design and characterization of the multi- energy monochromatic x-ray beam … · 2019-06-28 ·...
TRANSCRIPT
Design and characterization of the Multi-
Energy monochromatic X-ray Beam in
X-ray Imaging Systems
Daehong Kim
The Graduate School
Yonsei University
Department of Radiological Science
Design and characterization of the Multi-
Energy monochromatic X-ray Beam in
X-ray Imaging Systems
A Dissertation
Submitted to the Department of Radiological Science
and the Graduate School of Yonsei University
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Daehong Kim
August 2014
- i -
Table of Contents
List of Figures ··································································· iii
List of Tables ···································································· viii
Abstract ·········································································· ix
Chapter 1: Introduction ·························································· 1
1.1. Overview ·································································· 1
1.2. State-of-the-art of multi-energy X-ray imaging ······················ 4
1.3. Introduction and limitation of dual-energy imaging method ······· 9
1.4. Objectives of this study ··············································· 19
Chapter 2: Characteristics of emission and detection of X-ray ········· 21
2.1. Tube potentials and characteristics of filters ························ 22
2.2. Detector configuration ················································· 27
2.3. Process of emission and detection ··································· 29
Chapter 3: Simulation study of the proposed design for triple-energy
X-ray beam ··························································· 30
3.1. X-ray beam shaping ··················································· 31
3.2. Quantitative indices ···················································· 36
3.3. Measurement of designed X-ray beam ······························ 47
3.4. Monte Carlo simulation ················································· 50
3.5. Discussion ································································ 60
Chapter 4: Experiment with the designed X-ray beam ·················· 65
4.1. Evaluation of quantitative indices by experimental study ········· 66
- ii -
4.2. Linear attenuation coefficients and mean energy ···················· 70
4.3. Results of density map ················································ 75
4.4. Discussion ······························································ 78
Chapter 5: Summary and Conclusion ······································· 81
References ········································································· 84
Abstract (in Korean) ···························································· 91
- iii -
List of Figures
Figure 1.1. Multi-energy X-ray imaging devices and their characteristics of
operation.
Figure 1.2. Current types of multi-energy X-ray imaging systems for dual-
energy imaging by using a charge-integrating method with a broad
X-ray spectrum as a clinical device.
Figure 1.3. Signals were differentiated by the energies of their photons with a
one shot scan of a broad X-ray spectrum using the photon-counting
method.
Figure 1.4. Monochromatic beams produced by using Bragg diffraction on a
multilayer coating crystal.
Figure 1.5. Monochromatic beams produced by using a filter.
Figure 1.6. Relationship between polychromatic and monochromatic X-ray
beams for energy and X-ray intensity.
Figure 1.7. Phantom images acquired with energy subtraction, equivalent
thickness, and synthetic methods. (a) and (b) were obtained with 70
and 140 kV, respectively. Aluminum images were acquired with the
energy subtraction (c), equivalent thickness (e), and synthetic
methods (g). PMMA images were acquired by the energy
subtraction (d), equivalent thickness (f), and synthetic methods (h).
The arrow in (a) indicates the profile detailed in Figure 1.7 and 1.8.
Figure 1.8. Comparison of the profiles in the aluminum image acquired with
the energy subtraction, equivalent thickness, and synthetic methods.
Figure 1.9. Profiles of the PMMA image acquired with the energy subtraction,
equivalent thickness, and synthetic methods.
- iv -
Figure 2.1. Initial X-ray beam was simulated ROTANODETM
. Its operating
tube voltage ranges from 40 to 120 kV, and has a 0.7 mm
equivalent aluminum filter.
Figure 2.2. The micro-focus X-ray source tube for the experimental study with
photon-counting detector. The operating tube potential ranges from
20 to 90 kV, and has a 0.15 mm beryllium filter.
Figure 2.3. The X-ray spectra as functions of photon energy for various tube
potentials.
Figure 2.4. Filter materials for beam shaping used in this study.
Figure 2.5. The charge-integrating amorphous selenium (a-Se) detector for
acquiring signal from monochromatic X-ray beam for simulation
and experimental study.
Figure 2.6. The charge-integrating amorphous selenium (a-Se) detector for
acquiring signal from monochromatic X-ray beam for simulation
and experimental study.
Figure 2.7. Flow of emission and detection of X-ray from source to detector.
Figure 3.1. Illustration of geometry to acquire spectrum of designed X-ray
beam with initial X-ray source, filter, and a-Se detector.
Figure 3.2. The relationship between the number of photons and X-ray beam
shaping was simulated by using a Ba filter with increasing filter
thickness at 50 kV.
Figure 3.3. The alternation of relative X-ray beam shaping with increasing
filter thickness was simulated by using a Ba filter with increasing
filter thickness at 50 kV.
- v -
Figure 3.4. Mean energy with respect to tube potential using Ba filter at 2, 7,
and 8 HVL thicknesses and mean energy of K-edge, and without
filtration.
Figure 3.5. Mean energy using various filter materials corresponds to the
increasing tube potential at 7 HVL.
Figure 3.6. Results of mean energy ratio comparing various filter materials at 7
HVL through a 2 cm PMMA.
Figure 3.7. Results of mean energy ratio of comparing various filter materials
at 7 HVL through a 0.5 cm aluminum filter.
Figure 3.8. Illustration of geometry to acquire phantom image with designed
X-ray beam by using initial X-ray source, filter, and a-Se detector.
Figure 3.9. The signal (aluminum) and background (PMMA) were obtained to
evaluate contrast variation ratio and exposure efficiency by
simulation study. The effect of filtered X-ray beam was shown with
signal and noise of signal and background. The proton quantities of
unfiltered and filtered X-ray beam are each 3.8×106.
Figure 3.10. Contrast of the image obtained with filtered X-ray beam can be
higher than that acquired with unfiltered X-ray beam.
Figure 3.11. Exposure efficiency by considering the SNR and the number of
photons through 2 cm PMMA and 0.5 cm Al object for designed
beam obtained with Ba filter at various filter thickness.
Figure 3.12. Exposure efficiency considering the SNR and the number of
photons through 2 cm PMMA and 0.5 cm Al object for the designed
beam obtained with all filters at 7 HVL filter thickness.
- vi -
Figure 3.13. The recorded spectrum of the CZT detector and the simulated
incident spectrum at tube voltage of 50 kV and I filter. The spectra
were normalized with respect to the integrated energy.
Figure 3.14. The recorded spectrum of the CZT detector and the simulated
incident spectrum at tube voltage of 60 kV and Ba filter. The
spectra were normalized with respect to the integrated energy.
.
Figure 3.15. The recorded spectrum of the CZT detector and the simulated
incident spectrum at tube voltage of 70 kV and Gd filter. The
spectra were normalized with respect to the integrated energy.
Figure 3.16. X-ray spectra for proposed TE monochromatic X-ray beam by
generating I, Ba, and Gd filters with 50, 60, and 70 kV, respectively.
Figure 3.17. In photon-counting mode, energy binning was performed from 90
kV broad spectrum to match the energies of proposed TE
monochromatic X-ray beam.
Figure 3.18. The cubic phantom of I, Al, and PMMA is on the detector for
obtaining linear attenuation coefficient and thickness density map.
Figure 3.19. Linear attenuation coefficient maps of I, Al, and PMMA obtained
with proposed TE X-ray beams and photon-counting method. (a),
(b), and (c) are the attenuation coefficients at 50, 60, and 70 kV,
respectively, with I, Ba, and Gd filters, respectively. (d), (e), and (f)
are the attenuation coefficients map at 29.34, 37.57, and 45.87 keV,
respectively.
Figure 3.20. (a), (b), and (c) are thickness density maps of I, Al, and PMMA
acquired with TE X-ray beams. (d), (e), and (f) are thickness
density maps of I, Al, and PMMA with the photon-counting method.
Figure 3.21. The results of thickness density maps for I, Al, and PMMA.
- vii -
Figure 4.1. Mean energy ratio was estimated for images obtained with
proposed TE X-ray beam by measuring log intensity of the image
and known thickness of the phantom.
Figure 4.2. Contrast variation ratio was measured by the proposed and
conventional methods at E_1, E_2, and E_3.
Figure 4.3. Exposure efficiencies were measured by proposed and conventional
methods at E_1, E_2, and E_3.
Figure 4.4. Log intensity measurements by using the proposed method to
obtain linear attenuation coefficients with respect to increasing Al
thickness from 0.1 to 0.6 cm for E_1, E_2, and E_3.
Figure 4.5. Log intensity measurements by using proposed method to obtain
linear attenuation coefficients with respect to increasing PMMA
thickness from 1 to 6 cm for E_1, E_2, and E_3.
Figure 4.6. Log intensity measurements by using photon-counting method to
obtain linear attenuation coefficients with respect to increasing Al
thickness from 0.1 to 0.6 cm for E_1, E_2, and E_3.
Figure 4.7. Log intensity measurements by using the photon-counting method
to obtain linear attenuation coefficients with respect to increasing
PMMA thickness from 1 to 6 cm for E_1, E_2, and E_3.
Figure 4.8. (a) I, (b) Al, and (c) PMMA are obtained with the proposed TE
monochromatic X-ray beams with I, Ba, and Gd filters for 50, 60,
and 70 kV, respectively. (d) I, (e) Al, and (f) PMMA are the
material density maps obtained with the photon-counting method.
Figure 4.9. Thickness density maps of I, Al, and PMMA obtained by the
proposed TE X-ray beams and photon-counting methods.
- viii -
List of Tables
Table 2.1. Filter materials, Z number, density, and K-edge energy.
Table 3.1. Tube operating range summary for different quantitative indices
considering mean energy ratio, exposure efficiency, and contrast
variation ratio.
Table 3.2. Proposed triple-energy X-ray beam and binning of photon-counting
method.
Table 3.3. Linear attenuation coefficients and mean energies of I, Al, and
PMMA with Monte Carlo simulation for proposed method.
Reference energy is K-edge energies of I, Al, and PMMA.
Table 3.4. Linear attenuation coefficients and mean energies of iodine,
aluminum, and PMMA with Monte Carlo simulation for photon-
counting method. Reference energy is the energies as binned in the
photon-counting system.
Table 4.1. The experimental results of the linear attenuation coefficients and
mean energies of I, Al, and PMMA for proposed method.
Reference energy is K-edge energies of I, Al, and PMMA.
Table 4.2. The experimental results of the linear attenuation coefficients and
mean energies of I, Al, and PMMA for photon-counting method.
Reference energy is the energies of binned in photon-counting
system.
- ix -
ABSTRACT
Design and characterization of the Multi-
Energy monochromatic X-ray Beam in
X-ray Imaging Systems
Daehong Kim
Dept. of Radiological Science
The Graduate School
Yonsei University
Multi-energy X-ray imaging (or spectral imaging) is widely used in medical,
industrial, and security fields. In the medical field, multi-energy X-ray imaging
systems are suitable for contrast enhancement of lesions, quantitative analysis of
specific materials, and functional imaging of the human body. Therefore, the dual-
energy (DE) system was widely adopted for use in clinical examinations by operating
dual-source, dual-layer detectors, and fast kV-switching. Recently, a photon-counting
- x -
detector has been developed that can obtain multiple pieces of information about an
object by discriminating between the detected photon energies of the X-rays from
broad energy band by the application of specific integrated circuits (ASIC). Quasi-
monochromatic beam can be generated by using Bragg diffraction and filter design for
multi-energy X-ray imaging. The aim of this dissertation is to develop a triple-energy
(TE) monochromatic X-ray beam with filter designed to separate three materials, and
the results of an image acquired with the proposed TE monochromatic X-ray beam
were compared to an image obtained with the photon-counting method through both
simulation and experimental measurement.
Various monochromatic X-ray beams, having filter materials (Al, Cu, I, Ba, Ce, Gd,
Er, and W) with K-edge energy, were generated with a charge-integrating detector by
simulation based on empirical models. An appropriate filter thickness was decided
through comparison between the mean energy of a filtered beam and the K-edge
energy of the filter. Quantitative indices such as mean energy ratio, contrast variation
ratio, and exposure efficiency were estimated for each monochromatic beam using
Monte Carlo simulation. The mean energy of each filter material was characterized
with respect to increasing the tube potential due to the K-edge energy of the filter. The
values of mean energy ratio of the filtered beam were below that of the result without a
filter for all filter materials in a phantom study. This means that the filtered X-ray beam
is monochromatic, thereby maintaining minimal beam hardening by the K-edge filter.
Filtered X-ray beams obtained with I, Ba, and Ce were of a higher contrast than an
unfiltered X-ray beam, in accordance with tube potential. In exposure efficiency, the
- xi -
filtered beams using I, Ba, Ce, and Gd filters outperformed the unfiltered X-ray beams
at same tube potential.
The TE monochromatic X-ray beams were generated by I, Ba, and Gd filters at 50,
60, and 70 kV from the simulation results, respectively. The spectra of the simulated
TE monochromatic beams were compared to the experimental results obtained with the
photon-counting detector. The results indicate that the energy peaks of the simulated
spectra were well matched to those of experimental spectra. The thickness density map
that was acquired with TE monochromatic beams was compared to that obtained with
photon-counting method for both the simulation and experiment. In the simulation
results, the thickness map obtained by using TE monochromatic beams were estimated
to 1.00, 1.00, and 0.99 cm for iodine, aluminum, and PMMA, respectively, when the
true values of the thickness density were 1.00 cm for each. In the simulation results of
the photon-counting method, the thickness density maps of iodine, aluminum, and
PMMA were 1.00, 0.96, and 1.07 cm, respectively. The thickness density maps of
iodine, aluminum, and PMMA obtained with TE monochromatic beams were
compared with the photon-counting method. The resultant thickness densities of iodine,
aluminum, and PMMA were 0.57, 0.52, and 1.99 cm by the TE monochromatic
method when the true values of the thickness density were 0.50, 0.50, and 2.00 cm for
iodine, aluminum, and PMMA, respectively. In the photon-counting method, the
thickness densities of iodine, aluminum, and PMMA were 0.50, 0.51, and 2.05,
respectively.
