using CdTe-detectors with electronic spectrum
splitting
Charlotte Eriksson
2013-06-27
Institutionen f¨or medicinsk teknik
Department of Biomedical Engineering
Examensarbete
Optimization of Dual Energy data acquisition using
CdTe-detectors with electronic spectrum splitting
Examensarbete utf¨ort i Medicinsk Teknik vid Tekniska h¨ogskolan i Link¨oping
av
Charlotte Eriksson
LiTH-IMT/BIT30-A-EX--13/511–SE
Link¨oping 2013
Department of Biomedical Engineering Link¨opings tekniska h¨ogskola
Link¨opings universitet Link¨opings universitet
Optimization of Dual Energy data acquisition using
CdTe-detectors with electronic spectrum splitting
Examensarbete utf¨ort i Medicinsk Teknik
vid Tekniska h¨ogskolan i Link¨oping
av
Charlotte Eriksson
LiTH-IMT/BIT30-A-EX--13/511–SE
Handledare: Christer Ullberg
XCounter AB
Examinator: Michael Sandborg
IMH, Link¨opings universitet
Avdelning, Institution
Division, Department IMT
Department of Biomedical Engineering Link¨opings universitet
SE-581 83 Link¨oping, Sweden
Datum Date 2013-06-27 Spr˚ak Language ⇤ Svenska/Swedish ⇤ Engelska/English ⇤ ⇥ Rapporttyp Report category ⇤ Licentiatavhandling ⇤ Examensarbete ⇤ C-uppsats ⇤ D-uppsats ⇤ ¨Ovrig rapport ⇤ ⇥
URL f¨or elektronisk version
http://www.imt.liu.se http://ep.liu.se ISBN — ISRN LiTH-IMT/BIT30-A-EX--13/511–SE
Serietitel och serienummer
Title of series, numbering ISSN—
Titel
Title Optimization of Dual Energy data acquisition using CdTe-detectors with electronic spectrum splitting
F¨orfattare
Author Charlotte Eriksson
Sammanfattning
Abstract
Dual energy imaging has made it possible to enhance contrast in medical images using images containing different energy information, by combining low and high energy images. Dual energy data can either be acquired using dou-ble exposures or splitting the energy spectrum into two images using one exposure. This thesis presents investigations of dual energy imaging using a detector solution developed by XCounter which provides dual energy images in a single exposure with a threshold separating low and high energy images. Phantom experiments with phantoms of aluminum and plexiglas were performed using weighted logarithmic subtraction and basis material decomposition to produce dual energy images. Methods were validated and images were evaluated in terms of signal difference in noise ratio to find the threshold and tube voltage combination for optimum energy spectrum separation. The methods were also tested on biological materials using bone, soft tissue and iodine solution as contrast enhancer, to investigate K-edge imaging.
Optimal separation of plexiglas and aluminum were found at 70 kVp and the threshold parameter set within a range of 8 to 9, which corresponds to approximately 30 to 34 keV. For K-edge imaging, the optimum separation were found close to K-edge energy of iodine. The results found in the phantom study correlated with results from the biological material study.
Nyckelord
Abstract
Dual energy imaging has made it possible to enhance contrast in medical images using images containing different energy information, by combining low and high energy images. Dual energy data can either be acquired using double exposures or splitting the energy spectrum into two images using one exposure.
This thesis presents investigations of dual energy imaging using a detector solution developed by XCounter which provides dual energy images in a single exposure with a threshold separating low and high energy images. Phantom experiments with phantoms of aluminum and plexiglas were performed using weighted logarith-mic subtraction and basis material decomposition to produce dual energy images. Methods were validated and images were evaluated in terms of signal difference in noise ratio to find the threshold and tube voltage combination for optimum energy spectrum separation. The methods were also tested on biological materials using bone, soft tissue and iodine solution as contrast enhancer, to investigate K-edge imaging.
Optimal separation of plexiglas and aluminum were found at 70 kVp and the threshold parameter set within a range of 8 to 9, which corresponds to approxi-mately 30 to 34 keV. For K-edge imaging, the optimum separation were found close to K-edge energy of iodine. The results found in the phantom study correlated with results from the biological material study.
Sammanfattning
Tv˚aenergi har gjort det m¨ojligt att f¨orst¨arka kontrasten i medicinska bilder genom att utnyttja bilder tagna vid olika energier, genom att kombinera l˚ag- och h¨ogen-ergibilder. Tv˚aenergidata kan insamlas antingen genom att anv¨anda sig av dubbla exponeringer eller genom splittring av spektrum vid en exponering.
Det h¨ar examensarbetet presenterar unders¨okningar av bildtagning av tv˚aenergi med en detektor som tar tv˚aenergi-bilder i en exponering med en tr¨oskel som sep-arerar l˚ag- och h¨og-energibilder. M¨atningar med fantomer av aluminium och plexi-glas har utf¨orts d¨ar viktad logaritmisk subtraktion och basmaterialsammans¨attning har anv¨ants f¨or att ta fram tv˚aenergibilder. Metoderna har vailderats och bilderna har utv¨arderats med avseende p˚a signalskillnaden i f¨orh˚allande till brus f¨or att hitta den kombination av tr¨oskelv¨arde och r¨orsp¨anning som ger optimal sepa-ration av energispektra. Metoderna testades ¨aven p˚a biologiska material, ben, mjukv¨avnad och jodl¨osning som kontrastmedel, f¨or att unders¨oka bildtagning med K-kant.
Optimal separation av plexiglas och aluminum hittades vid 70 kVp med ett tr¨oskelv¨arde mellan 8 och 9, vilket motsvarar en ungef¨ar 30 till 34 keV. Optimum f¨or bildtagning av material med K-kant hittades n¨ara K-kanten f¨or jod. Resultat fr˚an m¨atningarna av fantomer sammanf¨oll med resultat fr˚an m¨atningar av biologiska material.
vii
Acknowledgement
I would like to thank all the employees at XCounter AB for the opportunity to do my master thesis at your company, a special thanks to Christer Ullberg and Mattias Urech for supervising and input during these weeks. I would also like to thank my parents, Mats and Monica for support and giving me comments on this report.
Last I want to thank my friends at the university for five great years and my best friends Sofie Pettersson and Salli Carlfjord for all encouragement.
