University of Ljubljana Faculty of mathematics and physics Department of physics. Tomography. Mitja Eržen. August 6, Menthor: Dr.

Transcription

1 University of Ljubljana Faculty of mathematics and physics Department of physics Tomography Mitja Eržen August 6, 2009 Menthor: Dr. Matjaž 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.

2 Contents 1 Introduction 2 2 X Ray X-Rays Image detection Mammography Computed Tomography Data-Acquisition Geometries First generation: Parallel-beam geometry Second generation: Fan beam, multiple detectors Third generation: Fan beam, rotating detectors Fourth generation: Fan beam, fixed detectors Fifth generation: Scanning electron beam Reconstruction principles Nuclear Medicine Radiopharmaceuticals Detectors SPECT Imaging process of SPECT Reconstruction methods PET Imaging process of PET Detectors Physical factor affecting resolution Conclusion 17 1

3 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 revolutionized medical radiology, because for the first time, doctors could obtain images of internal body structures. This enables them to make a diagnosis, without any surgery. Before tomography, radiography was used, which can also be used to make a diagnosis of some injuries. 2 X Ray X-ray radiography produces images of anatomy that are shadowgrams, based on 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 the x-rays at that point. Intensity difference relies on the fact that different parts of the anatomy absorb different amounts of x- rays. For better contrast we can use strong X-ray absorbers, like barium, which is often used for studying gastrointestinal tract [1]. When x-rays strike an object, they may either pass through unaffected or may undergo an interaction. Interaction is either the photoelectric effect (absorption of x-ray) or scattering (where the x-ray is deflected to the side with loss of some energy). Scattered x-rays can still reach the detector 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 anatomy and 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 been accelerated in vacuum from the cathode to the anode. The electrons are emitted from a filament mounted in the cathode. Emission occurs when the filament is heated by passing a current through it. When the filament is hot enough, some electrons obtain a thermal energy sufficient to overcome the energy binding the electron to the metal of the filament. Once the electrons have boiled off from the filament, they are accelerated by voltage difference (15-150kV) applied from the cathode to the anode. After acceleration electrons are stopped in the anode in a short distance. Most of the electrons energy is converted into heating of the anode, but a small percentage is converted to x-rays by two main mechanism. One relies on the fact that deceleration of a charged particle results in emission of electromagnetic radiation, called deceleration radiation. These x-rays have a wide, continuous distribution of energies, with the maximum being the total energy the electron had when reaching the anode. The second method occurs when an accelerated electron strikes an atom in anode and removes an inner electron from this atom. The vacant electron orbital will be filled by a neighboring electron and an x-ray may be emitted whose energy matches the energy change of the electron. The result is production of large numbers of x-rays at a few discrete energies. Energy of these characteristic x-rays depends on the material on the surface of anode. In mammography 2

4 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 absorbed and all they do is increase the dose to the patient. Because of that, aluminum or copper filters are used to remove low energy x-rays from the beam. Sometimes molybdenum filters are also used which filtr low energy x-rays and those x-rays that are above K edge could enrich the spectrum with x-ray energies in the range of 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 which uses light sensitive film as a meduim. But this film has a disadvantage, it has a poor response to x-rays, so it must be used with sensitive x-ray screens. These screens absorbs x-rays and their energy is converted to visible light, then this light exposes a negative image on the film. Such screens are usually made of 3

5 CaW o 2 or phosphorus using rare earth elements and the film is enclosed in a light-tight cassette in contact with screen on both sides. Efficiency of screens for x-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 for breast cancer. Mammogram is an x-ray shadowgram formed when x-rays irradiate 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 through tissue. The image system must have sufficient spatial resolution to delineate the edges of structure in tissue (breast). Structural detail as small as 50 µm must be resolved. Variation in x-ray attenuation among tissue structures in the breast gives rise to contrast, but because of random fluctuation (scattering,..) in the image appears noise. On figure 3 is one-dimensional profile of x-ray transmission, which illustrates the role of contrast, spatial resolution and noise in image 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 of contrans, spatial resolution and noise in image quality [1]. where one has similar properties as healthy tissue and one like cancer tissue and if we irradiate this model with monoenergetic x-rays of energy E, the number of x-rays recorded in a fixed area of the image is proportional to in the background (health tissue) and N b = N 0 (E) exp µt (1) N l = N 0 (E) exp µ(t t)+µ t (2) in the shadow (where is also cancer tissue). N 0 is the number of x-rays that would be recorded in the absence of tissue in the beam, µ and µ are the attenuation coefficients of healthy and cancer tissue. T and t are thickness of tissue. 4

