quantifying image quality

Linköping University Medical Dissertations No. 1050

Quantifying image quality indiagnostic radiology usingsimulation of the imagingsystem and model observers

Gustaf Ullman

Radiation Physics, Department of Medicine and HealthFaculty of Health Sciences

Linköping University, Sweden

Linköping 2008

ii

Gustaf Ullman, 2008

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

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

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

ISBN 978 91 7393 952 2ISSN 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 COMPUTATIONALMODEL OF THEIMAGING 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. FUTUREWORK ................................................................................................. 61

8. ACKNOWLEDGEMENTS ............................................................................... 63

9. REFERENCES...................................................................................................... 65

vi

Abstract

vii

ABSTRACT

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

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

In chest imaging the optimal tube voltage in detecting lung lesions wasinvestigated in terms of their SNR and the contrast of the lesions relative to theribs. It was found that the choice of tube voltage depends on whether SNR ofthe lesion or the interfering projected anatomy (i.e. the ribs) is most importantfor detection. The Laguerre Gauss (LG) Hotelling observer is influenced by theprojected anatomical background and includes this into its figure of merit,SNRhot,LG. The LG observer was found to be a better model of the radiologistthan the ideal observer that only includes the quantum noise in its analysis.The measures of image quality derived from our model are found to correlaterelatively well with the radiologist�’s assessment of image quality. ThereforeMC simulations can be a valuable and an efficient tool in the search for doseefficient 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 iodinecontrast media mammography. Phys. Med. Biol. 50, 3143�–3152 (2005)*

II. Gustaf Ullman, Michael Sandborg, David R Dance, Roger Hunt, andGudrun Alm Carlsson. Distributions of scatter to primary ratios andsignal to noise ratios per pixel in digital chest imaging. Radiat ProtDosim, 114, no 1 3, 355 358 (2005)*

III. Gustaf Ullman, Michael Sandborg, David R Dance, Roger A Hunt andGudrun Alm Carlsson. Towards optimization in digital chestradiography using Monte Carlo modelling. Phys Med Biol 51, 27292743 (2006)*

IV. Michael Sandborg, Anders Tingberg, Gustaf Ullman, David R Danceand Gudrun Alm Carlsson. Comparison of clinical and physicalmeasures of image quality in chest and pelvis computed radiography atdifferent tube voltages. Med. Phys. 33(11) 4169 4175 (2006)*

V. Gustaf Ullman, Alexandr Malusek, Michael Sandborg, David R. Danceand Gudrun Alm Carlsson. Calculation of images from ananthropomorphic chest phantom using Monte Carlo methods. Proc ofSPIE 6142, (2006)*

VI. Gustaf Ullman, Magnus Båth, Gudrun Alm Carlsson, David R Dance,Markku Tapiovaara, and Michael Sandborg. Development of a MonteCarlo based model for optimization using the Laguerre GaussHotelling 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, andGudrun Alm Carlsson. The influence of patient thickness, tube voltageand image detector on patient dose and detail signal to noise ratio indigital 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 chestradiography: 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, GUllman and G Alm Carlsson. Calculation of the properties of digitalmammograms using a computer simulation. Radiat Prot Dosim 114, no1 3, 395 398, 2005

4. D R Dance, R A Hunt, P R Bakic, A D A Maidment, M Sandborg, GUllman and G Alm Carlsson. Breast dosimetry using a high resolutionvoxel 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 Carlosimulation 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, AlmCarlsson G. (2002) A search for optimal x ray energy spectra in digitaliodine subtraction mammography using Monte Carlo simulation of theimaging chain. Digital Mammography IWDM 2002: Proceedings of theWorkshop, Bremen, Germany, June 2002. Ed. Peitgen H O (SpringerVerlag, 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 indigital chest radiography. Accepted for presentation at MedicalImaging, 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 breastimaging 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 andcalibration 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 CarlssonOptimisation of chest radiology by computer modelling of imagequality measures and patient effective dose Report no 97, ISRN ULIRAD R 97�—SE, 2004

4. Gustaf Ullman, M Sandborg, Anders Tingberg, D R Dance, Roger Huntand G Alm Carlsson Comparison of clinical and physical measures ofimage quality in chest PA and pelvis AP views at varying tube voltagesReport no 98, ISRN ULI RAD R 98�—SE, 2004

5. Gustaf Ullman, M Sandborg, D R Dance, M Båth, M Håkansson, SBörjesson, R Hunt and G Alm Carlsson On the extent of quantum noiselimitation in digital chest radiography Report no 99, ISRN ULI RAD R99�—SE, 2004

6. Gustaf Ullman, Michael Sandborg, David R Dance, Roger Hunt andGudrun Alm Carlsson Distributions of scatter to primary and signal tonoise ratios per pixel in digital chest imaging Report no 100, ISRN ULIRAD R 100�—SE, 2004

xi

Abbreviations

xiii

ABBREVIATIONS

AGD Average glandular doseALARA As low as reasonable achievableAPR Apical pulmonary regionAUC Area under the ROC curveBKE Background known exactlyBV Background varyingC ContrastCC Cranio caudalC/CB Nodule to bone contrastCrel Relative contrastDQE Detective quantum efficiencyE Effective doseFN False negativeFOM Figure of meritFP False positiveHt Equivalent doseHIL Hilar regionKc, air Collision air kermaLG Laguerre GaussLAT Lateral pulmonary regionLME Lower mediastinal regionLNT Linear non threshold hypothesisMC Monte CarloMTF Modulation transfer functionNPS Noise power spectrumPA Posterior AnteriorRET Retrocardial regionROC Receiver operating characteristicsSKE Signal known exactlySNR Signal to noise ratioSNRhot, LG Laguerre Gauss Hotelling observer signal to noise ratioSNRI Ideal observer signal to noise ratioSNRp Signal to noise ratio per pixelTN True negative

List of papers

TP True positiveUME Upper mediastinal regionVGA Visual grading analysisVGAS VGA score

Energy imparted per unit area from primary photonspAsA

p

Energy imparted per unit area from scattered photonsMean energy imparted per primary photonMean squared energy imparted per primary photon2

p

s Mean energy imparted per scattered photonMean squared energy imparted per scattered photon2

s

xiv

Introduction

1

1. INTRODUCTION

1.1. Radiation protection in diagnostic radiologyDiagnostic x ray examinations can support the radiologist with valuableinformation that can be utilised to give a patient an accurate diagnosis, andsubsequently a successful treatment. However, imaging with ionisingradiation is also associated with a small risk for cancer induction or geneticdetriment. When x ray photons are scattered or absorbed inside the cells of thehuman body, ionisations occur that can alter molecular structures and thusmake harm to the cell. The most important damage to the cell is damage in theDNA since this may induce mutations. Ultimately, the damage may lead tothat the cell is killed, and if enough cells are killed, the function of the tissue ororgan will be deteriorated. This type of acute harm due to large radiationexposures is referred to as a deterministic effect. However, at the relatively lowradiation exposures in diagnostic radiology, the damages caused by ionisingradiation are often rather easily repaired. Yet, sometimes the damage on theDNA is more complex. This can cause mutations or chromosome aberrations,which in turn may lead to a modified cell but with retained reproductioncapacity. In some cases, such modified cells can result in a cancer. In the casewhere the harmful effects of ionising radiation are only known statistically, itis referred to as a stochastic effect. The risk related to stochastic effects to ahuman from exposure from ionising radiation is often quantified with theeffective dose, E (ICRP 1991, ICRP 2007).

According to the linear non threshold (LNT) hypothesis, there is a linearrelation 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 thepopulation. The collective dose from medical radiography is according to theSwedish radiation protection authority (Andersson et al 2007) 8000 manSv peryear or 0.9 mSv on average per capita, and contributes the largest fraction ofthe total dose to the population from man made sources.

Diagnostic radiology is invaluable for the health care but due to the radiationrisks, radiation protection of the patient becomes an important issue. Threedifferent principles are used for radiation protection (ICRP 2007). The firstprinciple is justification. Ionising radiation should only be used in thosesituations 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 isjustified, doses should be kept as low as reasonable achievable. This is oftenreferred to as the ALARA (As Low As Reasonably Achievable) principle. Thethird principle is dose limits to the individual. However, this principle is moreapplicable for personnel rather than for patients in diagnostic radiology.

