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University of Ljubljana Faculty of mathematics and physics Department of physics Tomography Mitja Erˇ zen August 6, 2009 Menthor: Dr. Matjaˇ z Vencelj Abstract We’ll describe some methods for medical imaging.I’ll focus just on methods of tomography that relies on absorbtion or penetration of gamma or x-rays. We’ll describe the most common method of imaging in medical treatment (X-ray), later on we’ll show how CT and other methods work.

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Page 1: Tomography - University of Ljubljanamafija.fmf.uni-lj.si/seminar/files/2008_2009/tomography_final.pdf · University of Ljubljana Faculty of mathematics and physics Department of physics

University of LjubljanaFaculty of mathematics and physics

Department of physics

Tomography

Mitja Erzen

August 6, 2009

Menthor: Dr. Matjaz Vencelj

Abstract

We’ll describe some methods for medical imaging.I’ll focus just on methods oftomography that relies on absorbtion or penetration of gamma or x-rays. We’lldescribe the most common method of imaging in medical treatment (X-ray),later on we’ll show how CT and other methods work.

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Contents

1 Introduction 2

2 X Ray 22.1 X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Image detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Mammography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Computed Tomography 53.1 Data-Acquisition Geometries . . . . . . . . . . . . . . . . . . . . 6

3.1.1 First generation: Parallel-beam geometry . . . . . . . . . 63.1.2 Second generation: Fan beam, multiple detectors . . . . . 63.1.3 Third generation: Fan beam, rotating detectors . . . . . . 63.1.4 Fourth generation: Fan beam, fixed detectors . . . . . . . 73.1.5 Fifth generation: Scanning electron beam . . . . . . . . . 7

3.2 Reconstruction principles . . . . . . . . . . . . . . . . . . . . . . 7

4 Nuclear Medicine 84.1 Radiopharmaceuticals . . . . . . . . . . . . . . . . . . . . . . . . 84.2 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5 SPECT 115.1 Imaging process of SPECT . . . . . . . . . . . . . . . . . . . . . 115.2 Reconstruction methods . . . . . . . . . . . . . . . . . . . . . . . 12

6 PET 146.1 Imaging process of PET . . . . . . . . . . . . . . . . . . . . . . . 146.2 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146.3 Physical factor affecting resolution . . . . . . . . . . . . . . . . . 15

7 Conclusion 17

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1 Introduction

Tomography is imaging by sections. The word comes from the Greek word”tomos”, which means ”a section”, ”a slice” or ”a cutting”. Tomography rev-olutionized medical radiology, because for the first time, doctors could obtainimages of internal body structures. This enables them to make a diagnosis,without any surgery. Before tomography, radiography was used, which can alsobe used to make a diagnosis of some injuries.

2 X Ray

X-ray radiography produces images of anatomy that are shadowgrams, basedon x-ray absorption. The x-rays emerging through the body form a 2D image,where each point in the image has a brightness related to the intensity of thex-rays at that point. Intensity difference relies on the fact that different partsof the anatomy absorb different amounts of x- rays. For better contrast wecan use strong X-ray absorbers, like barium, which is often used for studyinggastrointestinal tract [1]. When x-rays strike an object, they may either passthrough unaffected or may undergo an interaction. Interaction is either thephotoelectric effect (absorption of x-ray) or scattering (where the x-ray is de-flected to the side with loss of some energy). Scattered x-rays can still reach thedetector and these x-rays reduce image contrast and thus degrade the image.This degradation can be reduced by the use of an air gap between the anatomyand the image receptor or by the use an antiscatter grid (collimator).

