A Novel Technique to Improve the Resolution of a Gamma

Home , Collimator, Gamma (agency), Gamma camera

A NOVEL TECHNIQUE TO IMPROVE THE

RESOLUTION OF A GAMMA CAMERA

A Thesis

Presented To

The Graduate Faculty of The University of Akron

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

Deepa Natarajamani

December, 2012

A NOVEL TECHNIQUE TO IMPROVE THE

RESOLUTION OF A GAMMA CAMERA

Deepa Natarajamani

Thesis

Approved: Accepted:

______Advisor Department Chair Dr. Dale H. Mugler Dr. Daniel B. Sheffer

______Co-Advisor Dean of the College Dr. Anthony M. Passalaqua Dr. George K. Haritos

______Committee Member Dean of the Graduate School Dr. Daniel B. Sheffer George R. Newkome

______Date

ABSTRACT

Nuclear medicine images have limited spatial resolution because of the limitations in the radiation detector and the associated electronics. Due to these limitations, the image of a point source of radiation is blurred. The degree of this blurring is called the point spread function of a gamma camera, the imaging device used in nuclear medicine. The aim of this study is to develop a technique to increase the spatial resolution and contrast by improving the point spread function of the system.

The basic idea of the proposed technique is to build a special collimator plate that replaces the conventional gamma camera collimator. Develop an algorithm that processes the images obtained with a gamma camera with the special collimator plate to improve the point spread function of the gamma camera. The images with the proposed gamma camera collimator plate method will be compared to the conventional collimator method.

Qualitatively the comparison is done by visually inspecting the images. Quantitative comparisons are done by the significant differences in their modulation transfer function.

Both comparisons indicate the proposed method is better than the conventional method.

iii

ACKNOWLEDGEMENTS

I would like to take this opportunity to express my deepest sense of gratitude to my mentor’s for their invaluable support, guidance and teaching throughout this project.

Thank you, Dr. Anthony Passalaqua, for introducing me to the fascinating science of nuclear imaging and for patiently listening to and answering all my questions anytime of the day. Thank you, Dr. Dale Mugler for your continued advice and support through each step in my Master’s life. Thank you, Dr. Daniel Sheffer for the invaluable suggestions and timely help given to me whenever needed. I am greatly indebted to Mr. Rick Neimer for assembling the materials needed for the experimental setup of this study in a crunch time. I am grateful to Sunil Das Thota for being motivational, supportive and helping me in achieving my goals. I would like to thank my friends Nirmala,Varsha,Sunitha,Pavan,

Ravi and Pavan for their support, encouragement and for making my Masters experience a memorable one. Finally, I would like to thank my parents, sister and brother-in-law for their continuous love, support and for instilling in me the values and morals which have helped me achieve my goals.

TABLE OF CONTENTS

Page

LIST OF TABLES ...... viii

LIST OF FIGURES ...... ix

CHAPTER

I INTRODUCTION ...... 1

1.1 Nuclear Medicine ...... 1

1.2 Goal of the Study ...... 3

1.3 Specific Goals ...... 3

1.4 Statement of Hypotheses ...... 3

1.4.1 Null Hypotheses ...... 4

1.4.2 Alternate Hypotheses ...... 4

II LITERATURE REVIEW ...... 5

2.1 Overview of Gamma Camera ...... 5

2.1.1 Collimators ...... 7

2.1.2 Detector ...... 8

2.1.3 Photomultiplier Tube ...... 8

2.1.4 X-, Y- Positioning Circuit ...... 8

2.1.5 Pulse-Height Analyzer ...... 9

2.1.6 Display and Recording Systems ...... 9

2.2 Image Reconstruction ...... 10

2.2.1 Filtered Back Projection ...... 11

2.2.2 Iterative Reconstruction Method ...... 14

2.3 Performance Parameters of Gamma Camera ...... 15

2.3.1 Spatial Resolution ...... 15

2.3.2 Methods to Improve Spatial Resolution ...... 16

2.4 Methods of Evaluating Spatial Resolution ...... 17

2.4.1 Line Spread Function...... 17

2.4.2 Modulation Transfer Function ...... 19

III MATERIALS AND METHODS ...... 22

3.1 Materials ...... 22

3.2 Special Plate Collimator ...... 22

3.3 Data acquisition ...... 24

3.4 Image processing ...... 27

3.4.1 FBP ...... 27

3.4.2 MLEM ...... 30

3.5 Method to find Spatial Resolution...... 31

3.6 Method for Statistical Test ...... 34

IV RESULTS ...... 35

4.1 Phantom results ...... 35

4.2 Experimental Results ...... 40

4.2.1 Point Source...... 40

4.2.2 Line Source ...... 41

4.2.3 Two Capillary tubes...... 42

4.3 Results for Spatial Resolution Experiments ...... 43

4.4 Results of Statistical test ...... 47

V DISCUSSION AND CONCLUSION ...... 49

5.1 Salient Features of the Proposed Technique ...... 50

5.2 Conclusions ...... 50

5.3 Future Work ...... 51

BIBILIOGRAPHY ...... 52

APPENDIX...... ………………………………………………………...... 53

vii

LIST OF TABLES

Table Page

4.1 FWHM and FWTM values obtained for the conventional and proposed method. .... 43

4.2 Results from Statistical test ...... 47

4.3 Statistical Analysis System results...... 48

viii

LIST OF FIGURES

Figure Page

2.1 Schematic electronics of gamma camera ...... 6

2.2 Flow chart-reconstructions...... 10

2.3 Theory of FBP...... 12 (a) Source of radioactivity (b) Projection data for 2 directions, 0 & 90 degrees (c) Back projection at 0 & 90 degrees (d) Back projection for multiple angles 0-360 degrees ...... 12