1.2. Optimisation of diagnostic radiologyOptimisation means to balance the diagnostic information (image quality) andpatient dose so as to maximize the ratio between the two; either to keep theinformation constant and minimize the dose or to increase information atconstant dose. The dose to the patient undergoing an x ray examination has, indigital systems, a close relation to the quantum noise in the image. Thequantum noise depends on the number of photons incident on the imagedetector and is approximately described with a compound poissondistribution, which takes the energy absorption properties of the detector intoaccount. If we use too few photons, the image will be noisy and it will make itdifficult or even impossible for the radiologist to give a correct diagnosis. Itmay also take longer time for the radiologist to give a diagnosis using a noisyimage. Yet, above a certain dose level, the quantum noise may becomenegligible in comparison to the noise naturally present in the projectedanatomy (Hoeschen et al 2005). There will therefore be limited benefit toincrease the dose above this level.

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

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

2

Introduction

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

However, the physical measures of image quality derived from simulationsmust in some sense give us information on the usefulness of the image for aradiologist to solve a specific clinical task. Our physical measures of imagequality must therefore correlate to clinical measures of image quality. Twomethods for assessment of clinical image quality are given attention in thiswork, receiver operating characteristics (ROC) (Metz 1986) and visual gradinganalysis (VGA) (Tingberg 2000). A challenge in this work has been to developa model, which includes realistic measures of image quality that takes theprojected anatomy into account.

3

Objective

5

2. OBJECTIVE

While patient doses are relatively straightforward to calculate, image qualityassessment is a more complex task and crucial for the optimisation process.The main objective of this thesis is therefore to further develop methods forassessment of image quality in x ray projection radiography. The mainmethod is Monte Carlo photon transport simulation (Monte Carlo model)through the whole x ray imaging system including a model of the imageobserver. As study cases, chest posterior anterior (PA) and mammographycranio caudal (CC) projections are used as these are particularly challengingfor the radiologist.

The specific objectives are:

To study how physical measures influencing image quality aredistributed over the image plane (paper II)

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

To develop patient models of higher realism and finer anatomicalstructures for calculation of synthetic x ray images to be used for imagequality analysis (papers V and VI)

To complete our model of the imaging system by including a morerealistic model observer that can be used to directly make any taskrelated clinical image quality assessment from synthetic imagescalculated by the model (papers V and VI)

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

Monte Carlo model

7

3. MONTE CARLO BASED COMPUTATIONAL MODEL OF THE

IMAGING SYSTEM

3.1. IntroductionThe Monte Carlo method relies on taking random samples from knowndistributions and is particularly useful for studying complex problems withmany degrees of freedom. One of the first applications of the method was inLos Alamos, USA, during the Second World War where it was used tosimulate neutron diffusion. Today, Monte Carlo methods are employed inwidely diverse fields, from the evaluation of shares on the stock market(Glasserman 2003) to the calculation of energy levels of molecules withquantum Monte Carlo (Ceperley and Alder 1986).

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

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

Monte Carlo model

organ and effective doses based on either measured air kerma area product orentrance air kerma values.

There are also Monte Carlo codes developed for optimisation in diagnosticradiology. Such codes rely on the fact that they are able to estimate both organor effective doses and measures of image quality. The main application of theMonte Carlo method is for estimating the negative effect of scattered photonsreaching the image detector. Chan and Doi (1985) used the Monte Carlomethod to characterise scattered radiation in x ray imaging. Chan et al (1985)also investigated the performance of anti scatter grids in screen film imagingwhereas Sandborg et al (1994a) did task dependent, anti scatter gridoptimisation for digital imaging. More recently McVey et al (2003) did anoptimisation study of lumbar spine radiography and Lazos et al (2003) havedeveloped a software package for mammography. The Lazos model alsoincludes a realistic model of the breast (Bliznakova et al 2003). Son et al (2006)have developed software that calculates images from the visual human (VIPman)(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 adaptedfor conditions usually encountered in diagnostic radiology. It originates fromDance and Day (1984) and Persliden (1986) who independently developedcomputer programs to estimate scattered radiation in the image plane inmammography and conventional radiography, respectively. A few years later,Dance et al (1992) and Sandborg et al (1994b) merged the codes and did furthervalidation of the computer programs. McVey et al (2003) replaced the simplehomogeneous water or tissue phantoms, used in the earlier versions of thecode, by a voxelised anthropomorphic male phantom developed by Zubal et al(1994). This step enabled more realistic organ dosimetry and made it possibleto describe how measures of physical image quality vary in the image planebehind the patient.

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

8

Monte Carlo model

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

A model of the imaging system. This comprises different sources ofinput data and the imaging geometry. Input data includes x rayspectrum, patient based voxel phantom, anti scatter grid, table or chestsupport couch and image detector.

Monte Carlo simulation of photon transport through the imagingsystem. The model uses different variance reduction techniques, brieflydescribed below, to increase the efficiency of the model.

Scoring variables such as organ and effective doses and calculation ofdifferent measures of image quality such as contrast and signal to noiseratio of nodule lesions or anatomical structures within the patientmodel.

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

3.2.1.1 Imaging geometryThe imaging geometries for the chest and mammography models are shown infigures 3.1 and 3.2, respectively. Examples of specific imaging configurationsare listed in table 3.1. Substantial variations of the imaging systemconfiguration were employed particularly in papers I, III and IV and to someextent also in papers II, V and VI.

9

Monte Carlo model

Figure 3.1. The simulated imaging geometry used in chest PA radiographyincluding an x ray source, voxel phantom, anti scatter grid and imagedetector.

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) breastsupport, 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.

TypicalvaluesFocus detector distance (cm) 180 65Tube voltage (kV) 90 150

) Cu Cu

Patient PA or breast thickness (cm) 0 28es 10 25 ocalcifications

Compression plate exiglaserial arbon fibre / Al

/ grid ratio

(mg/cm2)

20 55Total filtration (mm 0.1 0.5 mm 0.3 mm

25 m Rh2 2 8

Typical diagnostic tasks and size ofdetails

Nodulmm

Micrand soft tissuemasses3 mm pl

Grid interspace mat C Carbon fibreLamella frequency (cm 1) 40 / 12 60 / 5Image detector material BaFCl, CsI CsIImage detector thickness 100 100

.2.1.2 X ray spectrawas calculated with a computer program based on a

t

the VOXMAN model, the relative fractions of Bremsstrahlung and

3The x ray spectrumspectral model by Birch and Marshall (1979). The program calculatesBremsstrahlung and characteristic x rays from a tungs en or molybdenumanode target and allows the user to select appropriate thicknesses of addedfiltration of aluminum, copper or molybdenum. In paper I, tungsten,molybdenum and rhodium anode target spectra were instead calculated withMCNP4C Monte Carlo code since the Birch and Marshall program did notinclude a rhodium target or a rhodium filter.

Incharacteristic x rays were computed and a random number selected fromwhich of the distributions the photon emerged. If a Bremsstrahlung photonwas 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 phantomanthropomorphic voxel phantoms were

Voxel phantomstom

aA Mammography phanIn the mammography model, simple representation of the female breastused (Ullman et al 2005). The breast was assumed to be a cylinder withsemicircular cross section and made of a homogeneous mixture of glandularand adipose tissue in the central region surrounded by an adipose layer. Thetissue compositions were taken from Hammerstein et al (1979). The density ofglandular tissue was 1.04 g cm 3 and for adipose tissue 0.93 g cm 3. Theglandularity of the central part of the breast model was for the main part set to50%, but was allowed to vary between 10 90% to represent both dense andfatty breasts. BIn the chest model, three differentused as a model of the patient. The main phantom was the one developed byZubal 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 andbone marrow. It therefore allows for calculation of organ and effective doses.The female specific organs: breast, ovaries and uterus were added manually tothe male body to enable effective dose to be calculated (McVey et al 2003).However, the phantom has relatively large voxels (3x3x4 mm3) and istherefore not suitable for calculating realistic images (see figure 3.4 below). Inaddition, the lungs are comparably small since the phantom was based on aCT scan where the male patient was imaged with non inflated lungs and in anon upright position, contrary to the typical chest PA imaging situation.

igure 3.3. Volume rendered representation of the Zubal phantom (left) andFthe 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 phantomss (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: theAlderson phantom and the Kyoto Kagaku PBU X 21 phantom. The Aldersonphantom was used in paper V and did not include smaller vessels. The morerecent Kyoto Kagaku phantom was more realistic since it contained a morehuman like distribution of small and medium sized vessels. Simulated x rayimages of the Zubal, Alderson and Kyoto Kagaku phantoms are shown infigure 3.4 demonstrating an increasing realism from left to right.