In this paper, we proved that TE monochromatic X-ray beams are a reliable design
with tube voltages and additional filters for triple-energy imaging. The proposed
- xii -
additional filtration has proven its feasibility as the imaging method with a high
accuracy of material thickness over the three materials, and this method can be used in
the multi-energy X-ray imaging technique for medical imaging.
Keywords: Multi-energy X-ray imaging, monochromatic X-ray beam, charge-
integrating detector, photon-counting detector.
- 1 -
Chapter 1: Introduction
1.1. Overview
Multi-energy techniques have been developed to perform material segmentation in
X-ray imaging, based on dual-energy (DE) systems such as dual-energy digital
radiography (DEDR) and dual-energy computed tomography (DECT) in clinical
environments [1, 2]. Clinical interest in DEDR has been maintained over the years,
particularly for chest imaging and bone densitometry. DECT imaging has been also
introduced to clinical practices for detecting urinary stones and heart diseases [3, 4].
While DE imaging systems were of benefit for the contrast enhancement of
particular materials among other materials, the quantitative analysis of mixed material
and functional imaging for lung ventilation or perfusion imaging in the case of DECT,
DE imaging systems caused excessive radiation doses to the patient during
examination. Moreover, the X-ray spectra generated at low and high peak tube
potentials have a high degree of spectral overlap, resulting in smaller spectral
separation. The smaller spectral separation makes it harder to discriminate between two
materials, particularly for materials with close atomic numbers. Therefore, previous
work has reported that spectral separation could be increased by using additional
filtration for one or both tube potentials (kV) [5]. The work has demonstrated
- 2 -
optimizing the added filtration for DE imaging focused on chest radiography and
mammotomography [6].
The success of material decomposition for X-ray imaging is dependent on the
additional energy with DE. Therefore, triple-energy devices have been developed to
improve the accuracy of decomposition and to reduce the projection error in preclinical
environments for small animal imaging. These works proved that the decomposition
accuracy can be improved by using both triple-energy monochromatic X-ray beams
and triple-energy X-ray beams [7, 8].
More recently, many research studies have been focused on photon-counting
detectors for realizing multi-energy X-ray imaging, which can resolve energy fluence
since application-specific integrated circuits (ASIC) combined with semiconductor
detectors based on cadmium telluride (CdTe) and cadmium zinc telluride (CZT) can
discriminate between X-ray energies.
One possibility is the application of a photon-counting X-ray detector, which allows
for improvements of the contrast-to-noise ratio (CNR) by energy weighting from the
acquired image, counting each X-ray photon and measuring its energy in both
simulation and experimental study [9, 10]. Another advantage of the photon-counting
method is the possibility of K-edge imaging using a contrast agent with a K-edge such
as gadolinium and iodine [11–13]. It was shown that heavy metals could be
distinguished and quantified independently from a single scan. Photon-counting
detectors have been used to reduce radiation doses compared to conventional (charge-
integrating) detectors. Through photon-counting, projection-based weighting, and
image-based weighting, the expected dose reduction could be estimated by setting the
- 3 -
CNR to be the same as that of the flat-panel image acquired at a certain dose level, by
plotting CNR as function of air kerma [14] .
Generally, DE systems are able to use both single-energy (SE) and DE modes when
performing examinations. The energy spectra of these systems had a broad band-
window, thereby leading to giving an increased dose to patients and the decreased
contrast of the images. As mentioned above, since the devices use a triple-energy beam
with Bragg diffraction and a photon-counting detector to produce or read out the
information of specific photon energy, they can improve the image quality, reduce the
radiation dose, and discriminate between materials that share similar intensities on the
image. Current devices that use multi-energy X-ray imaging systems were specified
such as system name, institute of development, usage, and properties in figure 1.1.
Figure 1.1 Multi-energy X-ray imaging devices and their characteristics of operation.
- 4 -
1.2. State-of-the-art of multi-energy X-ray imaging
1.2.1 Dual-energy and photon-counting system
The signal acquisition mechanism of DE X-ray imaging systems includes dual-
source CT, rapid kV switching, and dual-layer detectors [15–18] as shown in figure 1.2.
The geometry of these systems means they must be able to acquire two images
successfully without patient motion during the examination. The dual-source systems
need two detectors that correspond to low- and high-energy X-ray sources
geometrically. The kV switching method is widely used for DEDR and DECT, which
alternate the tube potential during the scan to remove the motion artifact in a moment.
Dual-layer detectors use single source and stacked dual-layer detectors. The front and
rear detectors measure the low- and high-energy data, respectively. Since the aim of
clinical DE X-ray imaging systems is to reduce scan times and movement artifacts,
dual-source, kV switching, and dual-layer detectors were developed for image
acquisition.
As shown in figure 1.3, the photon energy from one shot scanning was measured by
the photon-counting method with complicated circuits such as ASIC. Therefore, a user
can select the energy bins prior to scanning with respect to the energy within the
photon energy ranges of the incident X-ray spectrum. The merit of the photon-counting
method is that it collects the various signal information effectively with one shot of X-
- 5 -
ray exposure [9], thereby enhancing image contrast, reducing radiation dose, and
separating the various materials.
Figure 1.2 Current types of multi-energy X-ray imaging systems for dual-energy
imaging by using a charge-integrating method with a broad X-ray spectrum as a
clinical device.
Figure 1.3 Signals were differentiated by the energies of their photons with a one shot
scan of a broad X-ray spectrum using the photon-counting method.
- 6 -
1.2.2 Monochromatic X-ray
Investigating the issue of radiation dose to the patient for procedures such as CT
examinations leads to reducing the radiation dose while maintaining image quality.
The goal of the usage of a monochromatic X-ray beam is to reduce the radiation dose,
improve the contrast of images, and suppress the fog of soft tissue. A monochromatic
imaging system using Bragg diffraction was developed by previous work [19]. They
dealt with the quasi-monochromatic X-ray beams, with tunable energy in a range of
26–72 keV, which was produced by Bragg diffraction on a Highly Oriented Pyrolytic
Graphite (HOPG) crystal. The image acquisition mechanism of a monochromatic beam
using Bragg diffraction is illustrated in figure 1.4.
Filter design technology was also introduced for obtaining a monochromatic X-ray
beam in a group [20], as shown in figure 1.5. The results of previous work have
reported that the filtered X-ray beams called with quasi-monochromatic X-ray beams
were produced by the initial X-ray beam having a broad energy range and using
additional filter materials with K-edge energies. They focused studying how the
monochromatic X-ray beam is expected to yield enhanced tomographic image quality
with a low dose. The effect of filter materials with different atomic numbers (Z)
provided the energy-tunable beam due to the K-edge energy of the filter material. The
shape of the quasi-monochromatic X-ray beam was dependent on both the filter
materials and the tube potentials. The low-energy beam was absorbed by the filter
material before the low-energy photons arrived at the object. The high tube potential
- 7 -
produced a spectrum tail over the peak energy of the monochromatic X-ray beam. Thus,
the design of filter requires the appropriate selection of filter materials, filter thickness,
and tube potentials.
Figure 1.4 Monochromatic beams produced by using Bragg diffraction on a multilayer
coating crystal.
Figure 1.5 Monochromatic beams produced by using a filter.
- 8 -
The merits of monochromatic X-ray beams are illustrated in figure 1.6. The contrast
of the X-ray imaging depends on the radiation energy; usually, high X-ray energies
result in a decreased contrast, while low energies are absorbed in the object, thus have
a smaller probability of reaching the detector. Polychromatic X-ray spectra contain a
large quantity of unnecessary photons and deliver images with deteriorated contrast.
Monochromatic X-ray beams reduce radiation dosage to an object, enhance the image
contrast, and increase the information given by a material. Multi-energy imaging is
possible with monochromatic X-ray beam, particularly TE X-ray imaging for its
generation of multiple X-rays with monochromatic energy.
Figure 1.6 Relationship between polychromatic and monochromatic X-ray beams for
energy and X-ray intensity.
- 9 -
1.3. Introduction and limitation of dual-energy
imaging method
1.3.1 Energy subtraction
In DR imaging, energy subtraction, equivalent thickness, and synthetic method
were used for enhancement of bone and tissue. The linear attenuation coefficient
)(E can be represented as a function of energy (E) that is a combination of
photoelectric absorption and Compton scattering within the diagnostic energy ranges
[21]. Hence, above the K-edge of a material for diagnostic radiography, the linear
attenuation coefficient can again be described by a set of basis functions [22, 23].
These basis functions are used to produce an energy-selective image such as bone and
tissue with a dual-energy technique in accordance with an empirical model due to the
characteristics of the bremsstrahlung x-ray spectrum [22]. Based on the previously
mentioned energy subtraction method, a dual-energy subtraction image was derived
from the difference between logarithmic intensity images utilizing low and high energy.
In case of a monoenergetic source, no beam hardening can occur because the X-ray
have only one energy. Therefore, the X-ray intensity can be measured at the detector
and described as:
xeII 0 , (1.1)
- 10 -
where 0I depicts the incident X-ray intensity, is the value of a linear attenuation
coefficient over the material thickness x [24]. If an object includes the soft-tissue
thickness st and bone thickness bt , with the low- and the high-energy beams (energy
level for i = 1 is 70 kVp and for i = 2 is 140 kVp), the log transmission measurements
)/ln( 0 ii II will be given by:
,)()()/ln( 111101 bbss tEtEYII (1.2)
,)()()/ln( 222202 bbss tEtEYII (1.3)
where s and b are linear attenuation coefficients of soft tissue and bone [24, 25].
By combining equations (1.2) and (1.3), the weighting factor for energy subtraction
can be given by the ratio of low- and high-energy linear attenuation coefficients:
),(/)( 21 EEw sss (1.4)
).(/)( 12 EEw bbb (1.5)
Therefore, the equations for the energy subtraction of bone and tissue images are:
),/ln()/ln( 202101 IIwIIBone s (1.6)
)./ln()/ln( 101202 IIwIITissue b (1.7)
- 11 -
In the case of polychromatic X-rays, is calculated as
,
)(
)()(
max
max
00
00
E
E
dEEI
dEEIE (1.8)
where )(0 EI is the incident x-ray spectrum and maxE is the maximum energy of
the spectrum. We generated the spectrum from the tungsten anode spectral model using
interpolating polynomials (TASMIP) code to calculate the weighting factors sw and
bw [26, 28]. The ratios of linear attenuation coefficients (i.e., weighting factors) in
equations (1.4) and (1.5) can be determined by the exposed dual energy spectra. The
mass attenuation functions of bone and soft tissue were computed from the NIST data
[27] within the diagnostic energy range.
- 12 -
1.3.2 Equivalent thickness and synthetic methods
According to the previous work, photoelectric effect and Compton scattering are
dominant at a diagnostic x-ray range. These two effects can be represented by two set
of basis functions )(1 Ef and )(2 Ef :
).(),,()(),,(),,,( 2211 EfzyxaEfzyxaEzyx (1.9)
In projection radiography, the relative detected X-ray photon flux is defined by
,exp)()(
),,,(
0
dEEDESI
I dsEzyx
(1.10)
where )(ES is the X-ray spectrum and )(ED is the detector efficiency. The
transmitted intensity is line integral in the direction of the beam of the attenuation
coefficient weighted by the incident X-ray spectrum and the detector efficiency. The
attenuation coefficient is expressed as
)()()( 2211 EfAEfAEU (1.11)
with
- 13 -
dszyxaA ii ),,( .2,1i (1.12)
Because aluminum is close to bone whereas PMMA behaves like soft tissue, the two
basis functions )(1 Ef and )(2 Ef can be replaced with energy dependence of these
two materials.
Thus equation (1.11) is rewritten as
alalPMPM tEtEEU )()()( (1.13)
where PM and al are the linear attenuation coefficient of PMMA and aluminum.
PMt and alt are the equivalent thickness of PMMA and aluminum. When the
monochromatic X-ray beams are used at two different energies, equations (1.10) and
(1.13) can be expressed as following
,)()()/ln( 111101 PMalPMPM tEtEYII (1.14)
,)()()/ln( 222202 alalPMPM tEtEYII (1.15)
where )/ln( 0 ii II is log measurement at two different energies. Equations (1.14) and
(1.15) can be inverted to
- 14 -
,213112 YaYatPM (1.16)
,223122 YaYatal (1.17)
where )/ln( 0 iii IIY . The a coefficients are function of the attenuation coefficients
PM and al . The two equations of (1.16) and (1.17) are only valid for
monochromatic X-ray beams. Therefore, the equations have to extended to
polychromatic X-ray beams as following
,3218
31172116
2215
211421311211 YaYaYYaYaYaYaYaatPM (1.18)
.3228
31272126
2225
212422312221 YaYaYYaYaYaYaYaatal (1.19)
The a coefficients in equations (1.18 and 1.19) were determined by using the known
combined thickness of PMMA and that of aluminum ( PMt and alt ) and the log
intensity measurements 1Y and 2Y corresponding to the thickness for the dual
energy calibration procedure as explained in the previous work [22]. In this work,
thickness of PMMA is 1, 2, 3, 4, 5, and 6 cm and thickness of aluminum is 0.1, 0.2, 0.3,
0.4, 0.5, and 0.6 cm. Thus we construct the matrix equation for aluminum and PMMA
thickness from equation (1.18) and (1.19). Then the a coefficients can be calculated by
using inverse matrix from the equations. The synthesized monochromatic image can be
formed from the equivalent thickness information, which is plotted on the basis
- 15 -
projection plane with characteristic angles. The equation with the two vectors is
expressed by
).sin()cos( alPM ttC
(1.20)
The scalar C represents the conversion of the equivalent thicknesses of PMMA and
aluminum to a unique equivalent thickness of a material having a characteristic angle
. The angle was determined by the equation of Lehmann et al. [23] as following
equation
.tan11
221
aa
aa
al
PM (1.21)
From this equation (1.21), it is possible to cancel any given material from the image
and fill the resulting cavity with any other given material. It is called with material
look-alike, which is within the synthesized monochromatic region and able to achieve
material cancellation.
