XCounter AB has developed a photon-counting gaseous avalanche detector with
no ...... The whole construction is mounted on a metal plate ... Figure 19:
Schematic of the rotating object container from the side (left) and from above (
Computed Tomography for Mammography
Jonas Nilsson [email protected]
A Master of Science Thesis in Engineering Physics
Supervisor: Dr Tom Francke Chief Executive Director, XCounter AB Danderyd, Sweden Examiner: Professor Andras Kerek Department of Physics, Particle and Astroparticle Group Royal Institute of Technology, KTH Stockholm, Sweden 2007
© 2007 Jonas Nilsson TRITA-FYS 2007:24 ISSN 0280-316X ISRN KTH/FYS/--07:24-SE
Abstract Mammographic screening has largely contributed to the reduced mortality in breast cancer observed in Sweden and several other countries. However, the conventional Xray projection technique has an inherent problem in the superimposition of breast structures, which in relatively many cases impedes a correct diagnosis. In recent years breast CT, which can provide three-dimensional breast visualisation, has gained increased attention. XCounter AB has developed a photon-counting gaseous avalanche detector with no electronic noise and highly efficient scatter rejection. Using this detector, prototype CT scans were performed on a small rodent. An algebraic iterative algorithm adapted to the specific system geometry was implemented to do volumetric reconstructions. For comparison purposes filtered backprojection slice-stacking reconstructions were also made. The results show that 3D visualisation of small high-contrast objects of sizes down to ~400 µm is possible when the projection data has very poor statistics, but does not suffer from electronic noise and scattered radiation. Anatomical structures were unfortunately not distinguishable. The results suggest that satisfactory visualisation of breast microcalcifications and anatomy may be hard to achieve at acceptable patient doses with breast CT.
Sammanfattning Mammografiscreening anses vara den viktigaste orsaken till den minskade dödlighet i bröstcancer som observerats i Sverige och flera andra länder. I konventionell röntgenteknik innebär projektionen av bröstet problem med överlappande vävnad som bidrar till den relativt stora andelen felaktiga diagnoser. Under de senaste åren har intresset för bröst-CT, som kan ge tredimensionell visualisering, ökat. XCounter AB har utvecklat en digital, foton-räknande röntgendetektor, fri från elektroniskt brus och med mycket effektiv bortsortering av Compton-spridd strålning. Med hjälp av denna gjordes CT-scans av en liten gnagare. En algebraisk iterativ lösare anpassad till den specifika geometrin implementerades för att göra 3Drekonstruktioner. För jämförelse gjordes även planvisa rekonstruktioner med hjälp av filtrerad bakåtprojektion. Resultaten visade att 3D-visualisering av små högkontrastobjekt (ned till ~400 µm) från projektionsdata fri från elektroniskt brus och spridd strålning, men med mycket dålig statistik, är möjlig. Inre organ kunde dock inte urskiljas. Resultaten antyder att tillräcklig god visualisering av små mikroförkalkningar och bröstanatomi kan vara svårt att uppnå med bröst-CT vid acceptabla patientdoser.
Acknowledgements First of all I would like to thank my supervisor Dr Tom Francke at XCounter for providing me with this exciting opportunity to apply my knowledge and skills. I would also like to express my appreciation for your experienced and enthusiastic guidance. Many thanks go to everyone at XCounter for contributing to an excellent working environment, you have made the work rewarding in many ways. I would especially like to mention Christer Ullberg, Leif Adelöw, Karin Lindman, Göran Hallengren and Niclas Weber for their helpfulness with many practical issues. Furthermore, I want to thank my examiner Professor Andras Kerek for profitable discussions and valuable comments on the report. My dear friend Andreas Tronsén deserves a special mention, thank you for proofreading and always being a supportive friend. Last but not least I wish to express my deep gratitude to my family and to Tola for all your support, encouragement and love.
Contents 1. 2.
Aims of this Thesis.........................................................................................1 Introduction .................................................................................................. 2 2.1. Mammography ........................................................................................... 2 2.1.1. Breast Cancer...........................................................................................................2 2.1.2. Mammographic Screening.....................................................................................3 2.1.3. Conventional Mammography ...............................................................................4 2.1.4. Digital Mammography ...........................................................................................8 2.2. Computed Tomography ............................................................................. 9 2.2.1. Brief History ............................................................................................................9 2.2.2. Basic Principles .....................................................................................................10 2.2.3. Inverting the Radon transform...........................................................................11 2.2.4. Algebraic Reconstruction Techniques...............................................................12 2.2.5. Three-Dimensional CT........................................................................................14 2.2.6. The Use of CT for Mammography....................................................................15 3. Technical Description..................................................................................16 3.1. XCounter’s Gaseous Avalanche Detector..................................................16 3.2. The XC Mammo-3T Mammography Prototype .......................................17 3.3. The Prototype CT Setup........................................................................... 20 4. Method ........................................................................................................ 22 4.1. Data Acquisition ....................................................................................... 22 4.1.1. Aligning the setup.................................................................................................22 4.1.2. Single slice scan using the XC Mammo -3T .....................................................22 4.1.3. Spiral scan using the module test setup.............................................................23 4.2. Reconstruction Method............................................................................ 23 4.2.1. Overview................................................................................................................23 4.2.2. System model ........................................................................................................24 4.2.3. Simultaneous Algebraic Reconstruction Technique........................................26 4.2.4. Implementation.....................................................................................................27 5. Results and Analysis ................................................................................... 28 5.1.1. Single slice scan using the XC Mammo -3T .....................................................28 5.1.2. Spiral scan using the module test setup.............................................................32 6. Discussion ................................................................................................... 40 7. Conclusions ..................................................................................................41 8. References ................................................................................................... 42
1. Aims of this Thesis The aims of this thesis are to make a prototype CT setup, collect data and do a true three-dimensional reconstruction of a small object. The work is carried out at XCounter AB in Danderyd. A multitude of reconstruction methods exist and a large part of the work will focus on adapting and implementing one of them for the geometry being used. For the computations normal commodity PCs will be used. The data collection will be done using XCounter’s detector module test setup or their digital mammography prototype system. The mechanical setup will be as simple as possible, only allowing for the object to be rotated in the X-ray beam and aligning the rotation axis with sufficiently small tolerance. The computational burden of 3D CT reconstructions is massive and therefore this thesis will be limited to making a method work, very little attention will be focussed on performance. Furthermore, to get a reasonably short reconstruction time the resolution and/or reconstruction volume will have to be limited.
2. Introduction 2.1. Mammography 2.1.1. Breast Cancer Breast cancer is the most common form of cancer among women in the western world today, and for women between 35 and 50 years it is the dominant cause of death . As many as one in ten of all women are expected to get the diagnosis during their lifetime. In Sweden, about 6500 new cases are found and approximately 1500 women die from breast cancer every year . Although the breast cancer rate has increased in the last centuries a drop in mortality has been observed, most likely due to improved diagnosis (with mammographic screening being one) and treatment. It should be noted that male breast cancer does also exist, but is very rare. The female breast is mainly composed of fat, connective tissue and milk-producing glandular tissue. Anatomically, the breast is divided into 15-20 lobes which themselves are subdivided into smaller lobules. Each lobule ends with milk-producing bulbs and the milk is transported by ducts (see figure 1).