Tmaterials with linear attenuation coefficients ( values resembling those ofhuman tissues. However, they failed to provide us with details of the atomiccompositions of the tissue substitute materials, which complicate a morerigorous comparison with real x ray images of their chest phantom (see paperVI). A more detailed description of the segmentation of the Kyoto Kagakuphantom is given in Malusek (2008). The Alderson and Kyoto Kagakuphantoms are used mainly for simulation of synthetic images with highresolution but are not yet segmented into organs and tissue types and cantherefore 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 gridas simulated by specifying the lamella thickness,

thesis. To the left the low resolution Zubal phantom, central the Aldersonphantom and to the right the Kyoto Kagaku phantom.

3The anti scatter grid winterspace 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 focusedgrid 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 simulatedby a separate Monte Carlo simulation in a parallel grid (Sandborg et al 1994b).

3.2.1.5 Image detectorge 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 transporttion is described by

nnnnn wE ,,,r

The response of the imamodel of a semi infinite layer of the image detector material. This model isincluded as a sub routine to the main VOXMAN program. Energy impartedper unit area was assumed proportional to the image detector signal. Theimage detector model does not include the transport of secondary electrons asthe kerma approximation was assumed. The transport of light photons wasalso neglected. In papers V and VI, the detector response was calculatedseparately with MCNP4C and was used for the calculation of primaryprojections (Malusek 2008).

Tcm-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 acomputed radiography (CR) fluorescent screen and finally in paper VI, aGd2O2S indirect flat panel (DR) fluorescent screen was employed.

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

(3.1)

here rn is the position, En is the energy, n is the solid angle and wn is the

.2.2.1 Photon interaction, cross sections and material compositions

wstatistical weight of the photon. Photon interaction types in the energy rangeof diagnostic radiology (10 150 keV) are: coherent scattering, incoherentscattering and photoelectric effect. The photon interactions are described bythe differential cross sections for these events based on the atomic compositionof the materials and tissue types in the geometry. A flow chart of the mainsteps in the Monte Carlo program is given in figure 3.6. A central part of theMonte Carlo method is the utilisation of a random number generator. In thiswork we have used the random number generators embedded in UNIX orLINUX operating systems.

3The differential cross section for coherent scattering is given by

14

Monte Carlo model

),()cos1(2

222

ZxFr

dd ecoh (3.2)

where re is the classical electron radius, x is defined by )2/sin(hcEx where h

is Planck�’s constant and c the speed of light. F is the atomic form factor, thescattering angle and Z the atomic number.

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

),(sin2

222

ZxSEE

EE

EEr

dd eincoh (3.3)

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

)cos1(1EE

2/ cmE e

(3.4)

where , me is the electron rest mass.

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

To describe these photon interactions we have used tabulated cross sectionsfrom the XCOM library by Berger and Hubbell (1987). Cross sections forcompounds were computed based on the relative weight of individualelements. 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 etal (1975).

In the voxel phantom model of the patient, each organ is identified with one offour 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 (1.18g 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 photonsPrimary transmission was calculated by first sampling the initial energy fromthe 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

nn dL

1(3.5)

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

dEEfeEr

Es LEpA ),(

)(2

,

Es , ),(

(3.6)

where is the source intensity, Ef is the detector absorption efficiencyfunction depending on the photon energy E and cosine of incidence angle,

cos

),(

, at the detector surface; r is the focus detector distance.

Equation 3.6 is calculated by two separate methods. In the original version ofthe VOXMAN program, this calculation was embedded inside the MonteCarlo code. It is then calculated by first sampling the photon energy E, fromthe x ray spectrum, subsequently the optical path L from the source to a pointin the detector is calculated. Finally the photon is transported in a semi infinitelayer corresponding to the detector thickness in order to calculate Ef

),(

.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. Inpapers I, III and IV, the energy imparted to the image detector per unit areafrom primary photons was therefore calculated to a very limited number ofpoints (1 15) in the detector plane corresponding to those points where theprojection of the contrasting detail or lesion was located. In paper II, V and VIthe Monte Carlo simulations where performed for 40 x 40 points in thedetector. This is rather time consuming and is only feasible to perform withhigh precision with a fast, modern computer.

In papers V and VI, a different method was implemented for the calculation ofprimary projections. The detector absorption efficiency function Ef wascalculated separately with MCNP4C (Malusek 2008) and the projections werecalculated analytically averaged over the energy spectrum. This allowed for aseparate calculation of primary projections with high resolution.

16

Monte Carlo model

3.2.2.3 Scattered photons and variance reduction techniquesThe simulation of scattered photons is time consuming. Therefore, differentvariance reduction techniques, described briefly below, were used to increasethe efficiency. Monte Carlo methods that do not employ any variance reducingtechniques are often referred to as analogue Monte Carlo methods. Analgorithm for sampling the free path of the scattered photon, referred to as theColeman�’s algorithm is also briefly described below.

A Coleman�’s algorithmThe free path of the scattered photon is sampled using an algorithm describedby Coleman (1968). The sampling of the free path consists of several steps.First, the distance to the first interaction point is sampled for a homogeneousmedium with the linear attenuation coefficient, max, corresponding to thematerial with highest attenuation (e.g. bone). The sampling is performed bytesting whether a sampled random number from a uniform distribution in theinterval [0,1] is less than the quotient / max, where is the attenuationcoefficient of the material at the interaction point. If yes then the new point isaccepted and the algorithm ends. If no then the sampling of the distance to thefirst interaction in the homogenous medium is repeated until the sampledrandom number is less than / max.

B Collision density estimatorAnalogue Monte Carlo methods are inefficient in estimating scattered photonsin the image plane due to the low probability that a scattered photon will passa given small target area in the image detector. Therefore in the VOXMANcode, the collision density estimator (Persliden and Alm Carlsson 1986) isused. The contribution to the energy imparted per unit area at a given point ofinterest in the image detector is obtained from each interaction point in thephantom. The contribution is derived throughs

sn

N

nnns Tw ,

1)( (3.7)

where n,s is the contribution from the n:th interaction and T( ) is theprobability for the photon of state n to be scattered to the point of interest; wn

is the photon weight. In the collision density estimator, incoherent andcoherent scattering are treated separately. The radiological path length fromthe interaction point to the point of interest in the detector is calculated withSiddon�’s algorithm as in the case of primary photons.

17

Monte Carlo model

C Analytical averaging of survival and Russian rouletteThe main purpose of the Monte Carlo model is to achieve an accurate estimateof scattered photons generated in the patient and emerging towards the imagedetector. If photons are absorbed in the patient they will not contribute to thisestimate. Therefore, a technique known as analytical averaging of survival isused which does not allow photons to interact by the photoelectric effect. Allinteractions in the phantom are therefore constrained to be either coherent orincoherent scatterings. The new statistical weight, wn+1, for the photon after then:th interaction is calculated from the cross sections for photoelectric, (E) andscattering processes, (E) to correct for the bias which this method wouldotherwise introduce.

EEE

ww nn (3.8)1

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

3.2.3. Scoring quantities3.2.3.1 Energy imparted to the image detectorEstimates of the mean energy imparted per unit surface area of the imagedetector from scattered photons, s

A and primary photons pA are computed.