The phantom images are displayed in Figure 1.7 for the three methods and two
materials. The comparisons of profiles of the phantom images are plotted in Figure 1.8.
When the results acquired with the cylindrical phantom were compared, the relative
intensity of aluminum with the equivalent thickness and the synthetic methods was
2.17 times higher than that obtained with the energy subtraction method in terms of the
- 16 -
profiles in Figure 1.8. The relative intensity of PMMA achieved with the synthetic
method was 5.69 times better than that achieved with the energy subtraction method, as
shown in figure 1.9. Although using the equivalent thickness method improved the
relative intensity of the PMMA, the method resulted in aluminum shadows in the
PMMA image. In contrast, the synthetic method can effectively remove the aluminum
hole shadows and enhance the PMMA intensity, as shown in Figure 1.9.
However, theses method for DE imaging such as energy subtraction, equivalent
thickness, and synthetic method were limitation in projection error in case of
superimposed three materials. Since the energy subtraction and the equivalent
thickness are assuming that the two basis materials for separating bone and tissue
image, the methods are limited for discriminating three materials. Synthetic method
produces a certain material by synthesize with characteristic angle two basis materials
such as aluminum and PMMA. However, the synthetic method was also generated
from two basis materials similar to equivalent thickness, and the method need complex
imaging process due to the polychromatic X-ray energy. Therefore, the monochromatic
triple-energy (TE) beam is needed to reduce projection error, maximize image contrast,
and minimize radiation dose.
- 17 -
Figure 1.7 Phantom images acquired with energy subtraction, equivalent thickness, and
synthetic methods. (a) and (b) were obtained with 70 and 140 kV, respectively.
Aluminum images were acquired with the energy subtraction (c), equivalent thickness
(e), and synthetic methods (g). PMMA images were acquired by the energy subtraction
(d), equivalent thickness (f), and synthetic methods (h). The arrow in (a) indicates the
profile detailed in Figure 1.8 and 1.9.
- 18 -
Figure 1.8 Comparison of the profiles in the aluminum image acquired with the energy
subtraction, equivalent thickness, and synthetic methods.
Figure 1.9 Profiles of the PMMA image acquired with the energy subtraction,
equivalent thickness, and synthetic methods.
- 19 -
1.4. Objectives of this study
It is challenging to discriminate between more than three materials using a DE
imaging system due to the lack of the information available through the DE method.
Moreover, spectral overlap causes inaccurate information in materials for multi-energy
X-ray imaging. The efforts of researchers to obtain monochromatic X-ray beams are
performed to maximize the performance metric (figure of merit) depending on several
parameters such as added filtration, kV setting, dose allocation, and tube loading.
However, there is a need for studies focused on DE imaging system that validate the
results with experimental data.
The purpose of this work was to perform simulation and experimental studies to
minimize the overlapped triple-energy X-ray spectra and to separate three materials
from the separated spectra. The significant accomplishment of this work is the
determination of X-ray beam for triple-energy imaging with imaging parameter
combinations of added filtration and kV settings.
In this doctoral thesis investigation, the development of material decomposition
methods with multi-energy technique in X-ray imaging system is reported that uses a
filter design with both simulated and experimental measurements.
In chapter 2, the process of emission and detection of X-ray spectra is investigated
with Monte Carlo and empirical simulation. Initial X-ray beam generation,
transmission through filters, and the detection of X-rays on the detector are reported.
The characteristics of the filter materials are discussed, and charge-integrating and
- 20 -
photon-counting detector are described for the purposes of the present study. Two
types of X-ray source are described: clinical X-ray source and micro focus X-ray
source were used for the charge-integrating and photon-counting detector.
In chapter 3, the Monte Carlo simulation of the X-ray beam design was performed
for TE X-ray imaging. The X-ray beam was designed with filter materials and tube
potential, then the designed X-ray beams were evaluated for their spectral distributions,
mean energy ratio, contrast variation ratio, and exposure efficiency in accordance with
tube potentials, filter materials, and their thickness compared with an unfiltered X-ray
beam at the same tube potentials. The spectra of the designed monochromatic TE
beams are compared to the spectra measured by photon-counting detector. Then, the
designed spectra were used for acquiring three materials imaging by a displayed
thickness density map.
In chapter 4, the performance of the triple-energy X-ray beams are evaluated
experimentally. The image quality between the designed TE X-ray beams and
conventional X-ray beams is evaluated by measuring their mean energy ratio, contrast
variation ratio, and exposure efficiency. The designed TE X-ray beams were
implemented to acquire a thickness density map of iodine, aluminum, and PMMA
images, and their results were compared with density maps acquired by the photon-
counting method.
Finally, the summary and conclusion of this study are presented in chapter 5.
- 21 -
Chapter 2: Characteristics of emission and
detection of X-ray
In this chapter, the emission and detection of X-rays emitted from a tube to a
detector were theoretically described with an X-ray source, filter materials, and
detector. This study was conducted using a tungsten anode spectral model that uses an
interpolated polynomials (TASMIP) simulation code developed by Siewerdsen et al.
that is based on an empirical X-ray generation model [28]. The model includes X-ray
spectra, the selection of elemental and compound filters, and the calculation of beam
quality characteristics. We simulated the X-ray spectra from a tungsten (W) target with
tube potentials ranging from 40 to 90 kVp in 10 keV increments, using both a 12°
anode angle and intrinsic tube filtration (0.7 mm aluminum equivalent) as shown in
figure 2.1, and with filter thicknesses ranging from 2 to 8 half-value layer (HVL).
Filter materials were selected in a range of Z=13 to 74, including K-edge energies for
generating a monochromatic X-ray beam.
- 22 -
2.1. Tube potentials and characteristics of filters
2.1.1 X-ray source
Radiation is generated by the deceleration of fast electrons entering a metal anode
(i.e. Bremsstrahlung).The radiation energy depends on the electron velocity, which in
turn depends on the acceleration voltage between the cathode and anode. The X-ray
spectrum has a broad energy band due to the emission origin. The empirical model
used in this study was designed to provide a flexible toll for the calculation of X-ray
spectra, the application of X-ray filters, and the analysis of spectral characteristics [28].
The initial spectrum was simulated with consideration of the tube potential (kV),
inherent filter (mm Al), and ripple voltage.
The X-ray source was modeled primarily as a tungsten target within a diagnostic X-
ray energy range of 40–90 kV and K-edge energy of filters. A tungsten target has
merits for low- to medium-energy X-ray imaging, which yields the ample modification
of beam currents, tube potential, and filtration. Therefore, a beam can be shaped with
an appropriate attenuating filtration. The tube potentials contribute in varying degrees
to the X-ray spectra as a function of the energy, as shown in figure 2.2. The simulated
X-ray spectra used in this study are referred to the commercial X-ray tube
(ROTANODETM
, Toshiba, Japan) for obtaining TE monochromatic X-ray beam with a
charge-integrating detector. The operating tube potential ranges from 40 to 120 kV,
and has an inherent filter (0.7 mm aluminum). The micro-focus X-ray source (L8601-
- 23 -
01TM
, Hamamatsu, Japan) was used for a photon-counting detector, which measures
the information of energy by binning, and the micro-focus of the source is illustrated in
figure 2.2. The operating tube voltage ranges from 20 to 90 kV, and has an inherent
filter (0.15 mm beryllium).
Figure 2.1 Initial X-ray beam was simulated ROTANODETM
. Its operating tube
voltage ranges from 40 to 120 kV, and has a 0.7 mm equivalent aluminum filter.
Figure 2.2 The micro-focus X-ray source tube for the experimental study with photon-
counting detector. The operating tube potential ranges from 20 to 90 kV, and has a
0.15 mm beryllium filter.
- 24 -
Initial X-ray spectra for 40, 50, 60, 70, 80, and 90 kV were generated by empirical
model in a commercial X-ray tube (ROTANODETM
), as shown in figure 2.3. The
shapes of spectra were calculated as functions of photon energy for various tube
potentials. From 40 to 70 kV, continuous energy spectra were illustrated. The peak
energies of tungsten target were shown at 80 and 90 kV. The K-edge and K-alpha
energies of tungsten target were 59.31 and 69.53 keV, respectively. With increasing
tube potential, the peak energy (i.e. characteristic X-ray) of the tungsten target material
was observed with continuous X-ray as well. The number of photons for 40, 50, 60, 70,
80, and 90 kV are as emitted per 1 mAs.
Figure 2.3 The X-ray spectra as functions of photon energy for various tube potentials.
- 25 -
2.1.2. Filter materials
The simulation and experiment were carried out for various filters consisting of
pure elemental materials in foil form (including Al, Cu, I, Ba, Ce, Gd, Er, and W). Al
(Z=13) and Cu (Z=29) are widely used as filters to reduce the low energy in X-ray
imaging devices. The K-edge energies of Al and Cu are 1.56 and 8.98 keV,
respectively. I (Z=53), Ba (Z=56), Ce (Z=58), Gd (Z=64), Er (Z=68), and W (Z=74)
have K-edge peaks from 30 to 70 keV, as shown in figure 2.4. Therefore, these
materials could be tailored to transmit lower energy X-rays with high flux rather than
X-rays at or greater than the K-edge. The specific information for each material (Z
number, density, and K-edge) is listed in table 2.2.
Figure 2.4 Filter materials for beam shaping used in this study.
- 26 -
Table 2.1 Filter materials, Z number, density, and K-edge energy.
Materials Z Density
(g/cm3)
K-edge
Aluminum (Al) 13 2.70 1.56
Copper (Cu) 29 8.96 8.98
Iodine (I) 53 4.93 33.17
Barium (Ba) 56 3.50 37.44
Cerium (Ce) 58 6.77 40.44
Gadolinium (Gd) 64 7.90 50.24
Erbium (Er) 68 9.07 57.49
Tungsten (W) 74 19.30 69.53
- 27 -
2.2. Detector configuration
2.2.1 Charge-integrating detector
The direct conversion detector (FDXD 1417, DRtech, Seongnam, Korea) composed
of thin-film transistor (TFT)-amorphous selenium (a-Se) was modelled through Monte
Carlo simulation study. GATE simulation used in this study toolkit models detector
signal as the absorbed energy of all primary and secondary absorption events [29]. It
has a size of 356×427 mm2, a 2,560×3,072 array of pixels, a pixel pitch of 139×139
μm2, and a thickness of 500 μm, as shown in figure 2.5. This detector used for
validating the multi-energy monochromatic X-ray beam on both simulated and
experimental measurement.
Figure 2.5 The charge-integrating amorphous selenium (a-Se) detector for acquiring
signal from monochromatic X-ray beam for simulation and experimental study.
- 28 -
2.2.2 Photon-counting detector
The photon-counting system (as shown in figure 2.6) that is able to perform both
DR and CT mode was constructed with CZT (eV2500, eV Products, Saxonburg, PA)
detector, which consisted of a linear row of four CZT crystals 12.8 mm in length, 3
mm in width, and 3 mm in thickness. Each crystal was divided into 16 pixels, yielding
a total of 64 pixels, with each pixel having an effective pitch of 0.8 mm. The linearity
of count rate range of this detector is less than 1.2×106 cps/mm
2 based on a thickness-
dependent study, thereby avoiding the pulse pile-up effect by high flux X-ray [10]. The
energy-resolving capability of the detector sorted the photons into user-definable
energy bins.
Figure 2.6 The photon-counting detector for validation compared to monochromatic
triple-energy X-ray beam.
- 29 -
2.3. Process of emission and detection
The schematic flow is illustrated for emission and detection of photons in figure 2.7.
If the primary X-ray beam is )(0 EI , the primary beam is shaping through the filter
),( Etfilter having a Z number, and the then filtered X-ray beam )(1 EI is produced.
The filtered X-ray beam )(1 EI is detected by reaching the detector ),( Etse . As
shown in figure 2.7, the filtered spectrum (narrow beam) was shaped in accordance
with the linear attenuation coefficients of the filter material.
Figure 2.7 Flow of emission and detection of X-ray from source to detector.
- 30 -
Chapter 3: Simulation study of the proposed
design for triple-energy X-ray beam
In this chapter, we report X-ray beam shaping in combinations with tube potentials
and filter materials with an empirical model. Appropriate filter thicknesses were
determined with mean energy with respect to increasing HVLs of materials at a given
tube potential. Filter materials were selected in a range of Z=13 to 74, including K-
edge energy for monochromatic X-ray beam. Appropriate filter thickness were decided
with reference to the results of variations of mean energy of filtered spectra. Then, the
filtered spectra were validated to mean energy ratio, contrast variation ratio, and
exposure efficiency as quantitative indices. Appropriate tube potentials and filter
materials were proposed for performing triple-energy X-ray imaging. The obtained
spectrum of triple-energy X-ray beam by simulation is compared to the experimental
results by photon-counting detector. The linear attenuation coefficients of iodine,
aluminum, and PMMA were produced by using a triple-energy beam for obtaining a
thickness density map of three materials. The thickness density map acquired with the
proposed triple-energy beam is compared to that obtained with the photon-counting
method.
