotelling observer is limited to perform
linear operations and is likely to more faithfully reflect the capabilities of
human observers (ICRU 1996). It has been described in detail for the problem
of image assessment in medical imaging by, e.g., in Barrett and Myers (2004).

Results of human observers were used in paper IV. To design and perform
human observer studies is time consuming and requires close collaboration
with radiologists. The main objective of this work was to create a complete
model of the imaging system including automatic performance evaluation,
which allows for rapid evaluation of image quality, so that a large number of
acquisition parameters can be tested. This is an important step towards the use
of our model for system optimisation. An inspiration was a recent study by
Son et al (2006), where they used simulated images and a model observer for
image quality assessment. The results of our model have repeatedly been
tested against results of human observer studies performed by our partners in
our network collaboration (Sweden Associated Imaging Laboratories, SAIL;
Göteborg, Linköping and Malmö). Through this collaboration, we have had
access to detailed information about the imaging systems used in their
experiments. Our efforts have been concentrated to finding model observers
that are capable of simulating the performance of human observers.

4.2.4. Figures of merit

4.2.4.1 Human observers
Clinical trials with human observers are essential in the assessment of image
quality. It is therefore of great importance to compare the results of our model
to what is relevant from the clinical point of view. As was pointed out above,
such comparisons have been performed in close collaboration with our
partners from Malmö and Göteborg. Two main types of human observer
studies were used in their clinical trials. The two types are: receiver operating
characteristic (ROC) and visual grading analysis (VGA) studies.

30

A ROC studies
Receiver operating characteristics (ROC) (Metz 1986, Metz 2000, ICRU 1996)
studies with human observers form the gold standard for assessment of image
quality.

When a human observer performs a specific task, for instance, decides
whether a signal is present or not present, there are four possible outcomes:
(1)  False Positive (FP): signal is absent – observer decides signal present
(2) True Positive (TP): signal is present – observer decides signal present
(3)  False Negative (FN): signal is present – observer decides signal absent
(4) True Negative (TN): signal is absent – observer decides signal absent

The decision maker also strives to minimize the cost. A false positive decision
may mean that the patient has to undergo extra examinations. A false negative
decision may mean that, for instance, a tumour is missed and the patient has
less probability for recovery if the tumour is discovered later. The strategy
used by the observer therefore depends on which kind of error (FP of FN) that
is most costly. The relation between the false positive fraction and the true
positive fraction is illustrated in the receiver operating characteristic (ROC)
curve, see figure 4.3. Each point on this curve corresponds to a threshold level
(observer strategy). The area under the ROC curve, AUC (also commonly
denoted Az in the literature), is a common figure of merit used in
discrimination tasks and can be translated to a value for the signal‐to‐noise
ratio SNR (Barrett and Myers 2004) using

(4.1) )12(2)( 1
−= −
AUCerfAUCSNR

where erf−1
is the inverse error function. The quantity SNR(AUC) is often
referred to as the detectability index dA. A short description of the
methodology is given below.

A recent review of ROC and related methods is given by Krupinsky and Jiang
(2008). To reach sufficient statistical power many images and several observers
are needed. Another problem in ROC studies is that the true answer has to be
known. This can be accomplished by using so called hybrid images where
lesions are simulated and paste into real images (Metz 2000).

31

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False positive fraction
Truepositivefraction

Figure 4.3. Illustration of an ROC curve. The area under the curve (AUC) is
used as a figure of merit and can be related to the SNR. In this figure: AUC=0.8
(SNR=1.19). The dotted line corresponds to AUC=0.5 (SNR=0), which means
that the observer is guessing.



B VGA studies
In a visual grading analysis (VGA) study, the observer is presented to two
images. One image is a reference image and used in every comparison. The
observer has to decide if the quality of the image compared to the reference
image is similar, better or worse.

In paper IV, results from a VGA study by Tingberg and Sjöström (2005) were
used to search for correlations between physical image quality parameters and
clinical image quality. In the VGA study, slightly modified CEC (Carmichael et
al 1996) image criteria were used. The criteria were based on structures in the
normal anatomy that are described in table 4.1 for chest PA and Pelvis AP
examinations. The radiologists were asked to give a graded response of the
fulfilment (=visibility of the structures) of the criteria compared to the
fulfilment of the criteria in the reference image. The grading was given in
quantitative terms as: clearly inferior (VGA=‐2), inferior (‐1), equal to (0),
superior (+1) or clearly superior (+2). The score was averaged over all criteria
and all radiologists to form an average score, VGAS.

32

Table 4.1. Structures used in the VGA evaluation
(Tingberg and Sjöström 2005)
Chest PA Pelvis AP
1 Vessels seen 3 cm from the pleural margin Sacrum (spongiosa)
2 Thoratic vertebra behind the heart Sacral foramina
3 Retrocardiac vessels Pubic and ishial rami
4 Pleural margin Sacroiliac joints
5 Vessels seen an face in the central area Femoral bilateral
6 Hilar region ‐

4.2.4.2 The ideal observer
For the Ideal observer used in this work, the background and the signal are
assumed to be known exactly, corresponding to a SKE/BKE task. From the
SNRMC (see section 3.2.4.2), the ideal observer signal‐to‐noise ratio, SNRI for a
given nodule is calculated from equation 4.2 as
222
DF
p
MI r
a
A
SNRSNR ⋅⋅= (4.2)
where A is the projected area of the nodule in the image plane, ap is the pixel
area and r2
DF is the signal to noise ratio degradation factor caused by the
system unsharpness. The quantity r2
DF includes effects on SNR of the imaging
system unsharpness (modulation transfer function, MTF) and correlated noise
(noise power spectrum (NPS)) as determined from experiments with the actual
detector type and additional detector noise. It is derived separately for each
nodule at its actual position in the anatomy, and depends on the nodule
projected area and the air kerma at the image detector. Geometrical (focal
spot‐ and magnification) unsharpness and motion unsharpness are taken into
account in addition to detector unsharpness. The latter is expressed in terms of
the pre‐sampled MTF (Sandborg et al 2003).