Charlotte Eriksson Link¨oping, June 2013
2.1 Example of energy spectrum . . . . 6 2.2 Example of beam hardening . . . . 8 2.3 Example of exiting spectrum after passing materials of I, Al and Pl 9 2.4 Illustration of pulse pileup . . . . 10 2.5 Illustration of equation 2.22. I–and I— are the basis images, linear
combination of these images forms the projection image I◊. . . . . 13 2.6 Illustration of the algorithm. The low and high energy images can be
seen as vectors with different intensity of plexiglas and aluminum, a linear operator ≠w is used to cancel out the intensity of plexiglas in the high energy image . . . . 15 3.1 Processing steps in basis material decomposition . . . . 19 3.2 Illustration of simulated exiting low and high spectra . . . . 24 3.3 Design image. To the left, image of an aluminum plate, to the right,
image of a plexiglas block . . . . 25 3.4 Regions of phantom 1, 2 and 3, composition of each block in Table
3.8 . . . . 26 3.5 Example of phantom setup . . . . 26 4.1 a) Single energy image of phantom 1 , b) Aluminum image of
phan-tom 1 . . . . 30 4.2 SDNR between different ROI:s in phantom 1, a,b) 50 kVp c,d) 60
kVp . . . . 31 4.3 SDNR between different ROI:s in phantom 1, a,b) 70 kVp c,d) 80
kVp e,f) 90 kVp . . . . 32 4.4 SDNR between different ROI:s in phantom 1 . . . . 34 4.5 a) Single energy image of phantom 2, b) Aluminum image of
phan-tom 2 . . . . 35 4.6 SDNR between different ROI:s in phantom 2 . . . . 36 4.7 a) Single energy image of phantom 3 , b) Aluminum image of
phan-tom 3 . . . . 37 4.8 SDNR between different ROI:s in phantom 3, a,b) 50 kVp c,d) 60
kVp, e,f) 70 kVp . . . . 38 4.9 SDNR between different ROI:s in phantom 3, a,b) 80 kVp c,d) 90
kVp . . . . 39 4.10 SDNR between different ROI:s in phantom 3 . . . . 40 4.11 Optimal threshold range for each kVp . . . . 41 4.12 This figure show the optimum weight for all investigated parameter
settings, i.e. the weight which corresponded to highest SDNR . . . 43 4.13 Calculated detected spectra from a) 0.2 mm I and b) 0.5 mm I . . . 44 4.14 The absolute value of the residuals of the returned fit for material
calibration data acquired at 45 kVp . . . . 45 4.15 The absolute value of the residuals of the returned fit for material
4.16 Standard deviation of the returned fit for material calibration data 46 4.17 Histograms of basis material images, image 1 . . . . 48 4.18 Histograms of basis material images, image 2 . . . . 48 4.19 High and low energy images of the fish eye (image 1) and the
result-ing dual energy images by basis material decomposition and weighted logarithmic subtraction . . . . 49 4.20 High and low energy images of the fish jaw (image 2) and the
result-ing dual energy images by basis material decomposition and weighted logarithmic subtraction . . . . 50 4.21 Logarithm of high and low energy images acquired at 8.5-70kVp and
double exposure at 40 kVp and 70kVp with 0.5mm Cu filtration. The images show scanning of a chicken joint . . . . 51 4.22 Resulting dual images of the chicken joint, using high and low energy
images shown in figure 4.21. . . . 52 4.23 SDNR for each weight and threshold . . . . 53 4.24 a) Single energy image, b) Iodine enhanced image . . . . 54 4.25 Single energy images of injection 2 and 3, and resulting iodine
en-hanced images using no filter and gaussian filter . . . . 55 4.26 Effect of pulse pile up on single energy image . . . . 57
Contents
1 Introduction 1
1.1 Problem formulation . . . 2
1.2 Purpose and goal . . . 2
1.3 Approach . . . 2
1.3.1 Difficulties and limitations . . . 3
2 Theory 5 2.1 Monochromatic projections . . . 5
2.2 Polychromatic projections . . . 6
2.3 Mass attenuation coefficient . . . 6
2.4 Beam hardening . . . 8
2.5 Dual energy imaging . . . 8
2.5.1 Energy spectra . . . 8
2.6 Energy spectrum splitting . . . 9
2.7 Basis material decomposition . . . 11
2.7.1 Basis projection image . . . 13
2.7.2 K-edge imaging . . . 13
2.8 Weighted logarithmic subtraction . . . 13
3 Material and methods 17 3.1 Contrast calculations . . . 17
3.2 Pre-processing of raw data . . . 17
3.2.1 Image correction . . . 17
3.3 Weighted logarithmic subtraction . . . 18
3.4 Basis material decomposition . . . 19
3.4.1 Material calibration of Aluminum and Plexiglas . . . 19
3.4.2 Material calibration, Iodine and Plexiglas . . . 20
3.4.3 Validation of inverse mapping functions . . . 22
3.4.4 Scatter . . . 22
3.5 Optimal parameter setting investigation, Aluminum and Plexiglas 22 3.6 Image acquisition, Plexiglas and Iodine . . . 23
3.7 Image acquisition using double exposures . . . 24
3.8 Phantoms . . . 25
3.8.1 Phantoms of plexiglas and aluminum . . . 25 xi
3.10 Pulse pile up investigation . . . 27
4 Results 29 4.1 Optimal parameter settings . . . 29
4.1.1 Phantom 1 . . . 30
4.1.2 Phantom 2 . . . 35
4.1.3 Phantom 3 . . . 36
4.1.4 Optimal threshold . . . 41
4.2 Validation of dual energy techniques . . . 42
4.2.1 Evaluation of basis material decomposition, Plexiglas and Aluminum . . . 42
4.2.2 Evaluation of weighted logarithmic subtraction, Plexiglas and Aluminum . . . 43
4.2.3 Validation of calibration data, Iodine and Plexiglas . . . 44
4.3 Images of biological materials . . . 47
4.3.1 Decomposition of bone and soft tissue, fish image . . . 47
4.3.2 Doble exposure comparison, chicken image . . . 51
4.3.3 Decomposition of iodine and soft tissue . . . 53
4.3.4 Scatter investigation . . . 56
4.4 Pulse pile up investigation . . . 56
5 Discussion 59 5.1 Aluminum and Plexiglas . . . 59
5.2 Iodine and Plexiglas . . . 61
5.3 Images of biological images . . . 61
5.4 Pulse pileup . . . 62
6 Summary and conclusion 63 6.1 Further work . . . 63
Chapter 1
Introduction
This master thesis is done on behalf of XCounter. XCounter develops and manu-factures photon counting detector solutions for X-ray imaging in medical, dental and industrial area. This study will focus on optimization of image acquisition for imaging methods used in the medical field.
Development of new blood vessels are common in cancerous tissue, a vascular contrast agent can be used to increase the detectability of tumors. To detect tumors in mammography, the standard method is to use contrast-enhanced MRI. Using iodine as a contrast-enhancer have been proven to enhance contrast in X-ray images, by advantage of the discontinuity in X-ray spectra behind iodine [1]. In conventional chest imaging when detecting long nodules it is convenient to mini-mize the intensity of the ribs [2]. By combining images acquired with low and high energy it is possible to extract more information from the scanned object, referred to as dual energy imaging. Dual energy imaging makes it possible to cancel out the intensity of one material to increase the detectability of other present materials. In this study a photon counting CdTe-detector with multiple energy levels is used to acquire low and high energy images. This detector solution provides dual energy imaging using one exposure where height analysis of each pulse classifies a photon as low or high energy. This solution have the potential to minimize dose level and motion artifacts compared to acquire two images at different energy spectra. The aim of this thesis is to find the optimal energy spectrum splitting to perform dual energy imaging of data acquired with this detector solution.
1.1 Problem formulation
Acquiring low and high energy images with double scans with different energy spectra give a distinct separation between the spectra, but it requires higher dose compared to a single exposure. As previously been mentioned, it is adequate to find the optimal threshold which splits the energy spectrum. The spectrum has to be separated to have enough number of photons in both images and to carry different energy information from the scanned object in order to reduce noise in the final images and increase signal difference between materials.
The detector used in this study is a dual-energy fast photon counting CdTe detec-tor with integrated charge sharing correction. Previous studies done by XCounter [3], [4], have evaluate the energy resolution of the detector with great results. Due to implemented charge sharing correction, the energy resolution is greatly enhanced which is important for acquisition of dual energy images. The electronic spectrum splitting was simulated in [3] accompanied with simulated dual energy images, showing possibilities for dual energy imaging. In [4], an experimental study of dual energy was done using a simple phantom composed of two materials, showing no contrast in the single energy image. Weighted logarithmic subtraction was used to enhance contrast between the materials, resulting in good separation of the materials. As an extension to this study, this thesis present an extensive in-vestigation of phantoms with different compositions at different parameter settings using two dual energy techniques.
1.2 Purpose and goal
In the detector system the separation between low and high energy photons is set by a threshold. The principal of this study is to find the threshold which corre-sponds to the low and high energy images which is best adapted for dual energy imaging, in order to achieve images with high image quality and detectability.
1.3 Approach
Two dual energy imaging methods, basis material decomposition and weighted logarithmic subtraction have been implemented to perform dual energy images at chosen parameter settings, section 3.5 and section 3.6, for decomposition of aluminum and plexiglas and of plexiglas and iodine respectively. The methods have been validated for this type of detector solution and the final dual energy images have been evaluated in terms of signal difference in noise ratio (SDNR) as measurement of contrast. SDNR is a measurement of signal difference in relation to noise, defined in section 3.1.
