Characterization and Optimization of Silicon-strip Detectors for Mammography and Computed Tomography

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Characterization and Optimization of Silicon-strip Detectors for Mammography and Computed

Tomography

HAN CHEN

Doctoral Thesis

Stockholm, Sweden 2016

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ISSN 0280-316X

ISRN KTH/FYS/--16:15--SE ISBN 978-91-7595-919-1

KTH Fysik SE-106 91 Stockholm SWEDEN Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan fram- lägges till offentlig granskning för avläggande av teknologie doktorsexamen i fysik torsdagen den 22 april 2016 klockan 10.00 i FA31, Tekniska Högskolan, Albanova, Roslagstullsbacken 21, Stockholm.

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Abstract

The goal in medical x-ray imaging is to obtain the image quality required for a given detection task, while ensuring that the patient dose is kept as low as reasonably achievable. The two most common strategies for dose reduction are: optimizing incident x-ray beams and utilizing energy information of transmitted beams with new detector techniques (spectral imaging). In this thesis, dose optimization schemes were investigated in two x-ray imaging systems: digital mammography and computed tomography (CT).

In digital mammography, the usefulness of anti-scatter grids was investigated as a function of breast thickness with varying geometries and experimental conditions. The general conclusion is that keeping the grid is optimal for breasts thicker than 5 cm, whereas the dose can be reduced without a grid for thinner breasts.

A photon-counting silicon-strip detector developed for spectral mammography was characterized using synchrotron radiation. Energy resolution,

∆E/Ein, was measured to vary between 0.11-0.23 in the energy range 15- 40 keV, which is better than the energy resolution of 0.12-0.35 measured in the state-of-the-art photon-counting mammography system. Pulse pileup has shown little effect on energy resolution.

In CT, the performance of a segmented silicon-strip detector developed for spectral CT was evaluated and a theoretical comparison was made with the state-of-the-art CT detector for some clinically relevant imaging tasks.

The results indicate that the proposed photon-counting silicon CT detector is superior to the state-of-the-art CT detector, especially for high-contrast and high-resolution imaging tasks.

The beam quality was optimized for the proposed photon-counting spectral CT detector in two head imaging cases: non-enhanced imaging and K- edge imaging. For non-enhanced imaging, a 120-kVp spectrum filtered by 2 half value layer (HVL) copper (Z = 29) provides the best performance. When iodine is used in K-edge imaging, the optimal filter is 2 HVL iodine (Z = 53) and the optimal kVps are 60-75 kVp. In the case of gadolinium imaging, the radiation dose can be minimized at 120 kVp filtered by 2 HVL thulium (Z = 69).

Key words: mammography, anti-scatter grid, photon-counting, spectral computed tomography, silicon strip, ASIC, energy resolution, Compton scatter, material decomposition, K-edge imaging

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Sammanfattning

Målet vid medicinsk röntgenavbildning är att erhålla den bildkvalitet som krävs för en given detektionsuppgift samtidigt som man säkerställer att patientdosen hålls så låg som det rimligen går att uppnå. De två vanligaste strategierna för att minska dosen är: att optimera de infallande röntgenstrålarna och att använda energiinformationen i de transmitterade strålarna med ny detektorteknik (spektral avbildning). I denna avhandling har metoder för att optimera dosen undersökts i två röntgenavbildningssystem: digital mammografi och datortomografi (CT).

Inom digital mammografi undersöktes användbarheten av antispridningsgaller som funktion av brösttjocklek för olika geometrier och experimentella förhållanden.

Den allmänna slutsatsen är att det är optimalt att behålla gallret för bröst tjockare än 5 cm medan det för tunnare bröst går att uppnå lägre dos utan galler.

En fotonräknande kiselstrippdetektor utvecklad för spektral mammografi karak- teriserades med hjälp av synkrotronljus. Energiupplösningen, ∆E/Ein, uppmättes till att variera mellan 0,11-0,23 i energiintervallet 15-40 keV, vilket är bättre än en- ergiupplösningen på 0,12-0,35 som uppmätts i ett fotonräknande mammografisys- tem av senaste generationen. Anhopning av pulser uppvisar ingen stor effekt på energiupplösningen.

Inom datortomografi utvärderades prestandan för en segmenterad kiselstrippdetektor utvecklad för spektral datortomografi, och en teoretisk jämförelse gjordes med den senaste generationens datortomografidetektor för några kliniskt relevanta avbildningsuppgifter. Resultaten tyder på att den föreslagna fotonräknande datortomografidetektorn av kisel kan ge bättre prestanda än datortomografidetektorn av senaste generationen, särskilt för avbildningsuppgifter med hög kontrast och avbildningsuppgifter som kräver hög upplösning.

Strålkvaliteten optimerades för den föreslagna fotonräknande spektrala datortomografidetektorn i två avbildningsfall för huvud: icke kontrastförstärkt avbildning och K-kantsavbildning. För icke kontrastförstärkt avbildning ger ett 120 kVp- spektrum filtrerat med två halvvärdesskikt (HVL) koppar (Z = 29) ger bäst prestanda. När jod används i K-kantsavbildning är det optimala filtret 2 halvvärdesskikt jod (Z = 53) och de optimala rörspänningarna är 60-75 kVp. I fallet med gadolin- iumavbildning minimeras stråldosen vid 120 kVp filtrerat med 2 halvvärdesskikt tulium (Z = 69).

Nyckelord: mammografi, anti-scatter grid, fotonräknande, spektral datortomo- grafi, kisel band, ASIC, energiupplösning, Compton scatter, material nedbrytning, K-kant imaging

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Publications

This thesis is based on the following papers:

I. H. Chen, M. Danielsson, C. Xu, and B. Cederström. "On image quality metrics and the usefulness of grids in digital mammography," J. Med. Imag., 2(1):013501–013501, 2015.

II. H. Chen, B. Cederström, C. Xu, M. Persson, S. Karlsson and M. Danielsson.

"A photon-counting silicon-strip detector for digital mammography with an ultrafast 0.18-µm CMOS ASIC," Nucl. Instr. and Meth. A, 749:1–6, 2014.

III. H. Chen, C. Xu, M. Persson and M. Danielsson. "Optimization of beam quality for photon-counting spectral computed tomography in head imaging:

simulation study," J. Med. Imag., 2(4):043504–043504, 2015.

IV. H. Chen, M. Danielsson and C. Xu. "Size-dependent scanning parameters (kVp and mAs) for photon-counting spectral CT system in pediatric imaging:

simulation study," Phys. Med. and Biol, 2016. Submitted for publication.

Reprints were made with permission from the publishers.

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The author has contributed to the following publications, which are to some extent related to the thesis but not included.

