Linköping University Medical Dissertations No. 1050
Quantifying image quality in diagnostic radiology using simulation of the imaging system and model observers
Gustaf Ullman
Radiation Physics, Department of Medicine and Health Faculty of Health Sciences Linköping University, Sweden
Linköping 2008
©Gustaf Ullman, 2008
Cover picture/illustration: An oil painting by Gustaf Ullman representing a chest radiograph
Published articles and figures have been reprinted with the permission of the copyright holder.
Printed in Sweden by LiU‐Tryck, Linköping, Sweden, 2008
ISBN 978‐91‐7393‐952‐2 ISSN 0345‐0082
ii
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
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iv CONTENTS
1. INTRODUCTION...... 1 1.1. Radiation protection in diagnostic radiology...... 1 1.2. Optimisation of diagnostic radiology ...... 2 1.3. Optimisation using a Monte Carlo based computational model ... 2
2. OBJECTIVE ...... 5
3. MONTE CARLO BASED COMPUTATIONAL MODEL OF THE IMAGING SYSTEM...... 7 3.1. Introduction...... 7 3.2. Computational model of the x‐ray imaging systems ...... 9 3.2.1. Model of the imaging system...... 9 3.2.2. Monte Carlo simulation of photon transport...... 14 3.2.3. Scoring quantities...... 18 3.2.4. Calculated quantities...... 19 3.3. Calculation of images from the high‐resolution phantom ...... 20 3.4. Uncertainties...... 22 3.4.1. Stochastic uncertainties ...... 22 3.4.2. Systematic uncertainties...... 22
4. ASSESSMENT OF IMAGE QUALITY ...... 25 4.1. Introduction...... 25 4.2. Image quality assessment as developed in this work...... 26 4.2.1. The task...... 26 4.2.2. Model of the imaging system and patient...... 27 4.2.3. Observers...... 29 4.2.4. Figures of merit ...... 30
5. RESULTS AND DISCUSSION ...... 41 5.1. Ideal observer with a simplified patient‐model ...... 41
v Contents
5.2. Low resolution voxel phantom ...... 43 5.3. High resolution voxel phantom...... 44 5.4. Ideal observer with simple anatomical background...... 46 5.5. Correlation to human observers ...... 49 5.6. Model observers with complex anatomical background ...... 52
6. SUMMARY AND CONCLUSIONS...... 59
7. FUTURE WORK ...... 61
8. ACKNOWLEDGEMENTS ...... 63
9. REFERENCES...... 65
vi Abstract
ABSTRACT
Accurate measures of both clinical image quality and patient radiation risk are needed for successful optimisation of medical imaging with ionising radiation. Optimisation in diagnostic radiology means finding the image acquisition technique that maximises the perceived information content and minimises the radiation risk or keeps it at a reasonably low level. The assessment of image quality depends on the diagnostic task and may in addition to system and quantum noise also be hampered by overlying projected anatomy.
The main objective of this thesis is to develop methods for assessment of image quality in simulations of projection radiography. In this thesis, image quality is quantified by modelling the whole x‐ray imaging system including the x‐ray tube, patient, anti‐scatter device, image detector and the observer. This is accomplished by using Monte Carlo (MC) simulation methods that allow simultaneous estimates of measures of image quality and patient dose. Measures of image quality include the signal‐to‐noise‐ratio, SNR, of pathologic lesions and radiation risk is estimated by using organ doses to calculate the effective dose. Based on high‐resolution anthropomorphic phantoms, synthetic radiographs were calculated and used for assessing image quality with model‐observers (Laguerre‐Gauss (LG) Hotelling observer) that mimic real, human observers. Breast and particularly chest imaging were selected as study cases as these are particularly challenging for the radiologists.
In chest imaging the optimal tube voltage in detecting lung lesions was investigated in terms of their SNR and the contrast of the lesions relative to the ribs. It was found that the choice of tube voltage depends on whether SNR of the lesion or the interfering projected anatomy (i.e. the ribs) is most important for detection. The Laguerre‐Gauss (LG) Hotelling observer is influenced by the projected anatomical background and includes this into its figure‐of‐merit,
SNRhot,LG. The LG‐observer was found to be a better model of the radiologist than the ideal observer that only includes the quantum noise in its analysis. The measures of image quality derived from our model are found to correlate relatively well with the radiologist’s assessment of image quality. Therefore MC simulations can be a valuable and an efficient tool in the search for dose‐ efficient imaging systems and image acquisition schemes.
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List of papers
LIST OF PAPERS
This thesis is based on the following papers
I. Gustaf Ullman, Michael Sandborg, David R Dance, Martin Yaffe, Gudrun Alm Carlsson. A search for optimal x‐ray spectra in iodine contrast media mammography. Phys. Med. Biol. 50, 3143–3152 (2005)* II. Gustaf Ullman, Michael Sandborg, David R Dance, Roger Hunt, and Gudrun Alm Carlsson. Distributions of scatter to primary ratios and signal to noise ratios per pixel in digital chest imaging. Radiat Prot Dosim, 114, no 1‐3, 355‐358 (2005)* III. Gustaf Ullman, Michael Sandborg, David R Dance, Roger A Hunt and Gudrun Alm Carlsson. Towards optimization in digital chest radiography using Monte Carlo modelling. Phys Med Biol 51, 2729‐ 2743 (2006)* IV. Michael Sandborg, Anders Tingberg, Gustaf Ullman, David R Dance and Gudrun Alm Carlsson. Comparison of clinical and physical measures of image quality in chest and pelvis computed radiography at different tube voltages. Med. Phys. 33(11) 4169‐4175 (2006)* V. Gustaf Ullman, Alexandr Malusek, Michael Sandborg, David R. Dance and Gudrun Alm Carlsson. Calculation of images from an anthropomorphic chest phantom using Monte Carlo methods. Proc of SPIE 6142, (2006)* VI. Gustaf Ullman, Magnus Båth, Gudrun Alm Carlsson, David R Dance, Markku Tapiovaara, and Michael Sandborg. Development of a Monte Carlo based model for optimization using the Laguerre‐Gauss Hotelling observer. (To be submitted to Med Phys)
*Reprints have been included with the permission from the publisher
ix List of papers
Other peer reviewed papers by the author not included in the thesis
1. Gustaf Ullman, Michael Sandborg, David R Dance, Roger Hunt, and Gudrun Alm Carlsson. The influence of patient thickness, tube voltage and image detector on patient dose and detail signal to noise ratio in digital chest imaging. Radiat Prot Dosim, 114, no 1‐3, 294‐297, 2005 2. Markus Håkansson, Magnus Båth, Sara Börjesson, Susanne Kheddache, Gustaf Ullman, Lars Gunnar Månsson. Nodule detection in digital chest radiography: effect of nodule location. Radiat Prot Dosim 114, no 1‐3, 92‐96, 2005 3. R A Hunt, D R Dance, P R Bakic, A D A Maidment, M Sandborg, G Ullman and G Alm Carlsson. Calculation of the properties of digital mammograms using a computer simulation. Radiat Prot Dosim 114, no 1‐3, 395‐398, 2005 4. D R Dance, R A Hunt, P R Bakic, A D A Maidment, M Sandborg, G Ullman and G Alm Carlsson. Breast dosimetry using a high‐resolution voxel phantom. Radiat Prot Dosim 114, no 1‐3, 359‐363, 2005 5. Roger A Hunt, David R Dance, Marc Pachoud, Gudrun Alm Carlsson, Michael Sandborg, Gustaf Ullman and Francis R Verdun. Monte Carlo simulation of a mammographic test phantom. Radiat Prot Dosim, 114, no 1‐3, 432‐435, 2005.
Conference presentations
1. Ullman G, Sandborg M, Dance D R, Skarpathiotakis M, Yaffe MJ, Alm Carlsson G. (2002) A search for optimal x‐ray energy spectra in digital iodine subtraction mammography using Monte Carlo simulation of the imaging chain. Digital Mammography IWDM 2002: Proceedings of the Workshop, Bremen, Germany, June 2002. Ed. Peitgen H‐O (Springer‐ Verlag, Berlin) pp152‐154, 2002 2. M. Båth, M. Håkansson, S. Börjesson, S. Kheddache, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, L. G. Månsson. Investigation of components affecting the detection of lung nodules in digital chest radiography. Accepted for presentation at Medical Imaging, 12‐17 February 2005, San Diego, USA. Proc. SPIE 5749, 231‐242, 2005.
x List of papers
Internal reports (not reviewed)
1. Gustaf Ullman, Michael Sandborg, Roger Hunt and David R Dance. Implementation of simulation of pathologies in chest and breast imaging Report no 94, ISRN ULI‐RAD‐R‐‐94—SE, 2003 2. Gustaf Ullman, Michael Sandborg and Gudrun Alm Carlsson. Validation of a voxel‐phantom based Monte Carlo model and calibration of digital systems. Report no 95, ISRN ULI‐RAD‐R‐‐95—SE, 2003 3. Gustaf Ullman, M Sandborg, D R Dance, R Hunt and G Alm Carlsson Optimisation of chest radiology by computer modelling of image quality measures and patient effective dose Report no 97, ISRN ULI‐ RAD‐R‐‐97—SE, 2004 4. Gustaf Ullman, M Sandborg, Anders Tingberg, D R Dance, Roger Hunt and G Alm Carlsson Comparison of clinical and physical measures of image quality in chest PA and pelvis AP views at varying tube voltages Report no 98, ISRN ULI‐RAD‐R‐‐98—SE, 2004 5. Gustaf Ullman, M Sandborg, D R Dance, M Båth, M Håkansson, S Börjesson, R Hunt and G Alm Carlsson On the extent of quantum noise limitation in digital chest radiography Report no 99, ISRN ULI‐RAD‐R‐‐ 99—SE, 2004 6. Gustaf Ullman, Michael Sandborg, David R Dance, Roger Hunt and Gudrun Alm Carlsson Distributions of scatter‐to‐primary and signal‐to‐ noise ratios per pixel in digital chest imaging Report no 100, ISRN ULI‐ RAD‐R‐‐100—SE, 2004
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Abbreviations
ABBREVIATIONS
AGD Average glandular dose ALARA As low as reasonable achievable APR Apical pulmonary region AUC Area under the ROC curve BKE Background known exactly BV Background varying C Contrast CC Cranio‐caudal C/CB Nodule‐to‐bone contrast Crel Relative contrast DQE Detective quantum efficiency E Effective dose FN False negative FOM Figure of merit FP False positive Ht Equivalent dose HIL Hilar region Kc, air Collision air kerma LG Laguerre‐Gauss LAT Lateral pulmonary region LME Lower mediastinal region LNT Linear non‐threshold hypothesis MC Monte Carlo MTF Modulation transfer function NPS Noise power spectrum PA Posterior Anterior RET Retrocardial region ROC Receiver operating characteristics SKE Signal known exactly SNR Signal‐to‐noise ratio SNRhot, LG Laguerre‐Gauss Hotelling observer signal‐to‐noise ratio SNRI Ideal observer signal‐to‐noise ratio SNRp Signal‐to‐noise ratio per pixel TN True negative
xiii List of papers
TP True positive UME Upper mediastinal region VGA Visual grading analysis VGAS VGA score
p ε A Energy imparted per unit area from primary photons s ε A Energy imparted per unit area from scattered photons
λ p Mean energy imparted per primary photon 2 λ p Mean squared energy imparted per primary photon
λ s Mean energy imparted per scattered photon 2 λ s Mean squared energy imparted per scattered photon
xiv Introduction
1. INTRODUCTION
1.1. Radiation protection in diagnostic radiology Diagnostic x‐ray examinations can support the radiologist with valuable information that can be utilised to give a patient an accurate diagnosis, and subsequently a successful treatment. However, imaging with ionising radiation is also associated with a small risk for cancer induction or genetic detriment. When x‐ray photons are scattered or absorbed inside the cells of the human body, ionisations occur that can alter molecular structures and thus make harm to the cell. The most important damage to the cell is damage in the DNA since this may induce mutations. Ultimately, the damage may lead to that the cell is killed, and if enough cells are killed, the function of the tissue or organ will be deteriorated. This type of acute harm due to large radiation exposures is referred to as a deterministic effect. However, at the relatively low radiation exposures in diagnostic radiology, the damages caused by ionising radiation are often rather easily repaired. Yet, sometimes the damage on the DNA is more complex. This can cause mutations or chromosome aberrations, which in turn may lead to a modified cell but with retained reproduction capacity. In some cases, such modified cells can result in a cancer. In the case where the harmful effects of ionising radiation are only known statistically, it is referred to as a stochastic effect. The risk related to stochastic effects to a human from exposure from ionising radiation is often quantified with the effective dose, E (ICRP 1991, ICRP 2007).
