The deepest gratitude to my supervisor Professor George Panayiotakis for offering me the opportunity to make this PhD and for his continuous support and guidance during all these years

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UNIVERSITY OF PATRAS

SCHOOL OF MEDICINE DEPARTMENT OF PHYSICS

INTERDEPARTMENTAL PROGRAM OF POSTGRADUATE STUDIES IN MEDICAL PHYSICS

Development of a Monte Carlo simulation model of the signal formation processes inside photoconducting materials for active matrix flat panel direct detectors in digital mammography

SAKELLARIS v. TAXIARCHIS

Three Members Advisory Committee

Professor George Nikiforides, Member of the Advisory Committee

Professor George Tzanakos, Member of the Advisory Committee

Professor George Nikiforides, Member of the Advisory Committee

Professor George Tzanakos, Member of the Advisory Committee

Professor Nikolaos Pallikarakis, Member of the Examination Committee

Professor Spiridonas Fotopoulos, Member of the Examination Committee

Associate Professor Alexandros Vradis, Member of the Examination Committee

Assistant Professor Eleni Costaridou, Member of the Examination Committee

Acknowledgments

The deepest gratitude to my supervisor Professor George Panayiotakis for offering me the opportunity to make this PhD and for his continuous support and guidance during all these years.

I am truly grateful and indebted to Dr. George Spyrou, for his precious help, guiding, ideas and advices he gave me during this work. His contribution has been essential.

I would like to thank Professor George Tzanakos for his participation and useful discussions we had all these years.

I would also like to thank Professor George Nikiforides for his co-operation and his support during this PhD thesis.

I am also grateful to Associate Professor Eleni Costaridou for the valuable help she offered by providing me with important bibliography relevant to this PhD thesis.

Also, I need to thank Associate Professor Alexandros Vradis for the useful meetings we had and the important advices he gave me.

I would like to express my gratitude to all my colleagues in the Department of Medical Physics as well, for the helpful discussions we had but also for the moments we lived together throughout all these years.

Finally, I would like to thank the State Scholarship Foundation of Greece (ÉÊÕ) that supported this research work by a grant.

Table Of Contents

Chapter 1

Introduction

1.1. Introduction

At present, the most important breast imaging technique is x-ray mammography. Mammography must be capable to reveal not only subtle differences in the density and composition of breast parenchymal tissue, but also the presence of minute calcifications typically 100 ìm in dimension. It is obvious that there is the need not only to maximize the subject contrast, for the detection of soft-tissue lesions, but also to obtain a high degree of resolution and low level of noise. In addition, due to the risks of ionizing radiation, the dose in the breast should be kept ‘as low as reasonably achievable’ according to the ALARA concept (ICRP 1991).

In trying to satisfy the above objectives and increase the sensitivity and specificity of the mammographic procedure, a fact that would led to a more accurate diagnosis and earlier breast cancer detection, research focuses on (a) the so-called computer-aided diagnosis (CAD), which deals with the application of image processing, image analysis and machine vision techniques on digitized mammographic images and (b) the optimization of image quality and the minimization of dose in breast with the design and refinement of dedicated mammographic equipment as well as the determination of optimum standards for the operational parameters of a mammography unit. The research in computer-aided diagnosis has a very remarkable progress to demonstrate. Nevertheless, its success depends on the quality of the mammographic image obtained at the x-ray image detector.

The x-ray image detector is one of the most important factors that affect the efficiency of the mammographic technique. Xeroradiography was the first step in producing mammographic images (Boag (1973)). It was introduced in the early 1970s and employed an amorphous selenium plate as the image sensor. The development of the screen-film mammography though offered superior performance in imaging low-contrast structures with distinct boundaries. This limitation of xeroradiography was largely due to the powder cloud development method used at the time. Screen-film mammography is still the gold standard in the examination of the female breast. Despite this fact, its dynamic range is limited (1:25) whereas masses and microcalcifications, important indicators of cancer, are hardly visualized in very dense breasts.