6 The difference in x-ray transmission gives rise to contrast which can be defined as: C 0 = N b N l N b + N l (3) if we have monoenergetic x-rays and we ignore scatter radiation we get: C 0 = 1 exp(µ µ)t 1 + exp (µ µ)t (4) Contrast would depend only on the thickness of the cancer tissue and the difference between its attenuation coefficient and background material. The figure 4 is shows x-ray attenuation coefficient of three types of materials found in the breast. Adiopose tissue (fat), normal fibroglandular breast tissue and infiltrating ductal carcinoma (tumor tissue). Figure 4: Measured x-ray linear attenuation coefficient for tissue found in breast vs x-ray energy [1]. 3 Computed Tomography The development of computed tomography (CT) was revolutionized in medical radiology in early 1970s. For the first time, physicians were able to obtain high-quality tomographic (cross-sectional) images of internal structures over the body. 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 technology has developed dramatically. Through time several different possibilities for CT were developed. The difference between them was in location, movement and types of detectors and x-ray sources. We can describe these variants as generations (figure 5). Current CT scanners use either third, fourth or fifth generation geometries, but each have its own pros and cons. 5

7 Figure 5: Different generations of CT scanner illustrating the parallel and fanbeam geometries [1]. 3.1 Data-Acquisition Geometries First generation: Parallel-beam geometry Multiple measurements of x-ray transmission are obtained using a single highly collimated x-ray pencil beam and detector. The beam is translated in a linear motion across the patient to obtain a projection profile. The source and detector are then rotated about the patient isocenter by approximately 1 and another projection profile is obtained. This tanslate-rotate scanning motion is repeated until the source and detector have been rotated by 180. Scan time of this time detector is long 5 min [1] Second generation: Fan beam, multiple detectors Scan times were reduced to approximately 30s with the use of a fan beam of x-rays and a linear detector array. A translate-rotate scanning motion was still employed. The reconstruction algorithms are more complicated than those for first generation, because they must handle fan beam projection data Third generation: Fan beam, rotating detectors A fan beam of x-rays is rotated 360 around the isocenter. No translation motion is used, but fan beam must be wide enough to completely contain the patient. A curved detector array consisting of several hundred independent detectors which 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 6

8 in 1s. This type have the advantage that thin tungsten septa can be placed between each detector in the array to reject scattered radiation Fourth generation: Fan beam, fixed detectors X-ray source and fan beam rotate around the isocenter, while the detectors array remains stationary. The detector array consists of independent detectors in a circle Fifth generation: Scanning electron beam Fifth-generation scanners are unique in that the x-ray source becomes an integral part of the system design. The detector array remains stationary, while a high energy electron beam is electronically swept along a semicircular tungsten strip anode as illustrated in figure 6. Projection data can be acquired in approximately 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 measured through all possible straight-line paths as in a plane of an object, and 2) the attenuation of an x-ray beam is estimated at point in the object. If we want to get a result we need computer processing procedures on the measurements of x-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 scattering processes as it passes through tissue (patient). The degree of attenuation depends on the energy spectrum of the x-rays as well as on the average atomic number and mass density of the patient tissues. The transmitted intensity is given by I t = I 0 exp L 0 µ(x)dx (5) where I 0 and I t are the incident and transmitted beam intensities. L is the length of the x-ray path and µ(x) is the x-ray linear attenuation coefficient, 7

9 which varies with tissue type and is a function of the distance x through the patients. The integral of the attenuation coefficient is then given by L 0 µ(x)dx = 1 L ln(i t/i 0 ) (6) If we measure the integral from many angles about isocentre, the reconstruction algorithm could reconstruct image of researched body. X-ray detectors used in CT systems must have a high overall efficiency to minimize the patient radiation dose, have a large dynamic range, be very stable with time an be insensitive to temperature variations. In CT are used solidstate detectors and gas ionization detectors (Fig. 7). Gas ionization detectors have excellent stability, however, they generally have a lower efficency than solid-state detectros. Figure 7: A solid state detector consist of a scintillator crystal and photodiode combination. Many such detectors are placed side by side to form a detector array that may contain up to 4800 detectors. Gas ionization detector arrays consist of high-pressure gas in multiple chambers separated by thin septa. The septa also act as electrodes and collect the ions created by the radiation and converting them into electrical signal [1]. 4 Nuclear Medicine Nuclear medicine can be defined as the practice of making patients radioactive for diagnostic and therapeutic purposes. The radioactive element is injected intravenously, rebreathed or ingested. These elements are called radiopharmaceuticals. 4.1 Radiopharmaceuticals Radiopharmaceuticals are radioactive-labeled pharmaceuticals, that distribute in different internal tissues or organs. Ideal characteristics of a radiopharmaceutical: - half-life similar to the length of the test - radionuclide should emit gamma rays - energy of gamma rays should be between kev 8