A Figure of merit corresponding to the VGAS in a VGA study
In paper IV we calculated a figure of merit that is intended to correspond to
the VGAS obtained in the VGA study (Tingberg and Sjöström 2005). For each
contrasting detail, denoted with index q, the SNRI,q relative to its value at the
reference tube voltage, SNRI,q(Uref), was computed (SNRI,q(U)/ SNRI,q(Uref)).
These ratios were then averaged for all the structures and a figure of merit
(FOM) was computed as given in equation 4.3. Here, unity was subtracted
from the average value in order to obtain the value zero for the reference tube
33

voltage and allow negative values when the image quality is inferior to that of
the reference system (corresponding to the ordinate scale of the VGAS)

( ) 1
)(1
)(
,
,
−∑=
q refqI
qI
USNR
USNR
N
UFOM , (4.3)

where N is the number of details.

4.2.4.3 Figures of merit using physical image quality measures

A Nodule to bone contrast
In Paper III we attempted to perform optimization using the Zubal phantom.
Since the SNRI as calculated in this work does not take into account anatomical
details and these are known to influence detectability, alternative figures of
merit were also used. The ribs obscure large parts of the lungs but are also
needed for the radiologist to orient himself in the image (Sven‐Göran
Fransson, personal communication). The contrast of the nodule relative to the
contrast of the ribs may indicate the disturbing influence of the ribs. We have
therefore defined a ‘nodule‐to‐bone’ contrast‐ratio by computing the quotient
C/CB. The C/CB is the nodule’s contrast divided by the contrast of a bone detail
of a thickness corresponding to a rib or transverse processes at the same
position in the image. The use of the nodule‐to‐bone contrast as a
complementary figure of merit was inspired from the work by Dobbins et al
(2003) and Samei et al (2005).

B Relative contrast
The radiologist often wants to adjust the contrast window. This choice of
contrast window affects the contrast of other objects in the image. We have
defined a relative contrast, Crel, as the signal difference in the image detector
divided by the dynamic range of the whole image of the chest
%5%95
21
εε
ε ε
−
−
=
pp
relC , (4.4)

where εp1 is the energy imparted to the detector per unit area in the presence of
the nodule, εp2 is the energy imparted in the absence of the nodule, and
ε95%−ε5% is the dynamic range in the chest image, here defined by the 95th
percentile minus the 5th percentile of the energies imparted to the image
detector in the whole chest image. The relative contrast is thus a measure of
the nodule’s contrast as a percentage of the dynamic range in the image. It
34

corresponds to the radiologist first impression of the image before adjusting
the contrast window.

4.2.4.4 The Hotelling observer
Ultimately, the measures of image quality should correspond to how an
observer (radiologist) performs a specific task with the aid of the image.  In
order to complete our model, we need an observer that can replace the human
observer and perform image quality assessment automatically using our
synthetic images. We therefore exploited (in paper VI), a model observer,
which is known to mimic human observers more closely than the ideal
observer. Such model observers are based on statistical decision theory. One of
the pioneers in using statistical decision theory for diagnostic radiology was
Wagner (Wagner et al 1979). A good thorough introduction to statistical
decision theory and model observers is given by Barrett and Myers (2004).

To describe the image, it is useful to represent the image as a vector

(4.5) nHfg +=

where H is an operator representing the imaging system, f a representation of
the object and n represents the noise.

If H1 denotes the hypothesis that the signal is present and H0 denotes the
hypothesis that the signal is absent, the Hotelling observer uses a test statistic
based on the likelihood ratio

)|(
)|(
)(
0
1
Hp
Hp
g
g
g =Λ
cΛ
)|( bap
(4.6)

to compare to a threshold in order to decide between H1 and H0. The
notation means the conditional probability of a given b (Jaynes 2003).
Under the assumption that g is described by a multivariate Gaussian
distribution, the performance of the Hotelling observer is given by (Barrett
and Myers 2004)

(4.7) gKg g ΔΔ=
−12 t
Hot
SNR

where gΔ is the mean difference of the image vector with signal absent and
signal present and Kg is the covariance matrix, which can take into account
35

both quantum noise and variations in anatomy. The superscript t means the
transpose of the vector. In the case where the signal s is known exactly (SKE)
this simplifies to

(4.8) sKs g
12 −
= t
Hot
SNR

The covariance matrix can be estimated from a set of images g. In the case
where g is real, the covariance matrix is defined by

(4.9) t
))(( ggggK −−=

where g is the mean image vector. If g is M dimensional, the resulting
covariance matrix will be M x M dimensional. The number of images g used to
estimate the covariance matrix must be larger than the number of pixels;
otherwise the covariance matrix is singular and non‐invertible. Even for a
relatively small region of interest of 100 x 100 pixels this would make the
covariance matrix virtually impossible to calculate since we would need at
least 104 images to perform the estimation. For a more accurate estimation of
the covariance matrix it would require an even larger set of images. Also, a
matrix of the size 104 x 104 is difficult to manage in the computer memory.