2.4 In filtered back projection, negative wings are introduced to eliminate blurring...... 12

2.5 Computer simulation of FBP (a) Sinogram (b) Filtered Sinogram (c-h) Steps of back projection………………...15

2.6 Flow Chart for MLEM……………………………………………………………….16

2.7 Point Source distribution (a) Ideal case and (b) Gamma camera ...... 18

2.8 FWHM and FWTM measurements………………………………………………….22

2.9.Basic principles of determining the MTF of an imaging device ...... 21

3.1 Pattern of the special collimator plate ...... 22

3.2 Special collimator plate on gamma camera………………………………………….26

3.3 Setup with plate and angular rotation instrument……………………………………26

3.4 Working of the plate a) Spread Function from the slit b) Summing up the spread function………...24

3.5 Line Source on the experimental setup ...... 25

3.6 Projection profiles at different angles a) 45 degree b) 90 degree ...... 27

3.7 Formation of Sinogram ...... 27

3.8 Reconstructed image ...... 28

3.9 Shepp-Logan phantom projection and reconstruction with special collimator plate .. 29

3.10 Image of flood source used for calibration ...... 31

3.11 Profile through the center of the image for PSF ...... 32

3.12 Point spread function and calculation of FWHM,FWTM………………………….35

3.13 MTF values from the PSF ...... 33

4.1 True Sinogram and true image for Shepp-Logan phantom ...... 36

4.2 Sinogram and reconstructed image with 1/2 of projection data ...... 37

4.3 Sinogram and reconstructed image with 1/4 of projection data ...... 38

4.4 Sinogram and reconstructed image with 1/8 of projection data ...... 39

4.5 Point source reconstruction with special collimator plate ...... 40

4.6 Line source reconstruction with special collimator plate……………………………44

4.7 Two line sources reconstruction with special collimator plate (a) Less gap in between (b) more gap in between……………………………...... 45

4.8 Point spread function and FWHM calculation for the conventional method ...... 44

4.9 Point spread function and FWHM calculation for the novel method ...... 45

4.10 Plot comparing the MTF’s for (a) Point and (b) Line Source ...... 46

CHAPTER I

INTRODUCTION

For many years photographic film was the principal means for storing medical images.

Computers have provided a new means for storing, processing, transferring and displaying images. With computers and digital image processing it is now possible to acquire data and perform mathematical operations to produce and improve images, all without film. Medical imaging incorporates Radiology, Nuclear Medicine, Endoscopy,

Thermography, Tomography, Medical Photography and Microscopy [1]. This work focuses on Nuclear Medicine Imaging.

1.1. Nuclear Medicine

Nuclear medicine enlists radioactive material for the diagnosis and treatment of diseases.

It is also referred to as molecular medicine or molecular medicine and therapeutics [2].

Nuclear medicine images organ function as opposed to simply organ morphology.

Nuclear medicine uses isotopes that emit gamma rays to diagnose various pathologies and the particles emitted are used for treatment of diseases. For

example, to identify tumors or fracture points in bones Tc-99m labeled phosphates are administered and the gamma rays from the tracer are detected by a suitable detector for further analysis. Gamma cameras are used as imaging device for Nuclear Imaging. The gamma camera produces an image of the radioactivity inside the body of a person. Thus this differs from Radiography, using X-ray, in that the source for X-ray radiation is external rather than within the patient as in Nuclear Medicine Imaging [2].

Radioactivity refers to the particles and gamma rays emitted when the unstable nuclei decay and emit radiation in the form of alpha, beta and gamma rays [3].In nuclear medicine a compound labeled with a radionuclide is administered to the patient and it localizes to a region of interest. This radioactive material is called a radiopharmaceutical.

As the radionuclide decays, gamma rays are emitted which when detected by the gamma camera give an image of distribution of the radiopharmaceutical in the organ of interest.

Alpha and beta particles cannot penetrate more than a few millimeters of a tissue and are hence useless for external imaging.

Single photon imaging uses radionuclide that decay by gamma-ray emission. A planar image is obtained by mapping the distribution of the radionuclide in the patient from one particular angle. This results in an image with no depth information. For Single Photon

Emission Computed Tomography (SPECT), data is collected from many angles around the patient. With computed tomography we get cross-sectional images of the distribution of the radionuclide providing the depth information missing from planar imaging. For this study, only planar images were obtained.

1.2. Goal of the Study

Nuclear medicine has the potential of producing images with a small dose of radiation to the patient, but the quality of the image is limited by the radiation detection and imaging system. The gamma camera has low spatial resolution and contrast. The goal of this study is to improve spatial resolution and contrast by improving the point spread function of the imaging system.

1.3. Specific Goals

Specific goals of the study are:

1. To design and build a special collimator plate to replace the conventional gamma

camera collimator.

2. To develop algorithms to convert the gamma camera plate collimator images into

higher resolution images.

3. To qualitatively compare the images obtained with the collimator plate technique

and those obtained by the conventional gamma collimator.

4. To quantitatively compare the spatial resolution of the collimator plate images

with that of the conventional gamma camera collimator.

1.4 Statement of Hypotheses

As explained in section 2.7.3, the Full Width Half Maximum (FWHM) gives the quantitative measure of the spatial resolution of an imaging system. Hence, the FWHMs with the conventional and proposed techniques were estimated and tested for statistical

difference. In addition to the qualitative (visual) analysis, the following null hypotheses were tested using the paired T-test.

1.4.1 Null Hypotheses

H01: There is no significant difference between the FWHM values obtained by the

conventional technique and the proposed technique.

1.4.2 Alternate Hypotheses

H02: There is a significant difference between the FWHM values obtained by the

conventional technique and the proposed technique.

CHAPTER II

LITERATURE REVIEW

2.1. Overview of Gamma Camera

Nuclear medicine uses radioactive tracers that emit gamma rays from within the body.

These tracers are generally short-lived isotopes linked to chemical compounds that permit specific physiological body processes to be evaluated. The radiopharmaceuticals can be given by intravenous injection, inhalation or orally. The first type is where single photons are detected by a gamma camera which can view organs from many different angles. The camera builds up an image from the points from which radiation is emitted; this image is enhanced by a computer and viewed by a physician on a monitor for indications of abnormalities.

The emitted gamma rays are of short wavelength and have high energy [3]. Gamma rays have sufficient energy to penetrate in body tissues and to be detected from deep-lying organs. The assessment of radionuclide distribution is performed with imaging systems that use Sodium Iodide (NaI) detectors. The principal imaging system used in nuclear medicine is the gamma camera.