This thesis will investigate dual energy images produced by low and high im-ages acquired at different energies and threshold settings for objects composed of aluminum and plexiglas. An additional study of dual energy images of
biolog-1.3 Approach 3
ical materials as bone, soft tissue and iodine as a contrast enhancer have been performed.
1.3.1 Difficulties and limitations
Energy spectrum separation
Dual energy imaging acquired with double exposures will have better separation between low and high energy images compared to single exposure dual energy imaging, i.e. better image quality. This is due to the energy threshold instead of using double exposures. Close to the threshold, there is an uncertainty between in the separation which introduces noise.
Motion artifacts
When comparing dual energy acquisition techniques, the disadvantage of motion artifacts when using double exposures in clinical use will be difficult to simulate in phantom measurements.
Pulse pile-up
If two events occur too close in time, the system will record the pulses as one event with combined pulse amplitude. For Dual Energy imaging two low energy pulses might be recorded as a high energy event, this is not corrected in the detector. The amount of pulse pileups increases at high photon flux. The effect of pulse pileups at the optimal kVp using measurements at different photon flux has been investigated.
Chapter 2
Theory
In this chapter the theory behind this thesis is presented. The theory behind x-ray projections and the formation of dual energy images are presented in sections 2.1 -2.5 and section 2.6 describes the spectrum splitting. The theory behind used methods to decompose dual energy images are presented in sections 2.7, 2.8. This chapter is mainly based on the work of Alvarez and Macovski in [5] and [6], and basic x-ray physics stated in [7] by Faiz M Khan and in [8] by Dendy and Heaton.
2.1 Monochromatic projections
Consider a monochromatic x-ray beam traveling through a material at fixed dis-tance, with the assumption that the photons can either be absorbed by the material or scattered away from the detector. The probability of photons interacting with the material depends on the attenuation coefficient, µ, further described in sec-tion 2.3. The relasec-tion between incident photons, photon reducsec-tion and material thickness can be described by
1
NdN = ≠µdx, (2.1)
where x is the thickness of the material and N is the number of photons. The same relation is found for the intensity, and the differential can be rewritten as
1
IdI = ≠µdx, (2.2)
where I is the intensity. Solving this differential yields Lambert-Beer’s law
I(x) = I0e≠µx, (2.3)
where I0are the incident intensity on the absorbing material, x the thickness of the
absorbing material and I(x) the transmitted intensity by the thickness x. When using the mass attenuation coefficient, described in equation 2.5, the material thickness x, should be expressed as flx, where fl is the density of the material [7].
2.2 Polychromatic projections
In practice, it’s hard to produce monoenergetic x-rays and the energy of a beam produced by an x-ray generator consists of a spectrum of photon energies where the attenuation coefficient depends on the photon energy. Figure 2.1 shows an example of a typical x-ray spectrum. The emission lines of tungsten produced in the W target are seen in the spectra. The seen emission lines are the K characteristic x-rays, other absorption edges are removed from the spectrum by inherent filtration. [7].
0 20 40 60 80 100 120
X−ray energy [keV]
Relative photon intensity
Figure 2.1: Example of energy spectrum
The log signal function of equation 2.3 show a linear relationship, which are not true for a polychromatic spectra. Instead Lambert Beer’s law are replaced by the integral form and the attenuation coefficient is energy dependent
N = ⁄ Sin(E)e≠ s µ(E)x dE, (2.4)
where µ(E) is the linear attenuation coefficient and Sin(E) is the incident photon
fluence for energy level E.
2.3 Mass attenuation coefficient
The attenuation of an absorbing material is caused by five types of interaction: Compton scattering, Rayleigh scattering, pair production, photo disintegration and the photoelectric effect. Photo disintegration is only important at photon energies above 10 MeV, therefor this interaction is omitted in the attenuation coefficient. The total attenuation coefficient can be summed together as
µ fl = µc fl + µR fl + µpp fl + µp fl (2.5) where µ
fl is the total mass attenuation coefficient, µc
fl ,
µR
fl and
µp
fl are the
2.3 Mass attenuation coefficient 7
the photoelectric effect respectively. The mass attenuation coefficient are given by dividing the linear attenuation coefficient µ with fl, the density of the interacting material. The resulting unit is g/cm2, which makes the mass attenuation
coeffi-cient independent of density and depends instead of atomic composition.
The Compton effect arise when a collision between a photon and an electron with much less binding energy compared to the photon energy. The photon interacts with the free electron, the electron receives part of the photon energy and are emitted at angle ◊, the photon with reduced energy are scattered at angle „. The Rayleigh scattering occurs when the photon interacts with an oscillating elec-tron and changing the direction of the photon. In this process the photon energy is preserved, this effect is most probably to occur at low energies and materials with high atomic numbers.
Pair production arise when the photon interacts with electromagnetic field of the nucleus, in the process an electron and a positron are created by the photon en-ergy. For this interaction, the photon energy must exceed 1.02 MeV since the mass energy of an electron/positron is 0.51 MeV.
In the photoelectric effect the photon is absorbed by the material. The pho-ton interacts with an atom and ejects an inner bound electron from its orbital. In this process the kinetic energy of the photon is transferred to the inner bound electron. Electrons of K, L, M or N shells can be ejected in this process, the pho-ton energy must exceed the bounding energies for electrons in the shells to cause the interaction. When the photon have exactly the same energy as the bounding energy, resonance occur and the photons are strongly absorbed. The probability of photon absorption decreases with energy, the mass attenuation coefficient are
1
E3, except at the bounding energies for each shell where attenuation coefficient is
much higher, which causes discontinuities in the x-ray spectra, so called absorption edges [7].
2.4 Beam hardening
As described in previous section, the attenuation is mainly caused by Compton scatter, Rayleigh scatter, pair production and the photoelectric process. When photons interact with matter, low energy photons are more likely to be absorbed, this is referred to as beam hardening. The effect of beam hardening in an incident polychromatic x-ray spectra are shown in figure 2.2, the incident spectrum was filtered with 10 mm aluminum which hardens the spectrum [8].
0 20 40 60 80 100 120
Relative photon intensity
X−ray energy [keV]
Incident spectra Exiting spectra
Figure 2.2: Example of beam hardening
2.5 Dual energy imaging
In dual energy imaging spectral information is utilized. The principal is to acquire two images at different energy spectra, one image at low energy and one image at high energy. Since different materials have different attenuation coefficients, the acquired images can be combined to enhance contrast of one material relative another or cancel out the intensity of one material in order to improve detectability. The high and low energy images can be acquired at different tube voltage using double exposure or splitting the energy spectrum into two images. The latter is used in this imaging system, described in section 2.6.
2.5.1 Energy spectra
In this study mainly three materials are present: aluminum, plexiglas and iodine. When the energy spectra produced by the x-ray tube passing different materials, the energy distribution changes due to the thickness of the material and the at-tenuation coefficient difference between materials. The exiting x-ray spectra after passing materials of aluminum and plexiglas have the same characteristics. The mean energy of the aluminum spectrum is somewhat higher compared to plexiglas spectrum because greater effect of beam hardening in aluminum. The character-istics of the exiting spectra after passing materials containing iodine differ from incident spectra.
2.6 Energy spectrum splitting 9
The K-absorption of iodine is about 33 keV caused by the photoelectric process, other absorption edges occur at lower energies and these energies are not present in the incident energy spectra, as seen in figure 2.1. Figure 2.6 plots an example of all exiting spectrums, the spectra were simulated with 0.2 mm iodine, 2 mm aluminum and 10 mm plexiglas respectively. The difference between these exiting spectra makes it possible to separate these materials from each other in dual energy imaging. Plexiglas is often used in phantom measurements since the attenuation of this material can be approximated with the attenuation of soft tissue, and the aluminum attenuation can be approximated with the attenuation of bone.