A Channelized Laguerre‐Gauss Hotelling observer
One solution to the problem mentioned above is to use channels to reduce the
size of the matrix (Myers and Barrett 1987).

gUν T
=
νKν ch ΔΔ=
−12
,
t
chHot
SNR
(4.10)

where U is a M x N matrix containing N channel profiles up as column vectors.
The vector v can be interpreted as the image seen through the channels. A
diagram of the channelized observer is shown in figure 4.4. The signal to noise
ratio for the channelized Hotelling observer is

(4.11)

where Kch is the N x N covariance matrix of the channelized images. In this
case the size of the covariance reduces significantly since often only 6‐50
channels are needed, depending on the type of task. Because of this dimension
reduction, the channelized covariance matrix can be estimated from a
relatively small number of images. Another advantage of the channelized
36

approach is that the channelized observer better models human performance
(Myers and Barrett 1987). To further increase the realism in simulating the
human observer, internal noise corresponding to neural noise and fluctuations
in observer decision criterion can be added (Burgess et al 1981, Zhang et al
2007).

u ν1
1
u2
u3
un
Image
vector
g
ν2
ν3
νn
Observer
Test statistic
λ(ν)

Figure 4.4. Diagram illustrating the channelized observer. The channelized
observer does not interpret the image vector g directly, but though a series (u1,
u2, …, un) of channels.

In paper VI we used Laguerre‐Gauss channels. Laguerre‐Gauss function is a
product between a Laguerre polynomial and a Gauss function. The Laguerre‐
Gauss channels are given by

)
2
()exp(
2
),( 2
2
2
2
a
r
L
a
r
a
arU nn
ππ−
= (4.12)

where a is a scaling factor that can be chosen iteratively to maximise the SNR, r
is the radial distance and Ln is the n:th Laguerre polynomial. The Laguerre‐
Gauss model assumes rotational symmetry. The LG channels of order 0, 3, 6
and 9 are shown in figure 4.5. Other authors have used the LG observer in
diagnostic radiography. Chawla et al (2007) studied observer performance in
mammography for normal and reduced doses. Pineda et al (2006) studied
tomosynthesis and compared with planar radiography. Son et al used the
Hotelling and LG Hotelling observer to search for calcifications in Monte
Carlo simulated images. Gabor channels (Chawla et al 2007) are sometimes
used. The Gabor channels are more accurate in modelling the human observer
since they do not assume rotational symmetry.

37

a b c d

Figure 4.5. Laguerre‐Gauss channels in different orders: a) 0:th, b) 3:rd, c) 6:th
and d) 9:th order LG channel.

B Laguerre‐Gauss Hotelling observer using a template
Instead of calculating SNR directly, it is also possible to simulate the observer
by using a template. In earlier versions of paper VI this method was used as a
compliment to the direct calculation. The direct calculation is used for the
reason that it is faster. The channelized Hotelling observer uses the template

sKw g
1−
=Hot
νwt
Hot=λ
t
(4.13)

and compares is to the (channelized) image vector with the scalar product

(4.14)

in order to calculate the decision variable λ. The model observer compares the
decision variable to a threshold λt in order to choose between the hypothesis
H1 (lesion absent) or H2 (lesion present). For instance, if λ λ≥ the model
observer may choose that the lesion is present. In this way, the model observer
can be used for ROC studies similar to those performed by human observers.
Two ROC curves for the channelized LG Hotelling observer are shown in
figure 4.6.

38


a
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1

b
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9

Figure 4.6. ROC curves calculated for the Laguerre‐Gauss Hotelling observer.
Figure 4.6a corresponds to figure 4.2b in the Hilar region with a lesion of the
same contrast (C=0.10) and diameter (D=10 mm). The AUC is approximately
0.99 (SNR=3.2). In figure 4.6b the situation is similar but with reduced contrast
(C=0.05). The AUC is approximately 0.87 (SNR=1.6). The dotted line
corresponds to the case when there is no signal.

39


40

Results and discussion
41
5.RESULTS AND DISCUSSION
5.1. Ideal observer with a simplified patient‐model
In paper I we used a simple model of the breast for optimisation of iodine
subtraction mammography. In subtraction imaging, the overlaying anatomical
structures are suppressed. The ideal observer signal‐to‐noise ratio, SNRI, is
here used in a situation where the detection or visibility of a lesion is only
limited by the quantum noise in the image. This in turn is determined by the
air kerma at the image detector and efficiency by which the image detector
absorbed the x‐ray quanta and converts it to an image signal.

The SNRI was calculated for a special case when iodine contrast media were
injected in the patients arm and images were acquired at set intervals before
and after injection in order to follow the leakage of contrast medium in the
vicinity of the breast tumor. During the whole image acquisition, the breast
remains compressed and images after injection of the contrast medium are
subtracted from the image prior to injection. In mammography such contrast
media may be valuable to distinguish between benign and malignant tumors
and for demonstrating tumors that might not otherwise be seen in dense tissue
and hence in providing a clearer picture of the extent of disease.
Figure 5.1 shows the SNRI
2
/AGD as a function of tube voltage for three
different anode‐filter combinations. The AGD is the average glandular dose
typically used as the radiation risk measure in mammography (Zoetelief et al
1996). For both the W/Cu and Rh/Cu spectra and at all breast thicknesses, a
maximum of the SNR2
/AGD was found at approximately 45 kV and a
minimum at 33 kV. The dominating K‐edge of iodine is at 33.17 keV (see
figure 5.2) and hence photons with energies just above this energy are
absorbed to a high degree and therefore provide a higher object contrast
compared to the background in the vicinity of the contrast‐filled vessel. At 45
kV and using copper filtration, a significant portion of the x‐ray spectrum has
energies in the optimal range just above the iodine K‐edge. Using 45 kV for the
Rh/Cu spectrum yields three to four times lower dose for 4 cm thick breasts
compared to using the Rh/Rh combination for producing images with equal
SNR for the iodine contrast medium. The SNR2
/AGD is approximately 1.8
times higher with 33.2 keV photons compared to its maximum value using the

poly‐energetic spectra from the W/0.3mmCu combination at 45 kV. The results
agree with Skarpathiotakis et al (2002).