Various designs of scintillation scanners have been proposed and made available but the

Anger camera with a single crystal is by far the most widely used. The Anger scintillation camera or the more commonly known Gamma Camera is a stationary imaging device. It can detect radiation from the entire field of view simultaneously. Thus the imaging time is less than other scanners.

Figure 2.1 Schematic electronics of gamma camera [3]

The gamma camera consists of several components: a detector, a collimator, photomultiplier (PM) tubes, a Pre- amplifier, an amplifier, a pulse height analyzer (PHA),

XY positioning circuit, and a display or recording device (Fig.2.1). The detector, PM

Tubes and amplifiers are housed in a unit called the detector head. This head can be moved up or down and rotated to position it in the field of view on the patient. The XY positioning circuits, PHA and recording devices are mounted in the console. The operation of the camera is performed by a built in computer [3].

The operation principle of the gamma camera is as follows, the γ rays from a source interact with the NaI detector, and light photons are emitted. The latter strike the photocathode of PM tubes, and a pulse is generated, which is then amplified by an amplifier and sorted out by a PHA. Finally the pulse is positioned by an XY positioning circuit on the recording device corresponding to the location of the γ ray interaction in the

NaI crystal.

2.1.1. Collimators

In a gamma camera, it is necessary to project the gamma rays from the source distribution onto the camera detector. Gamma rays cannot be focused; thus a “lens” principle similar to that used in photography cannot be applied. Absorptive collimation is therefore the most commonly applied principle for γ ray imaging. The absorptive collimator projects the image by allowing only those γ rays traveling in a specific direction, to reach the detector absorbing the rest. Thus “projection by absorption” is an inefficient method for utilizing radiation as most of the radiation travelling toward the detector actually is stopped by the collimator. This is one of the underlying reasons for the poor quality of radionuclide images [3].

Four basic types of collimators used are, pinhole, parallel, diverging and converging.

Pinhole is mostly used for magnification of images of small organs. The parallel hole collimator is the most commonly used and it projects a γ ray image of the same size as the source distribution onto the detector. Diverging collimators are used primarily on cameras with smaller detectors to permit imaging of large organs such as liver or lungs in a single view. Converging collimators produce an inverted magnified or minified image depending on its distance with the convergence point [2].

2.1.2. Detector

Na (I) crystals are the most commonly detectors used in the gamma camera [3].Increasing the thickness of the crystal increases the probability of absorption of γ rays and hence the sensitivity of the detector. Spatial resolution decreases in a thick crystal. Thin crystals decrease the sensitivity of the camera, because γ rays escape from the detector without interaction.

2.1.3. Photomultiplier Tube

PM tubes are used for converting the light photons in the Na (I) detector into pulses. An array of hexagonal PM tubes is used generally. The output of each PM tube is then used to define the X,Y coordinate of the point of interaction of the γ ray in the detector by the use of a X,Y positioning circuit and that is summed up by a summing circuit to form a pulse known as the Z pulse. The Z pulse is then subjected to pulse height-analysis and is accepted if it falls within the range of selected energies.

2.1.4. X-, Y- Positioning Circuit

The larger the number of PM tubes, the better the accuracy of the X, Y locations of all pulses on the image; that is, the better spatial resolution. The PM tubes are connected through capacitors to four output leads representing signals X+, X-, Y+ and Y-. Depending upon the light interaction, capacitance values are assigned and they are summed up to give values for X+, X-, Y+ and Y- . The sum of these four values gives the Z pulse. [3]

Z=X++X-+Y++Y-

Then the X, Y pulses correspond to the location where γ ray originated.

2.1.5. Pulse-Height Analyzer

After the Z pulses are formed by the summing circuit, the PHA analyzes their amplitude and selects only those of desired energy by the use of appropriate peak and window settings. The X and Y pulses are applied to the display only if the Z pulse is within the energy range selected by the PHA. If the Z pulse is outside this range, then X and Y pulses are discarded.

2.1.6. Display and Recording Systems

The pulses after pulse height analysis and X, Y positioning are projected on an oscilloscope to see the instantaneous image distribution. Data are collected for a preset interval of time or a preset number of gamma rays detected. The gamma rays detected form a single planar image. The single planar image is a two dimensional image of a 3 dimensional radionuclide distribution, similar to a conventional light photograph. In the past the data was collected directly to film but is currently stored in a computer and can be printed to film or viewed on a monitor.

After getting a proper sequence of planar images of the object under the camera, using computed tomography we get cross sectional images. Following, section consists of a brief overview of two different algorithms.

2.2. Image Reconstruction

Figure 2.2 Flow chart-reconstructions

The method of getting the image of the unknown source from the acquired data is called

Image reconstruction. The image reconstructions algorithms are broadly classified into analytical and iterative method (Fig.2.2). We are interested in the Filtered back projection and Likelihood methods of reconstruction.

2.2.1. Filtered Back Projection

Filtered back projection is the most commonly used reconstruction algorithm for SPECT images. The gamma rays that are released within the tissue experience a certain amount of attenuation before they are detected. The line integrals represent the total amount of attenuation. As a result, the projection data can be thought of as an indication of the density of the tissues in the object being imaged. A number of projections are taken from various angles [4].

Let us consider a 2-D image of only one point with highest intensity (fig.2.3.a).

Projections are taken at different angles (fig.2.3.b). The spike is the sum of all activity along the projection path. To reconstruct the image, we must re-distribute the activity in the spike back to its original path. The problem is that we do not know where along the path we need to put more activity and where along the path we need to put less. So, we put equal amounts of activity everywhere along the path, and the amount will be high at the projection spike. This is repeated for all projections taken from every angle

(fig.2.3.c). This is called back projection. If back projection is done for over 360 degrees we obtain an image like in (fig.2.3.d)

After back projection, the image is not quite the same as the original image, but rather is a blurred version of it. In order to sharpen the image, we apply special filtering to the projections by introducing negative wings (fig.2.4.a) before back projection. The use of the negative wings results in a clear image (fig.2.4.b).