Figure 1: Anatomy of the female breast .
It is in the glandular tissue and above all in the ducts that cancer develops. The process starts when a normal cell undergoes transformation into a cancer cell. If the immune system does not successfully recognize and destroy the cell, a lump of abnormal tissue, 2
a tumour, may form in the breast. From there it can invade other breast tissues or even spread to other parts of the body through the lymph and blood vessels.
Figure 2: The growth and spreading of breast cancer.
2.1.2. Mammographic Screening Since breast cancer is such a common disease and also relatively young women are affected, a lot of effort has been made to find the cancer at an early stage. This is absolutely crucial for a successful treatment, whether it is curative or palliative. Mammographic screening (examination of large segments of the population) is the best and most cost-effective method available today. It is anticipated that between 75% and 90% of the female breast cancer cases in Sweden are correctly diagnosed with mammography . Mammographic examination of healthy women started in the USA in the 1960’s and screening trials began in Sweden in the 1970’s . Based on the positive outcome the Swedish National Board of Health and Welfare (Socialstyrelsen) issued a recommendation in 1986 to start nation-wide mammographic screening . Similar programs exist or are being developed in many other western countries. Since the introduction of mammographic screening in Sweden the mortality has decreased even though the breast cancer rate in the population has increased. Part of this should be attributed to improved treatment methods, but the majority of the scientific evidence shows that mammographic screening also plays a very important role . Based on this, the National Board of Health and Welfare recommends that all women between 40 and 74 should be called to mammographic examination every 18-24 months. Since breast cancer is very rare among women younger than 40 the possible benefits for this group are not considered to outweigh the potential (albeit very small) risk associated with the X-ray dose. For women older than 74 breast cancer is no longer among the dominant causes of death. Therefore they are in general not being called to screening.
2.1.3. Conventional Mammography
22.214.171.124. Basic Principles Conventional mammography is an X-ray projection technique in which each breast is imaged from one or two views. Figure 3 shows a simple sketch of the geometry typically used. The breast is compressed between two plates in order to spread the anatomical structures over a larger area and reduce overlap. An X-ray tube operating at 20-30 kV irradiates the breast and the signal, differences in transmitted photon flux, is registered by the image receptor. Usually the image receptor is a high-contrast photosensitive film, but today more and more hospitals move to digital systems. X-ray tube
Figure 3: Geometry of conventional mammography.
The radiologist examining the mammograms looks for small abnormalities and microcalcifications, for which he or she must have specialist competence. To meet the demands the mammography system must have: • High contrast even for small attenuation differences, achieved by using a low X-ray tube voltage. • High dynamic range of the image receptor in order for the strongly absorbing microcalcifications as well as structures in the low-absorptive soft tissue to be visible. • High signal to noise ratio to make also small contrasts visible. • High spatial resolution in order for the often very small microcalcifications to be identifiable. • Small X-ray tube focal spot in order to minimise the geometrical unsharpness. Those technical demands make conventional mammography more difficult than most other classical X-ray imaging, for example of lungs and bones.
126.96.36.199. Contrast, noise and dose As a beam of X-rays traverses tissue some photons transfer energy to the matter via the photoelectric effect or Compton scattering. The linear attenuation coefficient, usually denoted by a µ and measured in cm-1, characterises how strongly the matter interacts with the photons and how quickly the beam is attenuated. The transmitted flux (photons per unit area) can be written as
I = I 0 ⋅ exp − ∫ µ ( x, y, z )ds ,
where the line integral is taken over the path of the X-ray. What forms the image on the image receptor are spatial variations of the incident Xray energy. A certain contrast between different objects within the tissue is necessary for them to be distinguishable. Consider the simple example below in figure 4 where the incident intensity is I0 and a volume with linear attenuation coefficient µ2 is embedded in a bigger volume with linear attenuation coefficient µ1. I0
Figure 4: Attenuation within an object composed of two tissue types
The contrast is usually defined as C=
I1 − I 2 , I1
which in complete analogy with equation (1) easily can be expressed as
C = 1 − exp[− (µ 2 − µ1 )d ] = 1 − exp(− ∆µ ⋅ d ) .
From this simplified example one can see that the contrast will depend on the difference in linear attenuation coefficients (∆µ) and the thickness of the target. A thick object and large ∆µ will give a high contrast.
Figure 5: Calculated contrast of 1 mm glandular tissue and 100 µm calcification relative to normal breast tissue .
Figure 5 shows the calculated contrast of glandular tissue and calcifications relative to typical breast tissue. It can be seen that lower X-ray energies give higher contrast, but if too low X-ray energies are used the patient dose will become unacceptably high. This illustrates the trade-off between contrast and dose that always has to be done. For mammography a tube voltage of 25-30 kV and a Molybdenum or Rhodium anode giving characteristic X-rays around 18 keV or 21 keV is a common choice .
Figure 6: Image blurring by scattered radiation and the common solution – a grid.
A rather large fraction of the photons will scatter as they traverse the tissue. This has a blurring effect and reduces the contrast of an object as illustrated in figure 6. In order to reduce the scattered radiation a movable grid restricting the angular acceptance of the “pixels” on the image receptor is usually used. Since the grid also absorbs some of
the information-carrying, directly transmitted radiation, a higher patient dose is necessary to maintain a high photon flux. This measure is necessary in conventional mammography but unfortunately it increases the patient dose with about a factor of two . In order for an object to be perceivable by the human eye it must not be swamped in the image noise, even if the object contrast itself is very high. One source of noise is the scattered radiation, another is (in the case of digital systems) electronic fluctuations within the system. Finally there are statistical fluctuations in the number of photons arriving at and being registered by the detector. The first two kinds of noise can in principle be minimised by intelligent system design, but the third, the statistical fluctuations, can never be completely removed. The number of photons being detected, N, follows Poisson statistics, which means the relative error goes as 1 / N . Thus, the only thing one can do is to make sure good statistics are maintained by using a high photon flux. Unfortunately an increased photon flux means higher patient dose. To summarise, we have seen that two trade-offs always must be made: • Patient dose vs. contrast. • Patient dose vs. signal to noise ratio. 188.8.131.52. Problems with conventional mammography Conventional mammography has several problems. One fundamental problem is that in projecting a three-dimensional object onto a two-dimensional image objects will inevitably overlap and possibly hide abnormalities. This gives rise to false-negatives, i.e. cases that are falsely reported not to have tumours. The superimposed structures may also mimic microcalcifications or tumours, leading to a high number of false-positives. According to Maidment et al. , as many as 25% of all biopsies taken following a mammographic screening examination are false-positives. One of the most serious drawbacks with conventional mammography is the difficulty to make high-quality images of thick or dense breasts, both with respect to contrast and noise. This is caused by an increase in scattered radiation, increased amounts of superimposed structure and a reduced transmitted flux giving poorer statistics. Since low-energy X-rays are necessary to get a good contrast the patient dose in mammography is relatively high compared to many other X-ray projection examinations . The glandular tissue in breasts is sensitive to ionising radiation and the dose must always be kept as low as possible. This is particularly important in mammographic screening since many healthy women are subject to the radiation. The critics of mammographic screening have argued that the benefits have been overestimated while the negative effects of the radiation exposure have not been taken into account properly .