Recent research has shown that digital mammography systems offer improved image quality as compared to screen-film systems as well as increased quantum efficiency, flexible image acquisition, processing and storage. Active matrix flat panel systems with an electroded x-ray phosphor as detection material have proved to be superior to other digital mammographic imaging modalities such as photostimulable phosphors and charge coupled devices (CCDs) (Zhao et al 1997, Zhao and Rowlands 1995). In particular, direct conversion digital flat panel systems, which directly convert x-rays to a charge cloud that is electrically driven and stored in the pixels, provide improved quantum efficiency, reduced blurring and high spatial resolution.

Among the most important components of direct detectors is the sensitive to the radiation material (photoconductor). Amorphous selenium (a-Se) is one of the most suitable materials mainly due to its ability to be coated over large areas with uniform imaging characteristics and due to its high intrinsic spatial resolution. Nevertheless, this material suffers from low x-ray absorption efficiency and x-ray sensitivity. Kasap and Rowlands (2000) discussed the properties of an ideal x-ray photoconductor for a direct conversion digital flat panel x-ray image detector. Materials like a-As2Se3, GaSe, GaAs, Ge, CdTe, CdZnTe, Cd0.8Zn0.2Te, ZnTe, PbO, TlBr, PbI2 and HgI2 satisfy some of these ideal characteristics and therefore are also potential candidates. Among them, the polycrystalline materials CdTe, CdZnTe, Cd0.8Zn0.2Te, PbO, PbI2 and HgI2 as well as the amorphous material a-As2Se3 are the most feasible candidates mainly due to the fact that they can be grown in large areas. On the other hand, the crystalline materials GaSe, GaAs, Ge, ZnTe and TlBr are difficult to be developed at such large areas with current techniques and therefore are less suitable. Nevertheless, the current preparation procedures are prone to improve.

To optimize the image quality and hence the diagnostic information acquired from direct detectors, a careful selection of the photoconducting material must be made with the simultaneous refinement of detector technology. This can be achieved with the investigation of the physics that governs the signal formation processes in the photoconductors mentioned since in this way important information relevant to the production of the final image is acquired. Research has mainly focused on the lag and ghosting phenomena (Bloomquist et al 2006, Bakueva et al 2006, Zhao et al 2005, Zhao and Zhao 2005), the x-ray sensitivity and photogeneration (Steciw et al 2002, Stone et al 2002, Street et al 2002, Kabir and Kasap 2002a, Kabir and Kasap 2002b, Kasap 2000, Blevis et al 1999) as well as the charge carrier drifting, multiplication, recombination and collection (Lui et al 2006, Cola et al 2006, Su et al 2005, Kasap et al 2004, Kabir and Kasap 2004, Miyajima 2003, Hunt et al 2002, Mainprize et al 2002, Miyajima et al 2002, Sato et al 2002, Kabir and Kasap 2002a, Fourkal et al 2001, Lachaine and Fallone 2000a, Lachaine and Fallone 2000b, Street et al 1999, Jahnke and Matz 1999).

The quality of the mammographic image is directly related to its characteristics. The x-ray induced primary electrons inside the photoconductor’s bulk comprise the primary signal which propagates in the material and forms the final signal (image) at the detector’s electrodes. Consequently, the characteristics of the mammographic image strongly depend on the characteristics of the primary electrons. Experimentally is not feasible to study exclusively the primary electrons. On the other hand, simulation studies in the materials mentioned have not dealt with the characteristics of primary electrons such as their number as well as their energy, angular and spatial distributions and furthermore with their influence on the characteristics of the final image.

In this PhD thesis an investigation has been carried out concerning the primary signal formation processes and the characteristics of primary electrons inside the photoconducting materials mentioned. In addition, the influence of the characteristics of primary electrons on the characteristics of the final signal together with the electric field distribution and the electron interaction mechanisms particularly for the case of a-Se, one of the most preferable photoconductors, have been studied at a first stage. The electric field distribution and the electron interactions are two crucial parameters in the development of a model that would simulate the final signal formation and hence study the influence of the characteristics of the primary electrons on the characteristics of the final image.