2.1 X-Rays

The standard device used for x-ray production is the rotating anode x-ray tube,as illustrated in fig.2. The x-rays are produced from electrons that have beenaccelerated in vacuum from the cathode to the anode. The electrons are emittedfrom a filament mounted in the cathode. Emission occurs when the filament isheated by passing a current through it. When the filament is hot enough, someelectrons obtain a thermal energy sufficient to overcome the energy binding theelectron to the metal of the filament. Once the electrons have boiled off fromthe filament, they are accelerated by voltage difference (15-150kV) applied fromthe cathode to the anode.After acceleration electrons are stopped in the anode in a short distance. Mostof the electrons’ energy is converted into heating of the anode, but a smallpercentage is converted to x-rays by two main mechanism. One relies on thefact that deceleration of a charged particle results in emission of electromagneticradiation, called deceleration radiation. These x-rays have a wide, continuousdistribution of energies, with the maximum being the total energy the electronhad when reaching the anode.The second method occurs when an accelerated electron strikes an atom in anodeand removes an inner electron from this atom. The vacant electron orbital willbe filled by a neighboring electron and an x-ray may be emitted whose energymatches the energy change of the electron. The result is production of largenumbers of x-rays at a few discrete energies. Energy of these characteristicx-rays depends on the material on the surface of anode. In mammography

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molybdenum is frequently used with characteristic x-rays of 20-keV (fig. 1) [1].

Figure 1: Comparison of tungsten and molybdenum target x-ray spectra [1].

Low energy x-rays are undesirable, because they are completely absorbedand all they do is increase the dose to the patient. Because of that, aluminumor copper filters are used to remove low energy x-rays from the beam. Sometimesmolybdenum filters are also used which filtr low energy x-rays and those x-raysthat are above K edge could enrich the spectrum with x-ray energies in therange of 17-20 keV[1].

Figure 2: X-ray tube [1].

2.2 Image detection

The most common method to make a radiographic x-ray image is method whichuses light sensitive film as a meduim. But this film has a disadvantage, it has apoor response to x-rays, so it must be used with sensitive x-ray screens. Thesescreens absorbs x-rays and their energy is converted to visible light, then thislight exposes a negative image on the film. Such screens are usually made of

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CaWo2 or phosphorus using rare earth elements and the film is enclosed in alight-tight cassette in contact with screen on both sides. Efficiency of screens forx-ray absorption is 30% for higher energy and 60% for lower energy of x-rays.This is also the reason why two screens on both sides of the film are used [1].

2.3 Mammography

Mammography is an x-ray imaging procedure for examination of the breasts forbreast cancer. Mammogram is an x-ray shadowgram formed when x-rays irra-diate the breast and the transmitted x-rays are recorded by an image receptor.The signal is a result of different attenuation of x-rays when passing throughtissue. The image system must have sufficient spatial resolution to delineatethe edges of structure in tissue (breast). Structural detail as small as 50 µmmust be resolved. Variation in x-ray attenuation among tissue structures in thebreast gives rise to contrast, but because of random fluctuation (scattering,..) inthe image appears noise. On figure 3 is one-dimensional profile of x-ray trans-mission, which illustrates the role of contrast, spatial resolution and noise inimage quality. If we have a model which is composed of two different materials,

Figure 3: Profile of a simple x-ray projection image, illustrating the role ofcontrans, spatial resolution and noise in image quality [1].

where one has similar properties as healthy tissue and one like cancer tissue andif we irradiate this model with monoenergetic x-rays of energy E, the numberof x-rays recorded in a fixed area of the image is proportional to

Nb = N0(E) exp−µT (1)

in the background (health tissue) and

Nl = N0(E) exp−µ(T−t)+µ′t (2)

in the shadow (where is also cancer tissue). N0 is the number of x-rays thatwould be recorded in the absence of tissue in the beam, µ and µ′ are the atten-uation coefficients of healthy and cancer tissue. T and t are thickness of tissue.

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The difference in x-ray transmission gives rise to contrast which can be definedas:

C0 =Nb −NlNb +Nl

(3)

if we have monoenergetic x-rays and we ignore scatter radiation we get:

C0 =1− exp(µ′−µ)t

1 + exp(µ′−µ)t(4)

Contrast would depend only on the thickness of the cancer tissue and thedifference between its attenuation coefficient and background material. Thefigure 4 is shows x-ray attenuation coefficient of three types of materials foundin the breast. Adiopose tissue (fat), normal fibroglandular breast tissue andinfiltrating ductal carcinoma (tumor tissue).