The total energy imparted is calculated as the sum of primary and scattercontributions sp

AAtA

p

. In order to estimate the signal to noise ratio andvariance in the image detector signal, the first and second moments of energyimparted per incident primary ( and ) and scattered (2

p s and )photon at the image detector was calculated (Dick and Motz 1981, Sandborgand Alm Carlsson 1992).

2s

18

Monte Carlo model

3.2.4. Calculated quantities3.2.4.1. ContrastA contrasting detail (e.g. corresponding to a lesion) is added to the model witha thickness and location specified by the user. The contrasting detail is notadded directly into the voxel phantom but in an artificial way in a subroutineinside the VOXMANmodel. The contrast of this detail is calculated as

11

21

11

psp

ppC (3.9)

where p1 is the mean energy imparted to the detector per unit area fromprimary photons with the nodule present, p2 the mean energy imparted perunit area from primary photons with the nodule absent and s is the meanenergy imparted per unit area from scattered photons.

3.2.4.2. Signal to noise ratiosThe program calculates two types of signal to noise ratios. The signal to noiseratio per pixel, SNRp is calculated as

22sspp

pA

pNN

SNR (3.10)

where N is the number of photons incident on a pixel. The indices p and sstands for contributions from primary and scattered photons, respectively. Thequantities and 2 are mean and mean squared values of the energy impartedto a specified pixel per incident photon.

Given the location and thickness of a specified lesion (detail), the computerprogram calculates the signal to noise ratio for this detail with a projectionarea corresponding to one pixel. It is here called the SNRMC and is given by

2211

2211

sspp

ppppMC

NN

NNSNR (3.11)

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

19

Monte Carlo model

3.2.4.1 Air collision kermaThe air collision kerma, Kc,air is given by

dE/EEEK airenEc,air

airen )/(

, (3.12)

where is the mass energy absorption coefficient for air and isthe differential photon fluence with respect to energy.

)( EE

tt HwE

3.2.4.2 Effective doseThe effective dose is the tissue weighted sum of the equivalent doses in allspecified tissues or organs of the body calculated according to ICRP 60 (ICRP1991).

(3.13)

where wt is the tissue or organ weighting factor and Ht the equivalent dose forthat tissue or organ. It is recognized that a new ICRP publication 103 (ICRP2007) has recently been adopted and uses slightly different values of the tissueweighting factors in the calculation of effective dose. A detailed analysis of theeffect on the figures of merit due to this change, for example signal to noiseratio per effective dose, SNR2/E, has not been performed here. The absolutevalues of SNR2/E may change, but the main conclusions on for example theappropriate tube voltage for chest PA radiography is unlikely to be affected bythe change of weighting factors, particularly since the weighting factors for thelungs are the same in ICRP 60 as in ICRP 103.

3.3. Calculation of images from the high resolution phantomThe scatter projection, SNRp and other quantities calculated with the MCmethod are rescaled (i.e. from 40 x 40 points) to fit the number of pixels in theprimary image. In paper V this number is 1760 x 1760, and in paper VI thenumber of pixels is 2688 x 2688. The rescaling is performed using a bilinearinterpolation function in MATLAB. The interpolated scatter projections areadded to the primary image to give the estimate of the mean energy impartedper unit area of the detector for the i:th pixel, s

,p

,t

, iAiAiA . Noise issubsequently added to the image. In paper V, white gaussian noise is addedwith the standard deviation

20

Monte Carlo model

ip,

p,

SNRiA

i .

The white noise is generated by adding sampled random numbers for eachpixel 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 powerspectrum (NPS) for the clinical system is needed. The NPS is then normalizedto correspond to unit variance. A random phase is added to the square root ofthe normalized NPS with the constraint that the random phase image ),( vushould have the symmetry ),(),( vuvu . By taking an inverse Fouriertransform of this spectrum a real and correlated noise image is created. Thevector is a multivariate random variable with mean corresponding to a nullvector and covariance matrix corresponding to the measured NPS. The noisefluctuation for each pixel is rescaled with the relation

�ˆ�ˆ

iAiiA ,, �ˆ . It isassumed that the NPS was invariant under a logarithmic transformation. Thetotal energy imparted to the detector per unit area including noise fluctuationsbecomes iA

tiAiA ,,

t,

t,iA

cbag iAi )ln( t,

. The pixel value in the i:th pixel is calculated by takinga logarithmic transformation of using the relation

(3.14)

where the parameters a, b and c are calculated with non linear regression tomake 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 theretrocardial 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. Uncertainties3.4.1. Stochastic uncertaintiesThe choice of the number of photon histories used in the simulation is a tradeoff between computer time and statistical precision. If the statistical precisionof 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 thescatter contribution to a synthetic image) on the computer Alpha (AMDOpteron processor 250, 2.4 GHz; 6.26 GB RAM) in 40 x 40 points of interest, atthe tube voltage 141 kV, with a precision of 1% (one standard deviation) takesapproximately 17 hours. The statistical uncertainty has to be kept low whenwe are calculating images, since if the statistical uncertainty is too high, thescatter projection often contains artifacts when it is interpolated to a higherresolution.

3.4.2. Systematic uncertaintiesThere are several sources of uncertainty that affect the results. These includeuncertainties in the cross sections, but also uncertainties in estimation of thedifferent 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 fromthis study is that the systematic uncertainty due to these factors in theestimated s/ p behind the grid is approximately 11%. Later, analysis ofvariance (ANOVA) and regression analysis was used to analyse similaruncertainties and the systematic uncertainty in s/ p behind the grid wasestimated to be approximately 9%. However, these relatively largeuncertainties only apply in those cases where we attempt to mimic a real x rayimaging system and compare measured quantities from that system with ourcalculated quantities. In the cases where we only use simulations to studyrelative differences between alternative acquisition schemes for an imagingsystem, the stochastic uncertainty is more relevant.

22

Monte Carlo model

23

Figure 3.6. Flow chart describing the most important steps in the Monte Carloprogram

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?

NoWas this the last history?

Calculate scoring quantities

Monte Carlo model

24

Assessment of image quality

25

4. ASSESSMENT OF IMAGE QUALITY

4.1. IntroductionImage quality assessment means quantifying the usefulness of an image tosolve a specific diagnostic task. It is preferred if this image quality assessmentis objective. There are, according to Barrett (1990), four criteria that areessential for objective assessment of image quality.

A. The taskImage quality can only be described in relation to a well defined task. Thisoften means detection of an object in a structured or homogeneousbackground. A summary of different tasks to be solved in chest radiography isgiven in ICRU 70 (ICRU 2003). Among those, the search for malignant nodulesat 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 calcificationsor masses (Burgess et al 2001). Several different types of tasks are discussed inthe literature (Barrett and Myers 2004).

B. Image and object propertiesWe need to understand the physical and statistical properties of the imagingsystem as well as the object being imaged. For example, the radiologist has aninternal model of both the human anatomy as well as a large �“data bank�” ofcommon pathologies in order be able to distinguish a malignant nodule fromnormal anatomy. The radiologist also needs to understand some of the physicsbehind the imaging technology in order to recognize some of the artefacts thatmay be present in the image.

C. ObserverAn observer that can perform the task is needed. This can be a human or amodel observer. It is the human observer (radiologist) that is the final decisionmaker. Therefore, measures of image quality should always take the humanobserver into account. Yet, clinical trials involving human observers are costlyand time demanding. Model observers may then be used to give insights intohow image quality depends on the physical and technical image acquisitionparameters.


D. Figure of meritThe figure of merit (FOM) is a number that tells us how well the observerperforms the task. The FOM depends on the detection task; a commonly usedFOM is the signal to noise ratio (SNR) or AUC, the area under the receiveroperating characteristic curve (ROC). In some cases, image quality is describedby physical properties derived from the image rather than by the performanceof 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 physicalimage quality.

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

4.2.1. The taskTwo main types of tasks are used in this work. The first task is to search for aknown signal (e.g. a nodule) in a known background, referred to as theSKE/BKE (signal known exactly/background known exactly) task. The secondtask 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 theoptimization of tube voltage and filtration in iodine subtractionmammography. The task was to detect a blood vessel filled with iodinecontrast 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 phantomand see in which image the structures corresponding to the image criteriawere most clearly visible (the VGA study). In some sense, the background canbe considered as known in this study since the same anthropomorphicphantom (the Alderson chest phantom) is used for all comparisons. Thus, theobserver may be able to remember the background. In addition, the phantomused in this study does not contain as fine and complex structural details asare present in real phantoms (see further figure 5.4).

