Design of a Multi-Pinhole Collimator and Its Evaluation for Application to High-Resolution Pre-Clinical SPECT system for Small Animal

Imaging

Hyun-Ju Ryu

The Graduate School

Yonsei University

Department of Radiological Science

Design of a Multi-Pinhole Collimator and Its Evaluation for Application to High-Resolution Pre-Clinical SPECT system for Small Animal

Imaging

A Master’s Thesis

Submitted to the Department of Radiological Science

and the Graduate School of Yonsei University

in partial fulfillment of the

requirements for the degree of

Master of Science

Hyun-Ju Ryu

January 2013

This certifies that the Masters

Thesis of Hyun-Ju Ryu is approved.

[s e]

Thesis Supervisor : Prof. Hee-Joung Kim

[s re]

Thesis Committee Member : Prof. Bong-Soo Han

[s re]

Thesis Committee Member : Prof. Yong-Hyun Chung

The Graduate School

Yonsei University

December 2012

iii

Acknowledgements

I must first express my gratitude towards my advisor, Prof. Hee-Joung

Kim. I deeply appreciate for his support and trust throughout my years of

research. Also, I thank him for giving me an opportunity to do this

research in Johns Hopkins University. I am fortunate to be educated by

Prof. Kim and Prof. Benjamin M.W. Tsui who generously and

wholeheartedly shared their knowledge to me. Especially for the work I

have done at Johns Hopkins, I deeply appreciate to Dr. Tsui for his care

not only academic but also for my life in Baltimore.

I am also grateful for Prof. Yong Hyun Chung for his invaluable

suggestions to the research, and Prof. Bong Soo Han for his precious

lessons for the fundamental theory.

I am lucky to have a team like a big family, Medical Physics and

Imaging Laboratory. Especially, Chang-Lae Lee, Hye-Sook Park, Dae-

Hong Kim, Seung-Wan Lee, Yu-Na Choi, Young-Jin Lee, Yeseul Kim, and

SuJin Park. I could feel lots of love and affection from their support. Also, I

would like to thank to Hyo-Min Cho, Chul-Pyo Hong and Do-Wan Lee for

unstinting support and trust. Additionally, I am fortunate to have been

studied with Dr. Jingyan Xu, Andrew rittenbach and Tao Feng who

supported me a lot on this research. And I thank to Dr. Taek-Soo Lee for

the words of encouragement. I would like to give a special thanks to

Dong-Hoon Lee who has inspired me by his constant love and

encouragement.

Finally and most importantly, I would like to express my greatest

appreciation to my family. They have always been my number one

supporters and I know that wherever life brings me, I have them. Words

will never be enough to express my love for them but I hope that by

offering this thesis to them, together with all my achievements in life, I

would be able to show how much they mean to me.

January 2013

From Hyun-Ju Ryu

iv

Table of Contents

Acknowledgements ·········································································· iii

Table of Contents ············································································ iv

List of Figures ················································································· vi

List of Tables ················································································· vii

Abstract in English ········································································· viii

1 Introduction ················································································ 1

2 Materials and Methods ································································· 3

2.1 Geometric configurations of the multi-pinhole imaging system

··························································································· 3

2.2 MPH collimator design optimization ······································· 5

2.3 Evaluation of the MPH collimator design and SPECT system

imaging performance using analytic computer simulation ······· 12

3 Results ····················································································· 14

3.1 MPH collimator design optimization ····································· 14

3.2 Sensitivity map and the optimum number of projections ········ 16

v

3.3 Evaluation of the Optimized MPH Collimator with hot-rod

resolution phantom ···························································· 19

4 Discussion ················································································ 24

5 Conclusion ················································································ 26

6 References ··············································································· 28

Abstract in Korean ·········································································· 31

Acknowledgements in Korean ·························································· 33

vi

List of Figures

Figure 1. Geometric configurations of the small animal SPECT Imaging

System. ············································································· 5

Figure 2. Geometric parameters of a pinhole collimator. ······················· 6

Figure 3. MPH collimator optimization process. ··································· 9

Figure 4. Detection efficiency and the number of pinholes. ················· 11

Figure 5. Eleven detectors in a row to present the projections through

MPH collimator. ······························································· 12

Figure 6. Center slice of a uniform sphere and a hot-rod resolution

phantom. ········································································· 13

Figure 7. Simulated Projection with a full CVOV sphere phantom with

different configurations of MPH collimators: 8% overlap (top)

and 18% overlap (bottom). ················································ 15

Figure 8. Sensitivity map of the backprojected image of a uniform

projection. ······································································· 17

Figure 9. Sensitivity profile from the central profile of the sensitivity map.