Figure 4: Measured x-ray linear attenuation coefficient for tissue found in breastvs x-ray energy [1].

3 Computed Tomography

The development of computed tomography (CT) was revolutionized in medi-cal radiology in early 1970s. For the first time, physicians were able to obtainhigh-quality tomographic (cross-sectional) images of internal structures over thebody. The first practical CT instrument was developed in 1971 by dr. G.N.Hounsfield in England and was used to image the brain. Since then, CT tech-nology has developed dramatically. Through time several different possibilitiesfor CT were developed. The difference between them was in location, move-ment and types of detectors and x-ray sources. We can describe these variantsas ”generations” (figure 5). Current CT scanners use either third, fourth or fifthgeneration geometries, but each have its own pros and cons.

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Figure 5: Different generations of CT scanner illustrating the parallel and fan-beam geometries [1].

3.1 Data-Acquisition Geometries

3.1.1 First generation: Parallel-beam geometry

Multiple measurements of x-ray transmission are obtained using a single highlycollimated x-ray pencil beam and detector. The beam is translated in a linearmotion across the patient to obtain a projection profile. The source and detectorare then rotated about the patient isocenter by approximately 1◦ and anotherprojection profile is obtained. This tanslate-rotate scanning motion is repeateduntil the source and detector have been rotated by 180◦. Scan time of this timedetector is long 5 min [1].

3.1.2 Second generation: Fan beam, multiple detectors

Scan times were reduced to approximately 30s with the use of a fan beam ofx-rays and a linear detector array. A translate-rotate scanning motion was stillemployed. The reconstruction algorithms are more complicated than those forfirst generation, because they must handle fan beam projection data.

3.1.3 Third generation: Fan beam, rotating detectors

A fan beam of x-rays is rotated 360◦ around the isocenter. No translation motionis used, but fan beam must be wide enough to completely contain the patient.A curved detector array consisting of several hundred independent detectorswhich are mechanically coupled to the x-ray source and both rotate together.As result these rotate-ony motions acquire projection data for a single picture

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in 1s. This type have the advantage that thin tungsten septa can be placedbetween each detector in the array to reject scattered radiation.

3.1.4 Fourth generation: Fan beam, fixed detectors

X-ray source and fan beam rotate around the isocenter, while the detectorsarray remains stationary. The detector array consists of 600-4800 independentdetectors in a circle.

3.1.5 Fifth generation: Scanning electron beam

Fifth-generation scanners are unique in that the x-ray source becomes an in-tegral part of the system design. The detector array remains stationary, whilea high energy electron beam is electronically swept along a semicircular tung-sten strip anode as illustrated in figure 6. Projection data can be acquired inapproximately 50ms, which is fast enough to image the beating heart.

Figure 6: Schematic illustration of a fifth-generation ultrafast CT system [1].

3.2 Reconstruction principles

CT is a two-step process: 1) the transmission of an x-ray beam is measuredthrough all possible straight-line paths as in a plane of an object, and 2) theattenuation of an x-ray beam is estimated at point in the object. If we want toget a result we need computer processing procedures on the measurements ofx-ray intensity. First CT scanner required 20 min to finish its reconstruction,but now we receive result (picture) on the fly.As we know the intensity of the x-ray beam is attenuated by absorption and scat-tering processes as it passes through tissue (patient). The degree of attenuationdepends on the energy spectrum of the x-rays as well as on the average atomicnumber and mass density of the patient tissues. The transmitted intensity isgiven by

It = I0 exp−∫ L

0µ(x)dx (5)

where I0 and It are the incident and transmitted beam intensities. L is thelength of the x-ray path and µ(x) is the x-ray linear attenuation coefficient,

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which varies with tissue type and is a function of the distance x through thepatients. The integral of the attenuation coefficient is then given by

∫ L

0

µ(x)dx = − 1Lln(It/I0) (6)

If we measure the integral from many angles about isocentre, the reconstruc-tion algorithm could reconstruct image of researched body.X-ray detectors used in CT systems must have a high overall efficiency to min-imize the patient radiation dose, have a large dynamic range, be very stablewith time an be insensitive to temperature variations. In CT are used solid-state detectors and gas ionization detectors (Fig. 7). Gas ionization detectorshave excellent stability, however, they generally have a lower efficency thansolid-state detectros.