0 20 40 60 80 100
X−ray Energy [keV]
Relative photon intensity
Al Pl I
Figure 2.3: Example of exiting spectrum after passing materials of I, Al and Pl The characteristic photons from the W-target are clearly seen in the image, as well as the K-edge of iodine. The K-edge of aluminum is not significant and is not visible in the x-ray spectra since it occur at low energies, about 1.559 keV. Photons at low energies are absorbed in the anode and do not reach the sorrounding, see figure 2.1 [7].
2.6 Energy spectrum splitting
The imaging system produces high energy and low energy images by splitting the spectrums into two images. When the a photon is absorbed by the CdTe, a cloud of electrons is generated, due to the bias voltage, the electrons are driven toward the pixel pads. The pulse is amplified before it reaches the counting system where the pulse could either be below or above a set threshold. The low energy image, ILE,
represents counts from 0 to a set energy threshold and the high energy image, IHE,
represents counts above this energy threshold. The threshold values represents digital-to-analog converter (DAC) values, table 2.1 present a rough estimation of the relation between threshold and energy (keV)
Table 2.1: Mapping from DAC values to keV
Threshold 5 6 7 8 9 10 11
Energy [keV] 18.8 22.5 26.3 30 33.8 37.5 41.3
Correct classification of the counts into two groups depends on the pulse resolution time. If to events occur too close in time, the system will not be able to detect these as two pulses and the system will record them as one pulse with added amplitude causing incorrect classification. The combination of two low-energy photons can either be erroneous classified as one low energy photon or one high energy photon, depending on the photon energy and energy threshold [9].
time true observed
Figure 2.4: Illustration of pulse pileup
The conversion material in the detector consists of CdTe. Incoming photons hit the detector and interact with the material, the photon energy is transferred to the crystal through Compton scattering and the photoelectric effect. The charge cre-ated by an entering photon can be recorded at two or more pixels, which decrease the energy resolution since pixels are triggered with charge lower than the primary charge. The conversion materials Cd and Te have K-edges at 23 keV and 27 keV respectively. At these energies secondary x-rays may escape out of the crystal,[3]. For these reasons a charge sharing correction is implemented in the detector to improve the energy resolution. The correction is based on the neighboring pixels: when two events is detected at the same time point, the charge is summed and detected to the pixel corresponding to the highest charge. The next neighbors are used as a compromise between energy resolution and counting speed [4].
2.7 Basis material decomposition 11
2.7 Basis material decomposition
The principal of this method is to decompose low and high energy images into basis images where each pixel corresponds to the actual thickness of the scanned object. This method is based on the assumption that the attenuation mainly depends on the photoelectric effect and Compton scattering within the diagnostic range, since pair production is only present at higher energies and Rayleigh scattering when low energy photons interact with matter of high atomic number, Z. With this assumption, the mass attenuation coefficient described in equation 2.5 can be approximated as
µ(E)
fl ƒ acfc(E) + apfp(E) (2.6)
where fcand fpare functions describing Compton scattering and the photoelectric
process, respectively and the coefficients acand ap are material specific constants.
The attenuation caused by photoelectric process have earlier been stated as ap-proximation I
E3 and the attenuation caused by Compton scatter can be
approxi-mated with the Klein-Nishina, which are described in [5],[6], the material constants depends on the atomic number of the interacting material. The mass attenuation coefficients for Compton scattering and photoelectric process are linearly indepen-dent and can be seen as a set of basis functions.
Since two linearly independent sums of two basis functions also are equivalent basis functions, the mass attenuation of two materials (–, —) can be used to de-scribe the attenuation of any other material (›)
µ(E)› fl› = a1 µ(E)— fl— + a2 µ(E)– fl– , (2.7) where a1= Ng›(Z 3.8 › ≠ Z—3.8) Ng–(Z–3.8≠ Z—3.8) , (2.8) and a2= Ng›(Z 3.8 › ≠ Z–3.8) Ng—(Z—3.8≠ Z–3.8) , (2.9)
where Ng are the electron mass density and Z is the atomic number [6].
Combining equation 2.3 and 2.7 gives
I(x) = I0e≠µ(E)–x–≠µ(E)—x—, (2.10)
where I are the exiting intensity and I0the incident intensity.
By splitting the energy spectrum into two images, a set of equations are acquired
IHE(x–, x—) = I0(EHE)e≠µ–(EHE)x–≠µ—(EHE)x—, (2.12)
where the intensity of low energy and high energy are expressed as functions of thickness of materials – and —. Solving the set of equations for the unknowns x–
and x— yields x–=µ—(ELE)log( ILE I0,LE) ≠ µ—(EHE)µ—(ELE)log( IHE I0,HE) ≠µ–(EHE)µ—(ELE) + µ—(EHE)µ–(ELE) , (2.13) x—= µ–(ELE)log( ILE I0,LE) ≠ µ–(EHE)µ–(ELE)log( IHE I0,HE) µ–(EHE)µ—(ELE) ≠ µ—(EHE)µ–(ELE) . (2.14)
Since the attenuation coefficients, µ and incident intensity, I0 are constant for
an energy level, thickness can be expressed as functions of low and high energy
x–(ILE, IHE) = c1log(ILE) + c2log(IHE), (2.15)
x—(ILE, IHE) = c3log(ILE) + c4log(IHE), (2.16)
and are referred as inverse mapping functions. As stated earlier, equations 2.15 and 2.16 are true for a monoenergetic spectra. The dual energy log signals at energy level ELE and EHE can be expressed as
(2.17) log(ILE) = log( ⁄ Sin(ELE)e≠µ–(ELE)x–≠µ—(ELE)x—)dE), (2.18) log(IHE) = log( ⁄ Sin(EHE)e≠µ–(EHE)x–≠µ—(EHE)x—)dE),
where I0,LE and I0,HE are the intensity of the incident beam and ILE and IHE
the intensity of the transmitted beam. Sin(ELE) and Sin(ELE are the incident
photon fluence for low and high energy spectra respectively. Since the log signals for a polychromatic spectra are nonlinear functions, polynomials of the log signals have been found empirical as inverse mapping functions. Linear, quadratic and cubic functions have been investigated [5],[10] as inverse mapping functions
(2.19)
xj(ILE, IHE) = c1+ c2log(ILE) + c3log(IHE),
(2.20)
xj(ILE, IHE) = c1log(ILE) + c2log(IHE) + c3log2(ILE)
+ c4log2(IHE) + c5log(ILE)log(IHE),
(2.21)
xj(ILE, IHE) = c1log(ILE) + c2log(IHE) + c3log2(ILE) + c4log2(IHE)
+ c5log(ILE)log(IHE) + c6log3(ILE) + c7log3(IHE).
2.8 Weighted logarithmic subtraction 13
2.7.1 Basis projection image
This method separates high and low energy images into basis images, by linear transformation these images can form a basis projection image. The basis projec-tion image is defined as
Iproj= I–cos(◊) + I—sin(◊) (2.22)
where I– and I— are the basis images. The resulting projection image can be a
synthesized monoenergetic image, for angles between approximately 10¶ to 70¶.
Material cancellation is for angles between 90¶ and 180¶, where 90¶ corresponds
to total cancellation of basis material – and 180¶ to total cancellation of basis
material —, [5].
Since I– and I— can be seen as basis vectors, the projection image can be
il-lustrated using a vector diagram.
I I
I
proj
Figure 2.5: Illustration of equation 2.22. I– and I— are the basis images, linear combination of these images forms the projection image I◊.
2.7.2 K-edge imaging
The assumption that the attenuation can be approximated by Compton scatter and the photoelectric process, equation 2.6, and that any material can be expressed by the combination of two other materials, equation 2.7, is true for any material above the K-edge. Since iodine have a significant absorption edge, these equations are not true for this material. Since equation 2.7 is not valid, iodine must be present in the material calibration. For equation 2.6 to be valid, the threshold has to be placed close to the bounding energy of the K shell (33.2 keV).