26


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

The two papers II and V were dedicated to describe the physicalcharacteristics of the simulated image rather than to solve a specific detectiontask. Paper II was dedicated to calculate the variation of the scatter to primaryratio s/ p in the image plane in a chest examination as well the variation in thesignal to noise ratio per pixel (SNRp). These quantities influence contrast andnoise and thus detectability of lesions varies with position in the imagedanatomy.

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

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

To allow for more realistic calculations of how the scatter to primary ratiosvaries at various positions in the anatomy behind large anatomical structureslike the spine, heart and lungs, a low resolution anthropomorphic phantom,the Zubal phantom, was used in papers II IV. In paper III the anatomy wasdivided 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 createdfrom CT images of an anthropomorphic (Alderson) phantom in paper V. Thisis 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) ofthe projected anatomical background strongly influence detectability (Kundelet al 1985, Samei et al 1999, Håkansson et al 2005b) and thus act as noise besidessystem (quantum) noise. In Paper VI a new and still more realistic highresolution anthropomorphic phantom (Kyoto Kagaku) was implemented inthe 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 ofdetectability using model observers. Figure 4.2 shows cut outs of a chest imagefrom 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 backgroundof quantum/system noise only. The figures clearly demonstrate the largedifference in difficulty between detecting a nodule in an image containinganatomical structures and in a pure quantum noise image, respectively.

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

28


a b

c d

Figure 4.2. Cut outs of a simulated chest image from the hilar region withoutlesion (4.2a) and with an added designer nodule (4.2b). Figures 4.2c and 4.2dshow corresponding images against a background of quantum noise only. Thecontrast (C=0.10) and size (D=10 mm) of the nodule are the same in images4.2b and 4.2d. The amount of quantum noise (corresponding to a collision airkerma Kc,air=0.3 Gy central in the image) is the same in all four images. Thedose level is kept unrealistically low for illustration purposes.

4.2.3. ObserversTwo model observers have been used, the ideal observer and the LaguerreGauss Hotelling observer. The method for calculating the ideal observer SNRI

was developed in the previous work by Sandborg et al (1994b) using anexpression from ICRU 1996. This observer is one who can make use of all theinformation in the image and is often used to describe the ultimate

29


performance of an imaging system. Also, this observer is able to perform nonlinear operations on the data. It works most easily under the condition ofSKE/BKE when the detection only is disturbed by system noise. The LaguerreGauss Hotelling observer was applied in Paper VI utilizing the method tosimulate high resolution images developed in paper V. This observer can alsobe used for the SKE/BV task. The Hotelling observer is limited to performlinear operations and is likely to more faithfully reflect the capabilities ofhuman observers (ICRU 1996). It has been described in detail for the problemof 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 performhuman observer studies is time consuming and requires close collaborationwith radiologists. The main objective of this work was to create a completemodel of the imaging system including automatic performance evaluation,which allows for rapid evaluation of image quality, so that a large number ofacquisition parameters can be tested. This is an important step towards the useof our model for system optimisation. An inspiration was a recent study bySon et al (2006), where they used simulated images and a model observer forimage quality assessment. The results of our model have repeatedly beentested against results of human observer studies performed by our partners inour network collaboration (Sweden Associated Imaging Laboratories, SAIL;Göteborg, Linköping and Malmö). Through this collaboration, we have hadaccess to detailed information about the imaging systems used in theirexperiments. Our efforts have been concentrated to finding model observersthat are capable of simulating the performance of human observers.

4.2.4. Figures of merit

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

30


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

When a human observer performs a specific task, for instance, decideswhether 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 decisionmay mean that the patient has to undergo extra examinations. A false negativedecision may mean that, for instance, a tumour is missed and the patient hasless probability for recovery if the tumour is discovered later. The strategyused by the observer therefore depends on which kind of error (FP of FN) thatis most costly. The relation between the false positive fraction and the truepositive 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 commonlydenoted Az in the literature), is a common figure of merit used indiscrimination tasks and can be translated to a value for the signal to noiseratio 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 oftenreferred to as the detectability index dA. A short description of themethodology 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 observersare needed. Another problem in ROC studies is that the true answer has to beknown. This can be accomplished by using so called hybrid images wherelesions 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 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

False positive fraction

True

pos

itive

frac

tion

Figure 4.3. Illustration of an ROC curve. The area under the curve (AUC) isused 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 studiesIn a visual grading analysis (VGA) study, the observer is presented to twoimages. One image is a reference image and used in every comparison. Theobserver has to decide if the quality of the image compared to the referenceimage is similar, better or worse.

In paper IV, results from a VGA study by Tingberg and Sjöström (2005) wereused to search for correlations between physical image quality parameters andclinical image quality. In the VGA study, slightly modified CEC (Carmichael etal 1996) image criteria were used. The criteria were based on structures in thenormal anatomy that are described in table 4.1 for chest PA and Pelvis APexaminations. The radiologists were asked to give a graded response of thefulfilment (=visibility of the structures) of the criteria compared to thefulfilment of the criteria in the reference image. The grading was given inquantitative terms as: clearly inferior (VGA= 2), inferior ( 1), equal to (0),superior (+1) or clearly superior (+2). The score was averaged over all criteriaand 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 AP1 Vessels seen 3 cm from the pleural margin Sacrum (spongiosa)2 Thoratic vertebra behind the heart Sacral foramina3 Retrocardiac vessels Pubic and ishial rami4 Pleural margin Sacroiliac joints5 Vessels seen an face in the central area Femoral bilateral6 Hilar region

4.2.4.2 The ideal observerFor the Ideal observer used in this work, the background and the signal areassumed to be known exactly, corresponding to a SKE/BKE task. From theSNRMC (see section 3.2.4.2), the ideal observer signal to noise ratio, SNRI for agiven nodule is calculated from equation 4.2 as

222DF

pMI r

aASNRSNR (4.2)

where A is the projected area of the nodule in the image plane, ap is the pixelarea and r2

DF is the signal to noise ratio degradation factor caused by thesystem unsharpness. The quantity r2

DF includes effects on SNR of the imagingsystem unsharpness (modulation transfer function, MTF) and correlated noise(noise power spectrum (NPS)) as determined from experiments with the actualdetector type and additional detector noise. It is derived separately for eachnodule at its actual position in the anatomy, and depends on the noduleprojected area and the air kerma at the image detector. Geometrical (focalspot and magnification) unsharpness and motion unsharpness are taken intoaccount in addition to detector unsharpness. The latter is expressed in terms ofthe pre sampled MTF (Sandborg et al 2003).

A Figure of merit corresponding to the VGAS in a VGA studyIn paper IV we calculated a figure of merit that is intended to correspond tothe VGAS obtained in the VGA study (Tingberg and Sjöström 2005). For eachcontrasting detail, denoted with index q, the SNRI,q relative to its value at thereference 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 subtractedfrom 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 ofthe reference system (corresponding to the ordinate scale of the VGAS)

1 )(1)(

,

,

q refqI

qIUSNR

USNRN

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 contrastIn Paper III we attempted to perform optimization using the Zubal phantom.Since the SNRI as calculated in this work does not take into account anatomicaldetails and these are known to influence detectability, alternative figures ofmerit were also used. The ribs obscure large parts of the lungs but are alsoneeded for the radiologist to orient himself in the image (Sven GöranFransson, personal communication). The contrast of the nodule relative to thecontrast of the ribs may indicate the disturbing influence of the ribs. We havetherefore defined a �‘nodule to bone�’ contrast ratio by computing the quotientC/CB. The C/CB is the nodule�’s contrast divided by the contrast of a bone detailof a thickness corresponding to a rib or transverse processes at the sameposition in the image. The use of the nodule to bone contrast as acomplementary figure of merit was inspired from the work by Dobbins et al(2003) and Samei et al (2005).