Figure 7: A solid state detector consist of a scintillator crystal and photodiodecombination. Many such detectors are placed side by side to form a detectorarray that may contain up to 4800 detectors. Gas ionization detector arraysconsist of high-pressure gas in multiple chambers separated by thin septa. Thesepta also act as electrodes and collect the ions created by the radiation andconverting them into electrical signal [1].

4 Nuclear Medicine

Nuclear medicine can be defined as the practice of making patients radioactivefor diagnostic and therapeutic purposes. The radioactive element is injectedintravenously, rebreathed or ingested. These elements are called radiopharma-ceuticals.

4.1 Radiopharmaceuticals

Radiopharmaceuticals are radioactive-labeled pharmaceuticals, that distributein different internal tissues or organs. Ideal characteristics of a radiopharma-ceutical:

- half-life similar to the length of the test

- radionuclide should emit gamma rays

- energy of gamma rays should be between 50-300 keV

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- chemically suitable

- readily available at the hospital site

- should localize only in the area of interest

- should be eliminated from the body with a half-life similar to the durationof the examination

- radiopharmaceutical should be simple to prepare

If half-life is very short, then the activity will have decayed to a very low levelbefore imaging has started, but if it is too long the patient will receive higherradiation dose. Another problem is with gamma energy, if energy is small thentissue could absorb too much gamma rays and we do not get enough gammarays to make an image. But if energy is too high more difficult it will be to stopthe gamma ray in the detector of the imaging device. It is also necessary toavoid those radionuclides that have alpha and beta emissions, which have shortrange and they just increase radiation dose to the patient.Radionuclides can be produced on three different ways: in the nuclear reactor,in the cyclotron or in a generator. Because of short half-life the most importantmethod of production is with generator. Generator depends upon the existenceof a long-lived parent to be supplied in the form of a generator, from which theshort-lived daughter can be chemically extracted when required. For the mostcommonly used in nuclear medicine technetium-99m , parent is molybdenum-99[2].

4.2 Detectors

Gamma rays are emitted isotropically. Simply using a detector would not showthe relationship between position at which the gamma ray hits the detector andthat from which they were emitted from the patient (fig.8 ).

Figure 8: In the absence of collimation (a) there is no relationship between theposition at which a gamma ray hits the detector and that from which it left thepatient. With collimator (b) we gain that relationship [2].

To avoid this problem the detector is used with collimator. It consist ofa lead plate through which an array of small holes runs and whose access isperpendicular to the face of collimator and parallel to each other. Only thosegamma rays that travel along a hole axis will pass into the scintillation crystal,

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while others are absorbed.Two main parameters describing collimator performance: spatial resolution andsensitivity. Resolution is a measure of sharpness of image, sensitivity is a pro-portion of gamma rays that absorbs in detector and gamma rays that do notreach the detector. Typically the sensitivity for a parallel hole collimator isonly 0.1%. 99.9% of gamma rays are absorbed by collimator or do not reachthe detector.

Because of small sensitivity it is necessary to have quality detectors whichperceive as much gamma rays as possible. To create a picture it’s necessary toconvert gamma rays into visible light in scintillation crystal, then this light isconverted to electrical signals by photo multiplayer tubes. Scintillator crystalshould have high efficiency for gamma rays and also high conversion of gammaray energy to visible light. This requirement increases sensitivity of the detector.Also, energy of gamma rays should be in the right range (fig.9)[2].

Figure 9: If we have too high x-ray energies the detector can’t stop them. If thedetector misses the x-rays we lose on sensitivity [2].