• C. Xu, H. Chen, M. Persson, S. Karlsson, M. Danielsson, C. Svensson, and H. Bornefalk. "Energy resolution of a segmented silicon strip detector for photon-counting spectral CT," Nucl. Instr. and Meth. A, 715 (2013): 11-17.

• L. Xuejin, H. Chen, H. Bornefalk, M. Danielsson, S. Karlsson, M. Persson, C.

Xu, and B. Huber. "Energy calibration of a silicon-strip detector for photon- counting spectral CT by direct usage of the x-ray tube spectrum," IEEE Trans. Nucl. Sci., 62.1 (2015): 68-75.

• C. Xu, M. Persson, H. Chen, S. Karlsson, M. Danielsson, C. Svensson, and H. Bornefalk. "Evaluation of a second-generation ultra-fast energy-resolved ASIC for photon-counting spectral CT," IEEE Trans. Nucl. Sci., 60.1 (2013):

437-445.

• L. Xuejin, H. Bornefalk, H. Chen, M. Danielsson, S. Karlsson, M. Persson, C. Xu, and B. Huber. "A silicon-strip detector for photon-counting spectral CT: energy resolution from 40 keV to 120 keV," IEEE Trans. Nucl. Sci., 61.3 (2014): 1099-1105.

• M. Persson, B. Huber, S. Karlsson, L. Xuejin, H. Chen, C. Xu, M. Yve- borg, H. Bornefalk. and M. Danielsson. "Energy-resolved CT imaging with a photon-counting silicon-strip detector," Physics in medicine and biology, 59, no. 22 (2014): 6709.

• H. Chen, M. Danielsson, and B. Cederström. "On imaging with or without grid in digital mammography," SPIE Medical Imaging. International Society for Optics and Photonics, 2014.

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Introduction

1.1 X-rays for medical imaging

Since the discovery of x-rays in 1895 by Wihelm Röntgen, x-rays have been widely used in medicine to visualize internal structures in human bodies. The valuable information provided by x-ray imaging can help to diagnose disease, support treat- ment planing, and guide medical personnel in surgical operations. Two main x-ray imaging procedures are projection radiography and computed tomography (CT). In projection radiography, a 2D projection image is produced by recording x-rays after transmitting through a patient. Typical clinical applications of projection radiography include mammography, chest imaging, and bone examinations. CT provides a 3D spatial distribution of the linear attenuation coefficients within a patient by acquiring a series of projection images at different angles [1]. One important advantage of CT over its counterpart magnetic resonance imaging (MRI) is its fast scanning speed. Today’s CT allows imaging of the whole body within 20 s with sub-millimeter isotropic resolution [2]. Such a fast scanning speed together with the accurate 3D information provided by CT has enabled CT to become one of the most widespread imaging modalities, especially for acute cases such as stroke, heart disease and trauma.

A major concern for the use of x-rays in medical imaging is the associated radiation dose to patients, especially for children who are more sensitive to radiation than adults due to their more rapidly dividing cells and longer life expectancy.

A report from the National council on Radiation Protection and Measurement (NCRP) indicated that the effective dose per individual in the U.S. population had increased from 3.6 mSv in the early 1980’s to 6.2 mSv in 2006 [3]. The primary reason for such increase is the radiation from x-ray imaging, mostly due to the higher use of CT which contributed 75% of the medical exposure of the US population [3].

Although the estimated risk to an individual is usually small, a considerable number of cancer cases can be induced when it comes to a large exposed population. The public health risks due to x-ray imaging have been investigated by many researchers.

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British researchers pointed out that 0.6% of cancers in UK are attributable to x-ray imaging and CT is the largest contributor [4]. A report by National Cancer Institute in U.S. estimated that 29 000 future cancer cases could be attributed to the 72 million CT scans performed in the country in 2007 [5]. While these estimations are disputed [6], the basic principle of x-ray imaging is widely accepted: the radiation dose should be kept as low as reasonably achievable (ALARA). The two most common strategies for dose reduction are: optimizing incident x-ray beams and utilizing energy information of the transmitted beam with new detector techniques (spectral imaging).

1.2 Optimization of x-ray beam

X-ray beam can be optimized in several ways, including beam collimation, beam filtration, tube current modulation and tube potential optimization.

1.2.1 Beam Collimation

In x-ray imaging, prepatient collimators positioned between x-ray sources and patients are usually implemented to irradiate regions of radiologists’ interest and avoid unnecessary radiation dose to patients. In spiral CT, a further reduction in radiation dose can be accomplished by introducing a dynamically adjustable prepatient collimator [7–9], which is able to reduce unnecessary dose due to overscanning. At the beginning and end of a CT scan, the pre-patient collimator width is dynamically changed to block part of the x-ray beam that is outside the reconstructed volume. The use of the dynamical prepatient collimator has shown a dose reduction of 5-50% with preserved imaging quality [8].

Another type of collimators is the post-patient collimator (a.k.a. anti-scatter grid) placed between the patient and the detector to reject object scatter. The major drawback for the use of post-patient collimators is that a considerable fraction of primary radiation is blocked from reaching the detector, resulting in reduced dose efficiency. Hence, the usefulness of post-patient collimators should be carefully assessed in x-ray imaging systems [10–12]. In today’s CT scanners, due to the large amount of object scatter usually encountered, post-patient collimators are standard configurations. In digital mammography, the general consensus has been that post- patient collimators can not improve image quality for thinner breasts (<4-5 cm), but is advantageous for the thicker breasts [13, 14]. However, some software-based scatter correction methods have been recently proposed to remove the effect of object scatter on image quality, thus replacing the post-patient collimator for all breast thicknesses [15]. In paper I, we showed that these post-processing methods do not improve image quality and post-patient collimators are still required for thick breasts.

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1.2. OPTIMIZATION OF X-RAY BEAM 3

1.2.2 Beam filtration

Since low-energy x-rays are mostly absorbed by patients and contribute little to image formation, filters are usually used in x-ray systems to remove low-energy x-rays. The most common materials for filters are aluminum and copper. In some imaging procedures, the filter materials are optimally selected to improve image quality. For example, a rhodium filter was found optimal to enhance breast tumors in digital mammography [16]. In dual-energy CT, an added filtration of tin allowed better separation of low-energy and high-energy spectra and was demonstrated to reduce image noise [17]. Bowtie filters are typically employed by CT scanners to reduce radiation dose in the peripheral region of a patient as well as reducing beam hardening. Bowtie filters can be specifically designed to adapt to different clinical applications (e.g. head, body, pediatric and cardiac imaging) [18, 19]. In cardiac imaging, the bowtie filters are shaped such that the exposure outside the area of the heart are efficiently reduced, leading to a dose reduction by 10-20% [19].