90 degree

180 degree 0 degree

360 degree

Figure 2.3 Theory of FBP

(a) Source of radioactivity (b) Projection data for 2 directions, 0 & 90 degrees

degrees [4]

90 degree

0 degree

Figure 2.4 In filtered back projection, negative wings are introduced to eliminate

blurring. [4]

algorithm in action. Fig. 2.5.(a) shows the projection sinogram. A sinogram is a way to display the projections, where projection data at one view is put in one row of the sinogram and the vertical direction represents the view angle. A point in the image corresponds to a sine wave in the sinogram. After the special filtering done by introducing negative wings, the sinogram shows two dark bands, which encapsulate each sine wave (see Fig 2.5(b)). The back projection step is shown in different stages in Fig

2.5(c to h). A perfect image is reconstructed when the back projection is performed over

180 degrees.

a) b)

Figure 2.5 Computer simulation of FBP (a) Sinogram (b) Filtered Sinogram (c-h) Steps of back

projection

2.2.2. Iterative Reconstruction Method

The iterative reconstruction algorithm is of two classes: analytical and statistical. The most commonly used algorithm in nuclear medicine is the Maximum Likelihood

Expectation maximization algorithm [5]. The name of the technique stems from the fact that each iteration has an expectation step that uses current parameter estimates in order to perform a reconstruction of the unobservable Poisson process, followed by a maximum likelihood step that uses this reconstruction to revise the parameter estimates. This method shows a high computational cost in terms of the time required to complete the reconstruction procedure and the computer memory needed.

Figure 2.6 Flow chart for MLEM [4]

2.3. Performance Parameters of Gamma Camera

2.3.1. Spatial Resolution

The spatial resolution of a gamma camera is a measure of the ability of the device to faithfully reproduce the image of an object, thus clearly depicting the variations in the distribution of radioactivity in the object. In other words, spatial resolution is the minimum distance between two points in the image that can be detected by the gamma camera. The overall spatial resolution (Ro) of a camera is the combination of the intrinsic resolution (Ri), the collimator resolution (Rg) and the scatter resolution (Rs), given by the following equation [3]

The smaller the Ro, the better the resolution of the gamma camera. The intrinsic resolution (Ri) arises due to the non-uniformities in the working of the different components of the detection system, as explained in the next section. Most modern cameras have an intrinsic resolution of about 4 mm full width at half maximum (FWHM) for Technetium-99m. The collimator or geometric resolution (Rg) depends on the type and design of the collimator used. There are four major collimator types: parallel-hole, pinhole, converging and diverging. Parallel-hole collimators are most routinely used in nuclear imaging. In collimator design, there is a tradeoff between collimator resolution and collimator efficiency. The scatter resolution (Rs) arises from the fact that radiations scattered by interaction with tissues in the patient, interact with the detector and are registered as counts in the wrong location on the image. The scatter resolution depends

on the composition of the scattering medium, the source configuration and the pulse- height analyzer (PHA) settings.

2.3.2. Methods to Improve Spatial Resolution

1. PM tubes: Modern cameras use a large number of smaller, efficient PM tubes and

have better optical coupling between the crystal and the PM tubes [3].

Disadvantages

a. There is a limit to the reduction in the size of the PM tubes.

b. As the number of PM tubes increases, the system becomes expensive.

2. Crystal Thickness: Intrinsic resolution depends on the crystal thickness. Thicker

crystals result in greater spreading of scintillation light before it reaches the PM tubes.

There is also a greater likelihood of detecting multiple Compton-scattered events in

thicker crystals . Hence, thinner crystals get better intrinsic resolution.

Disadvantages-Detection efficiency of the crystal decreases as high energy gamma

rays can penetrate the crystal and go undetected.

3. Collimator Design: The spatial resolution can be improved by having smaller, tighter

collimator apertures and by increasing the thickness of the collimator [3]

Disadvantages

a. The sensitivity of the system decreases as a large number of gamma rays

are absorbed by the collimator.

b. The scan time of the examination has to be increased in order to

compensate for the reduced sensitivity.

4. Another approach to improve spatial resolution is the use of iterative reconstruction

algorithms. In essence, these algorithms start with an initial estimate of the image and

approach the true image by successive approximations. These algorithms can be

incorporated with models of factors that degrade spatial resolution, like point spread

function and scatter radiation. So these algorithms can be used to obtain images with

improved resolution.

2.4. Methods of Evaluating Spatial Resolution

Image spatial resolution may be evaluated by subjective and objective means. A

subjective evaluation may be obtained by visual inspection of images of “organ

phantoms meant to simulate clinical images [2].To properly evaluate spatial

resolution, a quantitative approach using a point spread function (PSF) or a line

spread function (LSF) should be used.

2.4.1. Line Spread Function

The line spread or point spread function can be explained as follows. Consider a

small point being imaged under the gamma camera. It appears as a blurred image.

This is because of the spread function. In an ideal case all the gamma rays emitted

from the point source will pass through the collimator and hit the detector at the same

point. So, there will be a high intensity at that point and the projection will be a spike.

This is explained in Figure 2.4.1

But in the gamma camera, this is disturbed by the detector electronics and gives a

Gaussian-like distribution as in Fig. 2.7(b).

a) Ideal Case

b) Gamma Camera

Figure 2.7 Point Source distribution (a) Ideal case and (b) Gamma camera

The full width at half maximum (FWHM) of the LSF or PSF curve shown in fig.(2.8) gives the spatial resolution of the imaging device. The FWHM values of the LSF may not represent the true resolution, but the scatter and septal components fall in the tail part of the LSF and therefore are not accounted for. Hence the FWTM value gives a better estimate of spatial resolution.

Figure 2.8 FWHM and FWTM measurements

2.4.2. Modulation Transfer Function

A more comprehensive and quantitative representation of the spatial resolution is given by the modulation transfer function (MTF). The method of determining the MTF is illustrated by Fig.2.9. Suppose we have a source with a sinusoidal distribution of radioactivity. Such a distribution gives a spatial frequency (cycles per centimeter or cycles per millimeter). We can obtain a curve by calculating the MTF at changing spatial frequencies.