According to the linear non‐threshold (LNT) hypothesis, there is a linear relation between the effective dose and risk for cancer induction (ICRP 2005) and means that the collective dose can be used as a measure of the harm to the population. The collective dose from medical radiography is according to the Swedish radiation protection authority (Andersson et al 2007) 8000 manSv per year or 0.9 mSv on average per capita, and contributes the largest fraction of the total dose to the population from man‐made sources.
Diagnostic radiology is invaluable for the health care but due to the radiation risks, radiation protection of the patient becomes an important issue. Three different principles are used for radiation protection (ICRP 2007). The first principle is justification. Ionising radiation should only be used in those situations where it brings more good than harm. The second principle is
1 Introduction optimisation. It means that, in those cases where the use of ionising radiation is justified, doses should be kept as low as reasonable achievable. This is often referred to as the ALARA (As Low As Reasonably Achievable) principle. The third principle is dose limits to the individual. However, this principle is more applicable for personnel rather than for patients in diagnostic radiology.
1.2. Optimisation of diagnostic radiology Optimisation means to balance the diagnostic information (image quality) and patient dose so as to maximize the ratio between the two; either to keep the information constant and minimize the dose or to increase information at constant dose. The dose to the patient undergoing an x‐ray examination has, in digital systems, a close relation to the quantum noise in the image. The quantum noise depends on the number of photons incident on the image detector and is approximately described with a compound poisson distribution, which takes the energy absorption properties of the detector into account. If we use too few photons, the image will be noisy and it will make it difficult or even impossible for the radiologist to give a correct diagnosis. It may also take longer time for the radiologist to give a diagnosis using a noisy image. Yet, above a certain dose level, the quantum noise may become negligible in comparison to the noise naturally present in the projected anatomy (Hoeschen et al 2005). There will therefore be limited benefit to increase the dose above this level.
How to make the trade off between the dose to the patient and the image quality is a complex subject. A key aspect for the optimisation of diagnostic radiology is to understand the relative importance of the quantum noise in the image and the structures in the projected anatomy that act as noise. Several authors including Kundel et al (1985), Samei et al (1999), Burgess et al (2001) and Håkansson et al (2005b) have acknowledged the importance of projected anatomy in relation to quantum noise. The consensus from these studies is that at normal exposures, the projected anatomy is the most important factor in hampering the detection of subtle nodules in chest radiographs and mammograms.
1.3. Optimisation using a Monte Carlo based computational model One method that has been utilised to search in a systematic way for the optimal imaging parameters in diagnostic radiology is to use a model of the imaging system, including the patient and observer, and to simulate the photon transport through the imaging system using the Monte Carlo method.
2 Introduction
With this method it is possible to simultaneously calculate the dose to the patient and measures of image quality.
However, the physical measures of image quality derived from simulations must in some sense give us information on the usefulness of the image for a radiologist to solve a specific clinical task. Our physical measures of image quality must therefore correlate to clinical measures of image quality. Two methods for assessment of clinical image quality are given attention in this work, receiver operating characteristics (ROC) (Metz 1986) and visual grading analysis (VGA) (Tingberg 2000). A challenge in this work has been to develop a model, which includes realistic measures of image quality that takes the projected anatomy into account.
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Objective
2. OBJECTIVE
While patient doses are relatively straightforward to calculate, image quality assessment is a more complex task and crucial for the optimisation process. The main objective of this thesis is therefore to further develop methods for assessment of image quality in x‐ray projection radiography. The main method is Monte Carlo photon transport simulation (Monte Carlo model) through the whole x‐ray imaging system including a model of the image observer. As study cases, chest posterior‐anterior (PA) and mammography cranio‐caudal (CC) projections are used as these are particularly challenging for the radiologist.
The specific objectives are:
• To study how physical measures influencing image quality are distributed over the image plane (paper II)
• To develop methods for calculating physical image quality measures from simulated radiographs and search for correlations between these measures and measures of clinical image quality (papers III and IV)
• To develop patient models of higher realism and finer anatomical structures for calculation of synthetic x‐ray images to be used for image quality analysis (papers V and VI)
• To complete our model of the imaging system by including a more realistic model observer that can be used to directly make any task‐ related clinical image quality assessment from synthetic images calculated by the model (papers V and VI)
• To use our model of the imaging system towards optimisation of image quality and patient dose (paper I and III)
5
Monte Carlo model
3. MONTE CARLO BASED COMPUTATIONAL MODEL OF THE IMAGING SYSTEM
3.1. Introduction The Monte Carlo method relies on taking random samples from known distributions and is particularly useful for studying complex problems with many degrees of freedom. One of the first applications of the method was in Los Alamos, USA, during the Second World War where it was used to simulate neutron diffusion. Today, Monte Carlo methods are employed in widely diverse fields, from the evaluation of shares on the stock market (Glasserman 2003) to the calculation of energy levels of molecules with quantum Monte Carlo (Ceperley and Alder 1986).
In radiation physics, the Monte Carlo method is employed for simulating radiation transport, mathematically described by the Bolzmann equation. There are several general‐purpose computer codes available for the study of radiation transport, for example, MCNP (Monte Carlo N‐Particle transport) (Briesmeister 2000) developed in Los Alamos and designed to transport neutrons, electrons and photons; EGSnrc (Electron Gamma Shower) (Kawrakow and Rogers 2003, Nelson et al 1985), initially developed in Stanford, which transports photons and electrons; PENELOPE (PENetration and Energy Loss Of Positrons and Electrons) (Baro et al 1995) developed at University of Barcelona, and used to transports electrons, positrons and photons.
In diagnostic radiology, one of the most common applications of the Monte Carlo method is in patient dosimetry. There are several Monte Carlo computer codes that are used to estimate the effective dose. Jones and Wall (1985) used the Monte Carlo method to compute organ doses using a mathematical representation (Cristy 1980) of a human anatomy. Zankl and Wittman (2001) have developed a family of more realistic, segmented anthropomorphic voxel phantoms for organ dosimetry for external photon beams. Zankl and Petoussi‐ Henss (2002) calculated conversion factors based on the VIP man (Spitzer and Whitlock 1998) anthropomorphic model. The user‐friendly Monte Carlo computer program PCXMC by Servomaa and Tapiovaara (1998) calculates
7 Monte Carlo model organ and effective doses based on either measured air kerma‐area product or entrance air kerma values.
There are also Monte Carlo codes developed for optimisation in diagnostic radiology. Such codes rely on the fact that they are able to estimate both organ or effective doses and measures of image quality. The main application of the Monte Carlo method is for estimating the negative effect of scattered photons reaching the image detector. Chan and Doi (1985) used the Monte Carlo method to characterise scattered radiation in x‐ray imaging. Chan et al (1985) also investigated the performance of anti‐scatter grids in screen‐film imaging whereas Sandborg et al (1994a) did task‐dependent, anti‐scatter grid optimisation for digital imaging. More recently McVey et al (2003) did an optimisation study of lumbar spine radiography and Lazos et al (2003) have developed a software package for mammography. The Lazos model also includes a realistic model of the breast (Bliznakova et al 2003). Son et al (2006) have developed software that calculates images from the visual human (VIP man)(Xu et al 2000). They have used the EGSnrc code as a basis of the model, used model observers and calculated effective dose.
In this work we have used an in‐house Monte Carlo code VOXMAN adapted for conditions usually encountered in diagnostic radiology. It originates from Dance and Day (1984) and Persliden (1986) who independently developed computer programs to estimate scattered radiation in the image plane in mammography and conventional radiography, respectively. A few years later, Dance et al (1992) and Sandborg et al (1994b) merged the codes and did further validation of the computer programs. McVey et al (2003) replaced the simple homogeneous water or tissue phantoms, used in the earlier versions of the code, by a voxelised anthropomorphic male phantom developed by Zubal et al (1994). This step enabled more realistic organ dosimetry and made it possible to describe how measures of physical image quality vary in the image plane behind the patient.
The main focus of this thesis is on chest imaging. Therefore we have mainly used the VOXMAN model, adapted to simulate chest radiography. In paper I we used the version of the computer program dedicated for mammography. This computer program was further developed by Hunt et al (2005) to incorporate an anthropomorphic model of the breast developed by Bakic et al (2002). A brief description of the VOXMAN model is presented below.
8 Monte Carlo model
3.2. Computational model of the x‐ray imaging systems The Monte Carlo based computational method used in this thesis models the x‐ray imaging system and simulates photon transport from the source through patient, anti‐scatter grid and into the image detector. The computational method consists of the following components:
A model of the imaging system. This comprises different sources of input data and the imaging geometry. Input data includes x‐ray spectrum, patient‐based voxel phantom, anti‐scatter grid, table or chest support couch and image detector.
Monte Carlo simulation of photon transport through the imaging system. The model uses different variance reduction techniques, briefly described below, to increase the efficiency of the model.
Scoring variables such as organ and effective doses and calculation of different measures of image quality such as contrast and signal‐to‐noise ratio of nodule lesions or anatomical structures within the patient model.
3.2.1. Model of the imaging system The input data files are described below including geometry, x‐ray spectra, voxel phantom, anti‐scatter grid and image detector.
3.2.1.1 Imaging geometry The imaging geometries for the chest and mammography models are shown in figures 3.1 and 3.2, respectively. Examples of specific imaging configurations are listed in table 3.1. Substantial variations of the imaging system configuration were employed particularly in papers I, III and IV and to some extent also in papers II, V and VI.
9 Monte Carlo model
Figure 3.1. The simulated imaging geometry used in chest PA radiography including an x‐ray source, voxel phantom, anti‐scatter grid and image detector.
Figure 3.2. The simulated imaging geometry used in Cranio‐caudal (CC) mammography. Notations are a) focus‐detector distance; thickness of b) breast, c) compression plate, d) adipose layer, e) contrasting detail, f) breast support, g) anti‐scatter grid and h) image detector.
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Table 3.1. Examples of imaging system configurations for chest and breast imaging used in this work.
Typical imaging system component Chest PA Breast CC values Focus‐detector distance (cm) 180 65 Tube voltage (kV) 90‐150 20‐55 Total filtration (mm) 0.1‐0.5 mm Cu 0.3 mm Cu 25μm Rh Patient PA or breast thickness (cm) 20‐28 2‐8 Typical diagnostic tasks and size of Nodules 10‐25 Microcalcifications details mm and soft tissue masses Compression plate ‐ 3 mm plexiglas Grid interspace material Carbon fibre / Al Carbon fibre Lamella frequency (cm‐1) / grid ratio 40 / 12 60 / 5 Image detector material BaFCl, CsI CsI Image detector thickness (mg/cm2) 100 100
3.2.1.2 X‐ray spectra The x‐ray spectrum was calculated with a computer program based on a spectral model by Birch and Marshall (1979). The program calculates Bremsstrahlung and characteristic x‐rays from a tungst en or molybdenum anode target and allows the user to select appropriate thicknesses of added filtration of aluminum, copper or molybdenum. In paper I, tungsten, molybdenum and rhodium anode target spectra were instead calculated with MCNP4C Monte Carlo code since the Birch and Marshall program did not include a rhodium target or a rhodium filter.
