Design and characterization of the Multi- Energy monochromatic X-ray Beam … · 2019-06-28 ·...

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




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.


incident spectrum at tube voltage of 60 kV and Ba filter. The

spectra were normalized with respect to the integrated energy.

.


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




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 -


spectrum at tube voltage of 60 kV and Ba filter. The spectra were normalized with



spectrum at tube voltage of 70 kV and Gd filter. The spectra were normalized with


- 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


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


- 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

Design and characterization of the Multi- Energy monochromatic X-ray Beam … · 2019-06-28 ·...

Documents

Transcript of Design and characterization of the Multi- Energy monochromatic X-ray Beam … · 2019-06-28 ·...