2.8 Weighted logarithmic subtraction
The purpose of this method is to cancel the contrast between two materials. Log-arithm of equations 2.11 and 2.12 shows a linear relationship between log mea-surements and the attenuation. Since the equations are linear, the attenuation of
one material can be cancelled out by a weight
IDE
= log(I0(EHE)e≠µ1(EHE)x1≠µ2(EHE)x2) ≠ wlog(I0(ELE)e≠µ1(ELE)x1≠µ2(ELE)x2).
(2.23) The equation can be rewritten as
(2.24)
IDE = log(I0(EHE)) ≠ µ1(EHE)x1≠ mu2(EHE)x2
≠ log(I0(ELE)) + wµ1(ELE)x1+ wµ2(ELE)x2,
if cancellation of material 1 is wanted
0 = ≠µ1(EHE)x1+ wµ1(ELE)x1, (2.25)
should be satisfied, [1], [12], [13]. When an object are composed by several mate-rials equations 2.24 and 2.25 can be rewritten as
IDE= log(I0(EHE))≠
ÿ
µi(EHE)xi≠wlog(I0(ELE))+
ÿ
wµ1(ELE)xi, (2.26)
where i is the number of present materials. Any present material i can be cancelled if
0 = ≠µi(EHE)xi+ wµi(ELE)xi. (2.27)
Above equations are true for a monoenergetic spectra. For a x-ray spectrum, consider two path of x-rays passing through an object where the thickness of material – is constant and different thicknesses of material —
(2.28) I1,LE = ⁄ Sin(ELE)e≠µ–(ELE)x–≠µ—(ELE)x1,—dE, (2.29) I2,LE = ⁄ Sin(ELE)e≠µ–(ELE)x–≠µ—(ELE)x2,—dE, (2.30) I1,HE = ⁄ Sin(EHE)e≠µ–(EHE)x–≠µ—(EHE)x1,—dE, (2.31) I2,HE = ⁄ Sin(ELE)e≠µ–(EHE)x–≠µ—(EHE)x2,—dE,
where x1,— and x2,— are different thicknesses of material — and Sin(E) is the
incident photon fluende. To cancel out the intensity of material — the following equation should be fulfilled
log(I1,HE) ≠ wlog(I1,LE) = log(I2,HE) ≠ wlog(I2,LE), (2.32)
and the weight can be calculated as
w= log(I2,HE) ≠ log(I1,HE)
2.8 Weighted logarithmic subtraction 15 Plexiglas intensity Aluminum intensity IAl log(IHE) −w*log(ILE) log(ILE)
Figure 2.6: Illustration of the algorithm. The low and high energy images can be
seen as vectors with different intensity of plexiglas and aluminum, a linear operator
Chapter 3
Material and methods
This chapter presents the pre-processing of raw data and the methods to ac-quire dual energy images with enhanced contrast, basis image decomposition and weighted logarithmic subtraction, sections 3.3, 3.4. The parameter settings inves-tigated to find the optimal image acquisition for dual energy imaging is described in sections 3.5, 3.6, as well as the phantom study and dual energy imaging of biological materials in sections 3.8.1, 3.8.2.
3.1 Contrast calculations
As a measurement of contrast in this study, signal difference to noise ratio (SDNR) between regions of interest (ROI) was calculated as
SDNR = (‡SI1≠ SI2
2+ ‡1)/2 (3.1)
where ‡1 and ‡2 were computed as the standard deviation of the chosen regions.
SI1 and SI2 were defined as the mean signal of these regions in the final dual
energy image.
3.2 Pre-processing of raw data
The raw data is the uncalibrated readout data from the detector. This section describes the methods used to calibrate the data on a pixel by pixel basis.
3.2.1 Image correction
To calibrate the images, the images were gain corrected on a pixel by pixel basis in order to adjust the range of read out pixel values. The correction map was calculated as the mean pixel value of a calibration image divided by each pixel value. The calibration image could either consist of several calibration images
summed together or a single calibration image. The correction map was calculated for each low and high energy image according to
corrLE= meanq(qNimLE)
imLE , (3.2)
corrHE= meanq(qNimHE)
imHE , (3.3)
where N is the number of acquired calibration images.
3.3 Weighted logarithmic subtraction
As described in theory section 2.8, the intensity caused by a material can be cancelled using the following equation
IDE= log(IHE) ≠ w ú log(ILE). (3.4)
For decomposition of aluminum and plexiglas, the contrast difference is dominating in the high energy image. The weight were calculated as
w= ≠ln(SIHE,1) + ln(SIHE,2) ln(SILE,2) ≠ ln(SILE,1)
, (3.5)
were SIHE,1, SILE,1, SIHE,2and SILE,2are the mean signals of areas(1,2). The
scanned object composed of the same thickness of aluminum and different thick-ness of plexiglas in order to calculate the signal difference of plexiglas. To validate the calculated weighting factors the SDNR were calculated between areas of differ-ent composition of both plexiglas and aluminum. The weight were varied from 0.1 to 1 with increments of 0.01 to find the weight that corresponded to highest SDNR. For iodine enhanced images the images were calculated using equation 3.4, since the intensity difference between plexiglas and iodine is dominating in the high energy image as well. The weight were varied from 0 to 1 with increments of 0.01 to find the weight corresponding to highest SDNR.
3.4 Basis material decomposition 19
3.4 Basis material decomposition
By basis material decomposition algorithm, high and low energy images can be decomposed into aluminum and plexiglas images where the pixel value corresponds to the actual thickness of the scanned object. Using calibration data, high and low energy images can be nonlinear transformed into aluminum and plexiglas images and these images can be linear transformed into a final image with enhanced or cancelled out materials.
High energy image
Basis image Basis image
Low energy image
Projection image Inverse mapping
Linear transformation
Figure 3.1: Processing steps in basis material decomposition
In material calibration 16 calibration points were used, a polynomial of second degree were used to calculate the inverse mapping functions on a pixel by pixel basis using an iterative Newton-Gauss method. The polynomial of second degree was chosen considering the limited number of calibration points. Projection angle were set to ◊=[0,fi/2] in order to acquire images of plexiglas, aluminum and iodine only.
3.4.1 Material calibration of Aluminum and Plexiglas
In the material calibration of aluminum and plexiglas, filters with known thickness and material were used to determine the coefficients k1≠ k12. In this calibration
com-bined to form the calibration points. The area of the calibration filters were 28x28 mm2, designed just to cover the detector area (25.6x25.6 mm2).
Table 3.1: Filter thicknesses of material calibration of aluminum and plexiglas Aluminum thickness [mm] 0 2 4 6
Plexiglas thickness [mm] 0 10 20 30
Calibration data were acquired at parameter settings in table 3.5. The coefficients
k1≠k12were calculated pixel by pixel, using a iterative Gauss-Newton least square
method to minimize the expressions ÿ N (tal≠ Ial)2 (3.6) ÿ N (tpl≠ Ipl)2 (3.7)
were tpl and tal are known material thickness in mm and N the number of
cali-bration points. The method was evaluated by the returned fit of the calicali-bration data.
3.4.2 Material calibration, Iodine and Plexiglas
As described in theory section 2.7.2, iodine needs to be present in material cali-bration to be decomposed. In the calicali-bration, same filters of plexiglas were used as in material calibration of plexiglas and aluminum (10 mm, 20 mm and 30 mm). A square basin was constructed in plexiglas with inner dimensions of 10 mm x 35 mm x 35 mm to cover the detector area, the basin were filled with a solution of water and potassium iodide (KI) and acted as iodine (I) filters. The K-edge of Potassium is about 3 keV and does not change the characteristics in the detected spectra. The density of KI in the solution was recalculated to thickness of iodine (mm). Chosen iodine thicknesses in the calibration were 0.1 mm, 0.2 mm and 0.5 mm (table 3.2), combining the filters results in 16 calibration points.