In the VOXMAN model, the relative fractions of Bremsstrahlung and characteristic x‐rays were computed and a random number selected from which of the distributions the photon emerged. If a Bremsstrahlung photon was selected, the photon energy was chosen using rejection sampling (Sandborg et al 1994b).
11 Monte Carlo model
3.2.1.3 Voxel phantoms A Mammography phantom In the mammography model, a simple representation of the female breast was used (Ullman et al 2005). The breast was assumed to be a cylinder with semicircular cross‐section and made of a homogeneous mixture of glandular and adipose tissue in the central region surrounded by an adipose layer. The tissue compositions were taken from Hammerstein et al (1979). The density of glandular tissue was 1.04 g cm−3 and for adipose tissue 0.93 g cm−3. The glandularity of the central part of the breast model was for the main part set to 50%, but was allowed to vary between 10‐90% to represent both dense and fatty breasts.
B Low‐resolution chest phantom In the chest model, three different anthropomorphic voxel phantoms were used as a model of the patient. The main phantom was the one developed by Zubal et al (1994) and used in papers II, III and IV. The Zubal phantom (displayed in figure 3.3) was segmented into organs such as lungs, heart and bone marrow. It therefore allows for calculation of organ and effective doses. The female‐specific organs: breast, ovaries and uterus were added manually to the male body to enable effective dose to be calculated (McVey et al 2003). However, the phantom has relatively large voxels (3x3x4 mm3) and is therefore not suitable for calculating realistic images (see figure 3.4 below). In addition, the lungs are comparably small since the phantom was based on a CT scan where the male patient was imaged with non‐inflated lungs and in a non‐upright position, contrary to the typical chest PA imaging situation.
Figure 3.3. Volume‐rendered representation of the Zubal phantom (left) and the Kyoto Kaguku (PBU‐X‐21) phantom (right). An outline of the lungs, trachea, heart and breast are shown in the left image.
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C High‐resolution chest phantoms Two high‐resolution voxel phantoms (voxel size 0.97x0.97x0.6 mm) were created from CT scans of two different anthropomorphic thorax phantoms: the Alderson phantom and the Kyoto Kagaku PBU‐X‐21 phantom. The Alderson phantom was used in paper V and did not include smaller vessels. The more recent Kyoto Kagaku phantom was more realistic since it contained a more human‐like distribution of small and medium‐sized vessels. Simulated x‐ray images of the Zubal, Alderson and Kyoto Kagaku phantoms are shown in figure 3.4 demonstrating an increasing realism from left to right.
The manufacturer of the Kyoto Kagaku phantom claims that it is composed of materials with linear attenuation coefficients (μ values) resembling those of human tissues. However, they failed to provide us with details of the atomic compositions of the tissue substitute materials, which complicate a more rigorous comparison with real x‐ray images of their chest phantom (see paper VI). A more detailed description of the segmentation of the Kyoto Kagaku phantom is given in Malusek (2008). The Alderson and Kyoto Kagaku phantoms are used mainly for simulation of synthetic images with high resolution but are not yet segmented into organs and tissue types and can therefore not be used for direct calculation of effective dose.
Figure 3.4. Projection images of the three chest voxel‐phantoms used in this thesis. To the left the low‐resolution Zubal phantom, central the Alderson phantom and to the right the Kyoto Kagaku phantom.
3.2.1.4 Anti‐scatter grid The anti‐scatter grid was simulated by specifying the lamella thickness, interspace material and thickness as well as cover thickness and grid ratio. Typical grids are listed in table 3.1. In the Monte Carlo program the focused grid was simulated by an analytical transmission formula developed by Day
13 Monte Carlo model and Dance (1983). Scattered photons generated in the grid itself was simulated by a separate Monte Carlo simulation in a parallel grid (Sandborg et al 1994b).
3.2.1.5 Image detector The response of the image detector was simulated in a separate Monte Carlo model of a semi‐infinite layer of the image detector material. This model is included as a sub‐routine to the main VOXMAN program. Energy imparted per unit area was assumed proportional to the image detector signal. The image detector model does not include the transport of secondary electrons as the kerma approximation was assumed. The transport of light photons was also neglected. In papers V and VI, the detector response was calculated separately with MCNP4C and was used for the calculation of primary projections (Malusek 2008).
The image detector thickness was specified in terms of a surface density in mg cm-2 (see table 3.1). In paper I, the detector material was needle crystals of CsI; in paper II, III and IV an unstructured mixture of BaFCl grains simulating a computed radiography (CR) fluorescent screen and finally in paper VI, a Gd2O2S indirect flat panel (DR) fluorescent screen was employed.
3.2.2. Monte Carlo simulation of photon transport The physical state of the photon after the n:th interaction is described by
α = ()r Ω ,,, wE nnnnn (3.1)
where rn is the position, En is the energy, Ωn is the solid angle and wn is the statistical weight of the photon. Photon interaction types in the energy range of diagnostic radiology (10‐150 keV) are: coherent scattering, incoherent scattering and photoelectric effect. The photon interactions are described by the differential cross sections for these events based on the atomic composition of the materials and tissue types in the geometry. A flow chart of the main steps in the Monte Carlo program is given in figure 3.6. A central part of the Monte Carlo method is the utilisation of a random number generator. In this work we have used the random number generators embedded in UNIX or LINUX operating systems.
3.2.2.1 Photon interaction, cross‐sections and material compositions The differential cross‐section for coherent scattering is given by
14 Monte Carlo model dσ r 2 ecoh += θ 22 ZxF ),()cos1( (3.2) dΩ 2
E where re is the classical electron radius, x is defined by x = θ )2/sin( where h hc is Planck’s constant and c the speed of light. F is the atomic form factor, θ the scattering angle and Z the atomic number.
For incoherent scattering the differential cross‐section is given by the Klein‐ Nishina relation times the incoherent scattering function S(x,Z):
2 dσ r 2 ⎛ E′ ⎞ ⎛ E E′ ⎞ incoh = e ⎜ ⎟ ⎜ + − 2 θ ⎟ ZxS ),(sin (3.3) dΩ 2 ⎝ E ⎠ ⎝ E′ E ⎠
Here, E is the incident photon energy and E´ is the scattered photon energy given by the Compton relation
E E′ = (3.4) −+ θκ )cos1(1
2 where κ = / e cmE , me is the electron rest mass.
For the photoelectric effect, it is assumed that the photon is locally absorbed in interactions with atoms of low atomic number (such as carbon and oxygen). Elements with high atomic numbers such as those in the grid (lead) and detector materials (e.g. barium, gadolinium, cesium, iodine) may emit (high‐ energy) characteristic x‐rays if vacancies are created in the K‐ or L‐shells.
To describe these photon interactions we have used tabulated cross‐sections from the XCOM library by Berger and Hubbell (1987). Cross‐sections for compounds were computed based on the relative weight of individual elements. The atomic form factors, F(x,Z), were given by Hubbell and Överbö (1979) and the incoherent scattering functions, S(x,Z), were given by Hubbell et al (1975).
In the voxel phantom model of the patient, each organ is identified with one of four tissue types, with different densities: average soft tissue (1.03 g cm−3), healthy lung (0.26 g cm−3), cortical bone (1.49 g cm−3) and bone spongiosa (1.18 g cm−3). The tissue densities and compositions were taken from ICRU 46 (1992) except for cortical bone, which was obtained from Kramer (1979).
15 Monte Carlo model
3.2.2.2 Primary photons Primary transmission was calculated by first sampling the initial energy from the pre‐calculated energy spectrum, and use Siddon’s algorithm (Siddon 1985) to calculate the radiological path‐length from the focus to the detector
N = ∑ μ n dL n (3.5) n=1
The radiological path‐length can be used to calculate the contribution to the energy imparted per unit area from primary photons as
p Ω ,E Es )( −L ε A = ∫ ξξ ),( dEEfeE (3.6) r 2
where s Ω ,E is the source intensity, Ef ξ ),( is the detector absorption efficiency function depending on the photon energy E and cosine of incidence angle, ξ = cosθ , at the detector surface; r is the focus detector distance.
Equation 3.6 is calculated by two separate methods. In the original version of the VOXMAN program, this calculation was embedded inside the Monte Carlo code. It is then calculated by first sampling the photon energy E, from the x‐ray spectrum, subsequently the optical path L from the source to a point in the detector is calculated. Finally the photon is transported in a semi‐infinite layer corresponding to the detector thickness in order to calculate Ef ξ ),( . However, this did not allow for the calculation of high‐resolution images, since we were forced to run the Monte Carlo simulation for all these points. In papers I, III and IV, the energy imparted to the image detector per unit area from primary photons was therefore calculated to a very limited number of points (1‐15) in the detector plane corresponding to those points where the projection of the contrasting detail or lesion was located. In paper II, V and VI the Monte Carlo simulations where performed for 40 x 40 points in the detector. This is rather time‐consuming and is only feasible to perform with high precision with a fast, modern computer.
In papers V and VI, a different method was implemented for the calculation of primary projections. The detector absorption efficiency function Ef ξ ),( was calculated separately with MCNP4C (Malusek 2008) and the projections were calculated analytically averaged over the energy spectrum. This allowed for a separate calculation of primary projections with high resolution.
16 Monte Carlo model
3.2.2.3 Scattered photons and variance reduction techniques The simulation of scattered photons is time consuming. Therefore, different variance reduction techniques, described briefly below, were used to increase the efficiency. Monte Carlo methods that do not employ any variance reducing techniques are often referred to as analogue Monte Carlo methods. An algorithm for sampling the free path of the scattered photon, referred to as the Coleman’s algorithm is also briefly described below.
A Coleman’s algorithm The free path of the scattered photon is sampled using an algorithm described by Coleman (1968). The sampling of the free path consists of several steps. First, the distance to the first interaction point is sampled for a homogeneous medium with the linear attenuation coefficient, μmax, corresponding to the material with highest attenuation (e.g. bone). The sampling is performed by testing whether a sampled random number from a uniform distribution in the interval [0,1] is less than the quotient μ/μmax, where μ is the attenuation coefficient of the material at the interaction point. If yes then the new point is accepted and the algorithm ends. If no then the sampling of the distance to the first interaction in the homogenous medium is repeated until the sampled random number is less than μ/μmax.
B Collision density estimator Analogue Monte Carlo methods are inefficient in estimating scattered photons in the image plane due to the low probability that a scattered photon will pass a given small target area in the image detector. Therefore in the VOXMAN code, the collision density estimator (Persliden and Alm Carlsson 1986) is used. The contribution to the energy imparted per unit area at a given point of interest in the image detector is obtained from each interaction point in the ∗ phantom. The contribution ε s is derived through
N ∗ ε s = ∑ Tw nn )( λα ,sn (3.7) n=1
where λn,s is the contribution from the n:th interaction and T(α) is the probability for the photon of state αn to be scattered to the point of interest; wn is the photon weight. In the collision density estimator, incoherent and coherent scattering are treated separately. The radiological path‐length from the interaction point to the point of interest in the detector is calculated with Siddon’s algorithm as in the case of primary photons.