- 31 -
3.1. X-ray beam shaping
Initial X-ray beams were generated using an empirical model (i.e., TASMIP code),
and then filter materials were combinations with the initial X-ray beams. The
simulation tool for spectrum measurement and quantitative evaluation used a Geant4
Application for Tomographic Emission (GATE) Monte Carlo platform to model X-ray
beam through filter and object. GATE is well validated, with highly realistic
simulations [29]. The geometry of simulation was illustrated for monochromatic X-ray
beam design as shown in figure 3.1. The initial beam in accordance with alternations of
tube potentials is exposed to the detector through the filter. Detected X-ray beams are
sorted by number of photons and the photon energy in GATE. Therefore, we obtained
the filtered X-ray spectrum for each tube potential and filter material.
Figure 3.1 Illustration of geometry to acquire spectrum of designed X-ray beam with
initial X-ray source, filter, and a-Se detector.
- 32 -
We simulated the monochromatic X-ray beam by increasing filter thickness at each
tube potential. The filter thickness was increased from 2 to 8 HVL for observing the
reduction in photon number by filtering. The number of photons in filtered beam is
reduced to 128 times compared to the number of photons of initial beam at 7 HVL. The
mean energy of each filtered beam was distributed by tube potential at the filter
thickness of 7 HVL. Since tube loading can reduce the quantity of filtered beam to 128
times, the 7 HVL filter thickness was used to shape the X-ray beam. If 8 HVL is used
as filter thickness, it is insufficient because the photon quantity of the filtered beam is
reduced to 256 times. The plots of energy spectra in accordance with filter thickness
for absolute and relative numbers of photons are illustrated in figures 3.2 and 3.3,
respectively. Since maximum K-edge energy of a filter was about 70 keV, tube
potential of more than 100 kV is not sufficient for spectral shaping. Therefore, we
selected tube potential ranging from 40 to 90 kV. The relationship between the number
of photons and X-ray beam shaping by Ba filter was indicated as having a high-energy
range and narrow beam shaping, with increasing HVL at 50 kV, in figure 3.2. The
quantity of the initial X-ray beam of 50 kV is reduced to 128 times, but tube loading
can be controlled by increasing number of photons (i.e., mAs). The relative spectra by
using 2, 7, and 8 HVL Ba filter at 50 kV are shown in figure 3.3. The spectral quality
exhibits a complex distribution with higher tube potential (≥ 80 kV), where filtering
has a greater effect on controlling mean energy change. Filtered X-ray beam is more
narrow than the unfiltered X-ray beam. The mean energy of the narrow beam is
expected to be close to the mean energy of K-edge energy of a filter. From figure 3.3, it
- 33 -
can be seen that there is significant beam hardening for the unfiltered case, regardless
of tube potential.
Figure 3.2 The relationship between the number of photons and X-ray beam shaping
was simulated by using a Ba filter with increasing filter thickness at 50 kV.
Figure 3.3 The alternation of relative X-ray beam shaping with increasing filter
thickness was simulated by using a Ba filter with increasing filter thickness at 50 kV.
- 34 -
The mean energy of filtered X-ray spectrum is not dependent on the number of
photons; it is only affected by distribution of X-ray spectrum. A plot of the mean of the
filtered energy spectra for Ba at various filter thicknesses is shown in figure 3.4. The
K-edge energy of Ba is 37.44 keV, while with an unfiltered spectrum, mean energy
increases with increasing tube potential. Increasing filter thickness results in an
increase in the mean energy due to more efficient pre-hardening of the spectra and, as a
result, a qualitatively more quasi-monochromatic beam. When using 2 HVL
thicknesses, the trend of mean energy increases similarly to that of an unfiltered beam.
The trend of mean energy is similar between 7 and 8 HVL thicknesses at all tube
potentials. Mean energy is rapidly more increased over the 70 kV with 7 and 8 HVL
thicknesses than with the K-edge energy of Ba. Thus, K-edge peak of Ba does not
contribute to the spectrum due to the existence of high energy with high tube potential.
A plot of the mean of the filtered energy spectra for various filter materials at 7
HVL indicates relatively invariant mean energies within some tube potential operating
range with K-edge energy materials, as shown in figure 3.5. Mean energies of Al and
Cu filters increased corresponding to the increasing tube potential. Higher Z
corresponds to a higher mean energy within the range of 40 to 60 kV. The order of
increasing invariant mean energies corresponds to the increasing K-edge energies of
each material up to approximately 60 kV. However, the tungsten K-characteristic X-
rays bias the spectrum more than the filter’s K-edge at tube potentials greater than 60
kV and, hence, shift the mean energy of the spectrum, leading to an inversion of the
rank order of mean energies with increasing Z. Overall, mean energy is increasing
- 35 -
because the X-ray spectra is shifted to the high energy by filter. This means that the
shapes of spectra were broad to narrow.
Figure 3.4 Mean energy with respect to tube potential using Ba filter at 2, 7, and 8
HVL thicknesses and mean energy of K-edge, and without filtration.
Figure 3.5 Mean energy using various filter materials corresponds to the increasing
tube potential at 7 HVL.
- 36 -
3.2. Quantitative indices
We evaluated the filtered spectra as quantitative indices of mean energy ratio,
contrast variation ratio, and exposure efficiency. In this study, the quantity of photons
of filtered and unfiltered X-ray beam was set to 3.8×106 for evaluating the mean
energy ratio, contrast variation ratio, and exposure efficiency. Mean energy was
calculated as the ratio of post-object mean energy to pre-object mean energy as follows:
max
max
max
max
0
0
0
0
)(
)(
)(
)(
E
prepre
E
preprepre
E
postpost
E
postpostpost
obj
dEEI
dEEIE
dEEI
dEEIE
ME , (3.1)
where )(EI is the X-ray intensity at a given energy, dE . The smaller degree of
alternation of mean energy can be observed when objME mean energy of object of
pre- and post-object is close to unity. Blocks of aluminum (thickness of 0.5 cm) and
polymethyl methacrylate (PMMA) (thickness of 2 cm) were used for evaluating the
mean energy when X-ray photons pass through the matter in the proposed method.
Another way to characterize the effect of contrast when filtered X-ray beam is used
was to compare the contrast of unfiltered X-ray beam. Contrast (C) is defined with the
following equation:
- 37 -
back
signalback
S
SSC , (3.2)
where signalS is the signal obtained from image, and backS is the background of the
image. Therefore, the contrast variation ratio can be defined as the ratio of contrast
obtained in the beam-filtered case to contrast in the unfiltered beam case at the same
tube operating potential with the following equation:
unfiltered
filtered
C
CCvar , (3.3)
where filteredC is the contrast when X-ray beam is filtered, and unfilteredC is the
contrast when X-ray beam is unfiltered at same tube potential.
We used exposure efficiency to evaluate the influence of X-ray beam and tube
potential, which is assumed to be related to more desirable dose efficiency quantitative
index. The exposure efficiency is defined as:
osureN
SSEff
back
signalbackexp/
2
exp
, (3.4)
where, backS and signalS are the intensity of the background and of the signal,
respectively. N is the noise (standard deviation) in the background region.
- 38 -
Figure 3.6 shows results of mean energy ratio of comparing various filter materials
at 7 HVL through a 2 cm PMMA. Choice of an appropriate operating range for tube
potential is dependent on the filter material, with a wider range of tube potentials for
the higher Z materials (40–80 kV) than for the lower Z materials (40–50 kV), as
indicated by the values of kV for which the plot remains close to unity. However,
filters having low K-edge energy out of spectral energy such as Al and Cu are nearly
the invariant mean energy ratio in all tube potentials because their K-edge energy does
not contribute to shaping the X-ray beam. Mean energy ratio obtained with filtered X-
ray beam is lower than that acquired with unfiltered X-ray beam for all tube potentials.
Thus, filtered X-ray beam can reduce beam hardening by shaping a broad spectrum to
a narrow beam. The mean energy of the narrow beam is maintained after the X-ray
beam is through the object.
Figure 3.7 compares various filter materials at 7 HVL through a 0.5 cm Al. Mean
energy ratio of filtered beam is reduced with comparison to unfiltered beam at the same
tube potential. The mean energy ratio of I filter rapidly increases from 50 to 70 kV, and
reduces from 70 to 90 kV. The mean energy ratio of Ba filter increases from 60 to 80
kV, and reduces from 80 to 90 kV. The mean energy ratio of Ce filter increases from
60 to 90 kV. The mean energy ratio of Gd increases from 80 to 90 kV. The mean
energy of Al, Cu, Er, and W filters are almost equal. It is thought that K-edge energy of
Al and Cu is influenced by tube potential. Considering K-edge energy of Er and W, the
mean energy ratio of Er and W is expected to increase at more than 90 kV. The result
indicated the same trend in case of mean energy ratio of PMMA in figure 3.6.
- 39 -
Figure 3.6 Results of mean energy ratio comparing various filter materials at 7 HVL
through a 2 cm PMMA.
Figure 3.7 Results of mean energy ratio of comparing various filter materials at 7 HVL
through a 0.5 cm aluminum filter.
- 40 -
The geometry of simulation was illustrated for image acquisition with the design X-
ray beam, as shown in figure 3.8. The initial beam is emitted to the detector through
the filter and phantom. The phantom image was used to evaluate contrast variation
ratio and exposure efficiency.
Figure 3.8 Illustration of geometry to acquire phantom image with designed X-ray
beam by using initial X-ray source, filter, and a-Se detector.
In figure 3.9, the phantom images were acquired to evaluate contrast variation ratio
and exposure efficiency. Incident photon number was 3.8×106 for each simulation
condition. Aluminum is located at the center (white) as a signal, and the peripheral part
is PMMA as a background (black). The first row is the image when using Al filter with
7 HVL thicknesses. The images by using unfiltered and filtered X-ray beams with Cu,
I, Ba, Ce, Gd, Er, and W are displayed. The last row is the images made by using no
filtration from 40 to 90 kV. The results for contrast variation ratio and exposure
efficiency are illustrated in figures 3.9 and 3.10, respectively.
- 41 -
Figure 3.9 The signal (aluminum) and background (PMMA) were obtained to evaluate
contrast variation ratio and exposure efficiency by simulation study. The effect of
filtered X-ray beam was shown with signal and noise of signal and background. The
proton quantities of unfiltered and filtered X-ray beam are each 3.8×106.
- 42 -
As illustrated in figure 3.10, higher Z filters and higher tube potential appear to
have less gain than lower Z filters because the designed X-ray beam by filter at high
tube potential increases the transmission of the X-ray beam. Al and Cu are decreased
with increasing tube potentials due to the too low K-edge energy. If one is interested in
using the technique to reduce beam hardening without degrading contrast, then I, Ba,
and Ce are appropriate for filter materials. Contrast of image obtained with filtered X-
ray beam is higher compared with that acquired with unfiltered beam in this study.
Thus, filtered X-ray beam is efficient to enhance image contrast in a specific tube
potential range.
Figure 3.10 Contrast of the image obtained with filtered X-ray beam can be higher than
that acquired with unfiltered X-ray beam.
- 43 -
Mean energy only takes into account designed X-ray beam characteristics. Contrast
results are impacted by beam hardening in part but also take into account detector
characteristics. However, noise is not included in either of the above results. Thus, to
more completely characterize the system response, we include X-ray noise, detector
efficiency, and incident beam characteristics by examining the exposure efficiency.
The number of photons were 3.8×106 for each X-ray beam.
From the simulation results, exposure efficiency increased with increasing filtration
for almost all tube potentials. Figure 3.11 indicates the exposure efficiency considering
both signal-to-noise ratio and the number of photons (exposure) on images obtained
with monochromatic X-ray beam with increasing Ba filter thicknesses. In case of Ba
filter, exposure efficiency increases between 40 to 80 kV when using 2, 7, and 8 HVL
filter thicknesses. The exposure efficiency with changing tube potential illustrates that
more filtration for a given tube potential yields better exposure efficiency
(SNR2/exposure) in figure 3.11. The exposure efficiency is considered a reasonable
surrogate for dose efficiency, and is ultimately a more easily measured quantity. Al and
Cu filter reduced the exposure efficiency. The range of exposure efficiency with
filtered beam is higher than the conventional beam from 40 to 50 kV for all filters, as
shown in figure 3.12. The exposure efficiency obtained with monochromatic X-ray
beam with I, Ba, and Ce filters is increasing in the range of 50 to 60 kV compared to
that acquired with unfiltered beam at the same exposure. Overall, monochromatic X-
ray beam generated by I, Ba, Ce, and Gd filters were higher exposure efficiency than
that acquired with unfiltered X-ray beam. The evaluated quantitative indices for mean
- 44 -
energy ratio, contrast variation ratio, and exposure efficiency are summarized in table
3.1.
Figure 3.11 Exposure efficiency by considering the SNR and the number of photons
through 2 cm PMMA and 0.5 cm Al object for designed beam obtained with Ba filter
at various filter thickness.
- 45 -
Figure 3.12 Exposure efficiency considering the SNR and the number of photons
through 2 cm PMMA and 0.5 cm Al object for the designed beam obtained with all
filters at 7 HVL filter thickness.
From the simulation results for mean energy ratio, contrast variation ratio, and
exposure efficiency, the effect by using additional filter is summarized. As shown in
table 3.1, quantitative indices obtained with I, Ba, and Ce filters outperform other
filters at a certain range of tube potential. X-ray beam filtered by Al and Cu minimized
mean energy ratio for the full tube potential range and maximized exposure efficiency
from 40 to 50 kV. This means that mean energy of filtered spectra by using Al and Cu
was only shifted to high energy without spectral shaping by K-edge of filter. Since Gd,
Er, and W filters have high K-edge energies, the contrast is decreased compared to that
with X-ray beam without filter.