The iodine filters were chosen by simulation of exiting x-ray spectra with dif-ferent thicknesses of iodine. Since its adequate to chose filters were the K-edge is apparent. The returned exiting spectra from each iodine filter were calculated from calibration data and compared with simulated exiting spectra in order to find the threshold corresponding to the K-edge. The water basin consisted of a thickness of 4x2 mm plexiglas and 10 mm water, the attenuation of the basin was included in the plexiglas thickness as 18.5 mm. The attenuation of water and plexiglas are similar, allowing water to be approximated as plexiglas.
3.4 Basis material decomposition 21
Table 3.2: Iodine and plexiglas calibration filters
Iodine thickness [mm] 0 0.1 0.2 0.5
Plexiglas thickness [mm] 0 10+18.5 20+18.5 30+18.5
To make solutions of KI and water with the right concentration, conversion be-tween the solution and iodine thickness was necessary.
Assuming a cube of pure iodine, with dimensions 1cm x 1cm x 1cm, i.e. thickness of 10 mm. From table 3.3, the cube weight is 4.933 g, this reasoning gives a cube filled with water and 0.4933 g I, a thickness of 1 mm I. To calculate the amount of KI needed to get 1 mm of I in the cube
1 126.9 mol g 3 1 MI 4 ◊ 0.4933g(mI) ◊ 166 g mol(MKI) = 0.64529g(mKI) (3.8)
where mKI and mI are the mass of KI and I respectively. Since the inner thickness
of the used water basin is 1 cm, the concentration of KI needed in the water basin for 1 mm I is 0.64529 g/cm3. Concentrations for other filter thicknesses used were
calculated in the same way.
Table 3.3: Molar mass and density for KI
Molar mass Density
MI 126.9 g/mol flI 4.933 g/cm3 MK 39.10 g/mol flK 0.862 g/cm3 MKI 166.0 g/mol flKI 3.121 g/cm3
Table 3.4: Conversion from KI solution to I thickness for the water basin KI concentration Iodine thickness
0.64529 g/ml 1 mm
0.3226 g/ml 0.5 mm
0.1291 g/ml 0.2 mm
0.064529 g/mL 0.1 mm
calibration of plexiglas and aluminum, except ÿ
N
(tI≠ II)2. (3.9)
Calibration data were acquired at parameter settings in table 3.6.
The calculation of correction map for the material calibration images were cal-culated based on the images themselves in order to reduce noise in the inverse mapping functions, for both material calibrations respectively.
3.4.3 Validation of inverse mapping functions
The calculated inverse mapping functions were validated by the returned fit of the calibration data. The residual of each calibration point were calculated as
residual= ttrue≠ testimated, (3.10)
where ttrue is the thickness of filter used and testimatedthe mean estimated
thick-ness of the filter. Filter thickthick-nesses and estimated thickthick-nesses were measured in mm, and the unit of the residual is therefor in mm. The residual is used as a measure of the error in the estimated inverse mapping functions. By calculating the thickness of the material using the data used in the least square algorithm, the best result performed by the basis material decomposition algorithm is given. This is referred to as the return fit from the material calibration.
The residuals are also used as a measurement of deviation from the true val-ues when estimating material thickness in phantom experiments, the additional deviation from the true thickness now lies in the argument.
3.4.4 Scatter
Basis material decomposition does not consider the impact of scatter in the mate-rial calibration. Increased read-out counting values in the filters used in matemate-rial calibration due to scatter were investigated using a collimator. A collimator with a hole with a 2 mm radius were placed in front of the filter to allow passage of primary x-rays. This investigation were done for all plexiglas filters, (10, 20, 30 mm). The investigation was done for found optimal threshold-kVp combination for separation of plexiglas and aluminum.
3.5 Optimal parameter setting investigation,
Alu-minum and Plexiglas
To find optimal parameter settings, measurements were done at 50-90 kVp, at 10 mA. The threshold which separates the low and high energy spectrum was varied from 5.5 to 16, increments of 0.5. The acquisition time was adjusted to get
3.6 Image acquisition, Plexiglas and Iodine 23
approximately the same statistics an image without object at each kVp, i.e. the same amount of incident photons. At each parameter setting, 100 images were acquired and averaged to one image to reduce noise.
Table 3.5: Image acqusition parameters
Tube voltage Threshold Tube current Acqusition time
50 kVp 5.5 - 16 10 mA 25 ms
60 kVp 5.5 - 16 10 mA 15 ms
70 kVp 5.5 - 16 10 mA 10.5 ms
80 kVp 5.5 - 16 10 mA 8 ms
90 kVp 5.5 - 16 10 mA 6.5 ms
The above described methods: weighted logarithmic subtraction and basis material decomposition were used to form dual energy images at each threshold-kVp pair. In material calibration process, calibration data were acquired at each parameter setting. In the final images, SDNR, equation 3.1, was calculated between ROI:s.
3.6 Image acquisition, Plexiglas and Iodine
In iodine and plexiglas calibration, it is reasonable to use lower tube voltage com-pared to aluminum and plexiglas separation. Lower tube voltage resulting in greater intensity difference between high and low energy image if the spectrum is separated at the K-edge. The tube voltage must exceed the k-edge absorption energy, 33.2 keV, therefor data were acquired at 45 kVp and 50 kVp, table 3.6. For each threshold 100 images were acquired and averaged to one image in order to reduce noise.
Table 3.6: Image acqusition parameters
Tube voltage Threshold Tube current Acqusition time
45 kVp 3.5 - 20 10 mA 35 ms
50 kVp 3.5 - 20 10 mA 25 ms
The threshold were swept from 3.5 to 20 with increments of 0.5 for iodine filters 0.2 mm and 0.5 mm to investigate the detected spectra and clearly visualize the k-edge to find the that threshold corresponds to K-k-edge absorption energy. Material calibration data and phantom data were acquired within a range of threshold from 6.5 to 11 to cover the K-edge absorption energy.
3.7 Image acquisition using double exposures
As a comparison to acquire dual energy images using one exposure, low and high energy images were acquired using double exposures with different energy spectra. This was done for one of the biological material images, see section 3.8.2.
The low energy image was acquired at 40 kVp and the high energy image was acquired at 70 kVp. The high energy spectrum was filtered with 0.5 mm copper (Cu) to filter out the low energy photons. To illustrate the high and low energy spectra, the exiting spectra of 40 kVp and 70 kVp + 0.5 mm Cu through filters of 20 mm plexiglas and 2 mm Al were simulated. The plexiglas and aluminum filters were used as an approximation of the scanned object composition.
0 10 20 30 40 50 60 70 80
Relative photon intensity
X−ray energy [keV]
(a) Exiting low energy spectra
0 10 20 30 40 50 60 70 80
X−ray energy [keV]
Relative photon intensity
(b) Exiting high energy spectra
Figure 3.2: Illustration of simulated exiting low and high spectra
As seen in the figures, the high energy spectrum overlaps the low energy spectrum. Thicker filter of 1 mm Cu will filter out all photons below 40 keV, but only 5% of incident photons will pass through the filter. The filter of 0.5 mm Cu was chosen as a compromise between imaging time and low energy photons. To make the images comparable, the acquisition time was adjusted to have the same number of counts as in images acquired with threshold 8.5 at 70 kVp.
Table 3.7: Image acqusition parameters
Tube voltage Filter Tube current Acqusition time
40 kVp - 10 mA 45 ms
3.8 Phantoms 25
3.8 Phantoms
In this study two types of phantoms were used, phantoms of basis materials plex-iglas and aluminum and objects of biological material.