17 Monte Carlo model
C Analytical averaging of survival and Russian roulette The main purpose of the Monte Carlo model is to achieve an accurate estimate of scattered photons generated in the patient and emerging towards the image detector. If photons are absorbed in the patient they will not contribute to this estimate. Therefore, a technique known as analytical averaging of survival is used which does not allow photons to interact by the photoelectric effect. All interactions in the phantom are therefore constrained to be either coherent or incoherent scatterings. The new statistical weight, wn+1, for the photon after the n:th interaction is calculated from the cross‐sections for photoelectric, τ(E) and scattering processes, σ(E) to correct for the bias which this method would otherwise introduce.
σ ()E = ww (3.8) n+1 n ()+τσ ()EE
For high photon energies, E, the ratio wn+1/wn is less than, but close to 1 and the statistical weight is only slightly reduced at each interaction. However, as the photon energy is reduced the relative importance of photoelectric cross‐ sections increases, and the number of interactions before a scattered photon escapes from the phantom geometry may be large. Hence, the statistical weight of the photon may eventually be low and so its contribution to the estimated image detector signal. Therefore, an unbiased procedure called Russian roulette (Salvat et al 2003) is used. Once the weight is less than 0.05 a random number is selected and in 95% of the cases the photon history is terminated; in the other 5% of the cases the photon history continues with a twenty times higher (100%/5%) statistical weight wn+1 compared to the original weight. Photon histories are also terminated once the photon is scattered out of the boundaries of the phantom.
3.2.3. Scoring quantities 3.2.3.1 Energy imparted to the image detector Estimates of the mean energy imparted per unit surface area of the image s p detector from scattered photons, ε A and primary photons ε A are computed. The total energy imparted is calculated as the sum of primary and scatter t sp contributions A += εεε AA . In order to estimate the signal‐to‐noise ratio and variance in the image detector signal, the first and second moments of energy 2 2 imparted per incident primary ( λ p and λ p ) and scattered ( λ s and λ s ) photon at the image detector was calculated (Dick and Motz 1981, Sandborg and Alm Carlsson 1992).
18 Monte Carlo model
3.2.4. Calculated quantities 3.2.4.1. Contrast A contrasting detail (e.g. corresponding to a lesion) is added to the model with a thickness and location specified by the user. The contrasting detail is not added directly into the voxel phantom but in an artificial way in a subroutine inside the VOXMAN model. The contrast of this detail is calculated as
ε − ε pp 21 1 C = ⋅ (3.9) p1 1+ εεε ps 1
where εp1 is the mean energy imparted to the detector per unit area from primary photons with the nodule present, εp2 the mean energy imparted per unit area from primary photons with the nodule absent and εs is the mean energy imparted per unit area from scattered photons.
3.2.4.2. Signal‐to‐noise ratios The program calculates two types of signal‐to‐noise ratios. The signal‐to‐noise ratio per pixel, SNRp is calculated as
p ε A SNRp = (3.10) 2 2 NN ⋅+⋅ λλ sspp where N is the number of photons incident on a pixel. The indices p and s stands for contributions from primary and scattered photons, respectively. The quantities λ and λ2 are mean and mean squared values of the energy imparted to a specified pixel per incident photon.
Given the location and thickness of a specified lesion (detail), the computer program calculates the signal‐to‐noise ratio for this detail with a projection area corresponding to one pixel. It is here called the SNRMC and is given by
N λ N ⋅−⋅ λ pppp 2211 SNRMC = (3.11) 2 2 N 11 N ⋅+⋅ λλ sspp
where the index n=1 refers to a pixel in the image behind the nodule, and n=2 refers to the same pixel with the nodule absent.
19 Monte Carlo model
3.2.4.1 Air collision kerma
The air collision kerma, Kc,air is given by
c,air ∫ EK ΦE ()E ⋅⋅= ()μen ()E ρair dE/ , (3.12)
where μ en ρ )/( air is the mass energy absorption coefficient for air and Φ E E)( is the differential photon fluence with respect to energy.
3.2.4.2 Effective dose The effective dose is the tissue‐weighted sum of the equivalent doses in all specified tissues or organs of the body calculated according to ICRP 60 (ICRP 1991).
= ∑ HwE tt (3.13)
where wt is the tissue or organ weighting factor and Ht the equivalent dose for that tissue or organ. It is recognized that a new ICRP publication 103 (ICRP 2007) has recently been adopted and uses slightly different values of the tissue weighting factors in the calculation of effective dose. A detailed analysis of the effect on the figures of merit due to this change, for example signal‐to‐noise ratio per effective dose, SNR2/E, has not been performed here. The absolute values of SNR2/E may change, but the main conclusions on for example the appropriate tube voltage for chest PA radiography is unlikely to be affected by the change of weighting factors, particularly since the weighting factors for the lungs are the same in ICRP 60 as in ICRP 103.
3.3. Calculation of images from the high‐resolution phantom
The scatter projection, SNRp and other quantities calculated with the MC method are rescaled (i.e. from 40 x 40 points) to fit the number of pixels in the primary image. In paper V this number is 1760 x 1760, and in paper VI the number of pixels is 2688 x 2688. The rescaling is performed using a bilinear interpolation function in MATLAB. The interpolated scatter projections are added to the primary image to give the estimate of the mean energy imparted t p s per unit area of the detector for the i:th pixel, , , += εεε ,iAiAiA . Noise is subsequently added to the image. In paper V, white gaussian noise is added with the standard deviation
20 Monte Carlo model
p ε ,iA σ i = . SNR ip,
The white noise is generated by adding sampled random numbers for each pixel i from the appropriate distribution to the calculated image. In paper VI, correlated noise is added with a method similar to the one used in Båth et al (2005c). In order to add correlated noise, knowledge of the noise power spectrum (NPS) for the clinical system is needed. The NPS is then normalized to correspond to unit variance. A random phase is added to the square root of the normalized NPS with the constraint that the random phase image φ vu ),( should have the symmetry φ = −φ − −vuvu ),(),( . By taking an inverse Fourier transform of this spectrum a real and correlated noise image δεˆ is created. The vector δεˆ is a multivariate random variable with mean corresponding to a null vector and covariance matrix corresponding to the measured NPS. The noise fluctuation for each pixel is rescaled with the relation δε , σ ⋅= δεˆ ,iAiiA . It is assumed that the NPS was invariant under a logarithmic transformation. The total energy imparted to the detector per unit area including noise fluctuations t t becomes , ,iAiA += δεεε ,iA . The pixel value in the i:th pixel is calculated by taking t a logarithmic transformation of ε ,iA using the relation
t i = ε ,iA )ln( + cbag (3.14) where the parameters a, b and c are calculated with non‐linear regression to make the best fit to the real phantom images. The method to add primary, scattered and noise images is illustrated in figure 3.5.
+ + =
Figure 3.5. The method for calculating images illustrated in a cutout in the retrocardial region (see further figure 4.1.). From the left: primary projection, scatter projection, noise image and total image (to the right).
21 Monte Carlo model
3.4. Uncertainties 3.4.1. Stochastic uncertainties The choice of the number of photon histories used in the simulation is a trade off between computer time and statistical precision. If the statistical precision of the simulation is doubled, the computer time is increased by a factor of 4. For instance, the computer time for a typical simulation (for calculating the scatter contribution to a synthetic image) on the computer Alpha (AMD Opteron processor 250, 2.4 GHz; 6.26 GB RAM) in 40 x 40 points of interest, at the tube voltage 141 kV, with a precision of 1% (one standard deviation) takes approximately 17 hours. The statistical uncertainty has to be kept low when we are calculating images, since if the statistical uncertainty is too high, the scatter projection often contains artifacts when it is interpolated to a higher resolution.
3.4.2. Systematic uncertainties There are several sources of uncertainty that affect the results. These include uncertainties in the cross sections, but also uncertainties in estimation of the different parameters in the input files. In an internal report, Ullman et al (2003) studied the effects of uncertainties in x‐ray spectrum half value layer (HVL), field size, grid lamella thickness and detector thickness. The conclusion from this study is that the systematic uncertainty due to these factors in the estimated εs/εp behind the grid is approximately 11%. Later, analysis of variance (ANOVA) and regression analysis was used to analyse similar uncertainties and the systematic uncertainty in εs/εp behind the grid was estimated to be approximately 9%. However, these relatively large uncertainties only apply in those cases where we attempt to mimic a real x‐ray imaging system and compare measured quantities from that system with our calculated quantities. In the cases where we only use simulations to study relative differences between alternative acquisition schemes for an imaging system, the stochastic uncertainty is more relevant.
22 Monte Carlo model
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
Yes Terminate by Russian roulette?
Select new path length (Coleman’s algorithm)
Is the next Yes interaction within the phantom?
No Was this the last history?
Calculate scoring quantities
Figure 3.6. Flow chart describing the most important steps in the Monte Carlo program
23 Monte Carlo model
24 Assessment of image quality
4. ASSESSMENT OF IMAGE QUALITY
4.1. Introduction Image quality assessment means quantifying the usefulness of an image to solve a specific diagnostic task. It is preferred if this image quality assessment is objective. There are, according to Barrett (1990), four criteria that are essential for objective assessment of image quality.
A. The task Image quality can only be described in relation to a well‐defined task. This often means detection of an object in a structured or homogeneous background. A summary of different tasks to be solved in chest radiography is given in ICRU 70 (ICRU 2003). Among those, the search for malignant nodules at different positions in the lung is a common case treated in the literature (Samei et al 1999). In mammography it is common to search for calcifications or masses (Burgess et al 2001). Several different types of tasks are discussed in the literature (Barrett and Myers 2004).
B. Image and object properties We need to understand the physical and statistical properties of the imaging system as well as the object being imaged. For example, the radiologist has an internal model of both the human anatomy as well as a large “data bank” of common pathologies in order be able to distinguish a malignant nodule from normal anatomy. The radiologist also needs to understand some of the physics behind the imaging technology in order to recognize some of the artefacts that may be present in the image.
C. Observer An observer that can perform the task is needed. This can be a human or a model observer. It is the human observer (radiologist) that is the final decision maker. Therefore, measures of image quality should always take the human observer into account. Yet, clinical trials involving human observers are costly and time demanding. Model observers may then be used to give insights into how image quality depends on the physical and technical image acquisition parameters.
25 Assessment of image quality
D. Figure of merit The figure of merit (FOM) is a number that tells us how well the observer performs the task. The FOM depends on the detection task; a commonly used FOM is the signal to noise ratio (SNR) or AUC, the area under the receiver operating characteristic curve (ROC). In some cases, image quality is described by physical properties derived from the image rather than by the performance of an observer on a specific task, for example, the modulation transfer function (MTF) or the noise power spectrum (NPS). We will refer to this as physical image quality.
4.2. Image quality assessment as developed in this work In this work, different tasks and figures of merit have been used, changing along with an improved modeling of the imaging system including the patient and improved model observers. In some cases, figures of merit based on pure physical measures of image quality were used and correlated to measures of the performance of human observers in clinical trials. A summary of the development is given below.
4.2.1. The task Two main types of tasks are used in this work. The first task is to search for a known signal (e.g. a nodule) in a known background, referred to as the SKE/BKE (signal known exactly/background known exactly) task. The second task is to search for a known signal (e.g. a nodule) in a varying background, referred to as the SKE/BV (signal known exactly/background varying) task.
The SKE/BKE task was addressed in paper I, which was devoted to the optimization of tube voltage and filtration in iodine subtraction mammography. The task was to detect a blood vessel filled with iodine contrast of thickness 6 mg cm‐2 against a homogeneous background.
In paper IV the task was to compare two images from an x‐ray chest phantom and see in which image the structures corresponding to the image criteria were most clearly visible (the VGA study). In some sense, the background can be considered as known in this study since the same anthropomorphic phantom (the Alderson chest phantom) is used for all comparisons. Thus, the observer may be able to remember the background. In addition, the phantom used in this study does not contain as fine and complex structural details as are present in real phantoms (see further figure 5.4).