If Imax is the maximum intensity and Imin is the minimum intensity in the source, then the source/input modulation (Min) is given by [2]:

An ideal imaging system would image the source faithfully, that is the image would depict the same distribution with Imax and Imin as in the source. However, due to its limitations the system reproduces an image with Omax and Omin as maximum and minimum intensities respectively. So the image/output modulation (Mout) is given by:

The ratio of the output to input modulation is the MTF of a spatial frequency ‘k’:

An imaging system reproduces an image faithfully if it has a flat MTF curve with a value near unity. Good low-frequency response is needed to display coarse details of the image, so that large but low-contrast objects in the image can be detected. Good high-frequency response is necessary to display fine details and sharp edges, so that small lesions can be imaged faithfully. Practically, the MTF is not evaluated by the sinusoidal activity sources as described above. Instead, MTFs are determined by the mathematical analysis of the

PSF or LSF. Specifically, the MTF of a system is given by the amplitude of the Fourier transform (FT) of the LSF [2].

Figure 2.9.Basic principles of determining the MTF of an imaging device

We know that the FWHM of the LSF does not account for the scatter and septal penetration components. However, the MTF takes those into consideration and thus provides a comprehensive description of the spatial resolution of the system. The MTF method also simplifies the evaluation of the system spatial resolution by taking into consideration different components of the system. For example, if the MTF of the intrinsic resolution of the camera is MTFint (k) and that of the collimator is MTFcoll (k), then the overall system MTF is obtained by the element-by-element multiplication of individual MTFs [2]:

Thus, the overall MTF of the system is the product of the individual MTFs of all its components.

CHAPTER III

MATERIALS AND METHODS

3.1 Materials

The data for this study was collected at The Imaging Center, Stow, OH using a dual-head gamma camera manufactured by Trionix Inc. The gamma camera consisted of two NaI

(Tl) detectors placed 180o apart from each other. A low-energy, ultra-high resolution

(LEUR) collimator (Imaging Center, Stow) was used to acquire the data for conventional technique. This section describes the materials and methods for the study.

3.2. Special Plate Collimator

A tungsten plate of size 10.6 cm x 15.75 cm, was used for the study. The plate had 1mm apertures between 6mm tungsten bars. The design of the plate is as shown in fig.3.1.

Figure 3.1 Pattern of the special collimator plate

The plate was then placed on top of detector head of the gamma camera with a plate replacing the collimator. The experimental setup is shown in fig.3.2.

Figure 3.2 Special collimator plate on gamma camera

Data was collected using different sources of radioactivity placed on top of the plate. The data was collected for every angle of rotation from 0 to 360 degrees in steps of three degrees each. This was done as shown in Fig. (3.3)

Figure 3.3 Setup with plate and angular rotation instrument

As the plate has well defined slits, all gamma rays will pass through the particular slit and we will get a spread function for each slit as shown in Fig.3.4 (a). The distribution is summed up and placed in the center such that we get the ideal spike distribution from the spread function Fig 3.4 (b). Thus, we will get a spatial resolution equal to the width of the slit. In our case the width of the slit is 1mm and hence we were aiming at getting a spatial resolution of approximately 1mm.

a) Spread Function from the slit b) Summing up the spread function

Figure 3.4 Working of the plate

3.3 Data acquisition

Three types of data were acquired for this project: point source, line source, and two

line sources separated by a certain distance for evaluating the spatial resolution of the

techniques under comparison. Multiple acquisitions were made for statistical analysis.

The point source and line source were considered because we can see the point spread

function clearly. Two capillary tubes were used to see how well we can separate the

line sources when they are close to each other (1 mm and 2 mm).

The experimental setup was as follows:

1) The point source was prepared by placing a very small drop of a solution of Tc-99m

pertechnetate combined with small amount colored ink, to visualize the drop on a

piece of non-absorbing plastic. Line source was prepared by filling a capillary tube of

0.5 mm of diameter with Tc-99m pertechnetate combined with small amount of color

ink.

2) This source hence prepared was attached to the device used for angular measurement.

Figure 3.5 Line Source on the experimental setup

3) This was placed on top of the plate. The source should not be too far from the

detector.

4) The plate and angular measure device were all centered to the detector plate. In this

configuration tungsten plate was stationary and the gamma ray source was rotated.

5) The angular measuring device with the source was rotated by 3 degree increments

from 0 to 360 degrees and the image acquisitions were made.

6) After the acquisition, the imaging data were transferred to a personal computer and

reconstructions were performed.

The images acquired by the gamma camera were saved in the interfile format. It is a format widely used for the exchange of nuclear medicine information. The interfile formats consist of two separate files, the .hdr file and the .img file. The .hdr file is the header file and contains information such as the scaling factor, the number of images in a group, pixel size, size of the image, the date on which the images were taken etc. The actual image data is present in the .img file. The .hdr file can be accessed using a simple text editor but the .img file has to be ‘read in’ using a special MATLAB command.

These images were transferred to a personal computer and were read using the Image

Processing Toolbox of MATLAB (version R2009b) for further processing. Once the files are available for use in MATLAB’s working directory, these files are processed as explained in detail in the chapter that follows.

3.4 Image processing

3.4.1 FBP

Filtered back projection is the most common method of reconstruction of the images.

Considering a Shepp-Logan head phantom, we acquire the projection profile for each angle of the phantom as shown in Fig 3.6. A collection of the projection profiles at all angles together gives the projection data Fig 3.7.

80 100

90 70

80 60

50 60

40 50

30 40

20 30

20 10

10 0 0 5 10 15 20 25 30 35 0 0 5 10 15 20 25 30 35

a) 45 degree projection b) 90 degree projection Figure 3.6 Projection profiles at different angles a) 45 degree b) 90 degree

Figure 3.7 Formation of Sinogram

This projection data is filtered and back projected to get the source image. This is filtered back projection. The reconstructed image is given in Fig.3.8.