In particular, a Monte Carlo model that simulates the primary electron production inside a-Se, a-As2Se3, GaSe, GaAs, Ge, CdTe, CdZnTe, Cd0.8Zn0.2Te, ZnTe, PbO, TlBr, PbI2 and HgI2 has been developed. The model simulates the primary photon interactions (photoelectric absorption, coherent and incoherent scattering), as well as the atomic deexcitations (fluorescent photon production, Auger and Coster-Kronig electron emission). The results, obtained for both monoenergetic and polyenergetic x-ray spectra in the mammographic energy range, are grouped in four categories:

Energy distributions of: (i) fluorescent photons, (ii) primary and fluorescent photons escaping forwards and backwards, (iii) primary electrons.

Azimuthal and polar angle distributions of primary electrons.

Spatial distributions of primary electrons.

Arithmetics of: (i) fluorescent photons, (ii) primary and fluorescent photons escaping forwards and backwards, (iii) primary electrons.

In addition, a mathematical formulation has been developed for the drifting of primary electrons of a-Se in vacuum under the influence of a capacitor’s electric field and the resulting electron energy, angular and spatial distributions on the collecting electrode have been studied. The formulation has been based on the Newton’s equations of motion and the theorem for kinetic energy change.

Furthermore, the electric field distribution of Pang et al (1998) for a-Se detectors has been adopted and reexamined to adjust it to the simulation model of primary electrons. A code has been developed that calculates the distribution of the electric potential anywhere in a-Se over the pixel and the pixel gap, using the analytical solution of Pang, the boundary values of our case and appropriate numerical calculation methods.

Finally, the structure and the mathematical formulation of a model that would simulate the electron interactions inside a-Se have been developed. They were based on the model of Fourkal et al (2001) that has been reexamined and enriched with existing theoretical considerations, developed mainly by Ashley (1988), and simulation formalisms, developed mainly by Salvat et al (1985, 1987, 2003).The formulation has included the electron free path length, the decision on the type of electron interaction, the differential and total elastic scattering cross section and the differential and total inelastic scattering cross sections with inner shells (K and L shells) as well as with outer shells.

Based on the results of primary electron production, a comparative study between the various photoconductors is made concerning the number and the energy of fluorescent and escaping photons as well as the number, the energy and the angular and spatial distributions of primary electrons. Studying the primary electron production for the monoenergetic case, insights are gained into the related physics that lead to the investigation of the primary electron characteristics as well as the factors which affect them. The polyenergetic case provides information about the dependence of these characteristics on the incident mammographic spectrum. Moreover, the results obtained for a-Se primary electrons that drift in vacuum under the influence of a capacitor’s electric field and are being collected from the top electrode, although they pertain to an unrealistic case, yet give at a first approximation the influence of the characteristics of the primary signal on the characteristics of the final signal. Finally, the formulations for the electric field distribution and the electron interactions inside a-Se, can form the basis of developing a simulation model for the signal propagation inside the photoconductor’s bulk, a fact that would help to derive conclusive remarks on the correlation of primary and final signal characteristics and hence optimize the performance of direct detectors as well as select the most suitable materials for this kind of applications.

The layout of this PhD thesis has been built as follows:

The first two chapters deal with mammographic imaging issues. Chapter 2 describes briefly the mammographic imaging technique as well as the mammographic equipment whereas chapter 3 discusses and compares screen-film systems with digital mammographic detectors. Chapter 4 analyses the properties of some of the most suitable photoconductors for active matrix flat panel direct detectors such as a-Se, CdTe, CdZnTe, PbO, HgI2 and PbI2. The theoretical background of the physics related to the image formation processes is the subject of chapter 5. A detailed analysis of the physics of x-ray-matter interactions, atomic deexcitation mechanisms and electron interactions is made with a further discussion on charge carrier transport and recombination mechanisms inside a-Se. Chapter 6 discusses the mathematical foundation of Monte Carlo calculations and describes the basic Monte Carlo simulation methods. Chapters 7 and 8 deal with the x-ray induced primary electrons inside the selected photoconductors. The modeling of primary electron production is the subject of chapter 7 whereas the obtained results are presented and discussed in chapter 8. Chapter 9 presents the mathematical formulation for the drifting of primary electrons of a-Se in vacuum under the influence of a capacitor’s electric field and discusses the effect of this drifting on their characteristics. The electric field distribution and electron interactions inside a-Se are the subjects of chapters 10 and 11. The calculation method with the relevant analytical solution of Pang et al (1998) for the electric field distribution inside a-Se detectors as well as a derived electric potential distribution are presented in chapter 10. Chapter 11 gives the structure and the mathematical formulation of the simulation model for electron interactions inside a-Se. Finally, chapter 12 discusses the conclusions drawn in this PhD thesis as well as the research work that will be conducted in the near future.
1.4. Publications