························································································ 17

Figure 10. Simulated MPH projections with 3 rotational stops: 0° (top row),

24° (middle row) and 48° (bottom row). ······························ 18

Figure 11. Reconstructed image of the hot-rod resolution phantom with

different rotation and iteration numbers. ···························· 20

Figure 12. Reconstructed image of the hot-rod resolution phantom with

different rotation and iteration numbers. ···························· 21

Figure 13. Projection of the hot-rod resolution phantom without noise

(top), and with Gaussian noise (bottom). ····························· 22

Figure 14. Reconstructed image of the hot-rod resolution phantom without

noise (top), and with Gaussian noise (bottom). ···················· 22

vii

List of Tables

Table 1. System parameters of the small animal SPECT system. ··········· 4

Table 2. Optimized system parameters of the MPH collimator. ············ 16

viii

Abstract

Design of a Multi-Pinhole Collimator and Its Evaluation for

Application to High-Resolution Pre-Clinical SPECT system

for Small Animal Imaging

Hyun-Ju Ryu

Dept. of Radiological Science

The Graduate School

Yonsei University

A multi-pinhole (MPH) collimator was designed for a pre-clinical

SPECT system for small animal imaging to provide maximum detection

efficiency and highest image quality given a targeted system spatial

resolution and other system constraints. The performance of the

collimator was evaluated through simulation and experimental studies. The

optimum number of pinhole was calculated based on the geometry of the

small animal SPECT system for 24 mm common volume-of-view (CVOV)

with the target system resolution of 1 mm. The optimized MPH collimator

ix

design consisted of 15 pinholes with 0.56 mm effective pinhole diameter

and were placed 22.0 mm from the CVOV. In addition, the MPH

collimator-detector response (CDR) function was incorporated in the 3D

MPH maximum-likelihood expectation-maximization (ML-EL) image

reconstruction algorithm. With CDR modeling, even the smallest rods can

be differentiated. The reconstructed images of the phantom showed that

the MPH SPECT system gives a fine resolution for small animal imaging.

Key words: Multi-Pinhole Collimator, Pre-Clinical SPECT, Optimization,

High resolution, small animal imaging, Maximum-likelihood expectation-

maximization, Collimator-detector response modeling.

- 1 -

1 Introduction

Small animal nuclear medicine imaging techniques allow direct

visualization and quantification of three-dimensional (3D) distribution

of radiotracers in different organs in static or as a function of time.

Pinhole collimators have been widely used for small-animal single

photon emission computed tomography (SPECT) systems due to their

superior resolution and detection efficiency trade-off as compared to

conventional parallel-hole collimators for imaging small objects at

close range (Jaszczak et al. 1999, 425, Ogawa et al. 1998, 3122-3126).

High-resolution pinhole SPECT can be very useful in preclinical

research where small organs are usually imaged as a target (Ishizu et

al. 1995, 2282, Weber et al. 1994, 342). However, single pinhole

collimator system provides poor detection efficiency especially at high

spatial resolution (Schramm et al. 2003, 315-320). Due to its low

sensitivity, high doses of radio-tracers were injected into mice in

previous studies to achieve fine image resolution with appropriate

counts (Acton et al. 2002, 691-698, Habraken et al. 2001, 1863-1869).

The use of a multi-pinhole (MPH) collimator can increase the

detection efficiency which may reduce the dose to the small animal

while maintaining high resolution. Also, the additional data from MPH

- 2 -

collimator can reduce the data incompleteness of a single pinhole

collimator (Vunckx et al. 2008, 36-46, Rentmeester, Van Der Have,

and Beekman 2007, 2567).

A MPH collimator can be designed in various ways depends on the

objective of an imaging system. In this study, a MPH collimator was

designed for a small animal SPECT system to maximize the detection

efficiency without degrading the spatial resolution. The performance

of the MPH collimator was evaluated through analytic simulation, and

it was constructed for a preliminary evaluation study.