2.1.4. Digital Mammography There are several practical benefits of using an electronic detector to directly detect the X-rays. First of all the developing, managing and storing of the cassettes and films can be completely removed which decreases the procedural time for each exam. This makes the exam more cost-effective for both the hospital and the patient. The digital images can easily be processed to enhance certain structures, which has the potential to reduce the number of repeat examinations and improve the diagnostic quality. New digital detector technologies can also provide reduced noise and increase the efficiency to detect X-rays. Although traditional screen-film technology and computed radiography still are superior in terms of spatial resolution, new digital detector technologies have been shown to be able to offer higher image quality at lower patient doses [12, 13]. Because of the basic problem of conventional mammography with overlapping structures, methods for 3D imaging have attracted some interest over the years. Digital systems with higher efficiency have opened up for the possibility to simply obtain more views of the breast without increasing the total dose, which makes 3D computer reconstructions possible. Several studies indicate that the added depth perception does improve the diagnostic value of the images. For example Maidment et al. made a small clinical study with 3D images from small field-of-view digital mammography. They conclude: “In preliminary clinical evaluation we have demonstrated that 3-D morphologic analysis of calcifications is possible and can significantly increase the accuracy of diagnosis and reduce the number of benign biopsies required” . Similarly, Lehtimäki et al. write that ”Because of limitations of 2-D imaging TACT 3-D technology is an efficient method for studying difficult and ambiguous breast referral cases” .
2.2. Computed Tomography 2.2.1. Brief History The idea of reconstructing the interior of an object from its projections goes back to a paper by Radon published in 1917, in which the mathematical foundations were presented. Radon showed that it was possible to reconstruct a 2D distribution from its line integrals. Already in 1940 Gabriel Franck was granted several patents of ideas describing what resembles modern day CT, but it was not until the introduction of modern computer technology in the 1960’s that CT was made possible in practice. Cormack and Hounsfield, who shared the Nobel Prize in Physiology and Medicine in 1979, are usually recognised as the inventors of CT. Without knowledge of previous works Cormack developed methods to calculate absorption distributions and Hounsfield developed the first clinical scanner, which was put into service in 1972.
Figure 7: 3D reconstructions with sub-millimetre resolution from multi-slice spiral CT scanners .
The introduction of sectional imaging through computed tomography can be described as a revolution in modern medicine. In 1980, only eight years after Hounsfield’s first clinical scanner, 10 000 machines were in use . Since then the performance of CT systems have improved dramatically with respect to important parameters such as spatial resolution, scan time and patient dose. The introduction of multi-slice spiral CT scanners now allows full-body scans for 3D reconstruction to be done in less than 20 s.
2.2.2. Basic Principles The basic idea behind computed tomography in the plane is to record a series of X-ray projections of the object of interest, from which one infers what the inside of the object looks like. For each projection angle ϕ a one-dimensional intensity distribution along x’ is created from the two-dimensional object (see figure 8 below). X-rays
ρ ϕ x
Detector array Transmitted intensity x’
Figure 8: Projection of a two-dimensional object onto a one-dimensional detector array.
Since what is actually measured is the attenuation of the X-rays at each detector pixel position, the object can be thought of as a two-dimensional distribution of attenuation coefficients. Each ray hitting a detector pixel has been attenuated along its path through the object according to:
I = I 0 ⋅ exp − ∫ µ ( x, y )ds ,
where ds is a line element along the path of the ray. The projection of the ray at angle ϕ and offset ρ is defined as I (ρ , ϕ ) P (ρ , ϕ ) = − ln = ∫ µ ( x , y ) ds . I0
The process of scanning the object distribution generates a set of observations, where each observation practically is a line integral. This is the Radon transform – the twodimensional object has been expressed in terms of its line integrals. From here on the Radon transform of µ will be denoted ℜ [µ ] . Equation (5) can be rewritten as
ℜ[µ ](ρ , ϕ ) = ∫ µ ( x , y ) ds =
∫∫ µ ( x , y ) ⋅ δ (ρ − x cos ϕ − y sin ϕ )dxdy ,
which is the common definition of the Radon transform found in the literature . 2.2.3. Inverting the Radon transform Although this section only briefly describes the inversion of the Radon transform in the plane, the ideas are important for understanding the 3D case as well. It can be proven  that the one-dimensional Fourier transform along ρ for a given angle ϕ equals the two-dimensional Fourier transform of the object µ along the line in Fourier space defined by ϕ : F [µ ](υ , ϕ ) = Fρ [ℜ[µ ]](υ , ϕ ) ,
where F denotes the Fourier transform and ν is the complementary variable to ρ in the frequency domain. This important result is called the Fourier slice theorem. It allows us to understand that by measuring the projections of an object from a particular view, we actually sample the Fourier space in the radial direction along the corresponding line (see figure 9). ky
Figure 9: Measuring a projection view samples the Fourier space radially.
The Fourier slice theorem provides a way of reconstructing the object from its projections: first apply the one-dimensional Fourier transform along ρ for each projection view (each ϕ), then apply a two-dimensional inverse Fourier transform to take the object back to coordinate space. However, this scheme has some practical difficulties: since the Fourier space is sampled on a polar grid, and we normally want our object distribution µ(x,y) on a Cartesian grid, interpolation schemes in Fourier space have to be applied before inverting.
The most widely used reconstruction method is the filtered backprojection method, in which each projection view is filtered and then backprojected onto the Cartesian grid. It takes its starting point in a change to polar variables in the inverse Fourier transform of F[µ]:
µ ( x, y ) = ∫∫ F [µ ] ⋅ e
i 2π k x x + k y y
k x = υ cos ϕ dk x dk y = = υ ϕ = sin k y
= ∫ ∫ F [µ ] ⋅ υ ⋅ e i 2πυ ( x cos ϕ + y sin ϕ ) dνdϕ = ρ = x cos ϕ + y sin ϕ = 0 −∞
∞ = ∫ dϕ ∫ F [µ ] ⋅ υ ⋅ e i 2πυρ dυ 0 −∞ ρ π
= ∫ dϕ µ ( ρ , ϕ ) ∗ F −1 (| ν |) 0
(8) = x cos ϕ + y sin ϕ
ρ = x cos ϕ + y sin ϕ
The above formula suggests the following recipe: filter each projection with a ramp filter (multiply by |ν| in the frequency domain), take the inverse 1D Fourier transform along ν and backproject ( ∫ (K)dϕ ) onto the xy-grid. The ramp filter will have the effect of amplifying high frequencies, which on one hand is necessary – simply backprojecting will give a blurry image – but on the other hand also can cause problems with noisy data. In that case another filter such as a Hanning window may be used. 2.2.4. Algebraic Reconstruction Techniques In algebraic reconstruction techniques the X-ray projection process is modelled as a system of linear equations, usually written as Aµ = p ,
where the matrix A models the attenuation of the X-rays, µ is the attenuation coefficient distribution and p contains the projections . This formulation gives a large flexibility to model special geometries, and knowledge of for example noise characteristics may also be utilised when solving for µ. Equation (9) does not have any exact solution, since the system generally is over-determined and noise has introduced inconsistencies in the equations. The system matrix A also turns out to be too large to store in any practical implementation. Although it is sparse it does not possess any simple structure and approximate solutions must therefore be sought using iterative methods. This makes iterative methods computationally demanding, which together with the storage demands is the reason for its limited use in clinical applications.