B Relative contrastThe radiologist often wants to adjust the contrast window. This choice ofcontrast window affects the contrast of other objects in the image. We havedefined a relative contrast, Crel, as the signal difference in the image detectordivided by the dynamic range of the whole image of the chest

%5%95

21 pprelC , (4.4)

where p1 is the energy imparted to the detector per unit area in the presence ofthe nodule, p2 is the energy imparted in the absence of the nodule, and

5% is the dynamic range in the chest image, here defined by the 95thpercentile minus the 5th percentile of the energies imparted to the imagedetector in the whole chest image. The relative contrast is thus a measure ofthe 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 adjustingthe contrast window.

4.2.4.4 The Hotelling observerUltimately, the measures of image quality should correspond to how anobserver (radiologist) performs a specific task with the aid of the image. Inorder to complete our model, we need an observer that can replace the humanobserver and perform image quality assessment automatically using oursynthetic images. We therefore exploited (in paper VI), a model observer,which is known to mimic human observers more closely than the idealobserver. Such model observers are based on statistical decision theory. One ofthe pioneers in using statistical decision theory for diagnostic radiology wasWagner (Wagner et al 1979). A good thorough introduction to statisticaldecision 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 ofthe object and n represents the noise.

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

)|()|(

)(0

1

HpHp

gg

g

c

)|( bap

(4.6)

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

(4.7)gKg g12 t

HotSNR

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

35


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

(4.8)sKs g12 t

HotSNR

The covariance matrix can be estimated from a set of images g. In the casewhere 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 resultingcovariance matrix will beM xM dimensional. The number of images g used toestimate the covariance matrix must be larger than the number of pixels;otherwise the covariance matrix is singular and non invertible. Even for arelatively small region of interest of 100 x 100 pixels this would make thecovariance matrix virtually impossible to calculate since we would need atleast 104 images to perform the estimation. For a more accurate estimation ofthe covariance matrix it would require an even larger set of images. Also, amatrix of the size 104 x 104 is difficult to manage in the computer memory.

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

gU T

K ch12

,

tchHot

SNR

(4.10)

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

(4.11)

where Kch is the N x N covariance matrix of the channelized images. In thiscase the size of the covariance reduces significantly since often only 6 50channels are needed, depending on the type of task. Because of this dimensionreduction, the channelized covariance matrix can be estimated from arelatively 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 thehuman observer, internal noise corresponding to neural noise and fluctuationsin observer decision criterion can be added (Burgess et al 1981, Zhang et al2007).

u1

u2

u3

un

Imagevectorg

n

ObserverTest statistic

( )

Figure 4.4. Diagram illustrating the channelized observer. The channelizedobserver 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 aproduct between a Laguerre polynomial and a Gauss function. The LaguerreGauss channels are given by

)2()exp(2),(2

2

2

2

arL

ar

aarU nn (4.12)

where a is a scaling factor that can be chosen iteratively to maximise the SNR, ris the radial distance and Ln is the n:th Laguerre polynomial. The LaguerreGauss model assumes rotational symmetry. The LG channels of order 0, 3, 6and 9 are shown in figure 4.5. Other authors have used the LG observer indiagnostic radiography. Chawla et al (2007) studied observer performance inmammography for normal and reduced doses. Pineda et al (2006) studiedtomosynthesis and compared with planar radiography. Son et al used theHotelling and LG Hotelling observer to search for calcifications in MonteCarlo simulated images. Gabor channels (Chawla et al 2007) are sometimesused. The Gabor channels are more accurate in modelling the human observersince 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:thand d) 9:th order LG channel.

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

sKw g1

Hot

w tHot

t

(4.13)

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

(4.14)

in order to calculate the decision variable . The model observer compares thedecision variable to a threshold t in order to choose between the hypothesisH1 (lesion absent) or H2 (lesion present). For instance, if the modelobserver may choose that the lesion is present. In this way, the model observercan be used for ROC studies similar to those performed by human observers.Two ROC curves for the channelized LG Hotelling observer are shown infigure 4.6.

38


a

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1


True

pos

itive

frac

tion

b1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


True

pos

itive

frac

tion

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 thesame contrast (C=0.10) and diameter (D=10 mm). The AUC is approximately0.99 (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 linecorresponds 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 modelIn paper I we used a simple model of the breast for optimisation of iodinesubtraction mammography. In subtraction imaging, the overlaying anatomicalstructures are suppressed. The ideal observer signal to noise ratio, SNRI, ishere used in a situation where the detection or visibility of a lesion is onlylimited by the quantum noise in the image. This in turn is determined by theair kerma at the image detector and efficiency by which the image detectorabsorbed the x ray quanta and converts it to an image signal.

The SNRI was calculated for a special case when iodine contrast media wereinjected in the patients arm and images were acquired at set intervals beforeand after injection in order to follow the leakage of contrast medium in thevicinity of the breast tumor. During the whole image acquisition, the breastremains compressed and images after injection of the contrast medium aresubtracted from the image prior to injection. In mammography such contrastmedia may be valuable to distinguish between benign and malignant tumorsand for demonstrating tumors that might not otherwise be seen in dense tissueand 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 threedifferent anode filter combinations. The AGD is the average glandular dosetypically used as the radiation risk measure in mammography (Zoetelief et al1996). For both the W/Cu and Rh/Cu spectra and at all breast thicknesses, amaximum of the SNR2/AGD was found at approximately 45 kV and aminimum at 33 kV. The dominating K edge of iodine is at 33.17 keV (seefigure 5.2) and hence photons with energies just above this energy areabsorbed to a high degree and therefore provide a higher object contrastcompared to the background in the vicinity of the contrast filled vessel. At 45kV and using copper filtration, a significant portion of the x ray spectrum hasenergies in the optimal range just above the iodine K edge. Using 45 kV for theRh/Cu spectrum yields three to four times lower dose for 4 cm thick breastscompared to using the Rh/Rh combination for producing images with equalSNR for the iodine contrast medium. The SNR2/AGD is approximately 1.8times 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 resultsagree with Skarpathiotakis et al (2002).

20 25 30 35 40 45 50

50

0

100

150

200

250

300

350

55Tube voltage (kV)

SN

R2 /A

GD

(mG

y1 )

Figure 5.1. SNRI2/AGD as a function of tube voltage for a 4 cm thick breast and

50% glandularity. =Rh/25 mRh, O=Rh/0.3mmCu, =W/0.3mmCu.

105

20 25 30 35 40 45 50 55102

103

104

Photon energy (keV)

Cro

ss-s

ectio

n (b

arns

/ato

m)

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

42


5.2. Low resolution voxel phantomIn order to compare the result of the model with clinical image quality, it maybe useful to calculate distributions of physical image quality related quantitiesover the whole image and to study how these vary with position, patient sizeand imaging system configuration. The aim of paper II was to calculatedistributions of SNR per pixel (SNRp) and the scatter to primary ratio, s/ p interms of energy imparted per unit area to the image detector (see chapter 3 fordetails). Figure 5.3 shows scatter to primary ratios ( p/ s) and signal to noiseratios per pixel (SNRp) using the low resolution anthropomorphic chestphantom. The figures show that the p/ s varies significantly in the chest PAimage plane and is typically above 2 in the mediastinum and about 0.5 in thelungs. A comparison to measured s/ p in patient images (Jordan et al 1993)with calculated values in different regions shows that the mean values fromthe calculations agree reasonably well in the heart region (behind the wholeheart including the part covered by the spine), with average s/ p=2.0 (ourwork) vs. 1.9 (Jordan); in the lung region (entire lung) with average s/ p=0.6(our work) vs. 0.4 (Jordan).

As scattered photons add to the noise term in the SNRp expression (see chapter3), the SNRp is significantly reduced in the mediastinum compared to in thelungs. Therefore, if nodule detection were limited by quantum noise, thevisibility of such nodules would be higher in the lungs where the scatter toprimary ratio is lower than in the mediastinum.

43


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

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

Real phantom x ray images of those two phantoms are shown to the left infigures 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 simulationswere 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 acalculated image including scatter and statistical noise (b). An anti scatter gridwas used at the tube voltage 141 kV.