1.2.3 Modulation of tube current

A common way to reduce radiation dose is modulating the tube current based on patient weight or size [20–24]. A phantom study performed by Boone et al [24]

shows that with the same CT operation at 120 kVp, pediatric patients of 15 cm in diameter only required 5.4% of the tube current used for adults while image quality was maintained. The tube current can also be modulated angularly and longitudinally during a single CT scan to accommodate changes in attenuation due to patient anatomy, shape and size [25, 26]. Nowadays, x-ray tube current modulation has become a standard feature in most modern CT scanners. In the x-ray tube current modulation, someone can also take into account the radiation sensitivity for different human organs such as the eye or the female breast (i.e.

organ-based tube current modulation) [27, 28]. In this technique, the tube current is reduced when the x-ray tube is in front of the patient relative to the sensitive organ, and to maintain image quality, the tube current is increased when the x-ray tube is at the patient’s back.

1.2.4 Optimization of tube potential

Aside from the modulation of tube current, it is important to optimize the x-ray tube potential for different patient sizes and imaging tasks. A phantom study by Siegel et al [29] shows that decreasing tube voltage from 120 to 80 kVp can reduce dose in contrast-enhanced CT without compromising image quality. Kalender et al [30] investigated optimal tube potentials in different imaging tasks, showing that the conventional setting of 120-140 kVp is optimal for density imaging, whereas low tube potentials are preferable for imaging cases with high contrast materials (e.g.

iodine and calcium), Funama et al [31] demonstrated that when patient weight is below 80 kg, reducing the tube potential from 120 kV to 90 kV in abdominal CT led

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to as much as a 35% reduction in radiation dose without sacrifice of low-contrast detectability. The underlying principle of the improvement at low tube potentials is that low-energy x-rays contain more contrast information than high-energy x- rays, particularly in contrast-enhanced imaging where the attenuation coefficients of contrast agents are significantly increased at lower energies.

However, there are some practical problems in reducing the tube potential.

Radiologist are used to images at 120 kV and changing this means uncertainties in reference tube current settings [32]. The CT numbers of the imaged structures (e.g., soft tissue) resulting from low tube potentials might differ from those resulting from 120 kV; radiologists thus have to adapt to a different overall image impression [33].

Since low-energy x-rays are more likely to be attenuated, the tube currents required for larger patients perhaps exceed the maximum value achievable in x-ray tubes [30].

1.3 Spectral imaging

After passage through matter, the energy spectrum of a polychromatic x-ray beam contains valuable information about different tissue types as a result of the energy- and material-dependent linear attenuation coefficients. The potential benefits of using x-ray spectral information in medical imaging was realized early [34, 35] and its application in practice has become feasible as advances in detector technologies.

X-ray spectral information can be used to improve image quality either using energy weighting or material decomposition.

Energy weighting aims to maximize the detectability of a certain imaging target by optimally weighting the detected x-rays. Energy weighting can be realized by em- ploying a photon-counting spectral detector which is capable of measuring energies of individual x-rays. Some recent studies have demonstrated that energy weighting can improve the signal-difference-to-noise ratio (SDNR) by 10-45% compared to the conventional energy-integrating scheme at the same patient dose [36, 37].

An alternative way of utilizing the spectral information is material decomposition, originally proposed by Alvarez and Macovski [34]. The goal of this method is to differentiate and quantify different materials and tissues in an imaged volume by decomposing the energy dependent attenuation coefficients into a linear combination of several energy-dependent basis functions [34, 38]. This way can eliminate the beam-hardening artifacts [39], thus giving a potential advantage in improving the diagnostic accuracy. For substances containing only low atomic numbers, such as human tissues, two basis material functions are enough to achieve an accurate approximation of the attenuation coefficients. If a contrast agent is present in the imaged volume, the attenuation coefficient of the contrast agent must be added as a third basis function to capture the K-edge discontinuity in the energy spectrum.

Therefore, material decomposition can be used to quantitatively determine the distribution of contrast agents in the imaged volume (i.e., K-edge imaging) [40], which will benefit applications such as CT perfusion and CT angiography. Additionally, in diagnostic procedures requiring pre- and/or post-contrast images, multiple ex-

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1.4. DETECTOR TECHNOLOGY 5

posures can be avoided, offering a lower dose and less mis-registration caused by patient movement between exposures.

Today, several techniques have been developed to obtain spectral information.

Dual-source approach performs two spectrally distinct measurements by implement- ing two x-ray sources running at different voltages with two corresponding detectors [41–43]. Another approach is to switch the tube voltage at high frequency in order to obtain data for low and high kVp for each detector pixel [44, 45]. A third way to obtain dual energy images is by using a double layer detector, where the first layer will convert more of the low energy photons and the second layer more of the high energy photons [46, 47]. These approaches have shown promising results in clinical applications such as the quantitative evaluation of microcalcification in breasts [48], the lesion characterization in livers [49] and the characterization of renal stones and calcified plaques in vessels [50, 51].

However, the approaches mentioned above still use energy-integrating detectors and the overlapping of the spectra measured at low and high kVp would increase noise variance in material basis images [52, 53]. The number of basis functions for material decomposition is limited to two, which results in a biased estimation of contrast agents in K-edge imaging [54, 55]. Moreover, patient motion between spectrum measurements in the dual-source case would lead to mis-registration [56].

Another candidate technique for spectral imaging is to use photon-counting spectral detectors with multi-energy bins and excellent energy discrimination capability. See next section for a detailed description of photon-counting spectral detectors.

1.4 Detector technology

1.4.1 Current technology

Currently, most digital detectors used in x-ray imaging systems are based on energy- integrating techniques. An energy-integrating detector integrates the electric charge produced by all the interacting x-rays in a pixel during a given time period and outputs a signal proportional to the total produced charge. There are four problems associated with energy-integrating detectors in x-ray imaging:

(1) Energy-integrating detectors naturally place more weight to high-energy x- rays and this weighting scheme does not optimally utilize the contrast information carried in the detected x-rays .

(2) Electronic noise is integrated into signals. In low-exposure applications (e.g.

CT colonography [57]) or when imaging obese patients [58], electronic noise could have a significant impact on image quality.

(3) The contrast between a target and background will cancel if their effective attenuation coefficients weighted over the incident spectrum are similar. One classical example is the difficulty in differentiating between calcified plaques and iodinated blood.

(4) In CT, images reconstructed with data from energy integrating detectors suffer from beam hardening artifacts, thus degrading the diagnostic accuracy [59].

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These limitations associated with energy-integrating detectors can be solved by introducing photon-counting spectral detectors in x-ray imaging.