- 3 -

2 Materials and Methods

2.1 Geometric configurations of the multi-pinhole imaging

system

The small animal SPECT system used in the study was designed

to have eleven blocks of detector modules to form a complete

polygonal configuration. Each detector module consisted of a 48×

100 mm2 pixelated CsI(Tl) crystal with 1 mm pixel pitch and 0.1 mm

gap. The pixelated CsI crystal was attached to two 50×50 mm2

position-sensitive-photomultiplier tubes (PSPMT) (Model H9500,

Hamamatsu Photonics K. K, Hamamatsu City, Shizuoka, Japan) with

16×16 anodes. The distance from the center of the common-

volume-of-view (CVOV) to the face of the detector modules was

81.73 mm. Currently only eight detector modules were completed for

the polygonal SPECT system. Table 1 show the small animal SPECT

system design parameters.

- 4 -

Table 1. System parameters of the small animal SPECT system.

crystal

pixel pitch 1 mm

pixel thickness 4 mm

size 48×100 mm2

light guide thickness 2 mm

number of detector 11 (complete ring)

8 (completed)

CVOV to detector distance 81.73 mm

Photo-multiplier tube Hamamatsu H9500

The pixelated crystal could significantly alter the light

distribution compare to a continuous crystal due to the light blockage

at the edge of each pixels (Giokaris et al. 2004, 134-139). The

PSPMT (Hamamatsu H9500) with 16×16 anodes and 256 data

collection channels combined with the pixelated CsI(Tl) provided a

state-of-the-art high-resolution detector module for the small

animal SPECT system.

Figure 1 illustrates the polygonal SPECT system configuration

with the complete eleven detector modules (with eight completed).

The detector modules were attached to a rotational gantry. A MPH

collimator could be attached to the system and rotated with the

gantry for additional angular data sampling to acquire sufficient

number of projections for image reconstruction.

- 5 -

Figure 1. Geometric configurations of the small animal SPECT Imaging System.

2.2 MPH collimator design optimization

In this study, the goal of the optimized MPH collimator design is

to provide the maximum detection efficiency for a given total system

resolution under the constraints imposed by the SPECT system

configuration. To design the optimized MPH collimator for the small

animal SPECT system described above, first, we specified the target

system resolution to be 1.0 mm at the center of the common

volume-of-view (CVOV) of the multiple pinholes of the MPH

collimator. We then determined the optimum MPH collimator design

parameters that provide the highest possible detection efficiency

- 6 -

given the constraints of the SPECT system geometric parameters

including: the size of the CVOV for imaging, the distances between

the center of the CVOV to the face of the detector modules, and the

total area of the detector. The CVOV was set to 24 mm for imaging

mice and the distance between the axis-of-rotation and all pinhole

apertures were the same. To achieve this, the multiple pinholes were

placed on a cylindrically-shaped collimator sleeve made with high

density material and with its central axis coincided with the axis-of-

rotation of the small animal SPECT system.

- 7 -

Figure 2. Geometric parameters of a pinhole collimator.

The characteristics of a pinhole collimator with the geometric

parameters on Figure 2 were calculated using following equations

(Beekman, and van der Have 2007, 151-161). The parameters used

in the equations are the distance from the center of the CVOV to a

pinhole ( b ), the distance from the pinhole to the detector ( l ),

diameter of the pinhole aperture (d), the pinhole aperture angle (α),

and the attenuation coefficient of the collimator material (μ).

The geometric resolution of a collimator can be calculated by

𝑅𝑐𝑜𝑙𝑙 ≈ 𝑑𝑒𝑓𝑓(𝑏 + 𝑙)/𝑙

Equation 1.

where the effective pinhole diameter is

𝑑𝑒𝑓𝑓 = √𝑑[𝑑 + 2𝜇−1𝑡𝑎𝑛 (𝛼/2)]

Equation 2.

The total system resolution was calculated from the collimator

resolution and the system resolution:

𝑅𝑠𝑦𝑠 = √ [(𝑏/𝑙)𝑅𝑖𝑛𝑡]2 + 𝑅𝑐𝑜𝑙𝑙

2

Equation 3.

- 8 -

The detection efficiency of a pinhole collimator is

𝑔 ≈𝑑𝑒𝑓𝑓𝑐𝑜𝑠

3𝜃

16𝑏2

Equation 4.

And the geometric efficiency of multiple pinholes is

𝑔 ≈ 𝑑𝑒𝑓𝑓𝑐𝑜𝑠3𝜃/16𝑏2

Equation 5.