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

45


Figure 5.6. Calculated primary projection (a) and scatter projection (b) of theAlderson phantom. The intensity values are given in logarithmic scale inJ/m2. The average air kerma at the image detector was 5 Gy corresponding

to a sensitivity class of approximately 200.

The images of the scattered photons were computed in a coarse grid of points40 x 40 whereas the image of the primary photons was computed in the samenumber of pixels as the original real image (Alderson: 1760 x 1760 KyotoKagaku 2688 x 2688). The primary projection and the scatter projection werecombined to create a total image. Noise was added to the images. In paper Vgaussian noise was added with the aid of the calculated SNRp values. In paperVI we added correlated noise. However, at the point of writing this thesis, thecorrect noise power spectrum (NPS) for the system used in the clinical systemused for acquiring the real phantom images was not available. Instead, aprovisory NPS measured from a Fuji FCR 9501 CR Thorax system in Göteborgwas used. The simulated images were used in paper VI to assess image qualityusing the Laguerre Gauss Hotelling observer SNRhot,LG (see section 5.6). Weargue that the increased realism provided by the Kyoto Kagaku phantom isuseful for a more clinically realistic assessment of image quality.

5.4. Ideal observer with simple anatomical backgroundIn paper III the optimal tube voltage in detecting lung lesions with diameter 10mm but of varying thickness according to Håkansson et al (2005a) wasinvestigated in terms of the ideal observer SNRI in six anatomical regions ofthe 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 andtransverse processes, C/CB was derived, since these structures may interferewith the radiologist�’s detection of the lesion. The optimal tube voltage andscatter rejection technique were sought.

Figure 5.7 shows the figure of merit SNRI2/E, or the dose to information

conversion efficiency (Tapiovaara 1993) for a 25 mm thick lesion in the hilarregion and a 15 mm thick lesion in the lower mediastinal region. In both theseregions a low tube voltage results in a higher SNRI

2/E indicating superiorperformance. In the lower mediastinal region, a higher SNRI

2/E is found whenlarger grid ratios or longer air gaps are used. In the hilar region, withsignificantly lower scatter to primary ratio compared to the lower mediastinalregion (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 digitalchest PA radiography. The absorption of primary radiation in the grid reducesthe image quality and increases the bucky factor; this is avoided using the airgap technique.

Figure 5.7. SNRI2/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 cmthick 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 thecontrast 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 superiorcontrast of the lesion in comparison to the projected anatomical backgroundstructure such as rib or transverse process, at high tube voltages. Hence wehave two conflicting arguments for selecting the appropriate tube voltage.

In a similar study, Dobbins et al (2003) made both experiments and computerspectrum modelling to search for the optimum x ray spectrum for chestradiography for a CsI aSi flat panel image detector. They studied the SNRsquared per exposure, SNR2/X, and a contrast ratio similar to our, C/CB, as afunction of tube voltage and added filtration. The experimental results fromtheir study are essentially in agreement with our results. SNR2/X decreasesand C/CB increases with increasing tube voltage, and the tube voltage 120 kVwas considered to be optimal. We use SNR2/E instead of SNR2/X since theeffective dose is a better measure of radiation risk than exposure or incidentair 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 optimaltube voltage is reduced when the effective dose is used as a measure ofradiation risk instead of incident air collision kerma. We conclude that the choice of tube voltage depends on whether SNRI of thelesion or the interfering projected anatomy (i.e. ribs) is more important forlesion detection. The simple model of the patient used here is incapable ofmaking this selection and therefore alternative model observers and morecomplex anatomical background are needed for a proper treatment of thistask.

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 lowermediastinal region (c, d).

5.5. Correlation to human observersThe aim of paper IV was to study the dependence of image quality in digitalchest and pelvis radiography on tube voltage, and to explore correlationsbetween clinical and physical measures of image quality. The effect on imagequality of tube voltage was assessed using two methods. The first methodrelies on radiologists�’ observations of specified image criteria of images ofanthropomorphic phantoms (Visual grading analysis, VGA), and the secondmethod was based on computer modelling of the imaging system using ananthropomorphic voxel phantom.

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

49


Figure 5.9 and 5.10 show the clinical and physical image quality measures asfunction of tube voltage for the same effective dose to the chest phantom. Bothmeasures indicate that superior image quality is achieved at low tube voltagescompared to the reference system tube voltage 125 kV. Similar results wereobtained for the pelvis examination.

Chest PA

-0.5

0

0.5

1

1.5

2

VG

AS

-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 asfunction of the tube voltage. The VGAS values represent averages over allimaged structures and radiologists. The uncertainty bars show the readervariability (one standard error). The solid line (r2=0.90) indicates that there is alinear relationship between VGAS and tube voltage (data redrawn fromTingberg and Sjöström (2005)).

Chest PA

-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

60 70 80 90 100 110 120 130 140 150Tube Voltage (kV)

FOM

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

50


Chest PA

-2

-1

0

1

2

-0.5 -0.3 -0.1 0.1 0.3 0.5FOM

VG

AS

Figure 5.11. The correlation between VGAS and SNR (FOM) for a simulatedchest PA examination. The error bars correspond to one standard error and aredue to reader variability in the results of the observer studies (see Fig. 5.9). Ther2 of the fitted line (r2=0.91) indicates that the VGAS and FOM are linearlycorrelated. Lower tube voltages have positive VGAS and FOM and high tubevoltages negative values.

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

Arguments for and against this proposal are listed in paper IV and in Tingbergand Sjöström (2005). At low photon energies, the image detector�’s DQE(detective quantum efficiency) is higher and the contribution to effective doseper incident air collision kerma is lower. However, at low tube voltages, thetube charges typically increase compared to at higher voltages to maintain aconstant effective dose. Hence the risk for increased motion and focal spotunsharpness increases due to prolonged exposure time and focus sizeblooming, respectively. In examinations where iodine contrast media areemployed, the use of lower tube voltages than used today (approximately 70kV) 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 andSjöström (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 notrepresent numbers on an interval scale and one cannot assume equal stepsbetween the scale steps. This problem is solved with a closely related method,visual grading characteristics (VGC) (Båth and Månsson 2007). In this type ofstudy, the observer is asked to rate his/her confidence about the fulfilment ofimage quality criteria. The data is then analysed in a manner that is similar toROC studies, where the resulting figure of merit is the area under the VGCcurve. However, we have not been able to translate our results to a VGCstudy, since the question asked to the observer slightly differs between thosetwo types of studies.

Also, the importance of a clinical image quality measure such as VGA analysisthat relies on evaluation of structures in the normal anatomy may bequestioned. This is since the detection of pathological lesions may to a largedegree also depend on other objects in the image such as obscuring anatomicalbackground structures (Tingberg et al 2005).

5.6. Model observers with complex anatomical backgroundIn paper VI, The Laguerre Gauss Hotelling observer was implemented. Thisobserver is influenced by the anatomical background and includes this into itsfigure of merit, SNRhot,LG. Son et al (2006) and Chawla et al (2007) implementedsimilar observers. In the work by Son et al (2006), being an extension of thework by Winslow et al (2005), validation of their model is not considered dueto the use of a virtual phantom. We believe that it is important to verify thatthe computational model can faithfully reproduce variations in, e.g., tubevoltage since this is an important parameter influencing image quality andpatient dose. The implementation of the Laguerre Gauss Hotelling modelobserver, 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 asfunctions of tube voltage. The SKE/BV and SKE/BKE cases represent situationswhere the patient projected anatomy is assumed to act as noise (SKE/BV) or tobe known exactly (SKE/BKE). The figures show that for the SKE/BV task thereis 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 withincreasing 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. Intheir phantom study (a rabbit lung) they found a positive trend whenincreasing the tube voltage in the visibility of the carina and main bronchi, butno trend for the reproduction of central and peripheral vessels. Thoracicvertebrae were better visualized at low tube voltages. Their validation study(neonatal patients) showed no significant preference for any tube voltage inthe 40 90 kV range with regard to central and peripheral vessels but the carinawas better reproduced at the highest tube voltage in their study; 90 kV. Theseresults are in qualitative agreement with our work, although there aresignificant differences in the material as adult patients were studied in ourwork.