- 46 -
Table 3.1 Tube operating range summary for different quantitative indices considering
mean energy ratio, exposure efficiency, and contrast variation ratio.
Element
Mean energy ratio
minimized (kV)
Exposure efficiency
Maximized (kV)
Contrast variation
ratio maximized
(kV)
Al 40–90 40–50 …
Cu 40–90 40–50 …
I 40–50 40–60 40–60
Ba 40–60 40–80 50–80
Ce 40–70 40–80 60–80
Gd 40–90 40–60 …
Er 40–90 40–50 …
W 40–90 40–50 …
- 47 -
3.3. Measurement of designed X-ray beam
Designed TE monochromatic X-ray spectra by simulation are validated with
measured spectra obtained by using CZT detector in its spectrum collection mode,
where two thresholds separated by a small energy window were used to scan across the
full energy range. As obtained from the simulation results, filtered X-ray beams with I,
Ba, and Gd were measured with summation of detected signal by energy bin for each
tube potential. Figure 3.13 shows the comparison between the simulated and measured
filtered X-ray spectra at 50 kV with I filter. Both the simulated and the measured
spectra were compared with respect to the integrated energy above 20 keV. Although
the overall shapes of the measured spectrum agreed relatively well, especially K-edge
peak of I, distortions in the filtered spectrum can be observed with the simulation
spectrum. The measurement of spectrum of filtered X-ray beam obtained with Ba at 60
kV was performed. The simulation result for peak of K-edge energy of Ba is well
matched to the peak from the measurement spectrum, as illustrated in figure 3.14. The
shape of the measured spectrum agreed relatively well, especially the K-edge peak of
Ba, with the simulation spectrum, distortions in the filtered spectrum can also be
observed. The peak of Gd filter by measuring filtered X-ray beam is also matched to
the result from the simulation data in figure 3.15. In the three filtered X-ray beam, peak
energies by using experimental data are agreed with the simulation data. However, the
remaining energy regions were not matched to the simulation data.
- 48 -
In the spectrum measurement study, K-edge peak energies of designed X-ray beams
by measurement agreed well with those of spectra obtained with simulation. However,
spectral distortion by measurement data at the K-edge energy was observed. For
energies below 30 keV, the measured counts were significantly higher than the
simulated spectrum due to charge sharing effect of the photon-counting detector [30].
The efforts of reducing the charge-sharing effector of the photon-counting detector
have been studied by many groups. In this spectrum measurement, it is proved that the
three energy spectra can be separated by using K-edge filters with spectra measurement
study, as shown in figures 3.13, 3.14, and 3.15 for I, Ba, and Gd, respectively.
Figure 3.13 The recorded spectrum of the CZT detector and the simulated incident
spectrum at tube voltage of 50 kV and I filter. The spectra were normalized with
respect to the integrated energy.
- 49 -
Figure 3.14 The recorded spectrum of the CZT detector and the simulated incident
spectrum at tube voltage of 60 kV and Ba filter. The spectra were normalized with
respect to the integrated energy.
Figure 3.15 The recorded spectrum of the CZT detector and the simulated incident
spectrum at tube voltage of 70 kV and Gd filter. The spectra were normalized with
respect to the integrated energy.
- 50 -
3.4. Monte Carlo simulation
3.4.1 Beam selection
Based on the results of designed beam from simulated and measured spectra, linear
attenuation coefficients of PMMA, Al, and I were simulated with Monte Carlo
simulation prior to obtain the thickness density map of phantom containing three
materials such as I, Al, and PMMA. The results of linear attenuation coefficients
obtained with proposed TE X-ray beam were compared with the result of linear
attenuation coefficients acquired from photon-counting method in simulation study.
The linear attenuation coefficients were used as matrix to solve material density map
for I, Al, and PMMA.
Figure 3.16 illustrates the X-ray spectra by the number of photon of proposed TE
monochromatic X-ray beams. TE monochromatic beams are generated by using I, Ba,
and Gd filters at 50, 60, and 70 kV, respectively considering quantitative indices. The
mean energies of the proposed TE monochromatic X-ray beams were 31.47, 35.38, and
46.37 keV, respectively. Spectral separations for TE imaging were observed by
combinations of K-edge filter materials and tube potentials. Narrow spectra could be
able to discriminate the information including various materials in an object. In the
photon-counting method, three energy bins were selected to match the mean energy of
each TE X-ray beams. Therefore, the energy is binned into 21–33, 34–41, and 42–50
keV from X-ray spectrum at 90 kV tube potential, and the mean energies of each bin
- 51 -
are 29.34, 37.57, and 45.87, respectively, in photon-counting mode, as shown in figure
3.17.
Figure 3.16 X-ray spectra for proposed TE monochromatic X-ray beam by generating I,
Ba, and Gd filters with 50, 60, and 70 kV, respectively.
- 52 -
Figure 3.17 In photon-counting mode, energy binning was performed from 90 kV
broad spectrum to match the energies of proposed TE monochromatic X-ray beam.
The information of the X-ray beam on TE X-ray beam and photon-counting
method is given in table 3.2. In the proposed TE monochromatic X-ray method, E_1,
E_2, and E_3 were energies at 50, 60, and 70 kV, respectively, with I, Ba, and Gd
filters, respectively. The number of photons was 3.8×106 for each beam in the proposed
TE monochromatic X-ray. Since the photon number affects the image quality, such as
by inducing noise, the incident photon number is set to same level for multi-energy
imaging. In the photon counting method, the numbers of photons were 3.9×106,
3.7×106, and 3.8×10
6 for bin 1, bin 2, and bin 3, respectively. The limitation of count
rate of photon-counting system used in this study is 1.2×106, though the photon-
counting system can acquire the signal several times without effect of low-count rate.
- 53 -
Table 3.2 Proposed triple-energy X-ray beam and binning of photon-counting method.
Triple-energy X-ray beam Binning of photon-counting
Tube
potential &
filter
Mean
energy
(keV)
Number of
photons
(#/mAs)
Bin number
Mean
energy
(keV)
Number
of
photons
(#/mAs)
50 kV & I
(E_1)
31.47 3.8×106 1. 21-33 keV 29.34 3.9×10
6
60 kV & Ba
(E_2)
35.38 3.8×106 2. 34-41 keV 37.57 3.7×10
6
70 kV & Gd
(E_3)
46.37 3.8×106 3. 42-50 keV 45.87 3.8×10
6
3.4.2 Simulation setup
We try to discriminate three materials (I, Al, and PMMA) by density map when the
three materials are overlapped. To obtain density map, linear attenuation coefficients
for I, Al, and PMMA can be decided to calculate matrix in equation 3.6. GATE
simulation tool was used to obtain linear attenuation coefficients of I, Al, and PMMA.
The X-ray imaging system was designed with a SID of 100 cm. The phantom consisted
of I (100 mg/cm3), Al, and PMMA, as shown in figure 3.18. In the validation for
- 54 -
simulation of proposed method, the charge-integrating detector was modeled as
described in chapter 2. The energy-resolved photon-counting detector was modeled as
eV 2500, as described in chapter 2. The exposure condition is expressed for both
proposed and photon-counting method in table 3.2.
Figure 3.18 The cubic phantom of I, Al, and PMMA is on the detector for obtaining
linear attenuation coefficient and thickness density map.
3.4.3 Density map reconstruction
In case of three materials, the logarithmic intensity attenuation is described by the
well-known Beer’s law for three component systems, as in equation 3.4 [31].
PPAAII LLLIIT )/ln( 0 (3.5)
- 55 -
Equation 3.5 is assuming that the exposure is performed only at once to the object
containing three materials. If the object is scanned with triple-energy X-ray beam,
equation 3.5 can be extended to the following three-component system:
P
A
I
PAI
PAI
PAI
L
L
L
T
T
T
333
222
111
)3(
)2(
)1(
, (3.6)
where, T(1), T(2), and T(3) is log measurement by using three X-ray beam with added
filtration or three energy binning. iI , i
A , and iP is the linear attenuation
coefficient for I, Al, and PMMA, respectively. LI, LA, and LP are density map. We can
solve the system with matrix inversion. The density map reconstruction algorithm is
used to calculate the thickness of I, Al, and PMMA for both simulation and
experimental result.
3.4.4 Linear attenuation coefficients and mean energy
The linear attenuation coefficients and their mean energy of I, Al, and PMMA were
obtained by using Monte Carlo simulation. In table 3.3, the linear attenuation
coefficients and mean energies of I, Al, and PMMA for the values obtained with
proposed TE monochromatic X-ray beams. K-edge energies of I, Al, and PMMA were
used as a reference compared with simulated energies. As shown in table 3.3, the linear
- 56 -
attenuation coefficients and mean energies of I, Al, and PMMA are similar to those of
reference mean energies. In table 3.4, the linear attenuation coefficients and mean
energies of I, Al, and PMMA for photon-counting method. Reference energies are the
energies as binned in the photon-counting system. The mean energies of I, Al, and
PMMA are similar to those of binned mean energies. Resultant linear attenuation
coefficient maps of I, Al, and PMMA for the proposed and photon-counting methods
illustrated in figure 3.19. (a), (b), and (c) are the attenuation coefficients at 50, 60, and
70 kV, respectively, with I, Ba, and Gd filters, respectively. (d), (e), and (f) are the
attenuation coefficients map at 29.34, 37.57, and 45.87 keV, respectively. In figure
3.19 (a) and (d), since the mean energies of I are below those of the K-edge energy of I,
effective μ of I is lower than Al.
Linear attenuation coefficients of I, Al, and PMMA acquired with both TE X-tray
beams and photon-counting method were used as a matrix into equation 3.6 iI , i
A ,
and iP for producing thickness density map. The obtained images of figure 3.19 (a),
(b), and (c) and (d), (e), and (f) were used as a log measurement image into equation
3.6 T(1), T(2), and T(3) for proposed and photon-counting method, respectively.
- 57 -
Table 3.3 Linear attenuation coefficients and mean energies of I, Al, and PMMA with
Monte Carlo simulation for proposed method. Reference energy is K-edge energies of I,
Al, and PMMA.
Energy
Iodine Aluminum PMMA reference
Effective
μ
Mean
Energy
(keV)
Effective
μ
Mean
Energy
(keV)
Effective
μ
Mean
Energy
(keV)
Mean
energy
E_1 0.85 30.08 2.39 33.05 0.30 35.50 33.17
E_2 1.98 35.65 1.82 37.05 0.27 40.00 37.44
E_3 1.46 46.88 1.00 49.83 0.23 51.50 50.24
Table 3.4 Linear attenuation coefficients and mean energies of iodine, aluminum, and
PMMA with Monte Carlo simulation for photon-counting method. Reference energy is
the energies as binned in the photon-counting system.
Energy
Iodine Aluminum PMMA reference
Effective
μ
Mean
Energy
(keV)
Effective
μ
Mean
Energy
(keV)
Effective
μ
Mean
Energy
(keV)
Mena
energy
E_1 0.98 28.48 2.99 30.23 0.36 30.13 29.34
E_2 2.51 38.08 1.57 39.59 0.27 40.00 37.57
E_3 1.49 46.52 1.00 49.83 0.23 51.50 45.87
- 58 -
Figure 3.19 Linear attenuation coefficient maps of I, Al, and PMMA obtained with
proposed TE X-ray beams and photon-counting method. (a), (b), and (c) are the
attenuation coefficients at 50, 60, and 70 kV, respectively, with I, Ba, and Gd filters,
respectively. (d), (e), and (f) are the attenuation coefficients map at 29.34, 37.57, and
45.87 keV, respectively.
Figure 3.20 (a), (b), and (c) are thickness density maps of I, Al, and PMMA acquired
with TE X-ray beams. (d), (e), and (f) are thickness density maps of I, Al, and PMMA
with the photon-counting method.
- 59 -
Figure 3.20 (a), (b), and (c) shows thickness density maps of I, Al, and PMMA,
respectively, with the proposed method. (d), (e), and (f) are thickness density maps of I,
Al, and PMMA, respectively, with the photon-counting method. The true values of
thickness for I, Al, and PMMA are each 1.00. I, Al, and PMMA were well separated at
each thickness density map, as shown in figure 3.20. The resultant thicknesses of I, Al,
and PMMA were 1.00, 1.00, and 0.99, respectively, in proposed method. In the
photon-counting method, thickness densities of I, Al, and PMMA were 1.00, 0.96, and
1.02, respectively. The evaluation of thickness density is illustrated in figure 3.21. The
result indicated that the density map obtained with the proposed TE monochromatic X-
ray beam was similar to that acquired with photon-counting method.
Figure 3.21 The results of thickness density maps for I, Al, and PMMA.
- 60 -
3.5. Discussion
Filter designs and their results were validated in quantitative analysis by three
quantitative indices: mean energy ratio, contrast variation ratio, and exposure
efficiency by Monte Carlo simulation. The selection of filter materials, filter thickness,
and tube potential is discussed below.
Filter materials are selected as Al (Z=13), Cu (Z=29), I (Z=53), Ba (Z=56), Ce
(Z=58), Gd (Z=64), Er (Z=68), and W (Z=74) for obtaining the monochromatic X-ray
beam. Al is widely used as an intrinsic filter in X-ray imaging system to minimize low
energy X-ray photons, which cause the skin dose to the patient. Cu is used as an
intermediate filter for the DE imaging operating sandwich detector system. I and Ba
have been used in the previous work for the enhancement of I or Ba materials in the
phantom due to the matching for K-edge energies of contrast medium. Ba, Ce, Gd, and
Er are rare-earth materials, and the research of X-ray beam design included these due
to their K-edge energy within the diagnostic range. W is used as a collimator in gamma
camera system, which is used in this study for matching K-edge energy of tungsten
target of the X-ray source. In monochromatic imaging, since beam energy is generally
up to 70 keV, we used from Al to W (K-edge energy of 69.63 keV) material.