Figure 3 illustrates the procedures to optimize the process of

MPH collimator optimization. The total system resolution of a MPH

SPECT system is a function of the collimator resolution, collimator

geometry and the intrinsic resolution of the detector. There are a

large numbers of sets of design parameters which can provide a

targeted system resolution. Among them, it was our goal to find the

design parameters of the MPH apertures and their pattern that

provides the highest possible detection efficiency under the

constraints of the SPECT system configuration.

- 9 -

Figure 3. MPH collimator optimization process.

- 10 -

There are geometric constraints such as the diameter of the

CVOV, total detector area, the distance between the center of the

CVOV and the detector surface, the intrinsic resolution of the

detector, the photon energy, and the collimator material. The

optimization of the MPH collimator was processed based on the

geometric constraints

By changing the distance from the center of the CVOV to the

collimator aperture, the cone angle of the collimator and the size of

the projection were also affected. The maximum number of

projection at each distance from the CVOV to the collimator

aperture was calculated using total detector area divided by the area

of the projection. Then, the size of the collimator apertures were

calculated to provide 1 mm total system resolution. With different

collimator distances, the efficiencies of the MPH collimators were

calculated with maximum number of projections at each distance.

The optimal number of the pinholes was designed based on the

constraints of the MPH collimator design as plotted in Figure 4. As

shown in the figure, detection efficiency of the pinholes was

increased as the number of the pinhole increased to a certain point

and started to decrease after that. Therefore, the optimum number

of the pinholes could be found near the point with the maximum

- 11 -

efficiency.

Figure 4. Detection efficiency and the number of pinholes.

Once the number of pinholes that provided the highest detection

efficiency for the targeted system resolution was determined, the

arrangement of the pinhole apertures on the MPH collimator to

maximize the use of total detector area by the MPH projections with

less than 20% multiplexing were determined. To visualize and

present the patterns of the multiple pinhole projections onto the

detector surface, the 11-sided polygonal SPECT detector ring was

- 12 -

unfolded into a flat surface as shown in Figure 5. Detection

efficiency of the MPH collimator can be measured by plotting the

projections on the detector using a computer simulation.

Figure 5. Eleven detectors in a row to present the projections through MPH collimator.

2.3 Evaluation of the MPH collimator design and SPECT

system imaging performance using analytic computer

simulation

The MPH collimator design and SPECT system imaging

performance was evaluated using computer simulations. For the

projection simulation, a sphere phantom with a size of full CVOV

was used to evaluate the geometry of the MPH collimator. A

resolution phantom with different sizes of hot rods was used to

evaluate the MPH system performance. The sphere phantom and the

hot-rod resolution phantom are shown in Figure 6. The 3D

- 13 -

maximum-likelihood expectation-maximization (ML-EM) algorithm

was used to reconstruct the phantom projections.

Figure 6. Center slice of a uniform sphere and a hot-rod resolution phantom.

- 14 -

3 Results

3.1 MPH collimator design optimization

The optimum number of pinhole was calculated based on the

geometry of the small animal SPECT system for 24 mm CVOV with

the target resolution 1 mm and other constraints of the geometric

configuration of the small animal SPECT system. From the

calculations described in Chapter 2, various designs of 15 pinholes

were evaluated to pursue the maximum detection efficiency. The

pinhole projections were allowed to have less than 20% overlaps of

its area to maximize the use of the detector area compare to the

non-overlapping arrangements. The efficiency of the MPH

collimator design can be compared by measuring the intensity of the

projections in the detector area as compared in Figure 7. The

integrated intensity of 15 projections on 11 detectors were

compared to determine detected efficiency on the detector. The

arrangement of pinhole projections at the bottom of Figure 7 shows

18% overlap for each projection, which gives higher total detection

efficiency of the MPH collimator compared to the arrangement of

pinhole projections with 8% overlap.

- 15 -

Figure 7. Simulated Projection with a full CVOV sphere phantom with different

configurations of MPH collimators: 8% overlap (top) and 18% overlap (bottom).

The optimized MPH collimator for 1 mm system resolution with

24 mm CVOV was determined to have 15 pinholes placed at 22.0

mm from the axis-of-rotation and the diameter of each pinhole

projection was 65.2 mm on the detector surface. The cone angle of

the pinholes was 66.2 mm with 0.56 mm effective aperture diameter.

The optimized design parameters of the MPH collimator are shown

in Table 2.