1.4.2 Photon-counting spectral detectors

In photon-counting spectral detectors, the induced pulse height is measured for each x-ray with a number of programmable thresholds. Since the pulse height is proportional to the deposited energy for each x-ray, the x-rays can thus be sorted into different energy bins. The problem with electronic noise can be easily solved by setting a minimum threshold above the noise floor to reject false counts caused by electronic noise. Compared to conventional energy-integrating detectors, photon- counting spectral detectors can optimally weight detected x-rays in the different energy bins, thus improving the dose efficiency [35, 60].

A major challenge with spectral photon counting is the very high count rates in x-ray imaging, up to several million photons s⁻¹ mm⁻². Pile-up of pulses from different x-rays will cause a mis-registration of the energy and mistake two or more x-rays for one. It is therefore critical to develop readout electronics and x-ray sensor materials that are fast enough to handle high x-ray fluxes.

Promising sensor materials for photon-counting spectral detectors are cadmium telluride (CdTe), cadmium zinc telluride (CZT) and silicon. Because of the high atomic numbers, CdTe/CZT were used in most photon-counting detector projects to achieve high absorption efficiency [61–64]. However, CdTe/CZT have low hole mobility which would lead to incomplete charge collection and pulse pileup at high x-ray fluxes. One solution to handle high x-ray fluxes for CdTe/CZT detectors is by decreasing pixel size, but it also increases the spectrum distortion as a result of charge sharing and K-escape [65, 66]. Another problem limiting the use of CdTe/CZT at high fluxes is polarization due to the charge trapping and low hole mobility. The build-up of trapped holes would lead to a rapid decline of output count rate when the x-ray flux reaches above a critical level [67].

Silicon has the advantage of mature manufacturing technology. More impor- tantly, silicon has higher hole mobility than CdTe/CZT and does not suffer from K-escape and polarization. One commercial application for photon-counting silicon- strip detectors is the MicroDose digital mammography system supplied by Phillips [68, 69]. When the system was introduced in major breast cancer screening pro- grams, a dose reduction of around a factor of two was observed in combination with high cancer detection rate [70–72].

Silicon has also attracted attention for use in spectral CT. A photon-counting silicon-strip CT detector has been developed by our research group [73–75]. The pixel size of the silicon-strip detector is only around one-fifth as small as those of typical CT detectors, thus allowing for better visualization of small structures. The low absorption efficiency of silicon can be compensated for by operating the silicon- strip detector in edge-on geometry. The high fluxes in CT is handled by segmenting the silicon strips along the x-ray incident direction with each segment connected to an individual readout channel. One challenge for using silicon in CT is the high

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1.5. OUTLINE OF THE THESIS 7

fraction of Compton scatter, because of its low atomic number and the usually high x-ray energies (up to 140 kVp) encountered in CT. Compton scatter may lead to double counts if scattered x-rays are re-absorbed by the detector. Simulation studies in Chapter 4 have shown that the problem of Compton re-absorption is manageable by placing tungsten sheets between detector modules and the proposed photon-counting silicon CT detector can provide superior results compared to the state-of-the-art CT detector.

1.5 Outline of the thesis

The first part of the thesis is related to digital mammography. In order to explain the divergence of early results about the usefulness of anti-scatter grids in digital mammography, the possible dose reduction achieved from grid removal is investigated in Paper I and the results are summarized in Chapter 2. A photon-counting application specific integrated circuit (ASIC) has been developed for use in CT by our group [76–79]. The feasibility of using the new ASIC in digital mammography is investigated in Paper II by integrating the ASIC into a silicon-strip detector and the corresponding results are summarized in Chapter 3.

In the second part, the focus of the thesis is shifted towards the development of a segmented photon-counting silicon-strip detector for spectral CT. In Chapter 4, a performance evaluation of the proposed spectral CT detector is carried out using an analytical framework described in Paper IV and a theoretical comparison is made with the state-of-the-art CT detector for some clinically relevant imaging tasks. In Paper III, the beam quality for the proposed spectral CT detector in head imaging is optimized and the results are summarized in Chapter 5.

1.6 Author’s Contribution

The author is the principle contributor to all the results presented in this thesis. It should, however, be recognized that the measurements and simulations also depended on the contributions by others. The post-processing algorithm for scatter correction in Paper I was developed by Björn Cederström and the author. The ASIC in Paper II was designed by Christer Svensson and collaborators at Linköping University. The synchrotron measurements in Paper II were carried out by Cheng Xu, Mats Persson, Staffan Karlsson and the author. In Paper III and IV, Cheng Xu provided supports for Monte Carlo simulations. General contributions by several other people are listed in the Acknowledgments.

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Chapter 2

The usefulness of anti-scatter grids in digital mammography

2.1 Introduction

In mammography, image quality is degraded by an additional background caused by scattered radiation [80–82]. One solution for scatter reduction is using slot- or multislit-scanning geometries, which offer the potential advantage of inherent rejec- tion of scattered radiation [83–85]. Challenges with these geometries are increased image acquisition time and higher tube load. Scatter radiation can also be reduced by increasing the air gap between the breast and the detector, but the drawbacks of this technique include increased focal spot blurring due to the higher magnification, reduced effective field of view [86], and practical limitation on the separation between the breast support and the detector.

At present, the simplest and most practical solution for scatter reduction is placing an anti-scatter grid between the breast and the detector. Although this solution is imperfect and leads to partial absorption of primary radiation, the general consensus has been that anti-scatter grids improve image quality for the majority of breast types and sizes. Åslund et al [14] investigated the usefulness of a grid with a theoretical model, showing that a grid could not improve image quality for thinner breasts (<5 cm) but was advantageous for the thicker breasts. Similar results can be found in Gennaro et al’s study [13]. There is, however, inconsistency in the literature. Fieselmann et al [15] showed that by removing the grid and applying a software-based scatter correction technique, dose could be saved for any breast thickness without degrading image quality. Ducote and Molloi [87] also showed that software-based scatter correction can improve image quality in terms of contrast- to-noise ratio (CNR). To explain the divergence of the earlier results, simulations and experiments were performed in Paper I to estimate the dose reduction that can be achieved if the grid were to be removed, as a function of breast thickness.

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10 MAMMOGRAPHY

2.2 Methods

A commonly used linear grid, with a lead septa of 5:1 ratio and strip density of 31 lines/cm, was investigated. According to the European Guidelines [88], the image quality was quantified in terms of signal-difference-to-noise ratio (SDNR) measured using a thin aluminum (Al) foil on blocks of poly (methl methacrylate) (PMMA).

Images were acquired with and without the grid at a constant exposure. The dose reduction achieved from the grid removal was calculated as:

D = 1 − SDNR^grid SDNR^nongrid

²

, (2.1)

with SDNR^gridand SDNR^nongrid being the values obtained with and without the grid, respectively. A negative value of D stands for the dose increasing as a result of grid removal.

2.2.1 Simulation study

(x,y)

air gap

1.5 cm

PMMA primary

sca tter

detector plane incident photons

Figure 2.1: The schematic of Monte Carlo simulation for point spread function of scattered radiation.