20 25 30 35 40 45 50
50
0
100
150
200
250
300
350
55
Tube voltage (kV)
SNR
2
/AGD(mGy
−1
)

Figure 5.1. SNRI
2
/AGD as a function of tube voltage for a 4 cm thick breast and
50% glandularity. Δ=Rh/25μmRh, O=Rh/0.3mmCu, =W/0.3mmCu.

10
5
20 25 30 35 40 45 50 55
10
2
10
3
10
4
Photon energy (keV)
Cross-section(barns/atom)

Figure 5.2. Atomic cross‐section of iodine as a function of photon energy.

42

5.2. Low resolution voxel phantom
In order to compare the result of the model with clinical image quality, it may
be useful to calculate distributions of physical image quality related quantities
over the whole image and to study how these vary with position, patient size
and imaging system configuration. The aim of paper II was to calculate
distributions of SNR per pixel (SNRp) and the scatter to primary ratio, εs/εp in
terms of energy imparted per unit area to the image detector (see chapter 3 for
details). Figure 5.3 shows scatter‐to‐primary ratios (εp/εs) and signal to noise
ratios per pixel (SNRp) using the low‐resolution anthropomorphic chest
phantom. The figures show that the εp/εs varies significantly in the chest PA
image plane and is typically above 2 in the mediastinum and about 0.5 in the
lungs. A comparison to measured εs/εp in patient images (Jordan et al 1993)
with calculated values in different regions shows that the mean values from
the calculations agree reasonably well in the heart region (behind the whole
heart including the part covered by the spine), with average εs/εp=2.0 (our
work) vs. 1.9 (Jordan); in the lung region (entire lung) with average εs/εp=0.6
(our work) vs. 0.4 (Jordan).

As scattered photons add to the noise term in the SNRp expression (see chapter
3), the SNRp is significantly reduced in the mediastinum compared to in the
lungs. Therefore, if nodule detection were limited by quantum noise, the
visibility of such nodules would be higher in the lungs where the scatter to
primary ratio is lower than in the mediastinum.
43


Figure 5.3. Distributions of εp/εs (a) and SNRp (b) for a 24 cm thick patient. Figures
(c) and (d) show values of εp/εs and the SNRp along the vertical lines in the upper
figures.

5.3. High resolution voxel phantom
The images produced based on the low‐resolution voxel‐phantom VOXMAN
are useful for determining maps of physical measures of image quality such as
SNRp. Yet, they are of limited use for clinical image quality evaluation by
human or model observers due to its relatively coarse spatial resolution.
Anthropomorphic chest phantoms were therefore imaged in a CT scanner and
the reconstructed volume of CT‐numbers used to create high‐resolution voxel
phantoms (Malusek 2008). In paper V, the older Alderson phantom was
modelled and in paper VI, a more recently developed and more clinically
realistic (Kyoto Kagaku) phantom, was utilised.

Real phantom x‐ray images of those two phantoms are shown to the left in
figures 5.4 and 5.5 and simulated images calculated with the Monte Carlo
44

model are shown to the right. The parameters in the Monte Carlo simulations
were adjusted to fit the imaging conditions used in the real acquisition.

Figure 5.4. A real phantom image of the Alderson chest phantom (a) and a
calculated image including scatter and statistical noise (b). An anti‐scatter grid
was used at the tube voltage 141 kV.

Figure 5.5. A real phantom image of the Kyoto Kagaku chest phantom (a) and
a calculated image including scatter and statistical noise (b). An anti‐scatter
grid and 141 kV were used.

45


Figure 5.6. Calculated primary projection (a) and scatter projection (b) of the
Alderson phantom. The intensity values are given in logarithmic scale in
μJ/m2. The average air kerma at the image detector was 5 μGy corresponding
to a sensitivity class of approximately 200.

The images of the scattered photons were computed in a coarse grid of points
40 x 40 whereas the image of the primary photons was computed in the same
number of pixels as the original real image (Alderson: 1760 x 1760 Kyoto
Kagaku 2688 x 2688). The primary projection and the scatter projection were
combined to create a total image. Noise was added to the images. In paper V
gaussian noise was added with the aid of the calculated SNRp values. In paper
VI we added correlated noise. However, at the point of writing this thesis, the
correct noise power spectrum (NPS) for the system used in the clinical system
used for acquiring the real phantom images was not available. Instead, a
provisory NPS measured from a Fuji FCR 9501 CR Thorax system in Göteborg
was used. The simulated images were used in paper VI to assess image quality
using the Laguerre‐Gauss Hotelling observer SNRhot,LG (see section 5.6). We
argue that the increased realism provided by the Kyoto Kagaku phantom is
useful for a more clinically realistic assessment of image quality.