L2 µ2 L3 µ3 µ1 µ0
Figure 10: Geometrical interpretation of the Kaczmarz method. The approximate solution is sought by orthogonally projecting the initial guess onto the hyperplanes L1, L2, L3 and so on described by the equations.
Many iterative algorithms are developments of the Kaczmarz method, which was used in the first CT scanner. The method is commonly referred to as ART (Algebraic Reconstruction Technique) in the context of CT. Each row k in eq. (9), written ak µ = pk (where ak is the row vector and a k µ is the inner product of the row vector and the image vector), represents the attenuation of one projection ray and mathematically describes a hyperplane. In the ideal case the solution µ is the intersection point of the planes, but since no exact solution exists there will not be any common intersection point. In the Kaczmarz method the vector µ is iteratively projected orthogonally onto the hyperplanes, one after the other (see figure 10). The process is stopped when a solution considered “good enough” has been found. Of course the final vector will depend on the initial guess as well as the order in which the projections are done. The method can also be given a physical interpretation: For iteration q and subiteration k the forward projection of ray k is calculated from the current vector µk-1(q) and compared to the actual observation. The difference is distributed over the voxels crossed by the ray according to the weights in the row vector ak. This forms the next subiterate:
(q) k −1
− a kT µ k( q−1) ak . a kT a k
Hence ART is based on ray-by-ray corrections and therefore uses only one row of the system matrix A at a time.
2.2.5. Three-Dimensional CT Three-dimensional CT reconstructions began with “step and shoot” techniques in which several planes along the patient axis were reconstructed and simply stacked on top of another. Through the introduction of spiral CT scanners a continuous scanning mode was made possible, avoiding the constant acceleration/deceleration of the patient which caused motion-induced image artefacts. This meant a revival for the whole field of CT which since then has found many new exciting applications, for example in cardiac imaging.
Figure 11: In spiral CT the patient is translated and the source-detector gantry rotated, yielding an effective spiral trajectory as seen from the patient’s frame of reference .
As for 2D reconstruction there are numerous algorithms available for threedimensional CT. Many use interpolation approaches in which data from the spiral scan is interpolated to generate synthetic “classical” planar projections. From there on 2D reconstruction techniques can be applied in each plane . Other approaches are truly three-dimensional Fourier algorithms and yet another class of methods are the algebraic iterative ones. All methods share the common problem of being computationally extremely demanding, which explains why so much research and development has focused on algorithm improvements.
2.2.6. The Use of CT for Mammography Since one of the fundamental problems of conventional mammography is the superimposition of structures, it is possible that breast CT could improve image quality. Traditionally CT for mammography has not been considered a viable option because of patient dose and cost-effectiveness considerations . GE Medical Systems even designed a fan beam CT system for mammography in the 1970’s, but the clinical trials did not find it suitable for routine use, above all because of its poor spatial resolution and long scan times .
Figure 12: Illustration of the dedicated cone-beam breast CT setup proposed by Boone et al. .
Recent development of digital detectors has offered new possibilities and renewed the interest in the subject. Boone et al. , Chen and Ning  and Gong et al.  have studied dedicated breast CT setups with geometries as illustrated in figure 12 above, in which only the breast is subjected to the X-rays. The cone beam projects the breast, which does not need to be compressed, onto a flat panel detector. The studies have been carried out first with simulations and later on with prototype systems. The results have suggested that breast CT could provide improved detectability and location of breast tumours and lesions at glandular doses comparable to conventional mammography. Nelson et al. conducted a preliminary clinical trial from which they conclude that breast CT “provides high quality volume data that enhanced visualization of breast glandular tissue and architecture compared to other breast imaging methods” .
3. Technical Description 3.1. XCounter’s Gaseous Avalanche Detector XCounter AB has developed a gaseous avalanche detector based on the same principles as the Multiwire Proportional Chamber invented by Charpak at CERN in the 1960's. A detector module consists of two narrowly spaced plates between which a high voltage is applied. The space between the plates is filled with a gas, typically a Krypton-gas mixture. As X-rays interact with the gas ionisation occurs and electronion pairs are created. The liberated electrons and ions accelerate in the electric field towards the anode and cathode respectively. As they move in the field they gain energy which is transferred to other atoms through collisions. This creates many secondary electron-ion pairs and an electron avalanche is quickly built up, amplifying the original signal many times. The anode plane is equipped with strips, or antennas, which collect the signal and makes position determination along the detector module possible.
Figure 13: Working principle of XCounter’s gaseous avalanche detector .
Fast ASICs sitting at the ends of the anode strips count each pulse, which makes the detector truly photon-counting in contrast to many other technologies that are energy integrating. The strong amplification provided by the applied HV allows for the electronics to discriminate the X-ray photons from the electronic background noise, making the image noise dominated by the Poisson noise. The combination of a deep detector filled with a high atomic number gas makes it very efficient, about 80% of the photons are detected. Furthermore, the narrow slit design gives the detector module a very small angular acceptance which efficiently discards any scattered photons and thereby reduces image blur.
3.2. The XC Mammo -3T Mammography Prototype A mammography prototype, XC Mammo -3T, has been built using XCounter’s detector technology. 192 detector modules are mounted in a gas-filled camera box below the object table. Each module has 1024 channels and an effective pixel size of 60 µm, giving it a total length of roughly 6 cm. The modules are mounted in four columns (48 in each) and the strips point towards the X-ray tube focal spot. A collimator restricts the radiation to the solid angles covered by the detector modules. The breast is compressed between two plates and positioned similarly as in classical mammography. The camera and collimator move in a coordinated fashion to scan the breast, which results in 48 images obtained from different angles which are used to make a three-dimensional tomosynthesis image of the breast. Digital tomosynthesis can be thought of as a development of classical tomography and allows any plane through the object to be reconstructed from the acquired set of projections. In classical tomography only one plane is reproduced sharply in each scan. Planes out of focus also contribute to the image but are blurred.
Figure 14: The basic geometry of the XC Mammo -3T seen from the patient’s view. The camera with the detector modules is mounted below the object table. The collimator and camera move together to scan the breast.
Figure 15 below depicts a row of detector modules and the scanning geometry. The strips of each detector module are directed towards the focal spot and the scan is performed orthogonally to the arrays. X-ray tube focal spot
Scan direction Collimator plane
Object Pixel direction
Object Scan direction
Detectors directed towards source
Figure 15: Alignment of the detector modules and scan direction.
The beam has the half-fan shape typically used in mammography (see figure 16 below). The focal spot on the X-ray tube is located at a vertical distance of 650 mm and the collimator at 170 mm from the detector module. The focal spot is quite large, about 300 µm, while the collimator slit between the tube and the detector is smaller, 95 µm. This gives the X-ray beam an intensity profile of a trapezoid as sketched to the right in figure 16. The beam width through the object is in the range 150-200 µm.
x Beam profile z Detector module 1024 x 60µm
Figure 16: Fan beam geometry and beam profile of the XC Mammo -3T.