The scatter image S(x, y) on the detector plane was constructed by convolving the point spread function (PSF) of scattered radiation with the image field, which is a method similar to that described by Boone and Cooper [89],

S(x, y) = (FAl⊗ PSFAl)(x, y) + (Fbg⊗ PSFbg)(x, y) (FAl= 0, Fbg= 1; in the background

FAl= 1, Fbg= 0; beneath the Al filter

(2.2)

where Fbg and FAl refer to the background field and the field covered by an aluminum (Al) filter, respectively. PSFbg and PSFAl are their corresponding PSFs of scattered radiation.

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2.2. METHODS 11

The scattered PSFs were computed using PENELOPE Monte Carlo code [90].

For each PMMA thickness, the PSF_bg was obtained by tracking 10⁸x-ray photons that are normally incident at the center point of the PMMA surface (Fig. 2.1).

Both coherent and incoherent scatters were considered in the simulation. If the photons exited from the bottom of the PMMA layers, their positions on the detector plane were recorded as they passed through the air gap. We assumed that the deposited energy of each photon reaching the detector was completely absorbed in an ideal energy-integrating system. When the grid was present in the simulation, the transmission of each exiting photon through the grid was calculated using the analytical formulas derived by Day and Dance [91]. The secondary scattered radiation in the collimator was neglected because it has only a small effect, according to Boone et al’s study [86]. Similarly, PSFAl was generated by adding an extra 2-mm-thick Al foil on top of the PMMA in the simulation. For an Al foil of a given size, the scatter images S(x, y) with and without grid were constructed by taking the resulting PSFbg and PSFAl into Eq. (2.2). To investigate the influence of the size of the Al foil, two different sizes, 4 × 8 cm²and 1 × 1 cm², were applied in the simulation.

Ultimately, the phantom image I(x, y) was calculated by summing together the scatter image S(x, y) and its corresponding primary image P (x, y), given by

I(x, y) = S(x, y) + P (x, y);

(P (x, y) = Pbg; in the background

P (x, y) = PAl; beneath the Al foil (2.3) where PAl and Pbg refer to the primary radiation under the Al foil and in the background, respectively.

With properly selected regions of interest (ROI) in the simulated phantom images, the SDNR values for both grid-in and grid-less cases were calculated as

SDNR = |IAl− Ibg| pIbg

(2.4)

where Ibgand IAlrefer to the mean signal of ROI in the background and under Al, respectively.

2.2.2 Phantom study

The phantom study was performed on a full-field digital mammography system (Philips MammoDiagnost DR), with the same grid properties as the system used by Fieselmann et al [15]. PMMA layers 2 to 8 cm thick in 1 cm steps simulated breasts of different thicknesses. The SDNR values were determined by a 4×8 cm², 0.2 mm Al foil placed on top of the PMMA with its left edge superimposed on the center line of the PMMA layers (Fig. 2.2). Images were acquired in the manual exposure mode with an W-Rh anode-filter combination for all PMMA thicknesses. The tube potential and mAs were appropriately selected to ensure an adequate exposure.

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12 MAMMOGRAPHY

a PMMA 20-70mm

240mm X-ray

180mm

80mm

0.2mm Al 0.2mm Al

Front View ROI1 Top View

ROI2

60mm

(a) (b)

Figure 2.2: The experimental setup. (a) Front and (b) top view. A 4×8 cm², 0.2- mm-thick Al foil was placed on top of PMMA layers with a total thickness varying between 2 cm and 8 cm. The signals under the Al filter were determined by two 0.5×0.5 cm²ROIs, which are 6 cm from the chest wall. One (ROI1) was centered on the Al filter, and the other one (ROI2) at the edge. The reference ROIs in the background were symmetrically selected.

In each image, two 0.5×0.5 cm² ROI on the Al foil were selected to compute the SDNR, one (ROI1) at the center, as suggested by the 4th edition of the European Guidelines [92], and the other (ROI2) at the edge for comparison. The 4th edition of the European Guidelines do not specify the size of Al foil, but in a recently published supplement, a 1×1 cm²Al foil is suggested for SDNR measurement [88].

To study the effect of the size of Al foil on SDNR, the experiment was repeated with a small 1 × 1 cm² Al foil.

2.2.3 Scatter correction

The nonuniformity of scattered radiation can be removed by either using some types of deconvolution [87, 93] or simple subtraction of the spatial scatter profile.

Because the former method tends to further increase the noise variance [93], the latter method was used in this study, which consists of three steps:

Step 1: Subtract the grid-in image from the grid-less image with the same PMMA thickness, given by

I_s=Tp× I^nongrid− I^grid T_p− Ts

(2.5) where the primary transmission Tpand scatter transmission Tswere determined in the simulation.

Step 2: The low-frequency scattered radiation was obtained by smoothing the subtracted image Is with a low-pass filter

I_s⁰ = (Is)lowpass (2.6)

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2.3. RESULTS AND DISCUSSION 13

200 250 300 350 400 450 500 550 600

750 800 850 900 950 1000 1050

200 250 300 350 400 450 500 550 600

Figure 2.3: An example of removing scattered radiation for a 7-cm-PMMA phan- tom. (a) The original phantom image I^nongrid. (b) The scatter image I_sextracted from the original one. (c) The corrected image I_c has a more uniform distribution after the scatter has been removed. (the gray scale in each image is adjusted for visualization)

Step 3: The low-frequency scattered radiation was removed from the original images. For grid-less images, it was removed by

I_c^nongrid= I^nongrid− I_s⁰ (2.7) Considering that a small fraction of scattered photons still transmit through the grid, the images acquired with the grid were also corrected with

I_c^grid= I^grid− Ts× I_s⁰ (2.8) Fig. 2.3 shows an example of scatter removal for a 7-cm-PMMA phantom.

2.3 Results and discussion

The results of dose reduction that can be achieved from grid removal is shown in Fig. 2.4 as a function of PMMA thickness. Except when using a large Al foil with a central evaluation ROI, all experimental cases showed that the thickness below which removing the grid is beneficial is between 4.5 and 5 cm PMMA. This thickness is close to the center of the compressed breast thickness distribution of the female population. The finding is consistent with the earlier results by Åslund et al and Gennaro et al.

The Monte Carlo simulation in Fig. 2.5 illustrates that the scatter at the center of the large foil is lower than close to the foil edges and in the background, resulting in an underestimated scatter-to-primary ratio without grid. It explains why the experimental case with a large Al foil gives a different result (red squares in Fig. 2.4).