60 70 80 90 100 110 120 130 140 1500

1

2

3

4

5

6

7

8

Tube voltage (kV)

SNR

hot,L

G (S

KE/

BV

)

Figure 5.12. SNRhot,LG (SKE/BV) as function of tube voltage at the air kerma 5Gy 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), �‘+�’ uppermediastinum (UME).

53


60 70 80 90 100 110 120 130 140 1500

200

400

600

800

1000

Tube voltage (kV)

SNR

hot,L

G(S

KE/

BK

E)

Figure 5.13. SNRhot,LG (SKE/BKE) as a function of tube voltage at the air kerma5 Gy in the center of the image detector. The markers symbolize differentregions in the image: �’*�’ lateral pulmonary region (LAT), �’o�’ retrocardial region(RET), �’ �’ lower mediastinum (LAT), �’ �’ hilar region (HIL), �‘+�’ uppermediastinum (UME).

Figure 5.14 and 5.15 show SNRhot,LG for the SKE/BV and SKE/BKE tasks asfunctions 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 alarger increase in the SNRhot,LG with increasing dose level. For values of airkerma above 0.5 1 Gy, the values of SNRhot,LG are highest in the bony regionsLME and UME. In 5.15 for the SKE/BKE task, the SNRhot,LG increases inaccordance with the Rose model (Rose 1948).

54


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 51

2

3

4

5

6

7

8

Air kerma central in detector ( Gy)

SNR

hot,L

G(S

KE/

BV

)

Figure 5.14. SNRhot,LG (SKE/BV) as a function of incident air kerma at the imagedetector in the center of the image plane at 141 kV. The markers symbolizedifferent 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

00 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Air kerma central in detector ( Gy)

SNR

hot,L

G(S

KE/

BK

E)

Figure 5.15. SNRhot,LG (SKE/BKE) as a function of incident air kerma at theimage detector in the center of the image plane at 141 kV. The markerssymbolize 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 thepresence of normal patient projected anatomy including quantum noise and inimages with quantum noise only. They concluded that for the detection of thelung nodules, the quantum noise is of almost no importance at clinically useddose levels in chest radiography. The regions where lesion detection was leastinfluenced 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 etal. for images containing quantum noise only concerning the ranking of theregions with respect to the ease of detecting the lesions or SNRhot,LG. In thequantum noise images, the lower and upper mediastinum were by theseauthors ranked as the most difficult regions (most quantum noise) for lesiondetection and the hilar and lateral pulmonary regions as the least difficult(least quantum noise) ones in agreement with the results in figures 5.13 and5.14.

The results for the SKE/BV case agree relatively well with the results by Båth etal (2005a) for images where stationary noise (corresponding to structural noisein different regions) was used. In both cases, the hilar region is ranked as themost difficult region for lesion detection and the lower mediastinum ranked asthe least difficult one, in opposite order to the case with images containingquantum noise only. The results concerning ranking order also agreereasonably well for the retrocardial and lateral pulmonary regions. For theupper mediastinal region, however, the results disagree. This is probably dueto a less rich structural background in the anthropomorphic phantom in theupper mediastinum compared to in patient images. Although our model doesnot produce results that fully agree with nodule detection in a structuredanatomical background, our study shows that there are reasons to believe thatthe SKE/BV model is more realistic than the SKE/BKE model. The SKE/BVmodel also predicts that higher tube voltages result in a higher SNR incompliance with the tradition in Sweden of using high tube voltages in chestradiography. We conclude that the SNRhot,LG observer is a better model of theradiologist 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 scorewith the square root of the air kerma at the image detector in accordance withthe 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 airkerma at the image detector.

57

Summary and conclusions

59

6. SUMMARY AND CONCLUSIONS

We have developed patient models of high realism and fine anatomicalstructures for calculation of synthetic x ray images that can be used for imagequality analysis. The projection images from these images contain finestructure details such as small and medium sized vessels. This has allowed forimage quality assessment with increased realism.

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

Correlations between clinical and physical image quality measures weresought. In Paper IV we found a correlation between the VGA score and afigure of merit based on the quantum noise (ideal observer) signal to noiseratio, SNRI. In paper VI we implemented the Laguerre Gauss Hotellingobserver for the assessment of image quality in simulated high resolutionimages. A relatively good correlation was found between the Laguerre GaussHotelling observer figure of merit, SNRhot,LG for the SKE/BV task, and theclinical study by Båth et al (2005a) for images where stationary noisecorresponding to the structural noise in different regions was used. Theconclusion is therefore that the LG Hotelling observer mimics humandetection performance better than the ideal observer for tasks were theanatomical background varies.

In the special case of iodine subtraction mammography (Paper I) the optimaltube voltage was found to be significantly higher (45 kV) compared to what isstandard in conventional mammography. The optimisation of chestradiography with regard to tube voltage is more complex and depends on thetask. For tasks limited by quantum noise, or in those cases where the clearvisualisation of bone structures are essential, then low tube voltages (90 120)should be preferred. If we believe that the detection of soft tissue details (suchas 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 toperform optimisation of diagnostic radiology given a specific task. Asmentioned, a reliable and objective method for image quality assessment isneeded for this purpose. Our method using the Laguerre Gauss Hotellingobserver is in a rather early stage of development. An important future projectis therefore to further develop and validate this method against humanobservers. For instance, the Laguerre Gauss method assumes rotationalsymmetry, yet the anatomy is not rotationally symmetric. The Gabor Hotellingobserver does not assume rotational symmetry and would therefore, if it wereimplemented, provide a more accurate model of the human observer. Inaddition, another improvement is to add internal noise to the model observerto give a better agreement with human observers. One possible way tovalidate the model is to perform an ROC study where human observers andmodel observers are evaluating the same images, searching for the samepathologies. The methods for objective image quality assessment based onstatistical decision theory are also applicable in many other fields of radiationphysics, such as nuclear medicine and MR. Therefore; the work presented herecould serve as inspiration for future work for researchers in those fields.

Another possible future prospect is to develop a model for optimisation ofchest and breast tomosynthesis. It that case, the VOXMAN model needs to beimproved to calculate several projections for different angles. In the case ofbreast tomosynthesis, a realistic anthropomorphic breast model is also needed.Another improvement of the model is to segment the high resolutionanthropomorphic phantoms so that organ and effective doses can becalculated.

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

Acknowledgements

63

8. ACKNOWLEDGEMENTS

A common question from the opponent at the dissertation is, why did you choose tomake research in this specific field? My answer to that question is that I would havestudied 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 andartist 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 containssomething interesting. I stood at the seashore and picked up one grain of sand. Istudied this grain of sand in every detail and every aspect, and actually, it gave me adeeper understanding of the World. And even if I sometimes doubted, I found thatsome things inside were really interesting. So I thank this grain of sand, and return itto the seashore.

I want to express my gratitude to

My supervisorsMichael Sandborg and Gudrun Alm Carlsson for introducing me tothis field and for all the support during these years I have been working on thisthesis. 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 helpingme to attain a rather large production as a PhD student, and Gudrun for herenthusiasm. 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 myresearch. Especially during my visits in London where he taught me about theVOXMAN program. I also want to thank David for his hospitality during thesevisits.

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

Acknowledgements

Alexandr Malusek. For all your support with LINUX and UNIX. You have shownmuch patience with the �“LINUX lamer�” next door, who has asked many trivialquestions about even more trivial LINUX commands. Also for all interestingdiscussions during lunch about everything from TV programs on the discoverychannel to world politics.

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

My colleagues at the Radiation Physics Department

Jalil Bahar. For being a true friend, and for our discussions about Rumi (see the poemat 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 ofpreparing 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 duringmy PhD studies. Håkan Pettersson, for our common interest in music and for yourgood sense of humour that enriched my time as a PhD student. Anna Olsson for thetimes 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, JonasNilsson 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 readingand responding to the loads of emails about my successes and adversities as a PhDstudent. Lena Malmberg for your inspiration. Evelina Jansson, you have alsoinspired me, especially about art. All other friends, no one mentioned, no oneforgotten.

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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