5.4. Ideal observer with simple anatomical background
In paper III the optimal tube voltage in detecting lung lesions with diameter 10
mm but of varying thickness according to Håkansson et al (2005a) was
investigated in terms of the ideal observer SNRI in six anatomical regions of
the chest PA image. In addition to this figure‐of‐merit, the contrast of the
46

lesion in relation to structures in the normal anatomy such as ribs and
transverse processes, C/CB was derived, since these structures may interfere
with the radiologist’s detection of the lesion. The optimal tube voltage and
scatter rejection technique were sought.

Figure 5.7 shows the figure‐of‐merit SNRI
2
/E, or the dose‐to‐information
conversion efficiency (Tapiovaara 1993) for a 25 mm thick lesion in the hilar
region and a 15 mm thick lesion in the lower mediastinal region. In both these
regions a low tube voltage results in a higher SNRI
2
/E indicating superior
performance. In the lower mediastinal region, a higher SNRI
2
/E is found when
larger grid ratios or longer air gaps are used. In the hilar region, with
significantly lower scatter‐to‐primary ratio compared to the lower mediastinal
region (see paper II), the SNRI
2
/E is independent of grid ratio or air gap length.
The air gap results in significantly higher SNRI
2
/E than with the grid,
suggesting that the air gap is the superior scatter rejection technique for digital
chest PA radiography. The absorption of primary radiation in the grid reduces
the image quality and increases the bucky factor; this is avoided using the air
gap technique.

Figure 5.7. SNRI
2
/E as a function of tube voltage and scatter rejection
technique; grid ratio in (a) and (c) and air gap length (b) and (d), for a 20 cm
thick patient. Two anatomical regions were considered: the hilar region (a, b)
and the lower mediastinal region (c, d).
47


Figure 5.8 shows the ratio between the contrast of the lesion divided by the
contrast of a bone structure, C/CB in the same region. Contrary to the SNRI
2
/E,
the C/CB increases with increasing tube voltage, indicating relatively superior
contrast of the lesion in comparison to the projected anatomical background
structure such as rib or transverse process, at high tube voltages. Hence we
have two conflicting arguments for selecting the appropriate tube voltage.

In a similar study, Dobbins et al (2003) made both experiments and computer
spectrum modelling to search for the optimum x‐ray spectrum for chest
radiography for a CsI‐aSi flat panel image detector. They studied the SNR
squared per exposure, SNR2/X, and a contrast ratio similar to our, C/CB, as a
function of tube voltage and added filtration. The experimental results from
their study are essentially in agreement with our results. SNR2/X decreases
and C/CB increases with increasing tube voltage, and the tube voltage 120 kV
was considered to be optimal. We use SNR2/E instead of SNR2/X since the
effective dose is a better measure of radiation risk than exposure or incident
air collision kerma. However, conversion factors published by Hart et al (1994)
can be used to convert SNR2/X to SNR2/E. Such data shows that the optimal
tube voltage is reduced when the effective dose is used as a measure of
radiation risk instead of incident air collision kerma.
We conclude that the choice of tube voltage depends on whether SNRI of the
lesion or the interfering projected anatomy (i.e. ribs) is more important for
lesion detection. The simple model of the patient used here is incapable of
making this selection and therefore alternative model observers and more
complex anatomical background are needed for a proper treatment of this
task.

48


Figure 5.8. C/CB as a function of tube voltage and scatter rejection technique;
grid ratio in (a) and (c) and air gap length (b) and (d), for a 20 cm thick patient.
Two anatomical regions were considered: the hilar region (a, b) and the lower
mediastinal region (c, d).

5.5. Correlation to human observers
The aim of paper IV was to study the dependence of image quality in digital
chest and pelvis radiography on tube voltage, and to explore correlations
between clinical and physical measures of image quality. The effect on image
quality of tube voltage was assessed using two methods. The first method
relies on radiologists’ observations of specified image criteria of images of
anthropomorphic phantoms (Visual grading analysis, VGA), and the second
method was based on computer modelling of the imaging system using an
anthropomorphic voxel phantom.

The tube voltage is one of the independent variables that can be altered prior
to exposure of each patient and view. In the study, the effective dose to the
patient phantom was kept constant independent of tube voltage. The visual
grading study was performed by Tingberg and Sjöström (2005) but our group
performed the Monte Carlo simulation (see chapter 4).
49


Figure 5.9 and 5.10 show the clinical and physical image quality measures as
function of tube voltage for the same effective dose to the chest phantom. Both
measures indicate that superior image quality is achieved at low tube voltages
compared to the reference system tube voltage 125 kV. Similar results were
obtained for the pelvis examination.
Chest PA
-0.5
0
0.5
1
1.5
2
VGAS
-2
-1.5
-1
60 70 80 90 100 110 120 130 140 150
Tube voltage (kV)

Figure 5.9. The visual grading analysis score (VGAS) for the chest images as
function of the tube voltage. The VGAS values represent averages over all
imaged structures and radiologists. The uncertainty bars show the reader
variability (one standard error). The solid line (r2=0.90) indicates that there is a
linear relationship between VGAS and tube voltage (data redrawn from
Tingberg and Sjöström (2005)).
Chest PA
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
60 70 80 90 100 110 120 130 140 150
Tube Voltage (kV)
FOM

Figure 5.10. The average relative change in SNR (FOM) in chest PA
examination as a function of tube voltage.
50


Chest PA
-2
-1
0
1
2
-0.5 -0.3 -0.1 0.1 0.3 0.5
FOM
VGAS

Figure 5.11. The correlation between VGAS and SNR (FOM) for a simulated
chest PA examination. The error bars correspond to one standard error and are
due to reader variability in the results of the observer studies (see Fig. 5.9). The
r2 of the fitted line (r2=0.91) indicates that the VGAS and FOM are linearly
correlated. Lower tube voltages have positive VGAS and FOM and high tube
voltages negative values.