First, we found appropriate filter thickness for generating monochromatic X-ray
beam. The tube loading is considered to prevent usage of a thicker filter. An effective
thickness is 7 HVL, according to the results of mean energy evaluation. The calculated
mean energy between 7 HVL and 8 HVL is similar for all filter materials. The mean
- 61 -
energy by using Al and Cu filters was increasing because their K-edge energies were
1.56 and 8.98 keV, respectively. Since X-ray source generates the photon energy more
than 20 keV, K-edge energies of Al and Cu did not affect production of the
monochromatic X-ray beam, alternatively, the mean energy increases with filter
thickness increasing. Since the mean energies of I, Ba, Ce, Gd, Er, and W are close to
the K-edge energies of their materials at 7 HVL thicknesses, filters except for Al and
Cu for generating monochromatic beam are possible in 7 HVL thickness. Mean energy
is related to the beam hardening effect. Therefore, the accuracy of measurement
increases as mean energy approaches K-edge energy of filter.
The range of tube potential is decided from 40 to 90 kV. With increasing the tube
potential, the energy spectrum of X-ray beam is a broad band window. Since the
maximum K-edge energy of tungsten materials is 69.53 keV, high tube voltage is not
sufficient in this study. In diagnostic X-ray spectrum, the dominant interaction is
photoelelctric effect and Compton scattering [32–36]. The Compton scattering is
expected with increasing tube potential within the range from 30 to 150 keV [34–36].
Therefore, we limited the tube potential to 90 kV.
At 7 HVL of Al, Cu, I, Ba, Ce, Gd, Er, and W and tube potentials ranging from 40
to 90 kV, we evaluated mean energy ratio, contrast variation ratio, and exposure
efficiency. Mean energy ratio is the ratio of pre-mean energy to post-mean energy
through the phantom. Overall results indicated that filtered X-ray beams performed
better than in case of no filtration at equal tube potentials. Mean energy ratio of Al and
Cu is almost constant over all tube potentials. This phenomenon is due to the low K-
edge peak energy of Al and Cu. This means that the linear attenuation coefficients of
- 62 -
Al and Cu reduced exponentially at all tube voltages. The trend of alternations of I, Ba,
Ce, and Gd is remarkable in mean energy ratio. Mean energy ratio of I is nearly 1 in a
range from 40 to 50 kV. However, mean energy ratio of I is increasing from 50 to 70
kV, and then reducing from 70 to 90 kV. This effect is due to the increasing spectral
tail over the K-edge energy of I filter with increasing tube potential. However, the K-
edge effect of I filter was reduced when increasing the tube potential above 70 kV. The
trend is similar to those for K-edge energies of Ba, Ce, and Gd filters.
With respect to contrast variation ratio, I, Ba, and Ce, outperformed other filters.
However, the appropriate tube potential to improve contrast is limited by filter
materials. Contrast variation ratios of Al and Cu are reduced with increasing tube
potential. The enhancement of image contrast by using monochromatic beam was
assessed for this study with several filter materials at different tube potentials.
Therefore, it is expected that the monochromatic beam can improve the image contrast.
The trend of exposure efficiency of filter was reduced with increasing tube potential.
The exposure efficiency with changing tube potential illustrates that more filtration for
a given tube potential yields better SNR2/exposure. In exposure efficiency, I, Ba, Ce,
and Gd filters outperformed other filter materials. The exposure efficiency is
maximized at 40 kV for all filter materials. The exposure efficiency of I, Ba, Ce, and
Gd were maximized from 40 to 50 kV tube potentials. From the results of exposure
efficiency, a dose reduction effect for patients is expected.
According to results of quantitative indices from the simulation study, appropriate
filters for TE X-ray beam were I, Ba, Ce, and Gd filters, and resultant tube potentials
were 50, 60, and 70 kV, respectively. Therefore, we selected I, Ba, and Gd filters and
- 63 -
50, 60, and 70 kV tube potentials, respectively for TE X-ray imaging. To investigate
the spectrum of simulation results of the triple-energy beam, three spectra were
measured with a photon-counting detector. The experimental results of three beams
were matched to simulated spectra. The results indicated their peak energies is well
matched for their K-edge peak energies. However, experimental data on low energy
parts of the spectra were not matched to the simulation study. This effect is due to the
charge-sharing of the photon-counting detector [37–41].
From the TE X-ray beam, three materials decomposition was performed for I, Al,
and PMMA. Three materials can be decomposed by thickness density maps, which
require the information of linear attenuation coefficients of I, Al, and PMMA.
Therefore, the linear attenuation coefficients were obtained with attenuation coefficient
maps from simulation for the proposed method, and the results were compared to the
results obtained with the photon-counting method. The results of linear attenuation
coefficient were well matched to the known values for K-edge energy of the filter
materials. The results of thickness density map for I, Al, and PMMA indicated that the
decomposed image acquired with the proposed method was similar to the decomposed
image obtained with the photon-counting method.
In this chapter, we investigated appropriate filter materials, filter thickness, and tube
potentials. The quantitative evaluations were performed by the image metrics of mean
energy ratio, contrast variation ratio, and exposure efficiency by using the filter
materials, the filter thickness, and the tube potentials. Filter thickness of 7 HVL was
used in this study for considering efficiency. For generating monochromatic X-ray
beam, filters having K-edge energy within the tube potential range was effective for
- 64 -
enhancing contrast, shaping narrow beam, and reducing dose to patient. Therefore, the
TE monochromatic X-ray beam was well validated with simulation study by verifying
the quantitative image metric.
- 65 -
Chapter 4: Experiment with the designed
X-ray beam
In this chapter, we present the validation of the designed TE X-ray beams with both
DR and the photon-counting system by measuring quantitative indices such as mean
energy ratio, contrast variation ration, and exposure efficiency. Mean energy ratio was
measured from the image obtained with proposed TE monochromatic X-ray beam for
Al and PMMA phantom. Then, the result acquired with TE monochromatic beam were
compared with the results obtained with unfiltered X-ray beam at the same tube
potentials and same exposure conditions. Contrast variation ratio was measured for TE
monochromatic X-ray beam and for unfiltered X-ray beam at the same tube potentials
and same exposure doses. Exposure efficiency was also measured to compare between
SNR2/exposure between the proposed TE monochromatic X-ray beam and unfiltered
X-ray beam. To obtain the thickness density map, the linear attenuation coefficients of
I, Al, and PMMA were calculated by the designed TE X-ray beam and the photon-
counting method with step wedge phantom consisting of Al and PMMA. The value of
linear attenuation coefficients of I is used from the simulation results. Then, the
thickness density maps for I, Al, and PMMA are acquired with the designed TE
monochromatic X-ray beams and the photon-counting method, and their results were
displayed on image and evaluated quantitatively.
- 66 -
4.1. Evaluation of quantitative indices by
experimental study
Based on the results of information using the designed beam from simulation, the
experimental study was performed on both DR and the photon-counting system. In
figure 4.1, the mean energy ratio was estimated for images obtained with the proposed
TE monochromatic X-ray beam. In an ideal case, the value of mean energy ratio was
close to unity. Mean energy ratio of the image acquired with the proposed TE X-ray
beam was 1.04, 0.98, and 0.95 through the PMMA phantom. Mean energy ratio of the
image acquired with proposed TE X-ray beam was 0.95, 0.99, and 1.02 through the Al
phantom. Thus, proposed TE X-ray beams proved that monochromatic X-ray beam
reduced beam hardening due to the values of mean energy ratio being close to unity
experimentally.
- 67 -
Figure 4.1 Mean energy ratio was estimated for images obtained with proposed TE X-
ray beam by measuring log intensity of the image and known thickness of the phantom.
Based on the results of simulation studies with quantitative indices for the proposed
TE X-ray method, contrast variation ratio and exposure efficiency were each measured
at E_1, E_2, and E_3. In figure 4.2, contrast variation ratio was calculated as the ratio
of the contrast obtained with the TE monochromatic X-ray beam by using K-edge filter
to contrast acquired with unfiltered X-ray beam. Contrast improvement of the proposed
TE X-ray beam was 1.29 and 1.22 for E_1 and E_2. For E_3, contrast is decreased to
0.95 because the filtered X-ray beam removed low energy photons by K-edge Gd filter.
Therefore, the energy of the filtered X-ray beam is shifted to higher than that of the
unfiltered X-ray beam. The improvements of contrast by filtered X-ray beam were
29.00 and 22.00 % for E_1 and E_2, respectively. Thus, the appropriate filter is
- 68 -
effective to improve image quality compared to without filter. However, the
monochromatic X-ray beam has higher energy by filtering decreased image contrast
compared to unfiltered X-ray beam.
Figure 4.2 Contrast variation ratio was measured by the proposed and conventional
methods at E_1, E_2, and E_3.
Exposure efficiency was estimated as shown in figure 4.3. In the conventional
method, exposure efficiencies were 125.34, 91.47, and 86.05 at E_1, E_2, and E_3,
respectively. The exposure efficiencies obtained with proposed TE monochromatic X-
ray beam improved to 169.93 and 137.47 for E_1 and E_2, respectively. For E_3,
exposure efficiency was decreased to 73.59 due to reduced contrast. The improvement
of exposure efficiency by filtered X-ray beam was 35.57 and 50.29 % for E_1 and E_2,
- 69 -
respectively. This means that the proposed TE X-ray beam can reduce the exposure
dose to the object effectively. However, the energy spectrum generated by filter having
a high K-edge energy is considered to obtain the image without loss of image quality.
In this result, monochromatic X-ray beams acquired with low energy K-edge filter
improve the contrast and reduce the exposure dose from exposure efficiency.
Figure 4.3 Exposure efficiencies were measured by proposed and conventional
methods at E_1, E_2, and E_3.
- 70 -
4.2. Linear attenuation coefficients and mean energy
Linear attenuation coefficients and mean energies of I, Al, and PMMA were
measured by using both the proposed TE monochromatic X-ray beam and photon-
counting methods. Narrow X-ray beam could be more accurately measured to detected
signal. The log intensity images for Al and PMMA were acquired with Al and PMMA
block phantom. The linear attenuation coefficient can be calculated from the log
measurement data with known thickness and log intensity. The thickness of Al block is
0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 cm, and the thickness of PMMA block is 1, 2, 3, 4, 5, and
6 cm. The linear attenuation coefficient of I is used for simulation results due to the I
solution being used.
In figures 4.4 and 4.5, the results of log intensity in accordance with Al and PMMA
thickness, respectively, were illustrated by using the proposed TE monochromatic X-
ray beam. In figures 4.6 and 4.7, the results of log intensity in accordance with Al and
PMMA thickness, respectively, were plotted by using the photon-counting method by
setting three energy thresholds. In the values of linear attenuation coefficient by using
the proposed TE X-ray beam, the linear attenuation coefficients of Al was measured as
2.69, 1.79, and 0.94 for E_1, E_2, and E_3, respectively. The linear attenuation
coefficients of PMMA is 0.31, 0.29, and 0.24 for E_1, E_2, and E_3, respectively. In
the measurement by using the photon-counting method, the linear attenuation
coefficients of Al are 3.11, 2.02, and 1.38 for E_1, E_2, and E_3, respectively. The
- 71 -
linear attenuation coefficients of PMMA are 0.34, 0.29, and 0.23 for E_1, E_2, and
E_3, respectively.
Figure 4.4 Log intensity measurements by using the proposed method to obtain linear
attenuation coefficients with respect to increasing Al thickness from 0.1 to 0.6 cm for
E_1, E_2, and E_3.
Figure 4.5 Log intensity measurements by using proposed method to obtain linear
attenuation coefficients with respect to increasing PMMA thickness from 1 to 6 cm for
E_1, E_2, and E_3.
- 72 -
Figure 4.6 Log intensity measurements by using photon-counting method to obtain
linear attenuation coefficients with respect to increasing Al thickness from 0.1 to 0.6
cm for E_1, E_2, and E_3.
Figure 4.7 Log intensity measurements by using the photon-counting method to obtain
linear attenuation coefficients with respect to increasing PMMA thickness from 1 to 6
cm for E_1, E_2, and E_3.
- 73 -
As listed in tables 4.1 and 4.2, for reconstructing density map of three materials,
linear attenuation coefficients of I, Al, and PMMA were measured by using both the
proposed TE monochromatic X-ray beam and photon--counting methods. The results
of linear attenuation coefficient were used for calculating thickness density maps.
In table 4.1, the reference K-edge energies of E_1, E_2, and E_3 were 33.17, 37.44,
and 50.24 keV, respectively. Measured mean energies of E_1, E_2, and E_3 by using
proposed TE monochromatic X-ray beams were 31.66, 37.33, and 51.64 keV,
respectively, for Al. In PMMA, the measured mean energies of E_1, E_2, and E_3
obtained with proposed TE X-ray beams were 34.33, 36.75, and 47.67 keV,
respectively. The measured results of mean energy were well matched to the known K-
edge energy.
Table 4.1 The experimental results of the linear attenuation coefficients and mean
energies of I, Al, and PMMA for proposed method. Reference energy is K-edge
energies of I, Al, and PMMA.
Energy
Iodine (simulation) Aluminum PMMA reference
Effective
μ
Mean
Energy
(keV)
Effective
μ
Mean
Energy
(keV)
Effective
μ
Mean
Energy
(keV)
K-edge
energy
E_1 0.98 30.08 2.69 31.66 0.31 34.33 33.17
E_2 1.98 35.65 1.79 37.33 0.29 36.75 37.44
E_3 1.46 46.88 0.94 51.64 0.24 47.67 50.24
- 74 -
In table 4.2, reference mean energies of E_1, E_2, and E_3 were 29.34, 37.57, and
45.87 keV, respectively. These reference mean energies were calculated by each
energy bin with the photon-counting method. Measured mean energies of E_1, E_2,
and E_3 by using photon-counting method were 30.23, 39.59, and 49.83 keV,
respectively, for aluminum. In PMMA, measured mean energies of E_1, E_2, and E_3
obtained with photon-counting method were 30.13, 40.00, and 51.50 keV, respectively.