The large Al foil does not correspond well to the clinical imaging tasks, where targets and interesting structures are small, and the scattered radiation under those targets is very close to that of the surrounding background. The finding provides new insights for explaining the conflicting conclusions of earlier investigations, and

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14 MAMMOGRAPHY

1 2 3 4 5 6 7 8 9

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8

PMMA thickness (cm)

Dose reduction factor D Simulation results

ROI₁ ROI₂

ROI1 after correction ROI₂ after correction small Al filter

Figure 2.4: The dose reduction achieved from grid removal as a function of PMMA thickness, obtained from the simulation and the phantom studies.

the results by Fieselmann et al can probably be attributed to the large Al foil used.

For the case with the large foil, the underestimation of scatter can be eliminated by either using a smaller region of interest close to the edge of the large foil (Fig. 2.4 , cyan triangles), or by applying a technique of scatter correction to subtract the estimated scatter image(Fig. 2.4, diamonds).

Software-based scatter correction methods can remove the low-frequency background noise caused by scatter (as seen in Fig.2.3), and are useful for quantitative imaging, such as breast density estimation [87] and iodine concentration estimation [94]. But the procedure does not affect the properties of the local signal difference and the noise and, hence, does not affect SDNR (Fig. 2.4, crosses). The improvement in CNR in Ducote and Molloi’s study is becauuse they define CNR as contrast divided by noise (as the acronym suggests), which differs from the the conventional definition of CNR or SDNR as the signal difference divided by the noise, which is the definition used in this work as well as the European Guidelines and is based on the Rose model of visual perception. An analysis of the data provided in their article shows that when the conventional definition is used, the result corroborates the findings in this work.

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2.3. RESULTS AND DISCUSSION 15

0 50 100 150 200

2 2.1 2.2 2.3 2.4 2.5 2.6x 10⁵

x (mm)

Signal

primary distribution with 4 x 8cm² Al scatter distribution with 4 x 8cm² Al primary distribution with 1 x 1cm² Al scatter distribution with 1 x 1cm² Al

Figure 2.5: The simulated primary and scattered radiation for a 7-cm-thick PMMA without a grid, along a horizontal line 6 cm away from the chest wall, using Al foils of different sizes, 4×8 cm²and 1×1 cm².

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Chapter 3

Characterization of a

photon-counting spectral detector for mammography

3.1 Introduction

As mentioned in Chapter 1, photon-counting technology has several fundamental advantages compared to current-integrating front-end electronics in x-ray imaging.

However, the expected benefits available for photon-counting spectral detectors would be removed if the count rate linearity and energy resolution are severely degraded as a result of pulse pileup. It is therefore crucial to develop readout electronic circuits that are fast enough to handle high x-ray fluxes encountered in x-ray imaging. An ultra-fast application specific integrated circuit (ASIC) with 8 energy thresholds has been developed for spectral CT [76–79]. It might be de- sirable to implement the new ASIC in spectral mammography to mitigate pileup effect. The main differences compared to the current state-of-the-art ASIC used for mammography [68, 69] are shorter dead time and 8 energy thresholds instead of 2. Also the state-of-the-art ASIC has implemented an anti-coincidence circuit to eliminate charge-sharing effect, which is not the case for the new ASIC, because for CT the count rates are so high that it is much harder to successfully implement anti-coincidence schemes.

The feasibility of using the new ASIC in digital mammography was investigated in Paper II by integrating the ASIC into a silicon-strip mammography detector.

The count-rate linearity, energy resolution and the impact of charge sharing on detector performance were evaluated.

17

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18 SPECTRAL DETECTOR FOR MAMMOGRAPHY

Figure 3.1: Test board with 64 silicon strips wire-bonded to a new photon-counting ASIC.

3.2 Description of silicon detector

Fig. 3.1 shows the silicon detector, which was equipped on a test board. The detector consists of 64 p-type strips, each 50 µm wide and 11.3 mm long, that are implanted on a 500-µm-thick, n-type silicon substrate. The sensor has the same pitch as used in the-state-of-art photon-counting mammography system. The whole test board was mounted in a light-tight box to prevent the disturbance from natural light. A bias voltage of 200 V was applied to the backside of the detector. Under irradiation, x-ray photons deposit energy in the detector and excite electron-hole pairs. The resulting holes drift to the strip sides in the electric field and are collected by the electrodes, leading to electric pulses that are individually processed by the ASIC.

Cf

Detector CSA Differentiator

Cdet

Rf

Cs

Rs

Cpz

Rpz

PZC Circuit

Digital block 8 comparators

Vref0

Vref1

Vref7

Clk Globally distributed programmable thresholds

Gm-C Filter

Figure 3.2: Schematic of the analog part of the ASIC.

Of the 160 channels in the ASIC, 64 are wire-bonded to the detector. Each ASIC channel consists of an analog channel, 8 comparators, each with a threshold generated by a global 8-bit digital-to-analog converter (DAC), and a digital channel. The analog part of the ASIC, illustrated in Fig. 3.2, is composed of a charge-sensitive amplifier (CSA), a pole-zero cancellation circuit, a pulse shaper

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3.3. CHARACTERIZATION METHODS 19

and an offset calibration circuit. The electric pulses generated by x-ray interactions are firstly amplified by the CSA and then are converted by the pulse shaper into a common shape, with the amplitude proportional to the deposited energies. After pulse shaping, the pulse height is compared to the eight thresholds during a programmable time period, leading to a count in one of the energy bins that are formed by two neighboring thresholds. The offset calibration circuit is employed to reduce threshold dispersion between ASIC channels. The main frequency of the ASIC is 100 MHz, giving a clock cycle of 10 ns. The command input, data output, and the clock of the ASIC were controlled by a field-programmable gate array (FPGA) card, which was directly connected to the test board by a low voltage differential signaling (LVDS) interface.

3.3 Characterization Methods

Figure 3.3: Measured S-curve in one detector strip from threshold scanning of 20-keV x-rays, its corresponding fitting using a simple charge-collection model as described in Paper II, and the resulting spectrum.

The count-rate linearity of the detector was measured with polychromatic x- rays produced by a tungsten anode x-ray tube with 2-mm Al filtration. The energy resolution of the detector was evaluated by using monochromatic x-rays up to 40 keV provided by the beamline SYRMEP at Elettra. Different photon fluxes were obtained by placing aluminum slabs of different thicknesses in the beam. An ion- ization chamber was placed behind the slabs to monitor the photon flux. With

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20 SPECTRAL DETECTOR FOR MAMMOGRAPHY the detector being irradiated by a collimated x-ray beam, threshold scanning was performed to obtain the integrated spectrum seen by the detector. Fig 3.3 shows the threshold scanning curve (i.e., the S-curve) as a result of 20 keV x-rays. The measured S-curves were fitted with the integral of the equation:

S(E_th, E_in, σ_e, d) = S0

"

2d

(p + d)2E_inerfc Eth− Ein

√2σe

+ p − d

(p + d)σe

√2πexp

−(Eth− Ein)² 2σ_e²

# (3.1) where p is the strip pitch, σ_e is the electronic level, and S₀ is the number of registered counts at zero energy threshold in an ideal case without noise pollution.