Figure 5.11 shows the relation between clinical image quality measured using
visual grading analysis score (VGAS) and the physical measure of image
quality, quantified by the relative change in SNR and FOM. There is a positive
linear relationship between the two measures of image quality, indicating that
the SNR is related to the radiologists’ grading of the image criteria. Hence,
results by Tingberg and Sjöström (2005) and results from this study indicate
that, with modern digital imaging system, it would be favourable to use lower
tube voltages than traditionally used with screen‐film radiography.

Arguments for and against this proposal are listed in paper IV and in Tingberg
and Sjöström (2005). At low photon energies, the image detector’s DQE
(detective quantum efficiency) is higher and the contribution to effective dose
per incident air collision kerma is lower. However, at low tube voltages, the
tube charges typically increase compared to at higher voltages to maintain a
constant effective dose. Hence the risk for increased motion and focal spot
unsharpness increases due to prolonged exposure time and focus size
blooming, respectively. In examinations where iodine contrast media are
employed, the use of lower tube voltages than used today (approximately 70
kV) seems to be an advantage (Tapiovaara et al 1999, Wiltz et al 2005).
51


The statistical analysis of a relative VGA study, such as in Tingberg and
Sjöström (2005) and in paper IV is questionable since the scale steps used (e.g.
‐2 to +2) are an ordinal scale and the numerical representations do not
represent numbers on an interval scale and one cannot assume equal steps
between the scale steps. This problem is solved with a closely related method,
visual grading characteristics (VGC) (Båth and Månsson 2007). In this type of
study, the observer is asked to rate his/her confidence about the fulfilment of
image quality criteria. The data is then analysed in a manner that is similar to
ROC studies, where the resulting figure of merit is the area under the VGC
curve. However, we have not been able to translate our results to a VGC
study, since the question asked to the observer slightly differs between those
two types of studies.

Also, the importance of a clinical image quality measure such as VGA analysis
that relies on evaluation of structures in the normal anatomy may be
questioned. This is since the detection of pathological lesions may to a large
degree also depend on other objects in the image such as obscuring anatomical
background structures (Tingberg et al 2005).

5.6. Model observers with complex anatomical background
In paper VI, The Laguerre‐Gauss Hotelling observer was implemented. This
observer is influenced by the anatomical background and includes this into its
figure‐of‐merit, SNRhot,LG. Son et al (2006) and Chawla et al (2007) implemented
similar observers. In the work by Son et al (2006), being an extension of the
work by Winslow et al (2005), validation of their model is not considered due
to the use of a virtual phantom. We believe that it is important to verify that
the computational model can faithfully reproduce variations in, e.g., tube
voltage since this is an important parameter influencing image quality and
patient dose. The implementation of the Laguerre‐Gauss Hotelling model‐
observer, SNRhot,LG, is described in paper VI and chapter 4.

Figure 5.12 and 5.13 show SNRhot,LG for the SKE/BV and SKE/BKE tasks as
functions of tube voltage. The SKE/BV and SKE/BKE cases represent situations
where the patient projected anatomy is assumed to act as noise (SKE/BV) or to
be known exactly (SKE/BKE). The figures show that for the SKE/BV task there
is a small increase in SNRhot,LG with increasing tube voltage in the regions LAT,
RET and HIL. In the bony regions LME and UME the increase of SNRhot,LG with
increasing tube voltage is larger. For the SKE/BKE task, the SNRhot,LG steadily
52

decreases with increasing tube voltage as SNRI in paper III. Hansson et al
(2005) investigated the optimal tube voltage in neonatal chest radiography. In
their phantom study (a rabbit lung) they found a positive trend when
increasing the tube voltage in the visibility of the carina and main bronchi, but
no trend for the reproduction of central and peripheral vessels. Thoracic
vertebrae were better visualized at low tube voltages. Their validation study
(neonatal patients) showed no significant preference for any tube voltage in
the 40‐90 kV range with regard to central and peripheral vessels but the carina
was better reproduced at the highest tube voltage in their study; 90 kV. These
results are in qualitative agreement with our work, although there are
significant differences in the material as adult patients were studied in our
work.

60 70 80 90 100 110 120 130 140 150
0
1
2
3
4
5
6
7
8
Tube voltage (kV)
SNR
hot,LG
(SKE/BV)

Figure 5.12. SNRhot,LG (SKE/BV) as function of tube voltage at the air kerma 5
μGy in the center of the image detector. The markers symbolize different
regions in the image: ’*’ lateral pulmonary region (LAT), ’o’ retrocardial region
(RET), ’∇’ lower mediastinum (LME), ’ ’ hilar region (HIL), ‘+’ upper
mediastinum (UME).

53

60 70 80 90 100 110 120 130 140 150
0
200
400
600
800
1000
Tube voltage (kV)
SNR
hot,LG
(SKE/BKE)

Figure 5.13. SNRhot,LG (SKE/BKE) as a function of tube voltage at the air kerma
5 μGy in the center of the image detector. The markers symbolize different
regions in the image: ’*’ lateral pulmonary region (LAT), ’o’ retrocardial region
(RET), ’∇’ lower mediastinum (LAT), ’ ’ hilar region (HIL), ‘+’ upper
mediastinum (UME).