26 Assessment of image quality
The SKE/BV task was addressed in papers III and VI were the task was detection of nodules at various positions in the lungs. In paper III, the size and shape of the nodules corresponded to those used in the trial by Håkansson et al (2005b). The anatomical structures vary at different positions in a chest image and differ from patient to patient. When the background is unknown for the observer it hampers the detection of subtle details (Samei et al 2000).
The two papers II and V were dedicated to describe the physical characteristics of the simulated image rather than to solve a specific detection task. Paper II was dedicated to calculate the variation of the scatter‐to‐primary ratio εs/εp in the image plane in a chest examination as well the variation in the signal‐to‐noise ratio per pixel (SNRp). These quantities influence contrast and noise and thus detectability of lesions varies with position in the imaged anatomy.
4.2.2. Model of the imaging system and patient Knowledge of the imaging system is in this work translated into a model of the system including the patient. This model is used together with Monte Carlo techniques to calculate dosimetric and image quality parameters, needed for optimising the imaging system. The realism of the system, in particular the model of the patient, has been increased during the work. Details of the model and Monte Carlo calculations are given in Chapter 3. The development of the model of the patient can be summarised as follows.
In paper I the breast was modeled using a slab phantom with homogeneous materials and the detail (blood vessel) was modeled as a layer of iodine, see Figure 3.2.
To allow for more realistic calculations of how the scatter‐to‐primary ratios varies at various positions in the anatomy behind large anatomical structures like the spine, heart and lungs, a low‐resolution anthropomorphic phantom, the Zubal phantom, was used in papers II‐IV. In paper III the anatomy was divided into several regions corresponding to different anatomical properties, see figure 4.1. This approach was also used in paper VI.
In order to simulate images with realistic anatomical background variations, (see section 3.3) a high‐resolution anthropomorphic phantom was created from CT images of an anthropomorphic (Alderson) phantom in paper V. This is an important step in the model development, since it has been shown in
27 Assessment of image quality clinical trials that the fine details (such as small and medium sized vessels) of the projected anatomical background strongly influence detectability (Kundel et al 1985, Samei et al 1999, Håkansson et al 2005b) and thus act as noise besides system (quantum) noise. In Paper VI a new and still more realistic high‐ resolution anthropomorphic phantom (Kyoto Kagaku) was implemented in the model. A mathematical model of a lesion, referred to as a designer nodule (Burgess et al 1997) was inserted in the projection radiographs for studies of detectability using model observers. Figure 4.2 shows cut outs of a chest image from the hilar region without lesion (4.2a) and with an added designer nodule (4.2b). Figures 4.2c and 4.2d show corresponding images against a background of quantum/system noise only. The figures clearly demonstrate the large difference in difficulty between detecting a nodule in an image containing anatomical structures and in a pure quantum noise image, respectively.
Figure 4.1. The six anatomical regions of the chest PA image used in papers III and VI: APR: Apical pulmonary region, LAT: Lateral pulmonary region, RET: Retrocardial region, LME: Lower mediastinal region, HIL: Hilar region and UME: Upper mediastinal region.
28 Assessment of image quality
a b
c d
Figure 4.2. Cut outs of a simulated chest image from the hilar region without lesion (4.2a) and with an added designer nodule (4.2b). Figures 4.2c and 4.2d show corresponding images against a background of quantum noise only. The contrast (C=0.10) and size (D=10 mm) of the nodule are the same in images 4.2b and 4.2d. The amount of quantum noise (corresponding to a collision air kerma Kc,air=0.3 μGy central in the image) is the same in all four images. The dose level is kept unrealistically low for illustration purposes.
4.2.3. Observers Two model observers have been used, the ideal observer and the Laguerre‐
Gauss Hotelling observer. The method for calculating the ideal observer SNRI was developed in the previous work by Sandborg et al (1994b) using an expression from ICRU 1996. This observer is one who can make use of all the information in the image and is often used to describe the ultimate
29 Assessment of image quality performance of an imaging system. Also, this observer is able to perform non‐ linear operations on the data. It works most easily under the condition of SKE/BKE when the detection only is disturbed by system noise. The Laguerre‐ Gauss Hotelling observer was applied in Paper VI utilizing the method to simulate high‐resolution images developed in paper V. This observer can also be used for the SKE/BV task. The Hotelling observer is limited to perform linear operations and is likely to more faithfully reflect the capabilities of human observers (ICRU 1996). It has been described in detail for the problem of image assessment in medical imaging by, e.g., in Barrett and Myers (2004).
Results of human observers were used in paper IV. To design and perform human observer studies is time consuming and requires close collaboration with radiologists. The main objective of this work was to create a complete model of the imaging system including automatic performance evaluation, which allows for rapid evaluation of image quality, so that a large number of acquisition parameters can be tested. This is an important step towards the use of our model for system optimisation. An inspiration was a recent study by Son et al (2006), where they used simulated images and a model observer for image quality assessment. The results of our model have repeatedly been tested against results of human observer studies performed by our partners in our network collaboration (Sweden Associated Imaging Laboratories, SAIL; Göteborg, Linköping and Malmö). Through this collaboration, we have had access to detailed information about the imaging systems used in their experiments. Our efforts have been concentrated to finding model observers that are capable of simulating the performance of human observers.
4.2.4. Figures of merit
4.2.4.1 Human observers Clinical trials with human observers are essential in the assessment of image quality. It is therefore of great importance to compare the results of our model to what is relevant from the clinical point of view. As was pointed out above, such comparisons have been performed in close collaboration with our partners from Malmö and Göteborg. Two main types of human observer studies were used in their clinical trials. The two types are: receiver operating characteristic (ROC) and visual grading analysis (VGA) studies.
30 Assessment of image quality
A ROC studies Receiver operating characteristics (ROC) (Metz 1986, Metz 2000, ICRU 1996) studies with human observers form the gold standard for assessment of image quality.
When a human observer performs a specific task, for instance, decides whether a signal is present or not present, there are four possible outcomes:
(1) False Positive (FP): signal is absent – observer decides signal present (2) True Positive (TP): signal is present – observer decides signal present (3) False Negative (FN): signal is present – observer decides signal absent (4) True Negative (TN): signal is absent – observer decides signal absent
The decision maker also strives to minimize the cost. A false positive decision may mean that the patient has to undergo extra examinations. A false negative decision may mean that, for instance, a tumour is missed and the patient has less probability for recovery if the tumour is discovered later. The strategy used by the observer therefore depends on which kind of error (FP of FN) that is most costly. The relation between the false positive fraction and the true positive fraction is illustrated in the receiver operating characteristic (ROC) curve, see figure 4.3. Each point on this curve corresponds to a threshold level (observer strategy). The area under the ROC curve, AUC (also commonly denoted Az in the literature), is a common figure of merit used in discrimination tasks and can be translated to a value for the signal‐to‐noise ratio SNR (Barrett and Myers 2004) using
AUCSNR = erf −1 AUC − )12(2)( (4.1) where erf−1 is the inverse error function. The quantity SNR(AUC) is often referred to as the detectability index dA. A short description of the methodology is given below.
A recent review of ROC and related methods is given by Krupinsky and Jiang (2008). To reach sufficient statistical power many images and several observers are needed. Another problem in ROC studies is that the true answer has to be known. This can be accomplished by using so called hybrid images where lesions are simulated and paste into real images (Metz 2000).
31 Assessment of image quality
1
0.9
0.8
0.7
0.6
0.5
0.4
True positive fraction True 0.3
0.2
0.1
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 False positive fraction
Figure 4.3. Illustration of an ROC curve. The area under the curve (AUC) is used as a figure of merit and can be related to the SNR. In this figure: AUC=0.8 (SNR=1.19). The dotted line corresponds to AUC=0.5 (SNR=0), which means that the observer is guessing.
B VGA studies In a visual grading analysis (VGA) study, the observer is presented to two images. One image is a reference image and used in every comparison. The observer has to decide if the quality of the image compared to the reference image is similar, better or worse.
In paper IV, results from a VGA study by Tingberg and Sjöström (2005) were used to search for correlations between physical image quality parameters and clinical image quality. In the VGA study, slightly modified CEC (Carmichael et al 1996) image criteria were used. The criteria were based on structures in the normal anatomy that are described in table 4.1 for chest PA and Pelvis AP examinations. The radiologists were asked to give a graded response of the fulfilment (=visibility of the structures) of the criteria compared to the fulfilment of the criteria in the reference image. The grading was given in quantitative terms as: clearly inferior (VGA=‐2), inferior (‐1), equal to (0), superior (+1) or clearly superior (+2). The score was averaged over all criteria and all radiologists to form an average score, VGAS.
32 Assessment of image quality
Table 4.1. Structures used in the VGA evaluation (Tingberg and Sjöström 2005) Chest PA Pelvis AP 1 Vessels seen 3 cm from the pleural margin Sacrum (spongiosa) 2 Thoratic vertebra behind the heart Sacral foramina 3 Retrocardiac vessels Pubic and ishial rami 4 Pleural margin Sacroiliac joints 5 Vessels seen an face in the central area Femoral bilateral 6 Hilar region ‐
4.2.4.2 The ideal observer For the Ideal observer used in this work, the background and the signal are assumed to be known exactly, corresponding to a SKE/BKE task. From the
SNRMC (see section 3.2.4.2), the ideal observer signal‐to‐noise ratio, SNRI for a given nodule is calculated from equation 4.2 as
2 2 A 2 SNR I SNR M ⋅⋅= rDF (4.2) a p where A is the projected area of the nodule in the image plane, ap is the pixel 2 area and r DF is the signal to noise ratio degradation factor caused by the 2 system unsharpness. The quantity r DF includes effects on SNR of the imaging system unsharpness (modulation transfer function, MTF) and correlated noise (noise power spectrum (NPS)) as determined from experiments with the actual detector type and additional detector noise. It is derived separately for each nodule at its actual position in the anatomy, and depends on the nodule projected area and the air kerma at the image detector. Geometrical (focal spot‐ and magnification) unsharpness and motion unsharpness are taken into account in addition to detector unsharpness. The latter is expressed in terms of the pre‐sampled MTF (Sandborg et al 2003).
A Figure of merit corresponding to the VGAS in a VGA study In paper IV we calculated a figure of merit that is intended to correspond to the VGAS obtained in the VGA study (Tingberg and Sjöström 2005). For each contrasting detail, denoted with index q, the SNRI,q relative to its value at the reference tube voltage, SNRI,q(Uref), was computed (SNRI,q(U)/ SNRI,q(Uref)). These ratios were then averaged for all the structures and a figure of merit (FOM) was computed as given in equation 4.3. Here, unity was subtracted from the average value in order to obtain the value zero for the reference tube
33 Assessment of image quality voltage and allow negative values when the image quality is inferior to that of the reference system (corresponding to the ordinate scale of the VGAS)
1 ,qI USNR )( UFOM )( = ∑ − 1 , (4.3) N q , ()USNR refqI where N is the number of details.
4.2.4.3 Figures of merit using physical image quality measures
A Nodule to bone contrast In Paper III we attempted to perform optimization using the Zubal phantom.
Since the SNRI as calculated in this work does not take into account anatomical details and these are known to influence detectability, alternative figures of merit were also used. The ribs obscure large parts of the lungs but are also needed for the radiologist to orient himself in the image (Sven‐Göran Fransson, personal communication). The contrast of the nodule relative to the contrast of the ribs may indicate the disturbing influence of the ribs. We have therefore defined a ‘nodule‐to‐bone’ contrast‐ratio by computing the quotient
C/CB. The C/CB is the nodule’s contrast divided by the contrast of a bone detail of a thickness corresponding to a rib or transverse processes at the same position in the image. The use of the nodule‐to‐bone contrast as a complementary figure of merit was inspired from the work by Dobbins et al (2003) and Samei et al (2005).