The parameter d is charge-shared region within which the charges collected by the central strip are assumed to be linearly decreased from the incident energy Einto zero, as illustrated in Fig. 3.4. The first term in Eq 3.1 represents the spectrum resulting from charge-shared events accounting for a fraction of _p+d^2d in S0, and erfc is the complementary error function. The second term is related to the photons being totally absorbed by one single strip. This part of photons accounts for ^p−d_p+d in S0. The effect of charge sharing on detective quantum efficiency (DQE) was evaluated based on the derivation as described in Paper II.

Figure 3.4: The linear charge-collection model. The energy collected by the central strip with pitch p is plotted as a function of x-ray interaction position along the pitch direction. The parameter d is charge-shared region defined in Eq 3.1

3.4 Results

3.4.1 Count rate linearity

Fig 3.5 shows the output count rate of an individual ASIC as a function of input count rate for 120 kVp x-rays. The measured values were fitted with a semi-

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3.4. RESULTS 21

0 2 4 6 8 10

Input count rate per ASIC channel (Mcps)

Output count rate (Mcps)

Ideal count rate linearity Measured values Fitting

Figure 3.5: Count rate linearity of an individual ASIC for 120 kVp spectrum and the corresponding fitting with a semi-nonparalyzable model [79]

nonparalyzable model derived in [79]:

m = n

exp(−n(T_C− τ )) + nT_C, (3.2) where n and m are the input and output count rates, respectively, and TC is the time required to process one count in the ASIC and was set to be 120 ns in the evaluation. The dead time τ in Eq 3.2 was calculated to be 30.0±5 ns averaged over the 64 investigated strips on the detector. It is observed that the relationship between the input and output count rate is linear up to 2.5 Mcps. The count loss at the input count rate of 200 kcps is found to be 0.3%, as compared to 16% measured on the state-of-the-art mammography ASIC at the same input count rate [97].

3.4.2 Energy resolution

Fig. 3.6 (a) shows the energy resolution, ∆E/E_in, of 64 individual strips as a function of count rate in the range from 40 kcps to 1 Mcps. Two CSA resistance setting of 0.7 and 3.0 MΩ were selected in the measurement. The results indicate that 3.0 MΩ CSA feedback resistance yields a better energy resolution than the lower resistance, and the discrepancy is about 2%. This is because lower resistance leads to larger electronic noise. As a result of pulse-pileup effect, energy resolution is degraded with the increase in count rate. A linear least-squares fitting ξ = κm + ξ0

was used to fit the energy resolution, ξ, with count rate, m, with ξ0 being the energy resolution at zero count rate and κ being the deterioration rate of the energy resolution. For 3 MΩ CSA feedback resistance, the energy resolution degrades at a rate of 0.02 per Mcps and the energy resolution at zero count rate is 0.22. For 0.7 MΩ CSA feedback resistance, the deterioration rate and the energy resolution at

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22 SPECTRAL DETECTOR FOR MAMMOGRAPHY

(a) (b)

Figure 3.6: (a) Energy resolution of 64 individual strips as a function of count rate in the range from 40 kcps to 1 Mcps for 15-keV photons, as measured at two CSA resistance settings; (b) Average energy resolution ∆E/E_in, with and without the influence of charge sharing (cs), as a function of incident photon energy for 3.0 MΩ CSA feedback resistance. The dash lines are the fittings with the exponential functions.

zero input count rate is 0.03 per Mcps and 0.25, respectively. The results indicate that pulse pileup has little effect on energy resolution in the detector.

The energy resolution as a function of incident x-ray energy was investigated with four different energies 15, 20, 30, and 40 keV, which cover the energy range typically used in mammography. The measurement was performed with 3.0 MΩ CSA feedback resistance at a low count rate of around 50 kcps. Fig. 3.6 (b) shows the average energy resolution over 64 individual strips, with and without charge- sharing effect, as a function of incident photon energy, and their corresponding exponential fitting curves. The energy resolution without charge-sharing effect was estimated to be 0.08-0.21 in the energy range from 15 to 40 keV. With the influence of charge sharing, the spectrum peak was broadened, and consequently the energy resolution was degraded to 0.11-0.23. It is observed that the charge sharing has a relatively stronger effect on the energy resolution at higher energies because incident photons with higher energy yield on average longer attenuation length and thereby larger charge diffusion distance.

3.4.3 MTF and DQE

Fig. 3.7 (a) shows the pre-sampled modulation transfer function (MTFpre) derived from the charge-correction model, for 20 keV x-rays with three energy thresholds of 6, 10, and 14 keV (dashed lines). Because of the increase in double counts at lower energy thresholds, MTFpre at the 6 keV threshold drops faster along the spatial

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3.4. RESULTS 23

frequency than those at the other two thresholds, resulting in a lower cut-off point.

For comparison, the MTF_premeasured using a pencil beam in Paper II is plotted by solid lines in Fig. 3.7(a), showing good agreement with the estimated values from the charge-collection model.

(a) (b)

Figure 3.7: (a) Measured MTFpre curves using the pencil beam and the modeled MTFpre derived from the charge-correction model, for the energy thresholds of 6, 10, and 14 keV. (b) DQEs, with and without the charge-sharing (cs) effect, as a function of spatial frequency. A 30-kVp tungsten and 0.5-mm aluminum anode-filter combination with a 40-mm PMMA filtration was assumed in the calculation.

Fig. 3.7 (b) shows the detective quantum efficiency (DQE) at the three energy thresholds for a 30-kVp tungsten spectrum under the assumption of unity quantum efficiency. The 10-keV energy threshold provides a relatively higher DQE at low frequencies because the 6-keV-threshold setting suffered from more double counts whereas a considerable fraction of photons were unregistered at the 14-keV threshold, both of which degraded DQE. With the increase of spatial frequency, the 6-keV energy threshold instead yields a higher value. The ideal DQE without the impact of charge sharing is also plotted in Fig. 3.7 (b) for comparison. Since the com- parisons of DQE was made under the assumption of unity quantum efficiency, the absolute values are no of interest, only the relative differences. The results show that with a nearly optimal threshold setting of 10 keV, zero-frequency DQE only degrades by 5% due to the charge-sharing effect.