The research conducted during this PhD thesis resulted in publications in international journals and international conference proceedings.

Sakellaris T, Spyrou G, Tzanakos G and Panayiotakis G 2005 Monte Carlo simulation of primary electron production inside an a-selenium detector for x-ray mammography: physics Phys. Med. Biol 50 3717-38.

Sakellaris T, Spyrou G, Tzanakos G and Panayiotakis G 2007 Energy, angular and spatial distributions of primary electrons inside photoconducting materials for digital mammography: Monte Carlo simulation studies Phys. Med. Biol 52 6439-60.

Sakellaris T, Spyrou G, Tzanakos G and Panayiotakis G 2008 Photon and primary electron arithmetics in photoconductors for digital mammography: Monte Carlo simulation studies Nucl. Instrum. Methods A (accepted)

Sakellaris T., Spyrou G., Tzanakos G. and Panayiotakis G. “Digital Mammography using a-Se: Monte Carlo Generated Energy and Spatial Distributions of Primary Electrons”, X Mediterranean Conference on Medical and Biological Engineering and Computing, August 2004, Ischia, Italy.

Sakellaris T., Spyrou G., Tzanakos G. and Panayiotakis G. “Distributions of x-ray Generated Primary Electrons in a-Se: Monte Carlo Simulation Studies”, 1st International Conference "From Scientific Computing to Computational Engineering", September 2004, Athens, Greece.
1.5. Financial support

This PhD research work was supported by a grant from the State Scholarship Foundation of Greece (ÉÊÕ).

Chapter 2

Mammography

2.1. Introduction

Mammography is the examination of the female breast by the use of x-rays. The small x-ray tissue attenuation differences in the breast require the use of equipment specifically designed to demonstrate low contrast and fine detail at the same time. Due to the risks of ionizing radiation, techniques that minimize dose and optimize image quality are very important. Clinically, the determination of optimum standards for the operational parameters of a mammographic unit is crucial. In this chapter, the mammographic technique and the basic mammographic equipment are briefly discussed in conjunction with mammographic image quality issues.
2.2. Mammographic Equipment

The mammographic unit consists of two basic components mounted on opposite sides of a mechanical assembly: an x-ray tube and an image receptor. To accommodate patients of different height and due to the fact that the breast must be imaged from different aspects, the assembly can be adjusted vertically and can rotate about a horizontal axis. The system’s geometry is arranged as shown in figure 2.1. The radiation leaves the x-ray tube and passes through a metallic spectral-shaping filter, a beam-defining aperture and a plate that compresses the breast. The rays coming out from the breast can either be absorbed by an antiscatter grid or impinge on the image receptor. A fraction of x-rays passes through the receptor without interaction and is incident on a sensor used to activate the automatic exposure control mechanism of the unit (Yaffe 1995).

Figure 2.1. A typical mammographic unit.