B Relative contrast The radiologist often wants to adjust the contrast window. This choice of contrast window affects the contrast of other objects in the image. We have defined a relative contrast, Crel, as the signal difference in the image detector divided by the dynamic range of the whole image of the chest
ε − ε pp 21 C rel = , (4.4) − εε %5%95
where εp1 is the energy imparted to the detector per unit area in the presence of the nodule, εp2 is the energy imparted in the absence of the nodule, and th ε95%−ε5% is the dynamic range in the chest image, here defined by the 95 percentile minus the 5th percentile of the energies imparted to the image detector in the whole chest image. The relative contrast is thus a measure of the nodule’s contrast as a percentage of the dynamic range in the image. It
34 Assessment of image quality corresponds to the radiologist first impression of the image before adjusting the contrast window.
4.2.4.4 The Hotelling observer Ultimately, the measures of image quality should correspond to how an observer (radiologist) performs a specific task with the aid of the image. In order to complete our model, we need an observer that can replace the human observer and perform image quality assessment automatically using our synthetic images. We therefore exploited (in paper VI), a model observer, which is known to mimic human observers more closely than the ideal observer. Such model observers are based on statistical decision theory. One of the pioneers in using statistical decision theory for diagnostic radiology was Wagner (Wagner et al 1979). A good thorough introduction to statistical decision theory and model observers is given by Barrett and Myers (2004).
To describe the image, it is useful to represent the image as a vector
+= nHfg (4.5) where H is an operator representing the imaging system, f a representation of the object and n represents the noise.
If H1 denotes the hypothesis that the signal is present and H0 denotes the hypothesis that the signal is absent, the Hotelling observer uses a test statistic based on the likelihood ratio
g Hp 1 )|( g)( =Λ (4.6) g Hp 0 )|(
to compare to a threshold Λ c in order to decide between H1 and H0. The notation bap )|( means the conditional probability of a given b (Jaynes 2003). Under the assumption that g is described by a multivariate Gaussian distribution, the performance of the Hotelling observer is given by (Barrett and Myers 2004)
SNR 2 t −1 ΔΔ= gKg Hot g (4.7) where Δg is the mean difference of the image vector with signal absent and signal present and Kg is the covariance matrix, which can take into account
35 Assessment of image quality both quantum noise and variations in anatomy. The superscript t means the transpose of the vector. In the case where the signal s is known exactly (SKE) this simplifies to
SNR 2 = t −1sKs Hot g (4.8)
The covariance matrix can be estimated from a set of images g. In the case where g is real, the covariance matrix is defined by
−−= ggggK ))(( t (4.9) where g is the mean image vector. If g is M dimensional, the resulting covariance matrix will be M x M dimensional. The number of images g used to estimate the covariance matrix must be larger than the number of pixels; otherwise the covariance matrix is singular and non‐invertible. Even for a relatively small region of interest of 100 x 100 pixels this would make the covariance matrix virtually impossible to calculate since we would need at least 104 images to perform the estimation. For a more accurate estimation of the covariance matrix it would require an even larger set of images. Also, a matrix of the size 104 x 104 is difficult to manage in the computer memory.
A Channelized Laguerre‐Gauss Hotelling observer One solution to the problem mentioned above is to use channels to reduce the size of the matrix (Myers and Barrett 1987).
ν = T gU (4.10)
where U is a M x N matrix containing N channel profiles up as column vectors. The vector v can be interpreted as the image seen through the channels. A diagram of the channelized observer is shown in figure 4.4. The signal to noise ratio for the channelized Hotelling observer is
SNR 2 ν t K −1 ΔΔ= ν ,chHot ch (4.11)
where Kch is the N x N covariance matrix of the channelized images. In this case the size of the covariance reduces significantly since often only 6‐50 channels are needed, depending on the type of task. Because of this dimension reduction, the channelized covariance matrix can be estimated from a relatively small number of images. Another advantage of the channelized
36 Assessment of image quality approach is that the channelized observer better models human performance (Myers and Barrett 1987). To further increase the realism in simulating the human observer, internal noise corresponding to neural noise and fluctuations in observer decision criterion can be added (Burgess et al 1981, Zhang et al 2007).
ν1 u1
Image ν2 u2 vector Test statistic g ν3 Observer u3 λ(ν)
νn un
Figure 4.4. Diagram illustrating the channelized observer. The channelized observer does not interpret the image vector g directly, but though a series (u1, u2, …, un) of channels.
In paper VI we used Laguerre‐Gauss channels. Laguerre‐Gauss function is a product between a Laguerre polynomial and a Gauss function. The Laguerre‐ Gauss channels are given by
2 − r 2 2ππ r 2 arU ),( = L ()exp( ) (4.12) n a a 2 n a 2 where a is a scaling factor that can be chosen iteratively to maximise the SNR, r is the radial distance and Ln is the n:th Laguerre polynomial. The Laguerre‐ Gauss model assumes rotational symmetry. The LG channels of order 0, 3, 6 and 9 are shown in figure 4.5. Other authors have used the LG observer in diagnostic radiography. Chawla et al (2007) studied observer performance in mammography for normal and reduced doses. Pineda et al (2006) studied tomosynthesis and compared with planar radiography. Son et al used the Hotelling and LG Hotelling observer to search for calcifications in Monte Carlo simulated images. Gabor channels (Chawla et al 2007) are sometimes used. The Gabor channels are more accurate in modelling the human observer since they do not assume rotational symmetry.
37 Assessment of image quality
a b c d
Figure 4.5. Laguerre‐Gauss channels in different orders: a) 0:th, b) 3:rd, c) 6:th and d) 9:th order LG channel.
B Laguerre‐Gauss Hotelling observer using a template Instead of calculating SNR directly, it is also possible to simulate the observer by using a template. In earlier versions of paper VI this method was used as a compliment to the direct calculation. The direct calculation is used for the reason that it is faster. The channelized Hotelling observer uses the template
−1 Hot = g sKw (4.13) and compares is to the (channelized) image vector with the scalar product
t λ = w Hot ν (4.14) in order to calculate the decision variable λ. The model observer compares the decision variable to a threshold λt in order to choose between the hypothesis
H1 (lesion absent) or H2 (lesion present). For instance, if λ ≥ λt the model observer may choose that the lesion is present. In this way, the model observer can be used for ROC studies similar to those performed by human observers. Two ROC curves for the channelized LG Hotelling observer are shown in figure 4.6.
38 Assessment of image quality
a
1
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0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 False positive fraction
b
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True positive fractionTrue 0.3
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0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 False positive fraction
Figure 4.6. ROC curves calculated for the Laguerre‐Gauss Hotelling observer. Figure 4.6a corresponds to figure 4.2b in the Hilar region with a lesion of the same contrast (C=0.10) and diameter (D=10 mm). The AUC is approximately 0.99 (SNR=3.2). In figure 4.6b the situation is similar but with reduced contrast (C=0.05). The AUC is approximately 0.87 (SNR=1.6). The dotted line corresponds to the case when there is no signal.
39 Assessment of image quality
40 Results and discussion
5. RESULTS AND DISCUSSION
5.1. Ideal observer with a simplified patient‐model In paper I we used a simple model of the breast for optimisation of iodine subtraction mammography. In subtraction imaging, the overlaying anatomical structures are suppressed. The ideal observer signal‐to‐noise ratio, SNRI, is here used in a situation where the detection or visibility of a lesion is only limited by the quantum noise in the image. This in turn is determined by the air kerma at the image detector and efficiency by which the image detector absorbed the x‐ray quanta and converts it to an image signal.
The SNRI was calculated for a special case when iodine contrast media were injected in the patients arm and images were acquired at set intervals before and after injection in order to follow the leakage of contrast medium in the vicinity of the breast tumor. During the whole image acquisition, the breast remains compressed and images after injection of the contrast medium are subtracted from the image prior to injection. In mammography such contrast media may be valuable to distinguish between benign and malignant tumors and for demonstrating tumors that might not otherwise be seen in dense tissue and hence in providing a clearer picture of the extent of disease.
2 Figure 5.1 shows the SNRI /AGD as a function of tube voltage for three different anode‐filter combinations. The AGD is the average glandular dose typically used as the radiation risk measure in mammography (Zoetelief et al 1996). For both the W/Cu and Rh/Cu spectra and at all breast thicknesses, a maximum of the SNR2/AGD was found at approximately 45 kV and a minimum at 33 kV. The dominating K‐edge of iodine is at 33.17 keV (see figure 5.2) and hence photons with energies just above this energy are absorbed to a high degree and therefore provide a higher object contrast compared to the background in the vicinity of the contrast‐filled vessel. At 45 kV and using copper filtration, a significant portion of the x‐ray spectrum has energies in the optimal range just above the iodine K‐edge. Using 45 kV for the Rh/Cu spectrum yields three to four times lower dose for 4 cm thick breasts compared to using the Rh/Rh combination for producing images with equal SNR for the iodine contrast medium. The SNR2/AGD is approximately 1.8 times higher with 33.2 keV photons compared to its maximum value using the
41 Results and discussion poly‐energetic spectra from the W/0.3mmCu combination at 45 kV. The results agree with Skarpathiotakis et al (2002).
350
300
250 ) 1 −
200
/AGD (mGy 150 2 SNR 100
50
0 20 25 30 35 40 45 50 55 Tube voltage (kV)
2 Figure 5.1. SNRI /AGD as a function of tube voltage for a 4 cm thick breast and 50% glandularity. Δ=Rh/25μmRh, O=Rh/0.3mmCu, =W/0.3mmCu.
5 10
4 10
3 10 Cross-section (barns/atom)
2 10 20 25 30 35 40 45 50 55 Photon energy (keV)
Figure 5.2. Atomic cross‐section of iodine as a function of photon energy.
42 Results and discussion
5.2. Low resolution voxel phantom In order to compare the result of the model with clinical image quality, it may be useful to calculate distributions of physical image quality related quantities over the whole image and to study how these vary with position, patient size and imaging system configuration. The aim of paper II was to calculate distributions of SNR per pixel (SNRp) and the scatter to primary ratio, εs/εp in terms of energy imparted per unit area to the image detector (see chapter 3 for details). Figure 5.3 shows scatter‐to‐primary ratios (εp/εs) and signal to noise ratios per pixel (SNRp) using the low‐resolution anthropomorphic chest phantom. The figures show that the εp/εs varies significantly in the chest PA image plane and is typically above 2 in the mediastinum and about 0.5 in the lungs. A comparison to measured εs/εp in patient images (Jordan et al 1993) with calculated values in different regions shows that the mean values from the calculations agree reasonably well in the heart region (behind the whole heart including the part covered by the spine), with average εs/εp=2.0 (our work) vs. 1.9 (Jordan); in the lung region (entire lung) with average εs/εp=0.6 (our work) vs. 0.4 (Jordan).
As scattered photons add to the noise term in the SNRp expression (see chapter 3), the SNRp is significantly reduced in the mediastinum compared to in the lungs. Therefore, if nodule detection were limited by quantum noise, the visibility of such nodules would be higher in the lungs where the scatter to primary ratio is lower than in the mediastinum.
43 Results and discussion
Figure 5.3. Distributions of εp/εs (a) and SNRp (b) for a 24 cm thick patient. Figures
(c) and (d) show values of εp/εs and the SNRp along the vertical lines in the upper figures.