The detector’s response to photons is dependant on where between the anode and cathode planes the photon enters, since the electron avalanche must receive sufficient gain to exceed the threshold for detection. The beam profile is however aligned towards the cathode and falls within an active region of the detector with nearly flat response. Therefore it is safe to assume that the effective beam profile is identical to the one illustrated in figure 16 above. A small patient study comparing the reconstructed images with conventional screenfilm images has been conducted. The results have been very promising with better visualisation of anatomical structures and calcifications at glandular doses lower or comparable to the screen-film images [12, 13].
Figure 17: Comparison of mammograms of the same breast taken with the XCounter XC Mammo -3T (left) and ordinary screen-film technology (right). The arrow points out a ductal carcinoma (malignant cancer in the ducts) which is much better visualised in the left image .
3.3. The Prototype CT Setup For the prototype CT setup the XC Mammo -3T machine and a detector module test setup with identical geometry, but with only one detector module installed at a time, was used. Since these setups are fixed the object had to be rotated in the X-ray beam as illustrated in figure 18 below. For this purpose an object holder was built.
Figure 18: The object is rotated in the X-ray beam.
A PMMA (“Plexiglas”) cylinder with inner diameter 40.3 mm and outer diameter 50 mm was used as object container. Two fitting aluminium lids were made in a metal lathe, giving the outer diameters very low tolerance of only 20 µm. One of the lids was mounted on a step motor. A spring applies pressure to the opposite lid in order to stabilise the axis of rotation (A). The whole construction is mounted on a metal plate which can rotate on the base plate around axis B (see figure 19). The rotation around B is controlled with a micrometer screw. This allows the axis of rotation (A) to be aligned with the detector scan direction with high precision. Figure 20 on the next page shows a photo of the object holder. Lids Step motor
Spring Plexiglas cylinder B A
Figure 19: Schematic of the rotating object container from the side (left) and from above (right).
Figure 20: The object holder without the Plexiglas container.
4. Method 4.1. Data Acquisition 4.1.1. Aligning the setup When placing the CT setup on the object table of the imaging system it is important that the axis of rotation is as close to parallel to the scan direction as possible. In order to do this the edges of the metallic lids were used. The lids have very well-defined diameters and their X-ray projections have high contrast. By scanning the vertically aligned detector module from one lid to the other and comparing the channel numbers of the lid edges, the line-up could be adjusted with the micrometer screw. The precision is estimated to be within 200 µm, considering the tolerance of the lids (20 µm), the detector pixel size (60 µm) and the uncertainty in determining the position of the lid edges in the projection image. 4.1.2. Single slice scan using the XC Mammo -3T In order to get a practical idea what requirements the CT setup must meet, an initial single-plane scan was acquired in the XC Mammo -3T. At this point the setup was simpler than the one explained in section 3.3 on page 20, and the experiences learned from this led to the final design. The object was a simple plastic phantom with a few holes drilled in it. Silicon oxide balls with diameters roughly 0.5 mm and a thin glasscoated gold wire (gold diameter 25 µm) were also attached to it. The phantom was mounted directly on the axis of the step motor, but the rotation axis was at this point not stabilised by the spring. The axis of rotation was also not aligned with the scan direction as described in the previous section. 1000 projections per turn were collected. The acquired slice cut through the smaller outer diameter (2.5 mm) part of the phantom with hole diameters 2.5 mm, 3.3 mm and 5 mm respectively.
Figure 21: The simple plastic phantom used in the initial planar CT scans.
4.1.3. Spiral scan using the module test setup The detector module test setup with one detector corresponding to the vertical array (see figure 15, page 18) in the XC Mammo -3T was used to acquire spiral scan data. The spiral scan modality was realised by simultaneously rotating the object container and translating the table on which it was mounted. A small rodent was put in the PMMA cylinder and a copper wire was attached on the outside of the cylinder. A normal projection image was taken to get an overview picture. Due to limitations in the data acquisition system only small datasets corresponding to three turns could be collected in one scan. Six such short spiral scans were made of interesting regions of the rodent. A sequence of 20 scans was also made, each compromising three turns yielding a total scan length of 6.5 mm in 60 turns. A Wolfram rod on the outside of the cylinder was used as an aid for the reconstructions (see section 184.108.40.206 for details). Unfortunately the controller software did not state the correct acquisition and readout times, but they were adjusted to get 1080 projections per whole rotation. The step length between each acquisition was 0.1 µm, which gave a scan length of 108 µm per turn. All scans, except for the projection image, were acquired with 20 mA tube current at 40 kVp to get total exposures roughly comparable to those for mammography scans in the XC Mammo -3T.
4.2. Reconstruction Method 4.2.1. Overview An algebraic iterative algorithm for volumetric reconstructions, adapted to the system geometry, was implemented in C and Matlab. The implementation of filtered backprojection in fanbeam geometries in the plane included in the Matlab Image Processing Toolbox was used for slice-by-slice reconstructions, which could then be used for slice stacking. In the algebraic reconstruction method the forward projection process is modelled as a system of linear equations, Aµ = p ,
where p represents the recorded (and log-normalised, see equation 5, p. 10) projections and µ is the three-dimensional distribution of attenuation coefficients for which one seeks an approximate solution. The matrix A attempts to model the specific geometry of the XC Mammo -3T, including the divergence of the X-ray beam. The iterative algorithm is similar to the variant of SART (Simultaneous Algebraic Reconstruction Technique) described by Benson and Gregor . Limitations imposed by available computer memory only permits parts of A to be stored. Subsets of the system matrix are computed as they are needed and thrown away after they have been used. The algorithm simultaneously uses one whole subset of A in each sub-iteration, instead of only one ray at a time as in ART (section 2.2.4, p. 12).
4.2.2. System model The properties of the X-ray projection system, and the level of accurateness with which it is modelled, are completely incorporated in the system matrix A. A coordinate system (O-xyz) fixed to the object is defined. The source and the detector arrays are imagined to rotate around the origin (O) in a plane parallel to the x-y-plane. A second coordinate system (O-x’y’z) defines the directions of the detector array and the vertical line joining the source point (S) and the detector array (D). The z-axis coincides with the scan direction. Figure 22 below shows the described geometry together with the parameters defining the scan setup. RD, RS and d will define where along the array the projection of the object falls and RS and RK will define the beam divergence. y y’ φ x’ d O
x D RD
Figure 22: Definition of the geometry in the plane. The parameters RS, RK, RD and d define the scan setup.
Row i in eq. (11) describes the attenuation of projection ray i. The matrix element aij of A describes the influence of voxel j on the attenuation of ray i. If aij would be taken as the length sij of ray i through voxel j, each row would correspond to a discrete approximation of the projection formula:
pi = ∫ µ ( x, y, z )ds ≈ ∑ sij µ j = ∑ aij µ j . j
However, using the line lengths as matrix elements causes ring artefacts in the image  and does not take the finite beam size into account. In this model the fractional overlap in the xy-plane is instead calculated, as is the fraction of the intensity incident on the voxel in the z-direction, taking the beam profile into account. See figure 23 on the next page for an illustration.
S y ( ix, iy )
Beam profile Projection ray i
z iz1 iz2 iz3
Figure 23: Calculation of matrix elements is based on the fractional overlap in the xy-plane and the fraction of the intensity incident on the voxel along z.