Figure 5.14 and 5.15 show SNRhot,LG for the SKE/BV and SKE/BKE tasks as
functions of air kerma at the image detector in the center of the image plane.
Figure 5.14 shows that in the regions located in the lung (LAT and HIL),
increasing the dose level has a negligible influence on the SNRhot,LG. However,
in the regions containing more bony structures (LME and UME) there is a
larger increase in the SNRhot,LG with increasing dose level. For values of air
kerma above 0.5‐1 μGy, the values of SNRhot,LG are highest in the bony regions
LME and UME. In 5.15 for the SKE/BKE task, the SNRhot,LG increases in
accordance with the Rose model (Rose 1948).

54

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
1
2
3
4
5
6
7
8
Air kerma central in detector (μGy)
SNR
hot,LG
(SKE/BV)

Figure 5.14. SNRhot,LG (SKE/BV) as a function of incident air kerma at the image
detector in the center of the image plane at 141 kV. The markers symbolize
different regions in the image: ’*’ lateral pulmonary region (LAT), ’o’
retrocardial region (RET), ’∇’ lower mediastinum (LME), ’ ’ hilar region (HIL),
‘+’ upper mediastinum (UME).

700
600
500
400
300
200
100
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Air kerma central in detector ( μGy)
SNR
hot,LG
(SKE/BKE)

Figure 5.15. SNRhot,LG (SKE/BKE) as a function of incident air kerma at the
image detector in the center of the image plane at 141 kV. The markers
symbolize different regions in the image: ’*’ lateral pulmonary region (LAT),
’o’ retrocardial region (RET), ’∇’ lower mediastinum (LME), ’ ’ hilar region
(HIL), ‘+’ upper mediastinum (UME).

55


Båth et al (2005b) evaluated human detection of 10 mm lung nodules in the
presence of normal patient projected anatomy including quantum noise and in
images with quantum noise only. They concluded that for the detection of the
lung nodules, the quantum noise is of almost no importance at clinically used
dose levels in chest radiography. The regions where lesion detection was least
influenced by quantum noise were the hilar and lateral pulmonary regions.
The results for the SKE/BKE case in our work agree with the results in Båth et
al. for images containing quantum noise only concerning the ranking of the
regions with respect to the ease of detecting the lesions or SNRhot,LG. In the
quantum noise images, the lower and upper mediastinum were by these
authors ranked as the most difficult regions (most quantum noise) for lesion
detection and the hilar and lateral pulmonary regions as the least difficult
(least quantum noise) ones in agreement with the results in figures 5.13 and
5.14.

The results for the SKE/BV case agree relatively well with the results by Båth et
al (2005a) for images where stationary noise (corresponding to structural noise
in different regions) was used. In both cases, the hilar region is ranked as the
most difficult region for lesion detection and the lower mediastinum ranked as
the least difficult one, in opposite order to the case with images containing
quantum noise only. The results concerning ranking order also agree
reasonably well for the retrocardial and lateral pulmonary regions. For the
upper mediastinal region, however, the results disagree. This is probably due
to a less rich structural background in the anthropomorphic phantom in the
upper mediastinum compared to in patient images. Although our model does
not produce results that fully agree with nodule detection in a structured
anatomical background, our study shows that there are reasons to believe that
the SKE/BV model is more realistic than the SKE/BKE model. The SKE/BV
model also predicts that higher tube voltages result in a higher SNR in
compliance with the tradition in Sweden of using high tube voltages in chest
radiography. We conclude that the SNRhot,LG‐observer is a better model of the
radiologist than model observers that only includes the quantum noise (i.e.
ideal observer) in its analysis and suggest that such models have little validity.

Figure 5.15 shows that the SNRhot,LG(SKE/BKE)‐observer increases its score
with the square root of the air kerma at the image detector in accordance with
the Rose‐model whereas the SNRhot,LG(SKE/BV)‐observer (fig. 5.14) shows a
56

score, that in the hilar and lateral pulmonary regions, is independent of the air
kerma at the image detector.

57

Summary and conclusions
59
6.SUMMARY AND CONCLUSIONS
We have developed patient models of high realism and fine anatomical
structures for calculation of synthetic x‐ray images that can be used for image
quality analysis. The projection images from these images contain fine
structure details such as small and medium sized vessels. This has allowed for
image quality assessment with increased realism.

A study was also performed to investigate how physical measures influencing
image quality are distributed over the radiographic image. These physical
measures of image quality show a large variation in the chest PA image. The
scatter to primary ratio between spine and in the lung differs with a factor of 4.

Correlations between clinical and physical image quality measures were
sought. In Paper IV we found a correlation between the VGA score and a
figure of merit based on the quantum noise (ideal observer) signal to noise
ratio, SNRI. In paper VI we implemented the Laguerre‐Gauss Hotelling
observer for the assessment of image quality in simulated high‐resolution
images. A relatively good correlation was found between the Laguerre‐Gauss
Hotelling observer figure of merit, SNRhot,LG for the SKE/BV task, and the
clinical study by Båth et al (2005a) for images where stationary noise
corresponding to the structural noise in different regions was used. The
conclusion is therefore that the LG Hotelling observer mimics human
detection performance better than the ideal observer for tasks were the
anatomical background varies.

In the special case of iodine subtraction mammography (Paper I) the optimal
tube voltage was found to be significantly higher (45 kV) compared to what is
standard in conventional mammography. The optimisation of chest
radiography with regard to tube voltage is more complex and depends on the
task. For tasks limited by quantum noise, or in those cases where the clear
visualisation of bone structures are essential, then low tube voltages (90‐120)
should be preferred. If we believe that the detection of soft tissue details (such
as nodules) is hampered by bone details such as ribs, then high tube voltages
(120‐150) should be preferred.