The measured results of mean energies by using photon-counting method were well
matched to known mean energies of each bin.
Table 4.2 The experimental results of the linear attenuation coefficients and mean
energies of I, Al, and PMMA for photon-counting method. Reference energy is the
energies of binned in photon-counting system.
Energy
Iodine (simulation) Aluminum PMMA reference
Effective
μ
Mean
Energy
(keV)
Effective
μ
Mean
Energy
(keV)
Effective
μ
Mean
Energy
(keV)
Mean
energy
E_1 0.98 28.48 3.11 30.23 0.34 30.13 29.34
E_2 2.51 38.08 2.02 39.59 0.29 40.00 37.57
E_3 1.49 46.52 1.38 49.83 0.23 51.50 45.87
- 75 -
4.3. Results of density map
In the previous work, the projection error remained in density maps obtained with
DE algorithm when three materials existed on the projection plane. In this work, the
TE algorithm was applied to separate the three materials by using the TE
monochromatic X-ray beam. The projection error was removed by this method in
experimental results. Then, the density map obtained with the proposed TE X-ray beam
was similar to the result acquired with photon-counting method.
The linear attenuation coefficients of I, Al, and PMMA for both proposed TE
monochromatic X-ray beam and photon-counting method from experimental data were
used as a matrix with iI , i
A , and iP in equation 3.6 for producing thickness
density maps. The obtained phantom images consisting of I, Al, and PMMA were used
as log intensity images into T(1), T(2), and T(3), respectively, in equation 3.6 for the
proposed TE monochromatic X-ray beams and photon-counting method.
Figure 4.8 showed examples of the experimental images of the phantom at different
energies and the reconstructed density maps obtained for the TE method. In figure 4.8
(a), (b), and (c) are thickness density maps of I, Al, and PMMA, respectively, were
acquired with proposed TE monochromatic X-ray beam experimentally. Figure 4.8 (d),
(e), and (f) are the experimental images of thickness density maps of I, Al, and PMMA
with photon-counting method. Figure 4.8 indicates that the densities of I, Al, and
PMMA were enhanced from background material obtained by TE monochromatic X-
ray beam and photon-counting method.
- 76 -
Figure 4.8 (a) I, (b) Al, and (c) PMMA are obtained with the proposed TE
monochromatic X-ray beams with I, Ba, and Gd filters for 50, 60, and 70 kV,
respectively. (d) I, (e) Al, and (f) PMMA are the material density maps obtained with
the photon-counting method.
The true thickness values of I, Al, and PMMA were 0.50, 0.50, and 2.00 cm,
respectively. The three materials I, Al, and PMMA were well separated at each
thickness density map obtained with both the proposed TE X-ray beams and photon-
counting methods as shown in figure 4.8. The thicknesses densities of I, Al, and
PMMA were measured as 0.57, 0.52, and 1.99 cm, respectively, by the proposed TE
monochromatic X-ray beams. In the photon-counting method, thickness densities of I,
Al, and PMMA were 0.50, 0.51, and 2.05, respectively. The evaluation of thickness
density is illustrated in figure 4.9.
- 77 -
Figure 4.9 Thickness density maps of I, Al, and PMMA obtained by the proposed TE
X-ray beams and photon-counting methods.
- 78 -
4.4. Discussion
We measured and evaluated the effect of three designed X-ray beams by
quantitative indices of mean energy ratio, contrast variation ratio, and exposure
efficiency. In addition, density maps were reconstructed using the proposed TE beams
and photon-counting methods. Then, the results of density map were evaluated.
Mean energy ratio was estimated for the proposed TE monochromatic X-ray beams
and photon-counting methods in equation 3.1. In the simulation results, mean energy
ratio is closed to unity for E_1, E_2, and E_3. As shown in the results, mean energy
ratio obtained with the proposed TE X-ray beam is nearly balanced when the beams are
through Al and PMMA. Therefore, the proposed method contributes to improvement
of image contrast according to experimental findings.
Contrast variation ratio was measured at E_1, E_2, and E_3. Contrast variation ratio
was calculated as the ratio of the contrast with K-edge filter to contrast without filter.
The improvements of contrast when using filter were 29.00 and 22.00 % for E_1 and
E_2, respectively. However, contrast obtained with E_3 declined to 5.00 % because the
mean energy of X-ray beam by using filter is higher than that of unfiltered X-ray beam.
Higher energy X-ray beam caused decreasing image contrast. Thus, the
monochromatic X-ray beam is effective to improve the image contrast compared to
unfiltered X-ray beam.
Exposure efficiency was estimated at E_1, E_2, and E_3. The exposure efficiency
acquired with the proposed X-ray beam improved to 35.58 and 50.29 % for E_1 and
- 79 -
E_2, respectively. In E_3, exposure efficiency is decreasing to 14.48 %. Thus, the
proposed TE X-ray beam can reduce the exposure dose to the object effectively.
However, the energy spectrum generated by filter having a high K-edge energy is
considered to avoid loss of image quality. In this result, monochromatic X-ray beams
acquired with low energy K-edge filter improve the contrast and reduce the exposure
dose from exposure efficiency.
Prior to reconstructing density map for I, Al, and PMMA, linear attenuation
coefficients were decided by measuring the thickness of Al and PMMA blocks with the
TE X-ray beam and photon-counting methods. If the X-ray beam is monochromatic,
the linear attenuation coefficient is measured accurately [42, 43]. Log intensities for Al
and PMMA were increasing in accordance with thickness of the block. Effective linear
attenuation coefficients were calculated by using equation 3.1.
From the TE X-ray beam, three materials decomposition was performed for I, Al,
and PMMA. Three materials can be decomposed by thickness density maps, which
need the information of linear attenuation coefficients of I, Al, and PMMA. Therefore,
the linear attenuation coefficients were obtained with attenuation coefficient maps for
the proposed method, and the results were compared to the results obtained with the
photon-counting method. The resultant thicknesses of I, Al, and PMMA were 0.57,
0.52, and 1.99 cm, respectively, with the proposed TE X-ray beam. In the photon-
counting method, thickness densities of I, Al, and PMMA were 0.50, 0.51, and 2.05 cm,
respectively. The results of thickness density maps for I, Al, and PMMA indicated that
the decomposed image acquired with the proposed method was similar to the
- 80 -
decomposed image obtained with the photon-counting method according to the
experimental study.
In this chapter, we investigated the quantitative image metrics of contrast, variation
ratio, and exposure efficiency from the TE X-ray beam from the simulation study.
Then, the thickness density maps were acquired with both the proposed and photon-
counting methods. Monochromatic beam considering K-edge filter and tube potential
can improve the image contrast through contrast variation ratio evaluation. The trend
of exposure efficiency is similar to that in simulation results. Thus, a dose reduction
effect is expected with the proposed method. Therefore, the triple-energy X-ray beam
was well validated with experimental study by verifying quantitative image metrics.
- 81 -
Chapter 5: Summary and Conclusion
In this study, the TE X-ray method was introduced, and the effects of the design of
the X-ray spectra on system performances were evaluated using simulation and
experimental measurement for a spectral separation with the combinations of
additional filters and conventional tube voltage. The optimum energy spectra
determined based on the calibration for accurate linear attenuation coefficient
demonstrate that spectral separation can be achieved (i.e., without overlapping between
three spectra).
A mean energy of the filtered energy spectra for various filter materials at 7 HVL
indicates relatively invariant mean energies within given tube potential operating
ranges with K-edge energy materials. Higher Z corresponds to a higher mean energy
for all the tube potential ranges of 40 to 90 kV. The order of increasing invariant mean
energies corresponds to the increasing K-edge energies of each material up to
approximately 60 kV.
Mean energy ratio of comparing various filter materials at the 7 HVL through a 2
cm PMMA and a 0.5 cm Al. Choice of an appropriate operating range for tube
potential is dependent on the filter material, with a wider range of tube potentials for
the higher Z materials (40–80 kV) than for the lower Z materials (40–50 kV), as
indicated by the values of kV for which the plot remains close to unity. If one is
interested in using the technique to reduce beam hardening without degrading contrast,
then I, Ba, and Ce are appropriate for filter materials. The exposure efficiency with
- 82 -
changing tube potential illustrates that more filtration for a given tube potential yields
better SNR2/exposure.
Triple-energy beams are generated by using I, Ba, and Gd filters at 50, 60, and 70
kV considering quantitative indices. The mean energies of the proposed X-ray beams
were 31.47, 35.38, and 46.37, respectively. In the photon-counting method, three
energy bins were selected to match the proposed triple-energy X-ray beam. The energy
is binned into 21–33, 34–41, and 42–50 keV, and the mean energies of each bin are
29.34, 37.57, and 45.87 keV, respectively.
In the experimental work, the improvement of contrast when using a filter was
29.00 and 22.00 % for E_1 and E_2, respectively. The exposure efficiencies of the
proposed method improved to 35.58 and 50.29 % for E_1 and E_2, respectively. In
E_3, contrast and exposure efficiency is decreased by increasing the mean energy of
filtered beam compared to the conventional method. Therefore, the evaluation is
needed to optimize how the X-ray beam is appropriated to increase contrast when
using filtered beam and unfiltered beam.
In thickness density map, the results of I, Al, and PMMA were 1.00, 1.00, and 0.99,
respectively, in the proposed method. In the photon-counting method, thickness
densities of I, Al, and PMMA were 1.00, 0.96, and 1.02 cm, respectively, in the
simulation study. In experimental work, the resultant thicknesses of I, Al, and PMMA
were 0.57, 0.52, and 1.99 cm, respectively, in the proposed method, and 0.50, 0.51, and
2.05 cm, respectively, in the photon-counting method. Therefore, the proposed TE X-
ray beams are useful for the decomposition three different materials.
- 83 -
The present paper demonstrates that separated X-ray spectrum is a reliable design
for a TE with tube voltage and additional filters. In photon-counting mode, the studies
of bone mineral measurement and detection of breast cancer have been performed for
three materials decomposition [44, 45]. The proposed additional filtration method for
obtaining monochromatic X-ray beam has proven its feasibility as an imaging method
with high accuracy of material thickness over the three materials, and this method can
be used for multi-energy X-ray imaging for medical imaging.
- 84 -
References [1] D.-H. Kim, Y.-J. Lee, P.-H. Jeon et al., “Optimal contrast enhancement achieved by
the synthetic method for bone and tissue separation based on a dual-energy
radiographic system,” Journal of Instrumentation, 8, P07009, 2013.
[2] L. A, Lehman, R. E. Alvarez, A. Macovski et al., “Generalized image combinations
in dual kVp digital radiography,” Medical Physics, Vol. 8, pp. 659~667, 1981.
[3] P. Stolzmann, S. Leschka, H. Scheffel et al., “Characterization of urinary stones
with dual-energy CT: improved differentiation using a tin filter,” Investigative
Radiology, Vol. 45, No. 1, pp. 1~6, 2010.
[4] B. Ruzsics, H. Lee, P. L. Zwerner et al., “Dual-energy CT of the heart for
diagnosing coronary artery stenosis and myocardial ischemia initial experience,”
European Radiology, Vol. 18, No. 11, pp. 2414~2424, 2008.
[5] A. N. Primak, J. C. Ramirez Giraldo, X. Liu et al., “Improved dual-energy material
discrimination for dual-source CT by means of additional spectral filtration,” Medical
Physics, Vol. 36, No. 4, pp. 1359~1369, 2009.
[6] M. L. McKinley, M. P. Tornai, E. Samei et al., “Development of an optimal X-ray
beam for dual-mode emission and transmission mammotomography,” Nuclear
Instruments and Method in Physics Research A, Vol. 527, No. 1, pp. 102~109, 2004.
[7] P. V. Granton, S. I. Pollmann, N. L. Ford et al., “Implementation of dual- and
triple-energy cone-beam micro-CT for postreconstruction material decomposition,”
Medical Physics, Vol. 35, No. 11, pp. 5030~5042, 2008.
- 85 -
[8] G. Baldazzi, N. Lanconelli, S. Masetti et al., “A method to remove the projection
error in triple-energy radiography with contrast medium,” Nuclear Instruments and
Method in Physics Research A, Vol. 610, No. 1, pp. 222~224, 2009.
[9] P. M. Shikhaliev, “Computed tomography with energy-resolved detection: a
feasibility study,” Physics in Medicine & Biology, Vol. 53, No. 5, pp 1475~1495, 2008.
[10] P. M. Shikhaliev, “Energy-resolved computed tomography: first experimental
results,” Physics in Medicine & Biology, Vol. 53, No. 20, pp 5595~5613, 2008.
[11] E. Roessl, R. Proksa, “K-edge imaging in x-ray computed tomography using
multi-bin photon counting detectors,” Physics in Medicine & Biology, Vol. 52, No. 15,
pp 4679~4696, 2007.
[12] J. P. Schlomka, E. Roessl, R. Dorscheid et al., “Experimental feasibility of multi-
energy photon-counting K-edge imaging in pre-clinical computed tomography,”
Physics in Medicine & Biology, Vol. 53, No. 15, pp 4031~4047, 2008.
[13] S.Feuerlein, E. Roessl, R. Proksa et al. “Multienergy photon-counting K-edge
imaging: Potential for improved luminal depiction in vascular imaging,” Radiology,
Vol. 249, No. 3, pp 1010~1016, 2008.