The matrix element aij is calculated as: aij =
overlapping area incident intensity ⋅ . total pixel area total intensity
This choice will give very low weights to voxels that lie nearly out of the scanning plane or barely overlap the X-ray, which makes sense from a physical point of view since they do not contribute much to the attenuation of the ray. However, the dimension of a matrix element is no longer a distance, so equation (12) will strictly speaking not be completely true, but the chosen approach should better reflect the beam properties. Another possible model would be to divide each ray into several lines, calculate the lengths of the lines within each voxel and use the averages as elements. This would also take the finite size of the rays into account, but it has not been tried out.
4.2.3. Simultaneous Algebraic Reconstruction Technique To solve the system of linear equation a variant of SART (Simultaneous Algebraic Reconstruction Technique) was implemented. The algorithm was developed by Andersen and Kak  and is based on the idea of simultaneously applying correction terms to the image for all rays in a given projection, as opposed to “classical” ART which bases its corrections on single rays (section 2.2.4, p. 12). SART provides reasonable reconstructions much faster, already after one iteration, and is much less prone to “striping” artefacts than ART. Andersen and Kak also introduced other ideas such as heuristic weighting schemes along the backprojection rays, but this has not been applied in this case. The algorithm is based on the expression
) ]} c
µ (k,t +1 ) = µ (k,t) + AtT ⋅ p t − At µ (k,t) rt
where k is the iteration index, t is the subset/subiteration index, At is the subset of the system matrix (i.e. a set or rows) and pt is a vector containing the projections belonging to the subset. The division operator refers to element-wise division and rt and ct are the row- and column sums, i.e. rt ,i = ∑ a ij j
ct , j = ∑ aij ,
where St denotes the set of projections belonging to subset t. Equation (13) can also be written element-wise for the individual voxels as
(k,t +1 )
aij ( pi − ∑ aih µ h( k ,t ) ) h ∑ aim i∈S t ∑ (k,t) m = µj + . ∑ aij
The algorithm works as follows: I. Initiate with guess µ(0). Set k = 0, t = 0. II. For each iteration k: For each subiteration/subset t : 1. From the current image calculate the forward projection At µ(k,t) and the deviation from the actual observed projections ( pt − At µ ( k ,t ) ). 2. Weight the difference with the row sums, i.e. with the total overlap of each ray. 3. Backproject correction by multiplication with AtT (the result has the same dimensions as the image). 4. Weight with the column sums, that is with the sum of all overlaps for each voxel. 5. Add correction to image. III. Done.
Equation (13) can be given a more intuitive explanation if one considers what the row and column sums are. If the finite size of the rays are ignored and the projections are thought of as true line integrals, the row sum for ray i is rt ,i =
∫ ds , "ray i "
and the column sum for voxel j is ct , j = ∑
∫ ds .
i "ray i "
The factor aij/rt ,i which appears in (15) is the fractional length of the ray through voxel j compared to the total length through the object. Using rt,i as a weight when backprojecting the error corresponds to backprojecting in proportion to “how much” voxel j contributed to the total attenuation. Dividing the correction term for voxel j with ct,j is a way of taking the average of the correction terms generated by several projection rays. This seems wise since different rays may demand different corrections to the image. 4.2.4. Implementation The calculation of the system matrix and the SART reconstruction algorithm was implemented in C MEX-files for Matlab. Development started out in Matlab’s interpreted language but soon proved to be too slow. By using MEX-files data can easily be passed to and from the Matlab workspace, which makes pre- and posttreatment easier. The basic idea of the implementation is to calculate the subset of A as it is needed, use it in one sub-iteration and then throw it away. Subsets are defined on a view-basis; all projections with the same projection angle belong to one subset. For a spiral scan this means one projection per turn. One of the disadvantages of using iterative methods, the speed issue, becomes apparent immediately when the implementations are used. It is the calculation of the subsets of A that completely dominate the computational work.
5. Results and Analysis 5.1.1. Single slice scan using the XC Mammo -3T These initial measurements were used to try algorithms on single-plane reconstructions. Ifanbeam and iradon, the algorithms for fanbeam and parallel beam geometries included in Matlab’s Image Processing Toolbox, were applied on the data. Figure 24 below shows the acquired sinogram for the phantom. The channels have been normalised with a white image acquired with 40 mm PMMA. Two important features are visible in the sinogram. The horizontal arrows show what happens when the detector array is not perpendicular to the rotation axis. The silicon ball has left a trace in the first half of the sinogram, but has rotated out of plane in the lower half. Consequently the projections are incomplete, which may cause problems. The other important feature, which may be hard to notice in the printed image but is easy to see when zooming in, is the wiggly appearance of the cylinder edge. It was possible to fit a sine curve with period 2 s to the edge, which suggests that the axis of rotation was wobbling. In the reconstruction this will give the cylinder centre a small offset. The thin gold wire has left a thin sinusoidal trace which is hard to reproduce in print but is clearly visible when viewed on a computer screen.
Figure 24: Acquired sinogram of the plastic phantom.
Before reconstructing the sinogram was normalised and the logarithm was taken according to p = − ln(I / I 0 ) . I0 was estimated by averaging over a rectangular region where the radiation field is supposed to be homogeneous. In addition, a non-negativity constraint was applied to the projections from physical considerations. 28
Figure 25 shows various reconstructions produced with iradon (A) and ifanbeam (B, C, D) from 720 projections. The images have 650x650 pixels with a pixel width of about 60 µm. The reconstructions look reasonable, but the gold wire to the right in the image has been severely distorted in the images in the upper row. In the case of iradon (A) this is most likely due to the faulty assumption of parallel beam geometry. Ifanbeam assumes fan-beam geometry, which is a better approximation of the actual case. The artefacts on the gold wire in the upper right image (B) were first thought to also be due to discrepancies between the model and the actual geometry. However, when the order of the projections at a later point by chance was reversed, the artefacts on the wire disappeared! Unfortunately the silicon ball, for which the projections were incomplete, also disappeared (see image C). It was completely unexpected to see that the order of the projections should matter to the algorithm, but without insight into the implementation of ifanbeam it is hard to see why. The last image (D) is identical to (C) but with a non-negativity constraint applied, which is reasonable from a physical point of view since negative attenuation values would correspond to X-ray sources within the material. All the features visible in (C) are still there in this case, but the experience with other images has shown that removing the negative values can deteriorate the visibility of objects.
Figure 25: Reconstructions with iradon (A), ifanbeam (B), ifanbeam with reversed order of projections (C) and ifanbeam with reversed order of projections and a non-negativity constraint applied (D). Windowing has been applied to best enhance the visibility of the details in each image. The images have 650x650 pixels of size 60 µm x 60 µm.