5 10 15 20 25 30 Figure 3.8 Reconstructed image

The special collimator plate was designed in such a way that it will allow gamma radiations to pass through slits and block the rest. So, all information of data is not collected in a single acquisition. The projection data from the special collimator plate is given below in Fig.3.9 (a) the reconstructed image for that projection data with FBP is given in Fig.3.9 (b).

ytrue; true projections

Detector bins 60

100

120

20 40 60 80 100 120 Angle of rotation

(a) Projection data from Special Collimator plate

5 10 15 20 25 30 35 40 (b) Reconstruction with FBP

Figure 3.9 Shepp-Logan phantom projection and reconstruction with special

collimator plate and

As seen in the Fig.3.9 (b) filtered back projection will not provide and image because of the limited projection data. The only way to make filtered back projection work for the special collimator plate is to collect all of the missing data in the projection data. This can be done by moving the plate horizontally in five 1mm steps to acquire all the data missing from each projection. At each step we will have to acquire data for 120 angles.

We collect 600 images and post processing these images is time consuming process.

Hence, we prefer not to do FBP method of reconstruction. A modified MLEM algorithm has been shown to work for limited data reconstruction (Patel, 2007). We will now see if modified MLEM works for our projection data.

3.4.2. MLEM

The first and most important step in MLEM is the formation of the G matrix.

The G matrix depends on the type and geometry of the system. The G matrix, G (i,j), is the probability of emission of a particular pixel in the source being detected at particular pixel in the detector. The G matrix is also referred to as the ‘System matrix’.

The first row in the G matrix represents the probability of emission of the first pixel

(pixel (1, 1)) in the source to be detected at the detector. The second row represents the probability of emission of the second pixel (pixel (1, 2)) in the source to be detected at the detector and so on. Thus, each pixel in the source image corresponds to a row in the G matrix. Thus after we get the entire G matrix, we modify it according to our system geometry. Our special collimator plate is designed such that it will allow the radiation from the source to pass through only the apertures and block the others through the bars.

So, if we know the pixels through which the radiation will pass and pixels through which

the will not pass at the source side, we can calculate our system matrix. A calibration is necessary to determine which pixels in the source image are sampled at each angle. To calibrate the slit positions a flood source was placed on top of the special collimator plate and data was collected. The calibration image is given below in Figure 3.10.

Figure 3.10 Image of flood source used for calibration

The gamma rays have passed through the gap in between the tungsten bars. From these lines in the image we get the slit positions that have allowed gamma rays to pass through.

So, the system matrix is modified accordingly. Once the G matrix is formed we follow the flowchart as in Figure 2.6 to perform the Modified Maximum Likelihood

Maximization method of iterative reconstruction.

3.5. Method to find Spatial Resolution

After, we get the reconstructed image we calculate the LSF and MTF. The Line spread function is the profile through the center of the reconstructed image. From the LSF we

calculate the FWHM and FWTM. The profile taken is given in Fig.3.11. From the point

Spread function, FWHM and FWTM are calculated as in the Fig.3.12.

Figure 3.11 Profile through the center of the image for PSF

FWHM of Point source- Conventional technique

180 X: 135 Y: 188.9

160

140

120

X: 132.4 X: 138.9 100 Y: 93.2 FWHM Y: 91.62

Pixel Intensity 80

40 X: 129.7 X: 141.6 Y: 18.06 FWTM Y: 18.09 20

125 130 135 140 145 Pixel Number

Figure 3.12 Point Spread Function and calculation of FWHM, FWTM

The spatial resolution was estimated by the modulation transfer function method (MTF), since it is the most quantitative representation of the spatial resolution, as described in section 2.4.2. The MTF is calculated by taking Fourier transform of the Line spread function. The amplitude was normalized to 1.

For an imaging system a flat MTF curve with value near unity produces a faithful reproduction of the imaged object. Good low frequency response is needed to outline coarse details of the image, while higher frequencies are needed to portray finer details, sharp edges, etc. The MTF values are plotted against distance (mm) as in Fig.3.13.

MTF of Line Source

0.9

0.8

0.7

0.6

0.5 MTF

0.4

0.3

0.2

0.1

1 2 3 4 5 6 Spatial Frequency (lp/mm)

Figure 3.13 MTF values from the PSF

3.6. Method for Statistical Test

To prove that our special collimator plate gives a resolution significantly better than the conventional method statistically, we need more samples of the data. We considered a point source and we were able to collect four sets of data before the radioactivity decayed.

The four acquisitions were made by placing the point source at a different place each time. Refer to Appendix A for images.

The acquisitions were made with the special collimator plate and the FWHM was calculated on the reconstructed images. During each acquisition a planar image was captured by the gamma camera without the plate. From that image of the gamma camera we calculated the FWHM for the conventional method. At the end we got four FWHM values for the conventional method and four FWHM values for the proposed method.

These 2 sets of data were statistically tested by a paired t test.

The T-test works as follows. The difference between the observations is calculated for each pair, and the mean and standard error of these differences are calculated. Dividing the mean by the standard error of the mean yields a test statistic, ts, that is t-distributed with degrees of freedom equal to one less than the number of pairs. SAS (Statistical

Analysis System) gives the Pr-value also. The mean difference between the two groups is considered significant if the Pr value is less than 0.05 significance.

CHAPTER IV

RESULTS

4.1. Phantom results

The sample algorithm was developed and tested with the Shepp-Logan head phantom.

First, the algorithm was tested for the case that all the projection information were present. The result for the reconstruction of this case is given in Fig.4.1. Then, the algorithm was tested for the case when only 1/2, 1/4 and 1/8 of the projection data were present. The image size was 32 x 32. Number of angles was 120 and number of detector bins was 128. Fig.4.2, Fig.4.3, Fig 4.4 gives the results for the reconstruction of 1/2, 1/4 and 1/8 of the projection data.