- 16 -

Table 2. Optimized system parameters of the MPH collimator

Target resolution 1.0 mm Diameter of the CVOV 24.0 mm Distance from CVOV to pinhole 22.0 mm Distance from pinhole to the detector 59.7 mm Diameter of the projection 65.2 mm Cone angle of the pinhole 66.2° Optimal number of pinholes 15 Effective pinhole aperture 0.56 mm

3.2 Sensitivity map and the optimum number of projections

The reconstructed image field sensitivity map of the CVOV was

evaluated by backprojecting the uniform projections through the

MPH collimator. It showed the uniformity and the symmetry of the

reconstruction image space generated by the MPH collimator.

Examples of the reconstructed image field sensitivity maps with

different rotational stops are shown in Figure 8. Each rotational stop

provides 15 projections from the MPH collimator, and the rotation

was performed to generate equiangular views between rotational

stops.

- 17 -

Figure 8. Sensitivity map of the backprojected image of a uniform projection.

Figure 9. Sensitivity profile from the central profile of the sensitivity map.

- 18 -

The reconstructed image field sensitivity profiles along the

central line of each sensitivity map, as indicated on the first image

of Figure 8, were compared on Figure 9 with different rotational

stops. Three and four rotational stops of the 15-pinhole collimator,

which generate 45 and 60 projections, respectably, give more

uniform sensitivity profiles than those from no or one additional

rotational stop of the MPH collimator.

Figure 10. Simulated MPH projections with 3 rotational stops:

0° (top row), 24° (middle row) and 48° (bottom row).

By using the uniform sphere phantom, Figure 10 shows the

projections from the 15-pinhole collimator at three rotational stops

- 19 -

were simulated. The projections were obtained by rotating the MPH

collimator at equiangular stops of 24 degrees.

3.3 Evaluation of the Optimized MPH Collimator with hot-

rod resolution phantom

An analytical simulation was performed using the hot-rod

resolution phantom shown in Figure 6 without noise, and the

reconstruction was performed using a 3D MPH ML-EM image

reconstruction algorithm. The reconstructed images gave improved

resolution as the number of iteration increases in the noise-free

case.

The hot-rod phantom consists of six groups of rods with higher

intensity than the background. The diameters of the rods in each

group are the same and are 0.4 mm, 0.6 mm, 0.8 mm, 1.0 mm, 1.2

mm, 1.4 mm from the smallest to the largest. In Figure 11, the

reconstructed images with different numbers of rotational stops

were compared with the hot-rod phantom to evaluate the

performance of the MPH collimator.

- 20 -

Figure 11. Reconstructed image of the hot-rod resolution phantom

with different rotation and iteration numbers.

The reconstructed images from one stop to three stops showed

significant increases in resolution, but three and four rotational

stops showed a marginal difference. The results indicate the 15-

pinhole collimator required at least three rotational stops for a total

of 45 pinhole projections to achieve the highest possible

reconstructed image resolution using the 3D MPH ML-EM algorithm.

In addition, the MPH collimator-detector response (CDR)

- 21 -

function was incorporated in the 3D MPH ML-EL image

reconstruction algorithm. A comparison of the reconstructed images

of the hot rod phantom obtained with and without the CDR modeling

is shown in Figure 12. With CDR modeling, even the smallest rods

can be differentiated.

Figure 12. Reconstructed image of the hot-rod resolution phantom

with different rotation and iteration numbers.

To simulate the noisy projection, Gaussian noise was applied to

the projections of hot-rod phantom. The projections of the hot-rod

phantom with and without noise were shown in Figure 13.

- 22 -

Figure 13. Projection of the hot-rod resolution phantom

without noise (top), and with Gaussian noise (bottom).

Figure 14. Reconstructed image of the hot-rod resolution phantom

without noise (top), and with Gaussian noise (bottom).

The noisy projection was also reconstructed using 3D ML-EM,

and the CDR function was applied. As shown in Figure 14, 0.6 mm

- 23 -

rods can be differentiated from the reconstructed image of the hot-

rod phantom even with the noisy projections. A Butterworth filter

with Order2 and cutoff 0.4 was applied to the reconstructed image

from the noisy projections.