3.8.1 Phantoms of plexiglas and aluminum
The phantom consisted of basis materials aluminum and plexiglas to mimic the properties of bone and soft tissue. Two plates of aluminum with four equally sized parts with different thicknesses, 2 mm, 4 mm, 6 mm and 8 mm and seven blocks of plexiglas with a thickness of 10 mm. The idea behind the design is to combine the parts to create different thicknesses of aluminum and plexiglas in the image with approximately same statistics but different energy spectra.
14mm 10 mm 14 mm y x z = 8 mm z = 6 mm z = 2 mm 28 mm 14 mm 28 mm 14 mm z = 4 mm
Figure 3.3: Design image. To the left, image of an aluminum plate, to the right,
image of a plexiglas block
Three phantom combinations were used in the parameter setting evaluation. In phantom 1 the aluminum plate were positioned to leave some uncovered space in front of the detector, forming five areas with different aluminum thicknesses, seven plexiglas cubes were to form six areas of different combinations of aluminum and plexiglas. In phantom 2 an aluminum plate of 2 mm were placed to cover half of the detector area and a block of 20 mm plexiglas to cover the other half. To form three areas with different combinations a plexiglas cube were placed in front of the aluminum plate. In the third phantom the aluminum plate were positioned so the area of 2 mm and 6 mm covered half of the detector, all areas were combined with plexiglas cubes to form four areas with different compositions. All phantoms were placed as close as possible to the detector.
(a) 1 5 4 3 2 6 (b) 1 3 2 (c) 1 3 2 4
Figure 3.4: Regions of phantom 1, 2 and 3, composition of each block in Table 3.8
Table 3.8: Table of phantom composition of phantom 1, 2 and 3
Phantom 1 Phantom 2 Phantom 3
Al [mm] Pl [mm] Al [mm] Pl [mm] Al [mm] Pl [mm] 1 6 10 0 20 0 20 2 2 30 2 10 6 30 3 8 0 2 0 0 30 4 4 20 2 30 5 0 10 6 0 0
The phantom images were calibrated using a correction map based on a calibration image filtered by 10 mm plexiglas and 4 mm aluminum as a mean value of filters used in the material calibration. The correction image were acquired immediately after phantom image acquisition. As described, the components of plexiglas and aluminum were combined to form areas with different composition in front of the detector. Figure 3.5 shows the first combination of the phantom objects (phantom 1).
3.9 Imaging system and setup 27
3.8.2 Biological material objects
Three objects of biological materials were used to evaluate the dual energy imaging methods. To produce images of bone only and soft tissue only, the head of a fish were scanned. The fish were placed in a plastic bag and attached to a plexiglas disc of 4 mm and was adjusted so that the head of the fish were covering the detector. The image were calibrated in the same way as the phantom images. The second object used was a cutlet of meat, with the same setup as the fish. The object were placed so that the area covering the detector included both parts of muscles and fat in order to get contrast between soft tissue. The meat were injected with a 0.2 ml of a solution of KI and water of with a concentration of 0.098 g I / cm3 within the area covering the detector. These images were
cali-brated using a correction map based on a calibration image filtered by 0.2 mm iodine and 18.5 mm plexiglas (10 mm plexiglas filter and water basin) as a mean value of filters used in the material calibration. The image were acquired imme-diately after phantom image acquisition. Two additional experiments with this setup were done. Injection of solution with concentration of 0.047 g I / cm3 and
0.025 g I / cm3, 0.2 ml, were injected in other areas. These scans were performed
at found optimal threshold and kVp and images were corrected using calibration image filtered with 20 mm plexiglas.
The third objects was a chicken bone. The joint of the chicken bone was placed in front of the detector. For this object, dual energy data was acquired using found optimal threshold 8 and kVp, and double exposures at 40 kVp and 70 kVp + 0.5 mm Cu, described in section 3.7. After the scans of the chicken bone, the soft tissue was physically removed using a scalpel and the object was scanned again with single exposure at the same parameter setting. The images were corrected in the same way as the phantom images.
3.9 Imaging system and setup
The same detector was used in all measurement, a photon counting CeTd-detector developed by XCounter. The detector consists of 256x256 pixels, with a detector area of 25.6x25.6 mm2 and pixel size 0.1 mm. The detector is equipped with a
threshold for electronic spectrum splitting. The thresholds are fixed at specific energies i.e. independent of tube voltage. The threshold can be set at a specific level to separate the spectrums at chosen energy. All scanned objects, including filters for calibration, were placed as close as possible in front of the detector, the detector was positioned at a fixed distance of 65 cm from the tube.
3.10 Pulse pile up investigation
The effect of pulse-pile up on the detector was investigated by acquire white single energy images at different photon flux. The photon flux was changed by increasing
the tube current at fixed acquisition. Table 3.9 shows investigated parameter settings, 10 images were acquired at each parameter setting and averaged to one image. The raw data was not corrected since the mean value of each acquired image was of interest.
Table 3.9: Image acqusition parameters
Tube voltage Tube current Acqusition time
50 kVp 1 - 10 mA 25 ms
60 kVp 1 - 10 mA 15 ms
70 kVp 1 - 10 mA 10.5 ms
80 kVp 1 - 10 mA 8 ms
Chapter 4
Results
This chapter presents the results of following studies:
• Finding the optimal parameter setting for dual energy acquisition using a photon counting CdTe-detector. In this investigation the methods basis ma-terial decomposition and weighted logarithmic subtraction have been used to decompose raw data into dual energy images. The parameter settings tab-ulated in section 3.5 have been investigated, the acquisition time and tube voltage have been changed manually and the threshold has been automati-cally swept using XCounter’s software.
• Evaluation of methods. In this investigation the return fit of calibration data has been used as a measurement of how well the method works and are presented in this chapter. The different ways to calculate the weight in weighted logarithmic subtraction, described in section 3.3 have been com-pared and presented.
• Dual energy images of biological items. In this study the images of phantoms have been decomposed into dual energy images and the best results are presented.
4.1 Optimal parameter settings
Described phantom combinations in the method section 3.8.1 were used in this study. Raw data has been decomposed into aluminum and plexiglas images using basis material decomposition. Weights have been used to form aluminum images using weighted logarithmic subtraction. These images have been made from raw data acquired at 20 thresholds, yielding 60 dual energy images at each tube voltage setting. To find the optimal parameter setting, SDNR between regions of interest has been calculated for each image at each parameter setting.
4.1.1 Phantom 1
Figure 4.1 show a single energy image (low- and high energy image stacked to-gether) of phantom 1 and the revealed composition of aluminum in the final alu-minum image, black means low signal to the detector. Contrast has been measured between ROI 1 - ROI 4, ROI 2 - ROI 4 and ROI 3 - ROI 4. ROI 4 have been used as reference when calculating SDNR since this part of the phantom has ho-mogenous thickness of aluminum but inhoho-mogenous thickness of plexiglas, SDNR will peak when the signal difference in this area is cancelled out yielding a low standard deviation. Region 3 in the single energy image is not compared since there is no plexiglas to cancel out in that area.
50 100 150 200 250 50 100 150 200 250 2 5 4 3 1 6 (a) 50 100 150 200 250 50 100 150 200 250 ROI 1 ROI 2 ROI 3 ROI 4 (b)
Figure 4.1: a) Single energy image of phantom 1 , b) Aluminum image of phantom
1
Table 4.1: Material thickness of regions in figure 4.1 Single energy image Dual energy image Region Al [mm] Pl [mm] Region Al [mm] 1 6 10 ROI 1 6 2 2 30 ROI 2 2 3 8 0 ROI 3 4 4 4 20 ROI 4 0 5 0 10 6 0 0
4.1 Optimal parameter settings 31
The result of SDNR calculations between the above mentioned ROI:s in the final aluminum images using basis material decomposition and weighted logarithmic subtraction is shown in figure 4.2 and 4.3. When increasing the photon energy, more photons will pass through the objects yielding more statistics in the image, since the acquisition time is adjusted to have the same statistics in an image without object, statistics will increase with tube voltage (tube current is constant for all parameter settings). When moving the threshold, statistics will increase in the low energy image and decrease in the high energy image, resulting in narrower peak at lower kVp due to less statistic. SDNR is only calculated up to threshold 13 for 50 kVp and 13.5 for 60 kVp, at higher threshold there is not enough information left in the high energy image to calculate the inverse mapping parameters in a least square sense. Weighted logarithmic subtraction algorithm does not share that problem, at higher threshold the final image will end up with the same contrast as in the single energy image.