Detector Bins

Angle of rotation

5 10 15 20 25 30

Figure 4.1 True Sinogram and true image for Shepp-Logan phantom

ytrue; true projections

60 Detector Bins

100

120

20 40 60 80 100 120 Angle of rotation

Reconstructed Image; Iterations = 200

5 10 15 20 25 30

Figure 4.2 Sinogram and reconstructed image with 1/2 of projection data

ytrue; true projections

60 Detector Bins

100

120

20 40 60 80 100 120 Angle of rotation

Reconstructed Image; Iterations = 200

5 10 15 20 25 30

Figure 4.3 Sinogram and reconstructed image with 1/4 of projection data

ytrue; true projections

Detector Bins 60

100

120

20 40 60 80 100 120 Angle of rotation

Reconstructed Image; Iterations = 200

5 10 15 20 25 30

Figure 4.4 Sinogram and reconstructed image with 1/8 of projection data

4.2. Experimental Results

4.2.1. Point Source.

Experiments were conducted with a point source and it was reconstructed with the modified MLEM algorithm. The point source was created by placing a single drop of Tc-

99m on a small piece of paper and placing it under the gamma camera. The point source was imaged with the special collimator and also without the special collimator plate. The image size was 256 x 256 with 120 angles and 256 detector bins.

Conventional Method

Novel Method

Figure 4.5 Point source reconstruction with special collimator plate

4.2.2. Line Source

Experiments were also conducted for a line source. A capillary tube of 1mm diameter was filled with Tc-99m. The experiment was conducted with and without the special collimator plate. The data was processed with the modified MLEM algorithm. The image size was 256 x 256 with 120 angles and 256 detector bins.

Conventionalmethod MethodConventional Line-

100

150

200

250 0 250 200 Nove150 l Method 100 50

Figure 4.6 Line Source reconstruction with special collimator plate

4.2.3 Two Capillary tubes

To prove the improvement in spatial resolution we also conducted an experiment with

two capillary tubes separated by a distance of 1mm. The capillary tubes each had a

diameter of 0.5mm. The reconstruction was then performed with modified MLEM. The

images were then visually compared between the data from with and without the special

collimator plate. The image size was 256 x 256 with 120 angles and 256 detector bins.

250 200 150 100

Conventional Method 50 Novel Method 250

200

150

100 50

100 150 200 250

50 Conventional Method

250 Novel Method

200

150

100 50

Figure 4.7 Two line sources reconstruction with special collimator plate (a) less gap in

between (b) more gaps in between

4.3. Results for Spatial Resolution Experiments

The point spread function method is used to calculate the spatial resolution. A plot of pixel intensities through the centre of the image of the point source gives the point spread function. This is used to calculate the FWHM, FWTM and MTF. The values of FWHM and FWTM for the conventional and proposed method are listed below in Table.4.1. The

MTF plots are given in Figure 4.8 and Figure.4.9.The images of the point source and the measurement procedure of FWHM and FWTM are given in Appendix.

Table 4.1: FWHM and FWTM values obtained for the conventional and proposed method.

Conventional Novel Technique Technique

FWHM 3.96 mm 0.93 mm

FWTM 7.78 mm 1.84 mm

X: 176.1 Y: 218 200

150

100 X: 173.3 X: 179.3 Y: 109.2 Y: 107.9 Pixel Intensity

X: 170 X: 181.8 Y: 19.22 Y: 18.16

166 168 170 172 174 176 178 180 182 184 186 Pixel Number

FWHM FWTM Peak Intensity (M) X1 X2 X3 X4 (X2-X1) x 0.66mm (X4-X1) x 0.66mm

218 109 173.3 179.3 3.96 mm 22 170 181.1 7.78 mm

Figure 4.8 Point spread function and FWHM calculation for the conventional method

FWHM for Point source -Proposed technique

X: 178 Y: 114.6

100

X: 177.3 X: 178.7 Y: 59.25 Y: 57.96 60 Pixel Intensity

X: 176.6 X: 179.4 20 Y: 16.29 Y: 16.37

0 175 176 177 178 179 180 181 Pixel Number

FWHM FWTM Peak Intensity (M) X1 X2 X3 X4 (X2-X1) x0.66mm (X4-X1) x0.66mm

114 57 177.3 178.7 0.93 mm 10.48 176.6 179.4 1.84 mm

Figure 4.9 Point spread function and FWHM calculation for the novel method

COMPARISON OF MTF

0.9

0.8

0.7

0.6 MTF

0.5 Proposed Technique MTF Conventional Technique 0.4

0.3

0.2

0.1

0.5 1 1.5 2 2.5 SPATIALSPATIAL FREQUENCY FREQUENCY (lp/mm) a) MTF curves for point source

0.9

0.8

0.7 Conventional Technique Proposed Technique 0.6 MTF 0.5 MTF

0.4

0.3

0.2

0.1

0 0.5 1 1.5 2 2.5 3 SPATIAL FREQUENCYSpatial Frequency

b) MTF curves for Line Source

Figure 4.10 Plot comparing the MTF’s for (a) Point and (b) Line Source

The MTF curve that is closer to unity gives better frequency response of the imaging system. From the Fig.4.10, we conclude that the proposed technique gives a better MTF with respect to the plot above.

4.4 Results of Statistical test

As explained in section 2.4.2, the modulation transfer function (MTF) is the most quantitative measure of the spatial resolution of an imaging system. Hence, the MTFs with the conventional and proposed techniques are to be estimated and tested for difference. The MTF comparison curves will represent the fact. Further to test the experimental success, the experiment was repeated four times and the mean and standard deviation for the value of FWHM were calculated.

The statistical experiment was conducted by using a single point source and repeating the experiment 4 times. The FWHM values were calculated for the conventional and proposed technique. The results are listed in Table 4.2 below.

Table 4.2 Results from Statistical test

FWHM values (mm) Trial Conventional Method Proposed Method Position1 3.432 1.234 Position2 4.026 1.261 Position3 4.554 1.254 Position4 3.960 1.063

A paired t-test was then performed to test the null hypothesis [6]. The t-test is paired because the point sources were in four different locations for the four trials. The test results from SAS (Statistical Analysis System) are shown in Table 4.3.

Table 4.3 Statistical Analysis System results

The SAS System

The MEANS Procedure

Analysis Variable: diff

Mean Std Dev Std Error t Value Pr > |t|

2.790 0.456 0.228 12.25 0.0012

For t-test our results show that Pr value is 0.001. This value is less than 0.05. Thus we conclude there is a significant difference in the spatial resolution between the two methods and we reject the null hypothesis.