- 24 -

4 Discussion

In this study, a MPH collimator was designed based on achieving

the highest possible geometric detection efficiency given a target

MPH SPECT system resolution, theoretical formula of the imaging

characteristics of a MPH collimator as a function of its designed

parameters and under various system designed constraints. The

efficiency of a MPH collimator tends to increase at first as the number

of pinholes increases; however, it decreases with further increase of

the number of pinholes. As a result, there is an optimum number of the

pinholes for a given MPH SPECT system geometry to achieve the

target resolution with the most photon efficiency. Moreover, the

pattern of the pinholes was designed to fully utilize the detector area

with the projection.

Overlapping of the projections could generate artifacts on the

reconstructed image. However, if the projection contains relatively

less information on the edge compare to the center, the artifact can be

reduced by using iterative reconstruction method for limited

overlapping of the projections (of less than 20%) and at the same time

provide improved design optimization.

The minimum number of collimator rotations was determined by

- 25 -

comparing the reconstructed image field sensitivity map of the MPH

SPECT system, and the reconstructed images of the hot-rod

resolution phantom. The results show the 15-pinhole collimator with

minimum of three rotational stops generating a total of 45 pinhole

projections would achieve the highest possible resolution in the

reconstructed images using the 3D MPH ML-EM algorithm. The

simulation was performed with and without noise, and the

reconstructed images showed improved resolution with CDR modeling.

- 26 -

5 Conclusion

The optimum number of pinholes and the geometry of the MPH

collimator was designed to have the highest possible photon detection

efficiency for the given targeted system resolution and geometry of a

small animal SPECT system. By using analytic simulation methods,

MPH projections and the reconstructed image field sensitivity map

were generated with the optimized MPH collimator.

The reconstructed image of a hot-rod resolution phantom was

used to provide quality assessment of the system resolution obtained

with the MPH collimator. Image reconstruction was performed using a

3D MPH ML-EM image reconstruction algorithm with a minimum of

three rotational stops and a total of 45 simulated pinhole projections

can achieve the highest possible reconstructed image resolution. Also,

higher resolution can be achieved by incorporating model of the

collimator-detector response (CDR) function in the 3D MPH image

reconstruction algorithm. As shown in the reconstructed image of the

projections of hot-rod phantom with noise, the MPH SPECT system

could differentiate 0.6 mm which gives a fine resolution for the small

animal imaging.

Future studies will include Monte Carlo simulation and

- 27 -

experimental studies for further evaluation of the small animal SPECT

system fitted with the optimized MPH collimator.

- 28 -

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"Ultra high resolution pinhole SPECT for small animal study". Nuclear

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Rentmeester, M., F. Van Der Have and F. Beekman. 2007. "Optimizing

multi-pinhole SPECT geometries using an analytical model". Physics in

medicine and biology, 52(9): 2567.

Schramm, N., G. Ebel, U. Engeland, T. Schurrat, M. Behe and T. Behr.

2003. "High-resolution SPECT using multipinhole collimation". Nuclear

Science, IEEE Transactions on, 50(3): 315-320.

Vunckx, K., D. Bequé, M. Defrise and J. Nuyts. 2008. "Single and

multipinhole collimator design evaluation method for small animal

SPECT". Medical Imaging, IEEE Transactions on, 27(1): 36-46.

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Franceschi, H. Atkins, J. Coderre, H. Susskind and T. Button. 1994.

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"Pinhole SPECT: an approach to in vivo high resolution SPECT imaging

in small laboratory animals". Journal of nuclear medicine: official

publication, Society of Nuclear Medicine, 35(2): 342.