6 7 8 9 10 11 12 13 14 15 0 5 10 15 20
25 Basis material decomposition
Threshold SDNR ROI 1 ROI 2 ROI 3 (a) 6 7 8 9 10 11 12 13 14 15 0 5 10 15 20
25 Weighted logarithmic subtraction
Threshold SDNR ROI 1 ROI 2 ROI 3 (b) 6 7 8 9 10 11 12 13 14 15 0 5 10 15 20
25 Basis material decomposition
Threshold SDNR ROI 1 ROI 2 ROI 3 (c) 6 7 8 9 10 11 12 13 14 15 0 5 10 15 20
25 Weighted logarithmic subtraction
Threshold SDNR ROI 1 ROI 2 ROI 3 (d)
6 7 8 9 10 11 12 13 14 15 0 5 10 15 20
25 Basis material decomposition
Threshold SDNR ROI 1 ROI 2 ROI 3 (a) 6 7 8 9 10 11 12 13 14 15 0 5 10 15 20
25 Weighted logarithmic subtraction
Threshold SDNR ROI 1 ROI 2 ROI 3 (b) 6 7 8 9 10 11 12 13 14 15 0 5 10 15 20
25 Basis material decomposition
Threshold SDNR ROI 1 ROI 2 ROI 3 (c) 6 7 8 9 10 11 12 13 14 15 0 5 10 15 20
25 Weighted logarithmic subtraction
Threshold SDNR ROI 1 ROI 2 ROI 3 (d) 6 7 8 9 10 11 12 13 14 15 0 5 10 15 20
25 Basis material decomposition
Threshold SDNR ROI 1 ROI 2 ROI 3 (e) 6 7 8 9 10 11 12 13 14 15 0 5 10 15 20
25 Weighted logarithmic subtraction
Threshold SDNR ROI 1 ROI 2 ROI 3 (f)
Figure 4.3: SDNR between different ROI:s in phantom 1, a,b) 70 kVp c,d) 80 kVp
e,f) 90 kVp
As expected, the SDNR peaks close where the threshold separates the energy spec-trum into two images with approximately same statistics. The optimum threshold increases from low to high energy (50-90 kVp), which also is expected since higher
4.1 Optimal parameter settings 33
energy yields a broader spectrum. The calculated SDNR values are plotted in the graphs and approximated with a fourth degree polynomial. There will only be a single peak for each threshold sweep since at higher thresholds all counts end up in the low energy image.
When comparing the results from both methods, the graphs generated from ba-sis material decomposition and weighted logarithmic subtraction at the same kVp share the same pattern. SDNR peaks at approximately the same threshold and the SDNR vary slightly. Since there are no significant differences in SDNR between the thresholds sweep from both methods, the small variations probably derive from image correction and material calibration. To compare the optimized image at each kVp, the difference between the mean signal of each ROI and the true thickness, is tabulated in tables 4.2 - 4.3. Optimized threshold-kVp pairs chosen for this phantom are 7.5 - 50kVp, 8-60kVp, 9-70kVp, 9-80kVp and 9.5-90kVp. Since the pixel value in basis material images resulting from basis material decompo-sition corresponds to true thickness in millimeters, the residual of each ROI was compared in both plexiglas and aluminum images at optimized threshold for each kVp.
Table 4.2: Residuals of regions in aluminum image at optimal threshold. Al thickness (mm) ”50kV p ”60kV p ”70kV p ”80kV p ”90kV p ROI 1 -0.33 -0.57 -0.10 -0.16 -0.37 ROI 2 - 0.36 -0.49 -0.38 -0.32 -0.61 ROI 3 0.08 -0.14 -0.04 -0.09 -0.35 ROI 4 -0.12 -0.26 -0.01 - 0.23 -0.08
Table 4.3: Residuals of regions in plexiglas image at optimal threshold. Pl thickness (mm) ”50kV p ”60kV p ”70kV p ”80kV p ”90kV p 1 -2.7 -2.2 -0.4 -3.4 -2.0 2 - 3.0 -2.2 -2.4 -3.5 -3.0 3 2.7 1.3 2.3 1.5 0.1 4 0.4 0.2 0.0 - 2.1 -1.3 5 0.1 -1.7 -0.7 -3.1 -1.7 6 1.2 4.5 2.1 3.9 1.7
Overall the residuals for ROI 2, composed of 30 mm plexiglas and 2 mm aluminum corresponds to the maximum residual values for every kVp. In material calibra-tion, the pixel values at high plexiglas thickness increases due to scatter, since there are no scatter correction implemented in this method, the plexiglas thick-ness will be overestimated in phantoms with smaller area of plexiglas compared to filters used in material calibration. The result of scatter impact in the method
is shown in section 4.3.4. The tables show that 70 kVp gives the best estimation of true thickness in the aluminum image. In the plexiglas table there are big de-viations at area 2 for the same reason as in the aluminum table. In area 3 and 6 the big residual values can be explained by the composition of the phantom, these are the areas consisting of no plexiglas but surrounded by plexiglas cubes. Scatter from neighboring areas increase pixel counts in area 3 and 6, yielding an under estimation of plexiglas in the area.
SDNR graphs have been averaged and plotted in figure 4.4, the result from this also show the same pattern. The SDNR values are higher for basis material de-composition and resulted in better dede-composition for this phantom compared to images from weighted logarithmic subtraction.
6 7 8 9 10 11 12 13 14 15 0 2 4 6 8 10 12 14 16
Basis material decomposition
Threshold SDNR 50 kVp 60 kVp 70 kVp 80 kVp 90 kVp (a) 6 7 8 9 10 11 12 13 14 15 0 2 4 6 8 10 12 14 16
Weighted logarithmic subtraction
Threshold SDNR 50 kVp 60 kVp 70 kVp 80 kVp 90 kVp (b)
4.1 Optimal parameter settings 35
4.1.2 Phantom 2
Phantom 2 consists of three parts with different composition, resulting in two regions of interest in the aluminum image, visualized in figure 4.5. The calculated contrast between these regions has been plotted directly for all thresholds in figure 4.6. 50 100 150 200 250 50 100 150 200 250 1 2 3 (a) 50 100 150 200 250 50 100 150 200 250 ROI 1 ROI 2 (b)
Figure 4.5: a) Single energy image of phantom 2, b) Aluminum image of phantom
2
Table 4.4: Material thickness of regions in figure 4.5 Single energy image Dual energy image Region Al [mm] Pl [mm] Region Al [mm]
1 0 20 ROI 1 0
2 2 10 ROI 2 2
3 2 0
The graphs follow the same pattern as in phantom 1, with highest SDNR peak value at 70 kVp and peaks at the same threshold for every kVp. Comparing the results from the two methods in figure 4.6, the SDNR peak values at 60 kVp, 70 kVp and 80 kVp have a larger difference in basis material decomposition method compare to weighted logarithmic subtraction. The same behavior is seen in results from phantom 1, which proving that the difference depends on systematic errors, probably deriving from calibration. Comparing SDNR peak values between the two methods, the results from weighted logarithmic subtraction have about 0.5 higher SDNR value for each kVp than results from basis material decomposition. Basis material decomposition show greater SDNR differences between tube volt-ages compared to weighted logarithmic subtraction, this behavior is also seen in results from phantom 1.