CHAPTER V

DISCUSSION AND CONCLUSION

The aim of the study was to improve the spatial resolution of planar images. The spatial resolution obtained by the current technique of nuclear imaging is limited by the point spread function of the gamma camera. To validate this technique, a special collimator plate was developed and tested. The images obtained with the special collimator plate were compared with images obtained by the nuclear imaging technique currently in use.

The comparisons were made qualitatively and quantitatively.

First if we qualitatively (visually) compare the images obtained by the proposed and conventional method, we can see that the images with the proposed technique are crisper and have better contrast. Especially when we compare the images with two capillary tubes in Figure 4.7, with the conventional method we can see the two capillary tubes are overlapping each other.

Quantitatively when we compare the resolution of the two methods with their FWHM and MTF’s we find:

1) The smaller the FWHM and FWTM the better the resolution and hence the novel

method gives a better spatial resolution.

2) The MTF curve of an imaging system should be flatter and closer to unity. The

MTF curves of the conventional method approaches zero rapidly. The MTF curve

of the novel method varies slowly across the spatial frequency range indicating

that the response is better across varying frequencies.

3) Statistically to prove the performance of the proposed method, the experiment

was repeated 4 times and the FWHM values were calculated. The FWHM is

calculated mean of 1.20 ± 0.09.

5.1. Salient Features of the Proposed Technique

1) It improves the detector’s spatial resolutions.

2) Spatial resolution is limited by the special collimator plate configuration. Hence,

any resolution is theoretically realizable.

3) Hardware supports only small point and line source imaging for now.

5.2 Conclusions

This thesis presents a novel technique to increase the spatial resolution of the gamma camera. Based on the results from the visual comparisons and the quantitative tests performed, it was concluded that the proposed technique was successful and gave better spatial resolution images when compared to the conventional technique.

5.3 Future Work

1. The current method can be refined by making the process of acquisition automatic

and more precise by using a micro-controller.

2. The technique can be extended to tomographic (SPECT) imaging combined with

the use of iterative reconstruction algorithms because of the limited nature of the

dataset. Investigations as to the number of angles needed for sufficient

reconstruction data and the number of bins to be used for the reconstruction can

be made.

BIBLIOGRAPHY

[1] R.Chandra. Introductory Physics of Nuclear Medicine,Philadelphia,Lea & Febiger, 1976.

[2] S. R. Cherry, J. A. Sorenson, M. E. Phelps, Physics in Nuclear Medicine, 3rd Ed, Philadelphia, Saunders, 2003.

[3] G. B. Saha, Physics and Radiobiology of Nuclear Medicine,2nd Ed, New York, Springer, 2000.

[4] G.L.Zheng. Image Reconstruction- Tutorial. Utah : Univeristy of Utah, 2000.

[5] S. Vandenberghe, Y. D'Asseler, R. Van de Walle, et al, “Iterative reconstruction algorithms in nuclear medicine”, Compt. Med. Imaging Graphics, vol. 25, pp.105-111, 2001.

[6] J.Rohlf, R.Sokal, Biometry, 3rd Ed, San Francisco, W.H. Freeman & co, 1995.

[7] R. Patel, Maximum Likelihood - Expectation Maximum Reconstruction with Limited Dataset for Emission Tomography, Master’s Thesis, The University of Akron, 2007.

[8] Y.Vardi, L.A.Shepp, Maximum Likelihood Reconstruction for Emission tomography, IEEE Transactions on Medical Imaging, No-2, s.l. October 1982, Vols. MI-1.

[9] R. Raichur, A Novel technique to improve the resolution & contrast of Planar Nuclear medicine Imaging, Master’s Thesis, The University of Akron, 2008.

[10] S.Athawale,Use of Annular Coded Aperture in Nuclear Imaging, Master’s Thesis, The University of Akron, 2010.

APPENDIX STATISTICAL RESULTS

Co nventional Method Novel Method

100

150

200

250 50 100 150 200 250 Data 1

900 160 800

140 700

120 600

100 500

Pixel Intensity 400 Pixel Intensity

60 300

40 200

20 100

0 0 164 166 168 170 172 174 176 178 180 182 184 178 179 180 181 182 183 184 185 186 187 188 Pixel Number Pixel Number

X1(mm) X2(mm) FWHM(mm)

Conventional 173.7 178.91 3.43

Novel 178.61 180.41 1.23

Figure A.1 Data1- Reconstructed image and FWHM’S values

Conventional Method Novel Method

100

150

200

250 50 100 150 200 250

700

180 600

160

500 140

120 400

100

Pixel Intensity 300 Pixel Intensity 80

60 200

100 20

0 0 116 118 120 122 124 126 128 130 132 134 122 123 124 125 126 127 128 Pixel Number Pixel Number X1(mm) X2(mm) FWHM(mm)

Conventional 122.5 128.6 4.02

Novel 125.48 127.39 1.26

Figure A.2 Data2- Reconstructed image and FWHM’S VALUES

Conventional Method Proposed Method

100

150

200

250 50 100 150 200 250

450

400 200

350

300 150

250

Pixel Intensity 100 200 Pixel Intensity

150

50 100

0 136 138 140 142 144 146 148 150 152 154 0 145 146 147 148 149 150 Pixel Number

X1(mm) X2(mm) FWHM(mm)

Conventional 142.6 149.9 4.55

Novel 147.5 149.4 1.25

Figure A.3 Data3- Reconstructed image and FWHM’S values

Conventional Method Proposed Method

100

150

200

250 50 100 150 200 250

700

600 200

500

150 400

Pixel Intensity 300 Pixel Intensity 100

200

100

0 0 72 74 76 78 80 82 84 86 88 90 77 78 79 80 81 82 Pixel Number Pixel Number X1(mm) X2(mm) FWHM(mm)

Conventional 78.3 84.4 3.96

Novel 78.40 79.3 1.06

Figure A.4 Data4- Reconstructed image and FWHM’S values

Comparison of MTF-Statistical data

0.9

0.8 Proposed Method

0.7

0.6

0.5 MTF

0.4

0.3 Conventional method 0.2

0.1

0 1 2 3 4 5 6 Spatial Frequency (lp/mm)

Figure A.5 MTF plots for the statistical data against the MTF for conventional

method