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국 문 요 약

단일광자단층촬영장치의 공간 해상도 향상을 위한

다중 바늘구멍 조준기 설계 및 전임상적 적용가능성 평가

다중 바늘구멍 조준기는 소동물용 단일광자단층촬영장치 (SPECT) 에서

고해상도의 영상 얻으면서도 검출효율이 단일 바늘구멍 조준기에 비하여 높은

특성을 갖는다. 따라서 같은 SPECT 장치내에서 다중 바늘구멍 조준기를

사용함으로서 검출효율과 해상도를 함께 증가시킬 수 있는 장점이 있다. 본

논문에서는 시뮬레이션을 이용하여 소동물용 SPECT 장치 내에서 1 mm

이하의 고해상도를 가지면서도 검출 효율이 최대가 되도록 하는 다중

바늘구멍 조준기를 설계하였다. SPECT 장치 내 시야 ( common volume-of-

view, CVOV) 는 실험용 쥐를 모델링 하여 지름 24 mm 의 구 형태를 가지며,

이 때 전체 시스템의 해상도가 1 mm 가 되도록 조준기 설계를 최적화

하였다. 설계 된 다중 바늘구멍 조준기는 15 개의 바늘구멍을 가지는 튜브

형태의 텅스텐으로 이루어졌으며, 바늘구멍의 유효직경은 0.56 mm 이고

중심으로부터 바늘구멍까지의 거리는 22.0 mm 이다. 다중 바늘구멍 조준기의

상을 이용하여 영상을 재구성하기 위해서 3 차원 maximum-likelihood

expectation-maximization (ML-EM) 알고리듬이 사용되었으며, collimator-

detector response (CDR) 함수를 이용한 모델링도 추가적으로 적용되어 이를

이용해 재구성된 영상의 해상도 향상을 확인할 수 있었다. 영상의 노이즈

- 32 -

또한 시뮬레이션 되었으며, 노이즈를 포함한 상의 재구성 영상에서도 1 mm

이하의 해상도를 가짐을 확인하였다. 이러한 결과를 바탕으로 본 연구에서

설계 한 다중 바늘구멍 조준기는 소동물용 SPECT 에서 전 임상적 활용

가능성을 나타낸다.

Key words : 다중바늘구멍조준기, 전임상적 SPECT, 최적화, 고해상도,

소동물영상장치, Maximum-likelihood expectation-maximization,

Collimator-detector response modeling.

- 33 -

감사의 글

석사 논문을 마무리 하며 지금의 제가 있기까지 도움을 주신 모든 분들께 감

사의 뜻을 전합니다. 연세대학교 방사선학과에서 학부를 거쳐 석사과정을 마

치는 동안 다른 누구보다도 많은 경험을 할 수 있도록 기회를 주신 김희중교

수님께 가장 먼저 감사를 전하고 싶습니다. 학생들 보다도 더욱 열정적이신

교수님을 뵈며 학문적인 길 뿐만 아니라 삶의 자세에 대해서도 큰 배움을 얻

었습니다. 김희중 교수님의 배려로 기회를 얻은 존스홉킨스에서의 연구 과정

과 Benjamin M.W. Tsui 교수님을 만난 것 또한 저에게는 너무나도 감사한

시간이 되었습니다. 두 교수님의 가르침이 있었기에 이렇게 석사과정을 무사

히 마치게 되었습니다.

또한 학문에 대한 열정으로 항상 저의 부족한 부분을 짚어주시고 방향을 제시

해 주신 정용현 교수님과 탄탄한 이론 정립의 중요성을 다시한번 깨우치게 해

주신 한봉수 교수님께 깊은 감사를 드립니다.

대학원 생활을 하며 한 가족이 된 의학물리 및 영상 연구실의 모든 선후배들

께도 아낌없는 지지와 응원에 대해 고마운 마음을 전합니다. 특히 언제나 든

든한 창래오빠와 대홍, 조언을 아끼지 않고 후배들을 챙겨주는 혜숙언니, 처

음부터 지금까지 함께 마음을 나누어 준 승완오빠와 유나, 함께 고민하고 연

구해 준 고마운 영진과 수진, 연구실을 즐겁게 만들어주는 예슬이에게 감사를

표합니다. 끊임없는 격려와 지지를 보내주시는 박사 1기 홍철표, 조효민 부부

그리고 응원의 메시지를 잊지 않는 도완에게 고마운 마음을 보내며, 홉킨스에

서의 연구기간 동안 다양한 시각을 가질 수 있도록 도와주신 이택수 박사님께

도 감사드립니다. 학위 과정동안 더욱 집중할 수 있도록 사랑으로 지원 해 준

동훈에게도 고마운 마음을 전합니다.

멀리서도 언제나 언니를 믿어 준 동생 자영이와 오빠처럼 누나를 돌보아 준

정현이가 있기에 힘차게 달려올 수 있었습니다. 삶의 방향을 일깨워주시는 도

류스님과 청연스님, 함께 공부하기에 더 힘이 되는 은지언니, 영원한 멘토 안

현준 삼촌, 따뜻한 위로가 되는 김순명 숙모, 반짝반짝 빛이 나는 안채원과

안채린 모두가 저의 든든한 지원군입니다. 마지막으로 큰 사랑과 지원으로 항

상 그 곳에 있어주신 부모님께 말로 다 할 수 없는 감사를 드립니다.

2013년 1월

류 현 주 드림