[14] H. Le, J. Ducote, S. Molloi et al., “Radiation dose reduction using a CdZnTe-
based computed tomography system: comparison to flat-panel detectors,” Medical
Physics, Vol. 37, No. 3, pp 1225~1236, 2010.
[15] T. G. Flohr, C. H. McCollough, H. Bruder et al., “First performance evaluation of
a dual-source CT (DSCT) system,” European Radiology, Vol. 16, No. 2, pp 256~258,
2006.
- 86 -
[16] W. A. Kalender, W. H. Perman, J. R. Vetter et al., “Evaluation of a prototype
dual-energy computed tomographic apparatus. I. Phantom studies,” Medical Physics,
Vol. 13, No. 3, pp 334~339, 1986.
[17] D. T. Boll, E. M. Merkle, E. K. Paulson et al., “Coronary stent patency: dual-
energy multidetector CT assessment in a pilot study with anthropomorphic phantom,”
Radiology, Vol. 247, No. 3, pp. 687~695, 2008.
[18] D. T. Boll, E. M. Merkle, E. K. Paulson et al., “Calcified vascular plaque
specimens: Assessment with cardiac dual-energy multidetector CT in
anthropomorphically moving heart phantom,” Radiology, Vol. 249, No. 1, pp. 119~126,
2008.
[19] S. Masetti, L. Roma, P. L. Rossi, et al., “Preliminary results of a multi-energy CT
system for small animals,” Journal of Instrumentation, 4, P06011, 2009.
[20] R. L. McKinley, M. P. Tornai, E. Samei et al., “Simulation study of a quasi-
monochromatic beam for X-ray computed tomography,” Medical Physics, Vol. 31, No.
4, pp. 800~813, 2004.
[21] K. Bliznakova, Z. Kolitsi, N. Pallikarakis, “Dual-energy mammography:
simulation studies,” Physics in Medicine & Biology, Vol. 51, No. 18, pp. 4497~4515,
2006.
[22] W. R. Brody, G. Butt, A. Hall et al., “A method for selective tissue and bone
visualization using dual energy scanned projection radiography,” Medical
Physics, Vol. 8, No. 3, pp. 353~357, 1981.
- 87 -
[23] L. A. Lehmann, R. E. Alvarez, A. Macovski et al., “Generalized image
combinations in dual KVP digital radiography,” Medical Physics, Vol. 8, No. 5, pp.
659~667, 1981.
[24] F. C. Wagner, A. Macovski, D. G. Nishimura, “Dual-energy x-ray projection
imaging: two sampling schemes for the correction of scattered radiation,” Medical
Physics, Vol. 15, No. 5, pp. 732~748, 1988.
[25] S. J. Riederer, C. A. Mistretta, “Selective iodine imaging using k-edge energies in
computerized x-ray tomography,” Medical Physics, Vol. 4, No. 6, pp. 474~481, 1977.
[26] J. M. Boone, J. A. Seibert, “An accurate method for computer-generating tungsten
anode x-ray spectra from 30 to 140 kV,” Medical Physics, Vol. 24, No. 11, pp.
1661~1670, 1997.
[27] J. H. Hubbell et al., “Tables of x-ray mass attenuation coefficients and mass
energy-absorption coefficient”, Natl Inst. Stand. Technol.
[28] J. H. Siewerdsen, A. M. Waese, D. J. Moseley, “Spektr: A computational tool for
x-ray spectral analysis and imaging system optimization,” Medical Physics, Vol. 31,
No. 11, pp. 3057~3067, 2004.
[29] S. Jan, G. Santin, D. Strul et al., “GATE: a simulation toolkit for PET and SPECT,”
Physics in Medicine & Biology, Vol. 49, No. 19, pp. 4543~4561, 2004.
[30] X. Wang, D. Meier, S. Mikkelsen et al., “MicroCT with energy-resolved photon-
counting detectors,” Physics in Medicine & Biology, Vol. 56, No. 9, pp. 2791~2816,
2011.
- 88 -
[31] S. J. Riederer, C. A. Mistretta, “Selective iodine imaging using K-edge energies in
computerized X-ray tomography,” Medical Physics, Vol. 4, No. 6, pp. 474~481, 1977.
[32] R. A. Kruger, S. J. Riederer, C. A. Mistretta, “Relative properties of tomography,
K-edge imaging, and K-edge tomography,” Medical Physics, Vol. 4, No. 3, pp
244~249, 1977.
[33] A. N. Primak, J. C. Ramirez Giraldo, X. Liu et al., “Improved dual-energy
material discrimination for dual-source CT by means of additional spectral filtration,”
Medical Physics, Vol. 36, No. 4, pp. 1359~1369, 2009.
[34] M. M. Goodsitt, E. G. Christodoulou, S. C. Larson, “Accuracies of the
synthesized monochromatic CT numbers and effective atomic numbers obtained with a
rapid kVp switching dual energy CT scanner,” Medical Physics, Vol. 38, No. 4, pp.
2222~2231, 2011.
[35] L. A. Lehmann, R. E. Alvarez, A. Macovski, et al., “Generalized image
combinations in dual kVp digital radiography,” Medical Physics, Vol. 8, No. 5, pp.
659~667, 1981.
[36] W. R. Brody, G. Butt, A. Hall, A. Macovski et al., “A method for selective tissue
and bone visualization using dual energy scanned projection radiography,” Medical
Physics, Vol. 8, No. 3, pp. 353~357, 1981.
[37] C. Ponchut, “Correction of the charge sharing in photon-counting pixel detector
data,” Nuclear Instruments and Method in Physics Research A, Vol. 591, No. 1, pp.
311~313, 2008.
- 89 -
[38] H.-E. Nilsson, C. Frojdh, E. Dubaric, “Monte Carlo simulation of charge sharing
effects in silicon and GaAs photon-counting X-ray imaging detectors,” IEEE
Transactions on Nuclear Science, Vol. 51, No. 4, pp. 1636~1640, 2004.
[39] H.-E. Nilsson, E. Dubaric, M. Hjelm et al., “Simulation of photon and charge
transport in X-ray imaging semiconductor sensors,” Nuclear Instruments and Method
in Physics Research A, Vol. 487, No. 1-2, pp. 151~162, 2002.
[40] K. Mathieson, M. S. Passmore, P. Seller et al., “Charge sharing in silicon pixel
detectors,” Nuclear Instruments and Method in Physics Research A, Vol. 487, No. 1-2,
pp. 113~122, 2002.
[41] H.-E. Nilsson, B. Norlin, C. Frojdh et al., “Charge sharing suppression using
pixel-to-pixel communication in photon counting X-ray imaging systems,” Nuclear
Instruments and Method in Physics Research A, Vol. 576, No. 1, pp. 243~247, 2007.
[42] K. Achterhold, M. Bech, S. Schleede et al., “Monochromatic computed
tomography with a compact laser-driven X-ray source,” Scientific Reports, Vol. 3, pp.
1313, 2013.
[43] A. Sarnelli, H. Elleaume, A. Taibi et al., “K-edge digital subtraction imaging with
dichromatic X-ray sources: SNR and dose studies,” Physics in Medicine & Biology,
Vol. 51, No. 17, pp. 4311~4328, 2006.
[44] J. Swanpalmer, R. Kullenberg, T. Hansson, “Measurement of bone mineral using
multiple-energy X-ray absorptiometry,” Physics in Medicine & Biology, Vol. 43, No. 2,
pp. 379~387, 1998.
- 90 -
[45] H. Ding, S. Molloi, “Quantification of breast density with spectral mammography
based on a scanned multi-slit photon-counting detector: a feasibility study,” Physics in
Medicine & Biology, Vol. 57, No. 15, pp. 4719~4738, 2012.
- 91 -
국문 요약
엑스선 영상 시스템에서 필터를 이용한 다중에너지
단일화 엑스선 빔의 설계
연세대학교 대학원
방사선학과
김 대 홍
의료, 산업 및 보안 분야에서 다중에너지 엑스선 영상화 혹은 스펙트럴
영상화 방법이 널리 사용되고 있다. 이러한 다중에너지 엑스선 영상 시스템
은 의료 분야에서 관심 병변의 대조도 증강과 특정 물질의 정량적인 분석
및 인체의 기능적 영상에 적합하다. 그러므로, 이중 선원 조사 방식과 두
층 검출기 방식 및 관전압 전환 방식을 가진 이중에너지 엑스선 시스템이
다중에너지 시스템으로써 임상에서 사용되기 위하여 채택되었다. 최근에 광
자계수방식 검출기가 개발되었으며, 이 장치의 장점은 한 번의 엑스선 조사
- 92 -
를 통해서 여러 가지 물질들을 구별할 수 있고, 환자에 조사되는 선량을 줄
일 수 있다는 것이다. 광자계수방식 기반 영상화 방법의 영상 획득 개념은
넓은 대역의 에너지를 갖는 광자들의 에너지를 주문형 집적회로 (ASIC)를
통해서 각각의 에너지들을 구별할 수 있는 것이다. 또한, 브래그 회절
(Bragg diffraction) 의 원리를 이용한 방법과 필터 설계 방식을 이용한 단
색광 방사선 조사 장치가 다중 에너지 영상화 장치를 위하여 사용되고 있다.
본 연구의 목적은 세 가지 물질을 분리하기 위한 삼중에너지 단색광 엑스선
생성을 위한 필터 설계에 대한 것이다. 단색광 방사선은 환자에게 조사되는
선량도 줄일 수 있으며, 영상의 대조도 또한 향상시킬 수 있다. 또한, 이중
에너지 방법은 세 가지 물질의 분리에 있어서 프로젝션 오차를 발생시킬 수
있다. 그러므로, 본 연구는 전하누적방식 검출기를 사용하고, 다양한 필터와
관전압의 조합을 이용하여 단색광 삼중에너지 엑스선을 설계하고, 세 가지
물질의 분리에 사용하였다.
케이 특성 (K-edge) 에너지를 갖는 알루미늄, 구리, 요오드, 바륨, 세륨,
가돌리늄, 에르븀, 텅스텐 물질을 사용하여 다양한 단색광 엑스선 빔을 시
뮬레이션을 이용하여 생성하였다. 단색광 엑스선 빔을 생성하기 위한 필터
의 반가층 (HVL) 두께는 그 단색광 엑스선 빔의 평균 에너지의 분석을 통
하여 결정되었다. 각 단색광 엑스선 빔은 몬테 카를로 (Monte Carlo) 시뮬
레이션 결과를 통한 평균 에너지 비, 대조도 변화의 비, 조사 효율의 정량
적 지표를 이용하여 분석되었다. 관전압과 각 필터 물질의 조합을 통해 획
- 93 -
득한 단색광 엑스선 빔의 평균 에너지를 산출하였다. 단색광 엑스선 빔의
평균 에너지 비는 고식적인 엑스선 빔 보다 낮은 값을 보이고 있으며, 이는
필터를 투과한 엑스선 빔이 단색광 빔을 의미하며, 이를 통해서 선속 경화
(beam hardening) 현상이 감소하는 결과를 획득하였다. 대조도 변화의 비
의 평가 결과, 요오드, 바륨, 세륨 필터를 사용하여 획득한 엑스선 빔이 고
식적인 빔보다 대조도를 증가시키는 결과를 획득하였다. 조사 효율적인 측
면에서는 요오드, 바륨, 세륨, 가돌리늄 필터를 사용하여 획득한 단색광 엑
스선 빔이 고식적인 빔에 비하여 조사 효율 증가의 효과를 보였다.
삼중에너지 엑스선 빔의 설계를 위하여 평균에너지, 평균 에너지 비, 대
조도 변화 비와 조사 효율을 고려하였고, 이를 전산 모사방법의 결과와 실
험 결과를 비교하였다. 제안된 삼중에너지 빔을 사용하여, 요오드 조영제,
알루미늄, 아크릴이 존재하는 세 가지 물질을 분리하였고, 이 결과를 광자
계수방식 검출기를 이용한 결과와 시뮬레이션으로 비교하였다. 요오드 조영
제, 알루미늄, 아크릴 두께의 참값이 각각 1.00, 1.00, 1.00 cm 일 때, 제안
된 삼중에너지 단색광 엑스선 빔을 이용하여 얻은 요오드 조영제, 알루미늄,
아크릴의 두께 밀도 값은 1.00, 1.00, 0.99 cm 였고, 광자계수방식 검출기
를 사용하여 얻은 결과는 1.00, 0.96, 1.02로써 제안된 삼중에너지 방법을
이용한 결과가 이상적인 광자계수방식의 결과와 유사함을 시뮬레이션 결과
로써 검증하였다. 또한, 실험적인 방법으로써 획득한 요오드 조영제, 알루미
늄, 아크릴의 두께 밀도 값은 참 값이 0.50, 0.50, 2.00 cm 일 때, 각각
- 94 -
0.52, 0.52, 1.99 cm의 값을 제안된 삼중에너지 빔으로 획득하였고, 광자계
수방식 검출기로 획득한 결과는 0.50, 0.51, 2.05 cm 결과를 얻었다.
전산 모사방법의 결과와 실험적인 검증을 통하여 얻은 결과로 본 연구에
서 설계한 필터를 이용하여 삼중에너지 단색광 엑스선 빔을 제안하고, 세
가지 물질 분리의 정확성, 영상 대조도의 향상 및 선량 감소의 측면을 고려
하였을 때, 여러 가지 물질이 혼합되어 있는 경우의 여러 물질 분리에 활용
될 수 있는 자료 및 방법을 제공하는데 의의가 있다.
핵심 되는 말: 다중에너지 엑스선 영상화, 단색광 엑스선 빔, 전하누적방식
검출기, 광자계수방식 검출기