5.3. High resolution voxel phantom The images produced based on the low‐resolution voxel‐phantom VOXMAN are useful for determining maps of physical measures of image quality such as SNRp. Yet, they are of limited use for clinical image quality evaluation by human or model observers due to its relatively coarse spatial resolution. Anthropomorphic chest phantoms were therefore imaged in a CT scanner and the reconstructed volume of CT‐numbers used to create high‐resolution voxel phantoms (Malusek 2008). In paper V, the older Alderson phantom was modelled and in paper VI, a more recently developed and more clinically realistic (Kyoto Kagaku) phantom, was utilised.
Real phantom x‐ray images of those two phantoms are shown to the left in figures 5.4 and 5.5 and simulated images calculated with the Monte Carlo
44 Results and discussion model are shown to the right. The parameters in the Monte Carlo simulations were adjusted to fit the imaging conditions used in the real acquisition.
Figure 5.4. A real phantom image of the Alderson chest phantom (a) and a calculated image including scatter and statistical noise (b). An anti‐scatter grid was used at the tube voltage 141 kV.
Figure 5.5. A real phantom image of the Kyoto Kagaku chest phantom (a) and a calculated image including scatter and statistical noise (b). An anti‐scatter grid and 141 kV were used.
45 Results and discussion
Figure 5.6. Calculated primary projection (a) and scatter projection (b) of the Alderson phantom. The intensity values are given in logarithmic scale in μJ/m2. The average air kerma at the image detector was 5 μGy corresponding to a sensitivity class of approximately 200.
The images of the scattered photons were computed in a coarse grid of points 40 x 40 whereas the image of the primary photons was computed in the same number of pixels as the original real image (Alderson: 1760 x 1760 Kyoto Kagaku 2688 x 2688). The primary projection and the scatter projection were combined to create a total image. Noise was added to the images. In paper V gaussian noise was added with the aid of the calculated SNRp values. In paper VI we added correlated noise. However, at the point of writing this thesis, the correct noise power spectrum (NPS) for the system used in the clinical system used for acquiring the real phantom images was not available. Instead, a provisory NPS measured from a Fuji FCR 9501 CR Thorax system in Göteborg was used. The simulated images were used in paper VI to assess image quality using the Laguerre‐Gauss Hotelling observer SNRhot,LG (see section 5.6). We argue that the increased realism provided by the Kyoto Kagaku phantom is useful for a more clinically realistic assessment of image quality.
5.4. Ideal observer with simple anatomical background In paper III the optimal tube voltage in detecting lung lesions with diameter 10 mm but of varying thickness according to Håkansson et al (2005a) was investigated in terms of the ideal observer SNRI in six anatomical regions of the chest PA image. In addition to this figure‐of‐merit, the contrast of the
46 Results and discussion lesion in relation to structures in the normal anatomy such as ribs and transverse processes, C/CB was derived, since these structures may interfere with the radiologist’s detection of the lesion. The optimal tube voltage and scatter rejection technique were sought.
2 Figure 5.7 shows the figure‐of‐merit SNRI /E, or the dose‐to‐information conversion efficiency (Tapiovaara 1993) for a 25 mm thick lesion in the hilar region and a 15 mm thick lesion in the lower mediastinal region. In both these 2 regions a low tube voltage results in a higher SNRI /E indicating superior 2 performance. In the lower mediastinal region, a higher SNRI /E is found when larger grid ratios or longer air gaps are used. In the hilar region, with significantly lower scatter‐to‐primary ratio compared to the lower mediastinal 2 region (see paper II), the SNRI /E is independent of grid ratio or air gap length. 2 The air gap results in significantly higher SNRI /E than with the grid, suggesting that the air gap is the superior scatter rejection technique for digital chest PA radiography. The absorption of primary radiation in the grid reduces the image quality and increases the bucky factor; this is avoided using the air gap technique.
2 Figure 5.7. SNRI /E as a function of tube voltage and scatter rejection technique; grid ratio in (a) and (c) and air gap length (b) and (d), for a 20 cm thick patient. Two anatomical regions were considered: the hilar region (a, b) and the lower mediastinal region (c, d).
47 Results and discussion
Figure 5.8 shows the ratio between the contrast of the lesion divided by the 2 contrast of a bone structure, C/CB in the same region. Contrary to the SNRI /E, the C/CB increases with increasing tube voltage, indicating relatively superior contrast of the lesion in comparison to the projected anatomical background structure such as rib or transverse process, at high tube voltages. Hence we have two conflicting arguments for selecting the appropriate tube voltage.
In a similar study, Dobbins et al (2003) made both experiments and computer spectrum modelling to search for the optimum x‐ray spectrum for chest radiography for a CsI‐aSi flat panel image detector. They studied the SNR 2 squared per exposure, SNR /X, and a contrast ratio similar to our, C/CB, as a function of tube voltage and added filtration. The experimental results from their study are essentially in agreement with our results. SNR2/X decreases and C/CB increases with increasing tube voltage, and the tube voltage 120 kV was considered to be optimal. We use SNR2/E instead of SNR2/X since the effective dose is a better measure of radiation risk than exposure or incident air collision kerma. However, conversion factors published by Hart et al (1994) can be used to convert SNR2/X to SNR2/E. Such data shows that the optimal tube voltage is reduced when the effective dose is used as a measure of radiation risk instead of incident air collision kerma.
We conclude that the choice of tube voltage depends on whether SNRI of the lesion or the interfering projected anatomy (i.e. ribs) is more important for lesion detection. The simple model of the patient used here is incapable of making this selection and therefore alternative model observers and more complex anatomical background are needed for a proper treatment of this task.
48 Results and discussion
Figure 5.8. C/CB as a function of tube voltage and scatter rejection technique; grid ratio in (a) and (c) and air gap length (b) and (d), for a 20 cm thick patient. Two anatomical regions were considered: the hilar region (a, b) and the lower mediastinal region (c, d).
5.5. Correlation to human observers The aim of paper IV was to study the dependence of image quality in digital chest and pelvis radiography on tube voltage, and to explore correlations between clinical and physical measures of image quality. The effect on image quality of tube voltage was assessed using two methods. The first method relies on radiologists’ observations of specified image criteria of images of anthropomorphic phantoms (Visual grading analysis, VGA), and the second method was based on computer modelling of the imaging system using an anthropomorphic voxel phantom.
The tube voltage is one of the independent variables that can be altered prior to exposure of each patient and view. In the study, the effective dose to the patient phantom was kept constant independent of tube voltage. The visual grading study was performed by Tingberg and Sjöström (2005) but our group performed the Monte Carlo simulation (see chapter 4).
49 Results and discussion
Figure 5.9 and 5.10 show the clinical and physical image quality measures as function of tube voltage for the same effective dose to the chest phantom. Both measures indicate that superior image quality is achieved at low tube voltages compared to the reference system tube voltage 125 kV. Similar results were obtained for the pelvis examination.
Chest PA
2 1.5 1 0.5 0
VGAS -0.5 -1 -1.5 -2 60 70 80 90 100 110 120 130 140 150 Tube voltage (kV)
Figure 5.9. The visual grading analysis score (VGAS) for the chest images as function of the tube voltage. The VGAS values represent averages over all imaged structures and radiologists. The uncertainty bars show the reader variability (one standard error). The solid line (r2=0.90) indicates that there is a linear relationship between VGAS and tube voltage (data redrawn from Tingberg and Sjöström (2005)).
Chest PA
0.5 0.4 0.3 0.2 0.1 0 FOM -0.1 -0.2 -0.3 -0.4 -0.5 60 70 80 90 100 110 120 130 140 150 Tube Voltage (kV)
Figure 5.10. The average relative change in SNR (FOM) in chest PA examination as a function of tube voltage.
50 Results and discussion
Chest PA
2
1
0 VGAS
-1
-2 -0.5 -0.3 -0.1 0.1 0.3 0.5 FOM
Figure 5.11. The correlation between VGAS and SNR (FOM) for a simulated chest PA examination. The error bars correspond to one standard error and are due to reader variability in the results of the observer studies (see Fig. 5.9). The r2 of the fitted line (r2=0.91) indicates that the VGAS and FOM are linearly correlated. Lower tube voltages have positive VGAS and FOM and high tube voltages negative values.
Figure 5.11 shows the relation between clinical image quality measured using visual grading analysis score (VGAS) and the physical measure of image quality, quantified by the relative change in SNR and FOM. There is a positive linear relationship between the two measures of image quality, indicating that the SNR is related to the radiologists’ grading of the image criteria. Hence, results by Tingberg and Sjöström (2005) and results from this study indicate that, with modern digital imaging system, it would be favourable to use lower tube voltages than traditionally used with screen‐film radiography.
Arguments for and against this proposal are listed in paper IV and in Tingberg and Sjöström (2005). At low photon energies, the image detector’s DQE (detective quantum efficiency) is higher and the contribution to effective dose per incident air collision kerma is lower. However, at low tube voltages, the tube charges typically increase compared to at higher voltages to maintain a constant effective dose. Hence the risk for increased motion and focal spot unsharpness increases due to prolonged exposure time and focus size blooming, respectively. In examinations where iodine contrast media are employed, the use of lower tube voltages than used today (approximately 70 kV) seems to be an advantage (Tapiovaara et al 1999, Wiltz et al 2005).
51 Results and discussion
The statistical analysis of a relative VGA study, such as in Tingberg and Sjöström (2005) and in paper IV is questionable since the scale steps used (e.g. ‐2 to +2) are an ordinal scale and the numerical representations do not represent numbers on an interval scale and one cannot assume equal steps between the scale steps. This problem is solved with a closely related method, visual grading characteristics (VGC) (Båth and Månsson 2007). In this type of study, the observer is asked to rate his/her confidence about the fulfilment of image quality criteria. The data is then analysed in a manner that is similar to ROC studies, where the resulting figure of merit is the area under the VGC curve. However, we have not been able to translate our results to a VGC study, since the question asked to the observer slightly differs between those two types of studies.
Also, the importance of a clinical image quality measure such as VGA analysis that relies on evaluation of structures in the normal anatomy may be questioned. This is since the detection of pathological lesions may to a large degree also depend on other objects in the image such as obscuring anatomical background structures (Tingberg et al 2005).
5.6. Model observers with complex anatomical background In paper VI, The Laguerre‐Gauss Hotelling observer was implemented. This observer is influenced by the anatomical background and includes this into its figure‐of‐merit, SNRhot,LG. Son et al (2006) and Chawla et al (2007) implemented similar observers. In the work by Son et al (2006), being an extension of the work by Winslow et al (2005), validation of their model is not considered due to the use of a virtual phantom. We believe that it is important to verify that the computational model can faithfully reproduce variations in, e.g., tube voltage since this is an important parameter influencing image quality and patient dose. The implementation of the Laguerre‐Gauss Hotelling model‐ observer, SNRhot,LG, is described in paper VI and chapter 4.
Figure 5.12 and 5.13 show SNRhot,LG for the SKE/BV and SKE/BKE tasks as functions of tube voltage. The SKE/BV and SKE/BKE cases represent situations where the patient projected anatomy is assumed to act as noise (SKE/BV) or to be known exactly (SKE/BKE). The figures show that for the SKE/BV task there is a small increase in SNRhot,LG with increasing tube voltage in the regions LAT,
RET and HIL. In the bony regions LME and UME the increase of SNRhot,LG with increasing tube voltage is larger. For the SKE/BKE task, the SNRhot,LG steadily
52 Results and discussion
decreases with increasing tube voltage as SNRI in paper III. Hansson et al (2005) investigated the optimal tube voltage in neonatal chest radiography. In their phantom study (a rabbit lung) they found a positive trend when increasing the tube voltage in the visibility of the carina and main bronchi, but no trend for the reproduction of central and peripheral vessels. Thoracic vertebrae were better visualized at low tube voltages. Their validation study (neonatal patients) showed no significant preference for any tube voltage in the 40‐90 kV range with regard to central and peripheral vessels but the carina was better reproduced at the highest tube voltage in their study; 90 kV. These results are in qualitative agreement with our work, although there are significant differences in the material as adult patients were studied in our work.