The detectors in clinical nuclear medicine are NaI(TI) (Sodium Iodide dopedwith Thallium) crystals. The detector consists of a large number of crystals andevery crystal is connected with a light pipe. These pipes are connected to a PMT(photomultiplier tube) but in the way it indicates a row or a column. Crystalsare separated by lead septas to prevent scattered photons from one crystal tothe next. When large crystals became a reality, new ways to use them wereconceived. The Anger camera (fig. 10) is one of the first ones. It uses a singlecrystal which is large enough to image a significant part of the human body andhas an array off PMT on the back to give positional sensitivity[1].

Figure 10: Anger camera detector design [1].

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5 SPECT

Single-photon emission computed tomography (SPEC) is a medical imagingmodality that combines conventional nuclear medicine imaging techniques andCT methods. Different from x-ray CT, SPECT uses radiopharmaceuticals, thatdistribute in different internal tissues or organs instead of an external x-raysource. The spatial and uptake distributions of the radiopharmaceuticals de-pend on the biokinetic properties of the pharmaceuticals and the normal orabnormal state of the patient [1].

5.1 Imaging process of SPECT

The imaging process of SPECT we can simply describe with fig. 11. Gamma-rayphotons emitted from the internal distributed radiopharmaceutical penetratethrough the patient’s body and are detected by a single or a set of collimatedradiation detectors. When photons penetrate through body they could interactwith tissue. It could happen photoelectric effect, which absorbs all the energyof the photon and stops their emergence from the patient’s body. The othermayor interaction is Compton interaction, which transfers part of the photonenergy to the electrons, the original photon is scattered into a new directionwith reduced energy, that is depended on the scatter angle. Because primaryphotons have energy from 70-140 keV, the probability of pair production is zero[1].

Figure 11: Gamma-ray photons emitted from the internally distributed radioac-tivity may experience interactions. Photons that are not traveling in the direc-tion within the acceptance analog of the collimator will be intercepted by leadcollimator, photons will not have interactions and travel within the acceptanceangle of the collimator will be detected [1].

In SPECT is used Anger camera, with large (40 cm in diameter) scintillatorNaI(TI) crystal and an array of PMTs are placed at the back of the scintillationcrystal. The system could use one or more rotating cameras (fig. 12). Whenphoton hits and interacts with the crystal, the scintillation generated will bedetected by the array of PMTs. An electronic will evaluate signals and determi-nates the location of interaction. In SPECT, projection data are acquired fromdifferent views around the patient. On figure 13, 1-D projections of a distribu-tion of radioactivity comprising two point sources are shown for three positions

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of the detector. For reconstructing an image of the original distribution is themost common method ”back-projecting” each profile at the appropriate angleon to an image array in the computer (fig. 13). In other words, a constantvalue equal to the profile element is assumed for each point along that line inthe image array [2].

Figure 12: Examples of cameras for SPECT systems. (a) Single camera system.(b,c) Dual camera system. (d)Triple camera system. (d) Quadruple camerasystem [1].

Figure 13: a)Profiles relating to a single transactional section from a distributionof radioactivity. b) Back-projection of profiles from figure (a). Point source canbe indentifined but big background it’s noticed [2].

5.2 Reconstruction methods

In SPECT the goal of image reconstruction is to determine the distributionof radiopharmaceutical in the patient. However, the presence of photon at-tenuation affects the measured projection data. If conventional reconstructionalgorithms are used without proper compensation for the attenuation effects,inaccurate reconstructed images will be obtained. But first look what kind ofdata do we get.

Figure 14 shows schematic diagram of 2D image reconstruction problem.Left f(x, y) represent a 2D object distribution that is to be determined. A 1Ddetector array is oriented at angle θ with respect to the x axis of our laboratorysystem (x, y). Data collected into each element at location t is called the pro-jection data p(t, θ) and is equal to the sum of f(x, y) along a gamma ray. Thenthe projection data can be written as

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Figure 14: Schematic diagram of the two-dimensional image reconstructionproblem [2].

p(t, θ) = c

∫ α

−αf(x, y)ds, (7)

where (s, t) represents a coordinate system with s along the direction of the raysum and c is the gain factor of detection system. The angle between x and s isθ, then the relationship between position (x,y), the projection angle θ and theposition of detector is given by

t = y cos(θ)− x sin(θ). (8)