Future work
61
7.FUTURE WORK
The ultimate purpose for the model presented here is to serve as a tool to
perform optimisation of diagnostic radiology given a specific task. As
mentioned, a reliable and objective method for image quality assessment is
needed for this purpose. Our method using the Laguerre‐Gauss Hotelling
observer is in a rather early stage of development. An important future project
is therefore to further develop and validate this method against human
observers. For instance, the Laguerre‐Gauss method assumes rotational
symmetry, yet the anatomy is not rotationally symmetric. The Gabor Hotelling
observer does not assume rotational symmetry and would therefore, if it were
implemented, provide a more accurate model of the human observer. In
addition, another improvement is to add internal noise to the model observer
to give a better agreement with human observers. One possible way to
validate the model is to perform an ROC study where human observers and
model observers are evaluating the same images, searching for the same
pathologies. The methods for objective image quality assessment based on
statistical decision theory are also applicable in many other fields of radiation
physics, such as nuclear medicine and MR. Therefore; the work presented here
could serve as inspiration for future work for researchers in those fields.

Another possible future prospect is to develop a model for optimisation of
chest and breast tomosynthesis. It that case, the VOXMAN model needs to be
improved to calculate several projections for different angles. In the case of
breast tomosynthesis, a realistic anthropomorphic breast model is also needed.
Another improvement of the model is to segment the high‐resolution
anthropomorphic phantoms so that organ and effective doses can be
calculated.

If a user‐friendly version of the Monte Carlo model together with model
observers is created, it could be distributed to medical physicists who could
use it for study and optimisation purposes.

Acknowledgements
63
8.ACKNOWLEDGEMENTS
A common question from the opponent at the dissertation is, why did you choose to
make research in this specific field? My answer to that question is that I would have
studied every field of Science simultaneously if that had been possible.
Unfortunately, it is not possible. I would like to use a poem by the English poet and
artist William Blake as an illustration

To see a World in a grain of sand,
and a Heaven in a wild flower.
Hold Infinity in the palm of your hand,
and Eternity in an hour.

My belief is that any grain of sand, when studied in the depth, always contains
something interesting. I stood at the seashore and picked up one grain of sand. I
studied this grain of sand in every detail and every aspect, and actually, it gave me a
deeper understanding of the World. And even if I sometimes doubted, I found that
some things inside were really interesting. So I thank this grain of sand, and return it
to the seashore.

I want to express my gratitude to

My supervisors Michael Sandborg and Gudrun Alm Carlsson for introducing me to
this field and for all the support during these years I have been working on this
thesis. The time as a PhD student has been a process, from which I have learned a lot,
and it has made me develop as a person. I especially want to thank Micke for helping
me to attain a rather large production as a PhD student, and Gudrun for her
enthusiasm. She obviously loves her research, and that inspires others.

David Dance. As a co‐author of all my papers he has helped me greatly in my
research. Especially during my visits in London where he taught me about the
VOXMAN program. I also want to thank David for his hospitality during these
visits.

Magnus Båth. Magnus part in this thesis should not be underestimated. In the initial
stage of my PhD studies, being a Monte Carlo theorist, I was rather ignorant about
the clinical aspects of image quality. Largely due to Magnus, I was put out of this
ignorance. Nowadays we almost speak the same language and get similar results.

Acknowledgements
Alexandr Malusek. For all your support with LINUX and UNIX. You have shown
much patience with the “LINUX‐lamer” next door, who has asked many trivial
questions about even more trivial LINUX‐commands. Also for all interesting
discussions during lunch about everything from TV programs on the discovery
channel to world politics.

Other co‐authors: Martin Yaffe, Anders Tingberg, Markus Håkansson, Roger Hunt
and Markku Tapiovaara for their valuable contributions to the papers they have co‐
authored.

My colleagues at the Radiation Physics Department

Jalil Bahar. For being a true friend, and for our discussions about Rumi (see the poem
at the first page of this thesis) and our talks about beauty of different kinds.

Eva Lund. I think that you deeply understood my feelings during the final stages of
preparing this thesis. Our talks when I was feeling stressed really helped me.

Håkan Gustafsson, for our squash games. They helped me not to get too unfit during
my PhD studies. Håkan Pettersson, for our common interest in music and for your
good sense of humour that enriched my time as a PhD student. Anna Olsson for the
times you made me laugh. Pernilla Norberg for your kindness.

Magnus Gårdestig, Peter Larsson, Axel Israelsson, Sara Olsson, Agnetha Gustafsson,
Eilert Viking, Dan Olsson, Ebba Helmrot, Henrik Karlsson, Marie Karlsson, Jonas
Nilsson Althén, Peter Lundberg, Dan Josefsson, Muhammed Sultan, Håkan Hedtjärn,
Lotta Jonsson, Laura Antonovic, Kristian Seiron. Etc.

My friends

Gunnar Cedersund for all our discussions about religion and science, and for reading
and responding to the loads of emails about my successes and adversities as a PhD
student. Lena Malmberg for your inspiration. Evelina Jansson, you have also
inspired me, especially about art. All other friends, no one mentioned, no one
forgotten.

My family

Everyone in my family, my parents, siblings, uncles, cousins and (deceased)
grand parents. My grandmother Ebba Ullman who recently departed.

Finally, my precious, beloved Karin Wermelin.
64

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