8
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4 hot,LG
3 SNR
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Figure 5.12. SNRhot,LG (SKE/BV) as function of tube voltage at the air kerma 5 μGy in the center of the image detector. The markers symbolize different regions in the image: ’*’ lateral pulmonary region (LAT), ’o’ retrocardial region (RET), ’∇’ lower mediastinum (LME), ’ ’ hilar region (HIL), ‘+’ upper mediastinum (UME).
53 Results and discussion
1000
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0 60 70 80 90 100 110 120 130 140 150 Tube voltage (kV)
Figure 5.13. SNRhot,LG (SKE/BKE) as a function of tube voltage at the air kerma 5 μGy in the center of the image detector. The markers symbolize different regions in the image: ’*’ lateral pulmonary region (LAT), ’o’ retrocardial region (RET), ’∇’ lower mediastinum (LAT), ’ ’ hilar region (HIL), ‘+’ upper mediastinum (UME).
Figure 5.14 and 5.15 show SNRhot,LG for the SKE/BV and SKE/BKE tasks as functions of air kerma at the image detector in the center of the image plane. Figure 5.14 shows that in the regions located in the lung (LAT and HIL), increasing the dose level has a negligible influence on the SNRhot,LG. However, in the regions containing more bony structures (LME and UME) there is a larger increase in the SNRhot,LG with increasing dose level. For values of air kerma above 0.5‐1 μGy, the values of SNRhot,LG are highest in the bony regions
LME and UME. In 5.15 for the SKE/BKE task, the SNRhot,LG increases in accordance with the Rose model (Rose 1948).
54 Results and discussion
8
7
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4 hot,LG
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Figure 5.14. SNRhot,LG (SKE/BV) as a function of incident air kerma at the image detector in the center of the image plane at 141 kV. The markers symbolize different regions in the image: ’*’ lateral pulmonary region (LAT), ’o’ retrocardial region (RET), ’∇’ lower mediastinum (LME), ’ ’ hilar region (HIL), ‘+’ upper mediastinum (UME).
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Figure 5.15. SNRhot,LG (SKE/BKE) as a function of incident air kerma at the image detector in the center of the image plane at 141 kV. The markers symbolize different regions in the image: ’*’ lateral pulmonary region (LAT), ’o’ retrocardial region (RET), ’∇’ lower mediastinum (LME), ’ ’ hilar region (HIL), ‘+’ upper mediastinum (UME).
55 Results and discussion
Båth et al (2005b) evaluated human detection of 10 mm lung nodules in the presence of normal patient projected anatomy including quantum noise and in images with quantum noise only. They concluded that for the detection of the lung nodules, the quantum noise is of almost no importance at clinically used dose levels in chest radiography. The regions where lesion detection was least influenced by quantum noise were the hilar and lateral pulmonary regions. The results for the SKE/BKE case in our work agree with the results in Båth et al. for images containing quantum noise only concerning the ranking of the regions with respect to the ease of detecting the lesions or SNRhot,LG. In the quantum noise images, the lower and upper mediastinum were by these authors ranked as the most difficult regions (most quantum noise) for lesion detection and the hilar and lateral pulmonary regions as the least difficult (least quantum noise) ones in agreement with the results in figures 5.13 and 5.14.
The results for the SKE/BV case agree relatively well with the results by Båth et al (2005a) for images where stationary noise (corresponding to structural noise in different regions) was used. In both cases, the hilar region is ranked as the most difficult region for lesion detection and the lower mediastinum ranked as the least difficult one, in opposite order to the case with images containing quantum noise only. The results concerning ranking order also agree reasonably well for the retrocardial and lateral pulmonary regions. For the upper mediastinal region, however, the results disagree. This is probably due to a less rich structural background in the anthropomorphic phantom in the upper mediastinum compared to in patient images. Although our model does not produce results that fully agree with nodule detection in a structured anatomical background, our study shows that there are reasons to believe that the SKE/BV model is more realistic than the SKE/BKE model. The SKE/BV model also predicts that higher tube voltages result in a higher SNR in compliance with the tradition in Sweden of using high tube voltages in chest radiography. We conclude that the SNRhot,LG‐observer is a better model of the radiologist than model observers that only includes the quantum noise (i.e. ideal observer) in its analysis and suggest that such models have little validity.
Figure 5.15 shows that the SNRhot,LG(SKE/BKE)‐observer increases its score with the square root of the air kerma at the image detector in accordance with the Rose‐model whereas the SNRhot,LG(SKE/BV)‐observer (fig. 5.14) shows a
56 Results and discussion score, that in the hilar and lateral pulmonary regions, is independent of the air kerma at the image detector.
57
Summary and conclusions
6. SUMMARY AND CONCLUSIONS
We have developed patient models of high realism and fine anatomical structures for calculation of synthetic x‐ray images that can be used for image quality analysis. The projection images from these images contain fine structure details such as small and medium sized vessels. This has allowed for image quality assessment with increased realism.
A study was also performed to investigate how physical measures influencing image quality are distributed over the radiographic image. These physical measures of image quality show a large variation in the chest PA image. The scatter to primary ratio between spine and in the lung differs with a factor of 4.
Correlations between clinical and physical image quality measures were sought. In Paper IV we found a correlation between the VGA score and a figure of merit based on the quantum noise (ideal observer) signal to noise ratio, SNRI. In paper VI we implemented the Laguerre‐Gauss Hotelling observer for the assessment of image quality in simulated high‐resolution images. A relatively good correlation was found between the Laguerre‐Gauss
Hotelling observer figure of merit, SNRhot,LG for the SKE/BV task, and the clinical study by Båth et al (2005a) for images where stationary noise corresponding to the structural noise in different regions was used. The conclusion is therefore that the LG Hotelling observer mimics human detection performance better than the ideal observer for tasks were the anatomical background varies.
In the special case of iodine subtraction mammography (Paper I) the optimal tube voltage was found to be significantly higher (45 kV) compared to what is standard in conventional mammography. The optimisation of chest radiography with regard to tube voltage is more complex and depends on the task. For tasks limited by quantum noise, or in those cases where the clear visualisation of bone structures are essential, then low tube voltages (90‐120) should be preferred. If we believe that the detection of soft tissue details (such as nodules) is hampered by bone details such as ribs, then high tube voltages (120‐150) should be preferred.
59
Future work
7. FUTURE WORK
The ultimate purpose for the model presented here is to serve as a tool to perform optimisation of diagnostic radiology given a specific task. As mentioned, a reliable and objective method for image quality assessment is needed for this purpose. Our method using the Laguerre‐Gauss Hotelling observer is in a rather early stage of development. An important future project is therefore to further develop and validate this method against human observers. For instance, the Laguerre‐Gauss method assumes rotational symmetry, yet the anatomy is not rotationally symmetric. The Gabor Hotelling observer does not assume rotational symmetry and would therefore, if it were implemented, provide a more accurate model of the human observer. In addition, another improvement is to add internal noise to the model observer to give a better agreement with human observers. One possible way to validate the model is to perform an ROC study where human observers and model observers are evaluating the same images, searching for the same pathologies. The methods for objective image quality assessment based on statistical decision theory are also applicable in many other fields of radiation physics, such as nuclear medicine and MR. Therefore; the work presented here could serve as inspiration for future work for researchers in those fields.
Another possible future prospect is to develop a model for optimisation of chest and breast tomosynthesis. It that case, the VOXMAN model needs to be improved to calculate several projections for different angles. In the case of breast tomosynthesis, a realistic anthropomorphic breast model is also needed. Another improvement of the model is to segment the high‐resolution anthropomorphic phantoms so that organ and effective doses can be calculated.
If a user‐friendly version of the Monte Carlo model together with model observers is created, it could be distributed to medical physicists who could use it for study and optimisation purposes.
61
Acknowledgements
8. ACKNOWLEDGEMENTS
A common question from the opponent at the dissertation is, why did you choose to make research in this specific field? My answer to that question is that I would have studied every field of Science simultaneously if that had been possible. Unfortunately, it is not possible. I would like to use a poem by the English poet and artist William Blake as an illustration
To see a World in a grain of sand, and a Heaven in a wild flower. Hold Infinity in the palm of your hand, and Eternity in an hour.
My belief is that any grain of sand, when studied in the depth, always contains something interesting. I stood at the seashore and picked up one grain of sand. I studied this grain of sand in every detail and every aspect, and actually, it gave me a deeper understanding of the World. And even if I sometimes doubted, I found that some things inside were really interesting. So I thank this grain of sand, and return it to the seashore.
I want to express my gratitude to
My supervisors Michael Sandborg and Gudrun Alm Carlsson for introducing me to this field and for all the support during these years I have been working on this thesis. The time as a PhD student has been a process, from which I have learned a lot, and it has made me develop as a person. I especially want to thank Micke for helping me to attain a rather large production as a PhD student, and Gudrun for her enthusiasm. She obviously loves her research, and that inspires others.
David Dance. As a co‐author of all my papers he has helped me greatly in my research. Especially during my visits in London where he taught me about the VOXMAN program. I also want to thank David for his hospitality during these visits.
Magnus Båth. Magnus part in this thesis should not be underestimated. In the initial stage of my PhD studies, being a Monte Carlo theorist, I was rather ignorant about the clinical aspects of image quality. Largely due to Magnus, I was put out of this ignorance. Nowadays we almost speak the same language and get similar results.
63 Acknowledgements
Alexandr Malusek. For all your support with LINUX and UNIX. You have shown much patience with the “LINUX‐lamer” next door, who has asked many trivial questions about even more trivial LINUX‐commands. Also for all interesting discussions during lunch about everything from TV programs on the discovery channel to world politics.
Other co‐authors: Martin Yaffe, Anders Tingberg, Markus Håkansson, Roger Hunt and Markku Tapiovaara for their valuable contributions to the papers they have co‐ authored.
My colleagues at the Radiation Physics Department
Jalil Bahar. For being a true friend, and for our discussions about Rumi (see the poem at the first page of this thesis) and our talks about beauty of different kinds.
Eva Lund. I think that you deeply understood my feelings during the final stages of preparing this thesis. Our talks when I was feeling stressed really helped me.
Håkan Gustafsson, for our squash games. They helped me not to get too unfit during my PhD studies. Håkan Pettersson, for our common interest in music and for your good sense of humour that enriched my time as a PhD student. Anna Olsson for the times you made me laugh. Pernilla Norberg for your kindness.
Magnus Gårdestig, Peter Larsson, Axel Israelsson, Sara Olsson, Agnetha Gustafsson, Eilert Viking, Dan Olsson, Ebba Helmrot, Henrik Karlsson, Marie Karlsson, Jonas Nilsson Althén, Peter Lundberg, Dan Josefsson, Muhammed Sultan, Håkan Hedtjärn, Lotta Jonsson, Laura Antonovic, Kristian Seiron. Etc.
My friends
Gunnar Cedersund for all our discussions about religion and science, and for reading and responding to the loads of emails about my successes and adversities as a PhD student. Lena Malmberg for your inspiration. Evelina Jansson, you have also inspired me, especially about art. All other friends, no one mentioned, no one forgotten.
My family
Everyone in my family, my parents, siblings, uncles, cousins and (deceased) grand parents. My grandmother Ebba Ullman who recently departed.
Finally, my precious, beloved Karin Wermelin.
64 References
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