The integral 7 which transform object distribution to its projections is alsocalled Radon transform. Our goal of image reconstruction is to solve the inverseRadon transform [1]. In SPECT we measure distribution of radioactivity, so theequation 7 can be written as

p(t, θ) = c

∫ α

−αρ(x, y)ds, (9)

where ρ is the radioactivity concentration distribution of the object. This equa-tion is true if we ignore the effect of attenuation, scatter and collimator detectorresponse. If attenuation is taken into consideration Radon transformation canbe written as

p(t, θ0) = c

∫ α

−αρ(x, y)[−

∫ +α

(x,y)

µ(u, v)ds′]ds, (10)

where µ(u, v) is the 2D attenuation coefficient distribution and∫ +α

(x,y)µ(u, v)ds′

is the attenuation factor for photons that originate from (x,y), travel along

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the direction perpendicular to the detector array and are detected. A majordifficulty in reconstruction lies in attenuation factor, which makes the inverseproblem difficult to solve analytically. But small differences in attenuation co-efficient (different as in x-ray CT) are not as important in SPEC and then theattenuation coefficient in the body is aconstant and attenuated Radon transformcan be written as

p(t, θ0) = c

∫ α

−αρ(x, y)[−µl(u, v)]ds, (11)

where µ is constant attenuation coefficient and l(x, y) is the path length be-tween the point (x,y) and the edge of attenuator (patient’s body). The solutionof the inverse problem with constant attenuator has been a subject of severalinvestigations.As already mentioned reconstruction method called simple backprojectionwhere the reconstructed image is formed simply by spreading the values of themeasured projection data uniformly along the projection ray into the recon-structed image array. By backprojecting the measured projection data from allprojection views, an estimate of the object distribution can be obtained. Simplebackprojection is given by

ρ(x, y) =m∑j=1

p(y cos(θj)− x sin(θj), θj)4θ (12)

where θj is the j-th projection angle, m is the number of projection viewsand 4θ is the angular spacing between projections. The simple backprojectionimage f(x, y) is a poor approximation of the true object distribution f(x, y).For more accurate image reconstruction more complex methods are used.

6 PET

6.1 Imaging process of PET

PET imaging works on the same principle as SPECT, but with some differences.In PET imaging an active tracer is also injected, but here it emits positron andnot gamma ray. Positron then combines with an electron and these two particlesundergo the process of annihilation (eq. 13).

β+ + e− → 2γ (Eγ = 511keV ) (13)

The energy associated with the masses of positron and electron is 1.022MeV, this energy is divided equally between two photons that fly away from oneanother at 180◦ angle. Each photon has an energy of 511 keV. These high energygamma rays emerge from the body in opposite directions, which are detected bydetectors around the patient. When two photons are recorded simultaneouslyby a pair of detectors (coincidence) (fig. 15), it is possible that annihilationevent accures somewhere along the line connecting the detectors. When enoughdetection from all sides is collected then the picture can be reconstructed[1].

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Figure 15: Types of coincidences detected in a PET imaging system. A) Truecoincidence. B)Accidental coincidences, the two photons identified as arrivingin coincidence have originated from different disintegratios. C) Scatter, ne of thephotons has undergone Compton scattering before being detected. D) Multiplecoincidences. More than two photons arrive in coincidence. Apart from the truecoincidences , all other will result in incorrect spatial information. [2].

6.2 Detectors

PET system also uses scintillators detectors with PMTs but because of higherenergy of gamma rays the detector needs higher density crystals. Instead ofNaI(Tl) crystals BGO (Bismuth germanate) or LSO (lutetium orhosilicate) crys-tal are used. These have higher stopping power then NaI(Tl) [2].

In PET the arrangement of scintillators and PMTs are shown in figure 16.The ”individually coupled” design is capable of very high resolution, but thedisadvantages of this type of design are the requirement for many expensivePMTs. Second design is called ”a block detector design” and here are fivePMTs coupled to eight scintillator crystals. When one of outside four PMTsdetect an photon interaction, that means that interaction accured in one ofattached detectors. Center PMT is used to determine whether it was the inneror outer crystal. This is known as a digital coding scheme. We receive justsignal if detector was hit or not hit[1].