The iterative solver was also used to reconstruct the phantom. Figure 26 below shows the result after one iteration to the left and after five iterations to the right. The images have 800x800 pixels of size 56 µm x 56 µm and were reconstructed from 1000 projections. Both images appear very noisy, but the low contrasts between the air-filled holes and the PMMA are clearly visible with proper windowing. The glass-coated gold wire, situated near the right edge in the images, is reproduced in an acceptable fashion, although it is considerably broader than the 25 µm gold diameter. The silicon oxide ball has produced dark streaks tangentially to the phantom edge and also a white streak almost horizontally, and light shades are visible close to it. The artefacts are also present in figure 25, so they must be a result of the incomplete projections rather than the reconstruction method. The artefacts are also very similar to partial volume effects illustrated in an ImPACT slide show available online . In both images there is a clear tendency to over-estimate the edges of the phantom. This could be taken for a cupping artefact, a common problem in CT caused by beam hardening: As the beam passes through the object the low-energy photons are absorbed to a larger extent than high-energy photons, which makes the beam more penetrating as it passes through the object. This leads to an over-estimate of the absorption coefficient at the edges. However, the reconstructions in figure 25 do not have any significant cupping so what is visible in figure 26 must be a problem specific for the reconstruction algorithm. Wojciech and Beekman wrote that edge artefacts are a problem inherent to iterative methods and hypothesise that the cause is due to discretisation errors in the forward projection process during reconstruction . Furthermore they report that performing the reconstructions on a finer grid helps, which suggests that their hypothesis is correct. The method has been tried on this data but without success. Wojciech and Beekman used statistical reconstruction methods which take the statistical properties of the projection data into account, such as the maximum likelihood expectation maximisation method, but since their algorithms and the one used here share a forward projection step their results should be applicable. Hence, one can conclude that the edge artefacts are in this case most likely not due to discretisation errors in the forward projection.
Figure 26: Reconstruction with the iterative solver after one iteration (left image) and 5 iterations (right image). 800x800 pixels reconstructed from 1000 projections and non-binned pixels.
One interesting property with the solver is that it has provided an acceptable image after only one iteration, iterating more does not seem to provide any real improvement. The graininess in the right image in figure 26 has a slightly different character, but the most striking difference is that the streaking artefact from the silicon oxide ball has even been aggravated. It may be surprising that running more iterations does not necessarily give better images, but it is actually in agreement with what Andersen & Kak reported about SART . Figure 27 below shows the same object reconstructed from 360 binned projections (detector pixels binned two and two) with and without non-negativity constraint applied. The image is less noisy and the air-plastic contrasts are visible without any narrow windowing.
Figure 27: Reconstruction with the iterative solver with binned pixels. 350x350 pixels (pixel size 128µm x 128 µm) reconstructed from 360 projections without non-negativity constraint (A) and with non-negativity constraint (B).
These initial scans and the reconstructions following it stress the importance of aligning the setup correctly and making the correct geometrical assumptions. Experiences with the iterative solver show that it is crucial to feed it correct geometrical parameters to get meaningful reconstructions.
5.1.2. Spiral scan using the module test setup 220.127.116.11. Single slice reconstructions Figure 28 below shows a projection image of a rodent, about ten centimetres long, placed inside the cylinder. Because of the limitations of the data acquisition system mentioned in section 4.1.3, six very short spiral scans (only three turns each) were made at the positions marked below. Several small high-contrast objects are visible in the belly region. The objects could for example be gravel that the rodent has gotten with its diet or possibly some kind of calcifications. Their sizes have been estimated from figure 28, and some of them are clearly as small as ~300 µm, in other words about the same size as microcalcifications found in breasts. Naturally their X-ray attenuation properties remain unknown and can not be directly compared.
Figure 28: Projection image of the rodent.
Single slice reconstructions of the planes marked in figure 28 were made with the ifanbeam function. Slice 1 is interesting because it contains a lot of strongly absorbing materials such as teeth and bone. Figure 29 shows the sinogram of the first turn (windowed and inverted; white corresponds to low counts) together with a plot of the 300th projection. The counts are at some places as low as 10 photons, which implies a very noisy projection.
Figure 29: Sinogram of slice one with a plot of projection 300.
Figure 30 below shows the resulting reconstruction. A cross-section of the incisors (“gnawing teeth”) positioned nearly between the feet in the upper part of the image, the premolars (“chewing teeth”) and a part of the skull is visible. The copper wire has caused some metal streak artefacts and the image also appears streaky in general. The X-ray-dense objects almost completely absorb the photon flux, thereby introducing inconsistencies in the projections and impeding a correct reconstruction. Still, the image demonstrates that reconstructions from very noisy projection data are possible.
Figure 30: Reconstruction of slice one from 720 projections using ifanbeam. Image has 900x900 pixels of size 60 µm x 60 µm.
Figure 31: Comparison of reconstructions of slice 3 from binned (left) and non-binned data (right). Several of the small calcifications/gravel in the rodent are visible. The image reconstructed from binned detector pixels shows slightly improved contrast and lower noise.
Figure 31 above shows reconstructions of slice three made with ifanbeam using nonbinned and binned detector pixels. Binning the data has resulted in slightly improved contrast and lower image noise. 18.104.22.168. Spiral scan reconstructions Since the scan had to be separated into 20 shorter scans and the step motor rotated continuously, the projection angle at the start of the individual scans varied. In order to be able to test the reconstruction algorithms on the data it had to be re-bundled. This was done by fitting a sine curve to the high contrast Wolfram rod and rearranging the projections in the sinograms to get one long, continuous sine curve. Inconsistencies in depth information can be expected by doing this, since the projections are no longer ordered with monotonically increasing z. However, the beam width along z (about 200 µm at the detector) is large compared to the scanned length during one revolution (108 µm), so a considerable averaging in z-direction is done over one 2π spiral. A reconstruction of the scanned volume with 500x500x60 voxels was made from the re-bundled data. To limit the reconstruction time only 540 out of 1080 projections per turn were used. With the chosen resolution each voxel has dimensions 112x112x113 µm. The iterative solver adapted to spiral scans was run for only one iteration, which means it went through all projections one time. The total reconstruction time was five and a half hours on a 3.4 GHz Intel Xeon. Figure 32 on the next page shows a sequence of six planes perpendicular to the rotation axis. The planes in the image are separated about 340 µm. This particular sequence was chosen because it illustrates how some of the small high-contrast objects appear and disappear again. As an example, the ring marks a region where three objects move in and out of the image plane. Unfortunately the Wolfram rod proved to have a bit too high contrast; the streaking artefacts are quite severe. The images also appear a bit shady in the upper and lower parts.
Figure 32: Sequence of every third plane from six to 24. Each image has 500x500 pixels of size 112 µm x 112 µm. The separation between each image above is about 340 µm. The approximate location of the reconstructed region is marked in the small projection image. The white ring marks a region where several high-contrast objects move in and out of the image plane.
By studying the sizes in the image plane and the z-profile FWHM of some of the smallest but (subjectively) still clearly visible high-contrast objects, their sizes were estimated to be down to at least 400 µm, i.e. on the same order as microcalcifications in breasts.
Figure 33: Plot of z-profile of the marked object. FWHM about 3.5 plane separations, i.e. ~400 µm.
Using the VolumeViewer plugin for ImageJ the volume data was used to create a three-dimensional image. The result can be seen in figure 34 below. With appropriate thresholding the spine, several high-contrast spots and the tape wrapped around the rodent can be seen. The image has been cropped in order to exclude the Wolfram rod.
Figure 34: 3D visualisation of the reconstructed volume.