Figure 2.2. A typical mammographic x-ray tube.
2.2.1. X-ray tube

The x-rays used in mammography arise from bombardment of a metal target (anode) by electrons in a hot-cathode vacuum tube. The x-rays are emitted from the target over a spectrum of energies ranging up to the peak kilovoltage (kVp) applied to the x-ray tube (typically 30 kVp). A rotating anode design is used for modern mammographic x-ray tubes. The most common targets are those made of molybdenum (Mo). Nevertheless, targets made of tungsten (W), rhodium (Rh) or alloys combining these elements are being used as well. The anode has a beveled edge, which is at a steep angle to the direction of the electron beam. The exit window accepts x-rays that are approximately at right angles to the electron beam so that the x-ray source as viewed from the receptor appears to be approximately square even though the incident electron beam is slit-shaped. The resolution and optimal image quality required in mammography demands the use of very small focal spots for contact and magnification imaging. Typical focal spot sizes range from 0.3 to 0.4 mm for contact imaging and from 0.1 to 0.15 mm for magnification imaging. Most mammography tubes use beryllium (Be) windows between the evacuated tube and the outside world because glass or other metals would provide excessive attenuation of the useful energies for mammography. Since the high and low energies in the spectrum are suboptimal in terms of imaging the breast, added filtration (usually of the same element as the target) selectively attenuates and optimizes the beam spectrum. Collimation of the x-ray beam is accomplished usually by diaphragms. Diaphragm collimators are metal apertures with predetermined field sizes matched to the image receptor’s sizes (i.e. 18 x 24 cm2 or 24 x 30 cm2). Figure 2.2. presents a typical mammographic x-ray tube.

The compression to the breast is achieved with a compression paddle, a flat plate attached to a mechanical compression device. It is essential that the compression plate allows the breast to be compressed parallel to the image receptor and that the edge of the plate at the chest wall be straight and aligned with both the focal spot and image receptor to maximize the amount of breast tissue being included in the image. Compression causes the different tissues to be spread out, minimizing superposition from different planes and thereby improving conspicuity of structures. The use of compression decreases geometric blurring, the dose to the breast and the ratio of scattered to directly transmitted radiation that reaches the image receptor.

Scattered radiation comprises a considerable fraction of the radiation incident on the image receptor. It degrades the subject contrast according to the following rule (Yaffe 1995): Cs=Co/(1+SPR), where Cs is the subject contrast, Co is the contrast in the absence of scattered radiation and SPR is the Scatter-to-Primary x-ray Ratio at the location of interest in the image. The fraction of scattered radiation in the image can be reduced by the use of antiscatter grids or air gaps. Scatter rejection is best accomplished with an antiscatter grid for contact film/screen breast imaging. Antiscatter grids are composed of linear lead (Pb) septa separated by a rigid interspace material (usually paper). Generally, the grid septa are not strictly parallel but are focused toward the x-ray source. Due to the fact that the primary x-rays all travel along direct lines from the x-ray source to the image receptor while the scatter diverges from points within the breast, the grid presents a smaller acceptance aperture to scattered radiation than to primary and therefore discriminates against scattered radiation. Grids are characterized by their grid ratio (ratio of the path length through the interspace material to the interseptal width), which typically ranges from 3.5:1 to 5:1. When a grid is used, the SPR is reduced approximately by a factor of about 5, leading in the most cases to a significant improvement in image contrast. Nevertheless, the grid causes the overall radiation fluence to decrease. To compensate for losses and therefore to obtain a mammogram of proper optical density, the entrance

Figure 2.3. The geometrical characteristics of an antiscatter grid: h the height of lead strips, d the thickness of lead strips, D the thickness of paper, 1/(D+d) the strip density and h/D the grid ratio.
exposure to the patient is increased by a factor typically between 2 and 3 known as the Bucky factor. Figure 2.3. presents the geometrical characteristics of an antiscatter grid.
2.2.4. Image receptors

The image receptor forms the image by the absorption of energy from the x-ray beam. Image receptors must provide adequate spatial resolution, radiographic speed and image contrast. There is a variety of techniques used to visualize the distribution of energy being absorbed inside the receptor. The detectors are divided into two categories: (a) analog detectors (for example a high resolution fluorescent screen in conjunction with a radiographic film) that “reconstruct” the distribution in a continuous manner in the intensity scale and (b) digital detectors (for example an a-Se detector with an active matrix flat panel system) that sample the distribution in space and in intensity scale. The detectors used in mammography are discussed in detail in the next chapter.