6.3 Physical factor affecting resolution

There are some factors in PET, which result on spatial resolution of PET (fig.17). Size of the detector is critical in determining the system’s geometric reso-lution and if block design is used, there is a degradation in resolution for a 2.2mm. Also the angle between the paths of annihilation photons can deviatedfrom 180◦ as a result of some residual kinetic motion at the time of annihila-tion. The resolution of this effect increases with detector ring diameter. Also thedistance the positrons travels before annihilation, decrease spatial resolution[1].

These factors influence on resolution result for the center or axis of the to-

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Figure 16: The individually coupled design is capable of very high resolution andbecause the design is very parallel it is capable of very high data throughput. Ablock detector couples several PMT to a bank of scintillator crystals and uses acoding sheme to determine the crystal of interaction. [1].

Figure 17: Factors contributing o the resolution of PET tomograph. [1].

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mograph. The path of the photon from an off-center annihilation event typicallytraverses more than one detector crystal, as shown on fig. 18. This result thatresolution spread function along the radius of the transaxial plane. The loss ofresolution depends on the crystal density and the diameter of the tomographdetector ring [1].

Figure 18: Because annihilation photons can penetrate crystals to differentdepth, the resolution is not equal in all directions [1].

7 Conclusion

In described methods we must pay attention also on energy that is absorbedfrom gamma or x-ray, because if too much energy is absorbed it could come todamage of cells, tissues or organs. It is necessary to achieve that patient receiveas low absorbed dose as reasonably possible. Because of this, it is necessary todecide whether the imaging is necessary or not. Doses for different methods areshown in a table 1. For simple image is the most common method x-ray, but ifmore precise picture is needed, CT or MRI is used.

There are also some other methods which have their own pros and cons. Onfigure 19 are shown different pictures for different methods of imaging. Whilesome imaging scans such as CT and MRI isolate organic anatomic changes inthe body, PET and SPECT are capable of detecting areas of molecular biologydetail. These do this using radiolabeled molecular probes that have differentrates of uptake depending on the type and function of tissue involved. Picturesmade with MRI and CT are very similar, but there are some differences.First difference is that technology of MRI imaging is expensive method. Alsotime for image takes more than for CT. Images made with CT and MRI are notthe same because MRI operates in a different way.

MRI method of imaging uses a powerful magnetic field to align the nuclearmagnetization of atoms (usually) hydrogen atoms in water in the body. Ra-dio frequency (RF) fields are used to systematically alter the alignment of thismagnetization, causing the hydrogen nuclei to produce a rotating magnetic fielddetectable by the scanner. This signal can be manipulated by additional mag-netic fields to build up enough information to construct an image of the body.

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CT, however, exploits absorption of gamma or x-rays in tissues. Absorptiondepend on the atomic composition of the tissue and not just on one nucleus.

Method Absorbed dose [mSv]Dental radiography 0.005Chest radiography 0.02

Mammography 2Head CT 2-4Chest CT 5-7

Abdomen CT 8-11Background (/year) 2.5

Table 1: Comparison of absorbed dose for different types of imaging [3] [4].

Figure 19: First picture is made with MRI, second with CT and third withSPECT and PET method [4].

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References

[1] K. M. Mudry, R. Plonseyand and J. D. Bronzino, Biomedical Imaging.CRC, Boca Raton, 1st Edition, 2003.

[2] P. F. Sharp, H. G. Gemmell and A. D. Murray, Practical Nuclear Medicine.Springer, London, 3rd Edition, 2005.

[3] J. K. T. Lee,S. S. Sagel, R. J. Stanley and J. P. Heiken Computed body to-mography with MRI correlation. Lippincott Williams and Wilkins, Philadel-phia, 4th Edition, 2005.

[4] http://www.colin-studholme.net/software/rview/rvmanual/viewlayout2.htm

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