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Chapter 4

Photon-counting spectral CT versus the state-of-the-art CT

4.1 Introduction

A photon-counting spectral silicon-strip detector has been developed for CT application by our group [73–75]. Fig 4.1 shows a photograph of a single detector module. The detector module is fabricated on a 0.5-mm-thick high-resistivity n- type silicon substrate with p-type electrodes implanted. The detector width of 20 mm is divided into 50 strips with a strip pitch of 0.4 mm. As a result, a pixel size of 0.5×0.4 mm² is given for each detector strip by orienting the module with its edge directed towards the x-ray beam (i.e. edge-on geometry). The active absorption path along the x-ray incident direction is 30 mm, along with a dead layer of 0.6 mm at the front edge. In order to overcome the problem of high photon fluxes encountered in CT imaging, the detector strip is subdivided into 16 segments along the x-ray incident direction. The segment length is exponentially increased, providing a nearly uniform count rate over all segments. Five 160-channel ASICs as described in Chapter 2 are stud bonded to the detector module to manage 800 detector elements (50 strips × 16 segments). The previously published measurements on the detector module have shown high count rate linearity with only 1% count loss at an incident photon flux of 300 Mphotons s⁻¹mm⁻² [73], an RMS energy resolution varying from 1.5 keV for 40 keV photons to 1.9 keV for 100 keV photons [74], and a temperature stability of 0.1 keV threshold variation per kelvin at 30 keV [75].

Since silicon has a high fraction of Compton scattering for high-energy x-rays, which may limit its use in CT, a question may arise whether the photon-counting spectral silicon-strip CT detector would outperform the state-of-the-art CT detector? To answer the question, simulations were performed in this chapter to evaluate the performance of a full CT detector, including the derogatory effects of Compton scatter, charge sharing and object scatter, and a theoretical comparison was made with a modeled energy-integrating detector for some clinically relevant imaging

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26 STATE-OF-THE-ART CT

1

16

Segment

Strip 1 50

x-rays enter along this edge ASIC

D2

D1

D3

Front-side electrode x-rays

(a) (b)

Figure 4.1: (a) Photograph of a single detector module with 50 silicon strips, 16 segments and 5 160-channel ASICs stud bonded. The corresponding detector elements managed by different ASICs are illustrated by thick white lines. (b) A magnified view of two detector elements with detector thickness D1=0.5, strip pitch D2=0.4 mm and electrode width D3=0.125 mm.

tasks. In order to separate the influences of contrast resolution and spatial resolution on the detector performance, two figure of merits, SDNR and detectability index d⁰², were used for system comparison. Another commonly used measure for evaluating the performance of x-ray imaging systems is detective quantum efficiency (DQE). However, DQE can not fully capture the performance of a photo-counting spectral system, because the noise and signal properties would be varied when weight factors are applied to different energy bins. Also, the enhanced contrast through optimal energy weighting is not taken into account in DQE.

4.2 Description of two CT systems

4.2.1 Photon-counting spectral CT system

The geometry of a full CT detector is illustrated in Fig. 4.2. The full CT detector consists of a large number (1500-2000) of detector modules. Each detector module is aligned with its front edge pointing towards x-ray source. To facilitate the cooling and mounting of electronics, the detector modules are stacked in two different layers, with the lower detector layer offset by one module thickness along the x-axis relative to the upper layer. The backside of each detector module is covered by a 50-µm tungsten sheet to reduce internal scatter radiation between different detector modules, resulting in a geometric detection efficiency of 0.95. In order to reject the scatter radiation from objects, the tungsten sheets at the upper detector layer are

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4.2. DESCRIPTION OF TWO CT SYSTEMS 27

(a) (b)

Figure 4.2: Illustration of a full CT detector with a two-layer design. The detector modules are stacked in two different layers, with the lower detector layer offset by one module thickness along the x-axis relative to the upper layer.

extended by 2.5 cm towards x-ray source, acting as a one-dimensional anti-scatter grid.

Figure 4.3: Schematic of the simulation setup with a full CT detector. The 30- cm-diameter soft-tissue phantom is irradiated by a fan beam with a width of 1 cm along the z-axis at the isocenter. An imaging target of diameter dtis embedded in the phantom center

Simulation studies are performed based on the geometry of a commercial CT scanner (GE Lightspeed VCT) as shown in Fig. 4.3. The source-to-isocenter distance is 541 mm and the source-to-detector distance is 949 mm, giving a geometric magnification of 1.75. The phantoms are irradiated by a uniformly distributed x-

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28 STATE-OF-THE-ART CT ray fan beam with a width of 1 cm along the z-axis at the ioscenter. The x-ray tube equipped in GE LightSpeed VCT is Performix Pro 100 which has a target angle of 7 degree and a focal spot size of 0.6×0.7 mm²[98]. After the filtration of an inherent flat filter equivalent to 0.43-cm-thick aluminum (Al), x-rays are subsequently filtered by a GE body bowtie filter. The geometry of the bowtie filter was measured using the method described in Appendix A of Paper IV. A soft-tissue cylinder with diameter of 30 cm is placed at the isocenter to mimic an adult patient. The axial lengths of the phantom is 14 cm. An image target of diameter dtis centered in the phantom.

4.2.2 Modeled energy-integrating CT system

The energy-integrating CT system applies the same gantry geometry as used for the photon-counting spectral CT system. It is assumed that the energy-integrating detector has unity absorption efficiency, no object and detector scatter, and no electronic noise. In contrast to the pixel size of 0.5×0.4 mm² for the photon- counting spectral system, the pixel size of the energy-integrating system is 1.2×1.2 mm² with an effective absorption area of 1×1 mm². The resulting geometrical efficiency is around 0.7, a typical value for commercial CT systems.

4.3 Theoretical framework

4.3.1 SDNR

Statistical detection theory

Statistical decision theory, which is based on hypothesis testing, is extensively used to evaluate image quality in medical imaging [99–101]. A comprehensive description of this theory can be found in the publication by Harrison H et al [102]. To apply the theory to our photon-counting spectral imaging system, we assume two hypotheses, h0and h1, representing the absence and presence of an imaging target, respectively.

The task is then defined as deciding whether the imaging target is present or not.

Let g be a N×1 column vector g = (g1, g2, ..., gN)^T, with entries being the outcomes of N energy bins. Under the hypothesis hm(m ∈[0, 1]) described above, the expectation value of g is expressed as ¯g^m = hg|hmi. The squared SDNR between the imaging target and the background is then given by:

SDNR²= (w∆¯g)²

w(K¹+ K⁰)w^T (4.1)

where w is the bin weighting vector [ω1, ..., ω_N], ∆¯g is the signal difference between two hypotheses, i.e. ¯g¹− ¯g⁰, and K^m is the N ×N covariance matrix of g under hypothesis h_m, with entries given by:

K_ij^m= h(g_i− ¯g_i)(g_j− ¯g_j)|h_mi, m = 0, 1. (4.2)

Characterization and Optimization of Silicon-strip Detectors for Mammography and Computed Tomography