22.214.171.124. Multi-plane reconstructions For comparison purposes slice-by-slice reconstructions were made with the Matlab implementation of FBP for fanbeam geometries, ifanbeam. Each slice was reconstructed by using one turn, the next plane using the following turn and so on. The re-bundled spiral scan data described in the previous section was used, but due to limitations in the release of ifanbeam used each turn had to be interpolated from 1080 projections to 720. 60 planes were reconstructed, just as for the “truly” volumetric reconstructions. Figure 36 on the next page shows a sequence of planes in the same region as figure 32. Again, the spine, the tape wrapped around the rodent, several calcifications/gravels and the streaky Wolfram rod are visible. Ifanbeam neglects that: 1. The beam is half-fan shaped rather than fan shaped. 2. Each spiral turn contains projections from several reconstruction planes due to the beam divergence (having a width of roughly two voxels in z-direction) and the translation. Despite this the reconstructions in figure 36 are more appealing to look at than those in figure 32. They suffer less from streaks and the contrasts are higher. Figure 35 below shows the same 3D view as figure 34. The streaks are still there, but the “tails” on the spots are not as long. The overall improved contrast has also made thresholding easier which enhances visibility of objects. Part of the improved performance of ifanbeam with respect to streaks and contrast can be explained by the increased number of projections used, but comparisons carried out with equal number of views for both methods have indicated that part of it should be attributed to the algebraic reconstruction algorithm itself.
Figure 35: 3D visualisation of the FBP slice stacking reconstruction.
Figure 36: Sequence of every third plane from plane six to 27, each image above separated about 325 µm. Resolution of each plane is 500x500 pixels, pixel size 120 µm x 120 µm. The approximate location of the reconstructed region is marked in the small projection image.
126.96.36.199. Dose considerations The exposure times and X-ray tube currents were chosen to roughly correspond to normal mammography exposures. For mammography, the average glandular dose (AGD) and entrance skin air kerma (ESAK) are normally used to quantify the patient dose. The ESAK is the kinetic energy released per unit mass in air right before the entrance skin, and is important since the entrance skin receives a dose from low energy photons in the beam which is not negligible. The ESAK is measured at specific positions in the mammography unit and is used to calculate the AGD. Although the AGD can not be directly measured it is a very important estimate since the breast glandular tissue is considered particularly sensitive to ionising radiation. The spiral scan was done in 60 turns, each turn taking 2 s and compromising 108 µm, giving a scan speed of 54 µm/s. The tube voltage was 40 kVp and the current was set to 20 mA. In the clinical studies conducted with the XC Mammo -3T a tube voltage of 30-35 kVp and currents of 140-180 mA were used . The scan speed is 30 mm/s and 48 detectors in a row scans the object. The delivered dose is proportional to the X-ray tube current and the number of detector modules that scans the volume. Furthermore it should be inversely proportional to the scan speed. Thus, a relevant measure for comparing the dose delivered in the spiral scan with the clinical tomosynthesis scans should be # detectors ⋅ tube current , scan speed
which gives the result (48·180 mA)/(3·103 µm/s) ~ 0.28 mAs/µm for the tomosynthesis scan and (1·20 mA)/(54 µm/s) ~ 0.37 mAs/µm for the spiral CT scan. For reference, the average glandular dose in the clinical trials was about 1.5 mGy and the entrance skin air kerma about 5 mGy. Of course the rodent in the plastic cylinder differs substantially from a breast. Apart from having slightly different attenuation properties, the sizes differ: The outer diameter of the cylinder was 5 cm, and an uncompressed breast may have a diameter of 10-15 cm. Although the object diameter has increased a few times, this can be compensated for by using higher photon energies. For example Boone et al. used 80 kVp . The rough estimates and the discussion above should be viewed as an attempt to get at least reasonably realistic statistics in the spiral scan.
6. Discussion As described in section 5.1.2 both the volumetric iterative reconstruction algorithm and the slice-by-slice filtered backprojection (FBP) reconstructions provided 3D visualisation of highly absorptive structures within the rodent. Although the FBP reconstructions looked more appealing the benefits of a truly volumetric reconstruction should become visible when reconstructing regions sampled by detector modules at larger angles, where the region sampled in one turn deviates more from a plane. The effort of taking the spiral trajectory into account should also start to pay off when larger distances are covered in each turn (i.e. with larger pitch, to use the spiral CT nomenclature). Both reconstruction methods show that it is possible to do CT reconstructions from projection data with very poor statistics, at least with data from XCounter’s detector, which has no electronic noise and very efficient scatter rejection. A tube voltage of 3540kVp was used, but a higher kVp setting would give better statistics and probably be more suitable (for reference, Boone et al. used 80 kVp ). As the photon energy increases, so does the Compton scattering and thereby also the virtues of using XCounter’s detector compared to for example a flat panel detector. Some of the artefacts in the reconstructions in section 5.1.2 are common for the two methods, but some are not and must therefore be attributed to the algorithms themselves. In particular, the iterative reconstructor gave shady images and the streak artefacts were more severe. The problem with streaks could possibly be viewed as a question of “maturity” of the algorithm. For example it has been noted that the order in which the projections are treated has great influence on the final image. The shades may of course be a result of bugs in the implementation, but also due to a bad system model. As pointed out by Andersen and Kak  as well as Mueller  the approach of using the area overlaps is not the best choice from a signal theoretical point of view. It should also be noted that the data acquisition used for the volumetric reconstructions could not be preceded by the careful line-up described in section 4.1.1. Since the algorithm was found to be very sensitive to incorrect geometrical parameters, this could also be an explanation for the shady appearance. The reconstructions show that volumetric visualisation of object sizes on the order of larger microcalcifications is possible. Real microcalcifications can however be even smaller, even below 100 µm, and no such objects have been identified. The internal organs of the rodent, characterised by small differences in attenuation coefficients, were also not distinguishable in the images. Due to the absence of electronic noise and scattered photons the noise level is completely determined by the photon flux, i.e. the patient dose. Therefore, arbitrarily small features and differences in attenuation coefficients should in principle be possible to make visible given a high enough dose. Of course the patient dose will in practice have to be limited, especially for screening purposes, and it is unlikely that a new imaging modality will be accepted unless it offers a dose reduction. Since CT requires many views the dose per view must be kept very small, so noise will be a major issue. It is possible that breast tomosynthesis, which allows higher doses per view at the cost of less depth information, is a better choice for mammography. Another drawback of the breast CT geometry illustrated in figure 12 is that it will probably not allow for the breast muscle to be imaged, which is important for finding possible metastases in the lymph vessels. 40
7. Conclusions The aim of this Master Thesis was to make volumetric CT reconstructions from X-ray projection data using XCounter’s equipment and a prototype CT setup. An iterative algorithm adapted to the system geometry was implemented and was used to reconstruct limited volumes of a small rodent. For comparison purposes slice-by-slice reconstructions used for slice-stacking were also made using Matlab’s implementations of filtered backprojection. Upon comparison the iterative algorithm, taking the details of the system geometry into account, does not provide any advantages for volumes sampled by detectors nearly perpendicular to the rotation axis. The results have shown that three-dimensional reconstructions from noisy projection data are feasible, at least when the data is free from electronic noise and scattered radiation as when using XCounter’s detectors. In breast CT, especially for mammographic screening, the patient dose is a great concern and data will therefore by necessity be noisy. In the reconstructions of the small rodent several highly absorptive objects of sizes down to 400 µm were clearly identifiable, but internal organs were not distinguishable. This suggests that breast CT may not be able to provide satisfactory visualisation of the sometimes very small (< 100 µm) breast microcalcifications as well as anatomical structure, at least not at as low patient doses (1-2 mGy AGD) as with XCounter’s breast tomosynthesis system.
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