10 - 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 duration of the examination - radiopharmaceutical should be simple to prepare If half-life is very short, then the activity will have decayed to a very low level before imaging has started, but if it is too long the patient will receive higher radiation dose. Another problem is with gamma energy, if energy is small then tissue could absorb too much gamma rays and we do not get enough gamma rays to make an image. But if energy is too high more difficult it will be to stop the gamma ray in the detector of the imaging device. It is also necessary to avoid those radionuclides that have alpha and beta emissions, which have short range 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 important method of production is with generator. Generator depends upon the existence of a long-lived parent to be supplied in the form of a generator, from which the short-lived daughter can be chemically extracted when required. For the most commonly 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 show the relationship between position at which the gamma ray hits the detector and that from which they were emitted from the patient (fig.8 ). Figure 8: In the absence of collimation (a) there is no relationship between the position at which a gamma ray hits the detector and that from which it left the patient. With collimator (b) we gain that relationship [2]. To avoid this problem the detector is used with collimator. It consist of a lead plate through which an array of small holes runs and whose access is perpendicular to the face of collimator and parallel to each other. Only those gamma rays that travel along a hole axis will pass into the scintillation crystal, 9

11 while others are absorbed. Two main parameters describing collimator performance: spatial resolution and sensitivity. Resolution is a measure of sharpness of image, sensitivity is a proportion of gamma rays that absorbs in detector and gamma rays that do not reach the detector. Typically the sensitivity for a parallel hole collimator is only 0.1%. 99.9% of gamma rays are absorbed by collimator or do not reach the detector. Because of small sensitivity it is necessary to have quality detectors which perceive as much gamma rays as possible. To create a picture it s necessary to convert gamma rays into visible light in scintillation crystal, then this light is converted to electrical signals by photo multiplayer tubes. Scintillator crystal should have high efficiency for gamma rays and also high conversion of gamma ray 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 the detector misses the x-rays we lose on sensitivity [2]. The detectors in clinical nuclear medicine are NaI(TI) (Sodium Iodide doped with Thallium) crystals. The detector consists of a large number of crystals and every 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. Crystals are separated by lead septas to prevent scattered photons from one crystal to the next. When large crystals became a reality, new ways to use them were conceived. The Anger camera (fig. 10) is one of the first ones. It uses a single crystal which is large enough to image a significant part of the human body and has an array off PMT on the back to give positional sensitivity[1]. Figure 10: Anger camera detector design [1]. 10

12 5 SPECT Single-photon emission computed tomography (SPEC) is a medical imaging modality that combines conventional nuclear medicine imaging techniques and CT methods. Different from x-ray CT, SPECT uses radiopharmaceuticals, that distribute in different internal tissues or organs instead of an external x-ray source. The spatial and uptake distributions of the radiopharmaceuticals depend on the biokinetic properties of the pharmaceuticals and the normal or abnormal state of the patient [1]. 5.1 Imaging process of SPECT The imaging process of SPECT we can simply describe with fig. 11. Gamma-ray photons emitted from the internal distributed radiopharmaceutical penetrate through the patient s body and are detected by a single or a set of collimated radiation detectors. When photons penetrate through body they could interact with tissue. It could happen photoelectric effect, which absorbs all the energy of the photon and stops their emergence from the patient s body. The other mayor interaction is Compton interaction, which transfers part of the photon energy to the electrons, the original photon is scattered into a new direction with reduced energy, that is depended on the scatter angle. Because primary photons have energy from kev, the probability of pair production is zero [1]. Figure 11: Gamma-ray photons emitted from the internally distributed radioactivity may experience interactions. Photons that are not traveling in the direction within the acceptance analog of the collimator will be intercepted by lead collimator, photons will not have interactions and travel within the acceptance angle of the collimator will be detected [1]. In SPECT is used Anger camera, with large (40 cm in diameter) scintillator NaI(TI) crystal and an array of PMTs are placed at the back of the scintillation crystal. The system could use one or more rotating cameras (fig. 12). When photon hits and interacts with the crystal, the scintillation generated will be detected by the array of PMTs. An electronic will evaluate signals and determinates the location of interaction. In SPECT, projection data are acquired from different views around the patient. On figure 13, 1-D projections of a distribution of radioactivity comprising two point sources are shown for three positions 11

13 of the detector. For reconstructing an image of the original distribution is the most common method back-projecting each profile at the appropriate angle on to an image array in the computer (fig. 13). In other words, a constant value equal to the profile element is assumed for each point along that line in the 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 camera system [1]. Figure 13: a)profiles relating to a single transactional section from a distribution of radioactivity. b) Back-projection of profiles from figure (a). Point source can be indentifined but big background it s noticed [2]. 5.2 Reconstruction methods In SPECT the goal of image reconstruction is to determine the distribution of radiopharmaceutical in the patient. However, the presence of photon attenuation affects the measured projection data. If conventional reconstruction algorithms are used without proper compensation for the attenuation effects, inaccurate reconstructed images will be obtained. But first look what kind of data 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 1D detector array is oriented at angle θ with respect to the x axis of our laboratory system (x, y). Data collected into each element at location t is called the projection data p(t, θ) and is equal to the sum of f(x, y) along a gamma ray. Then the projection data can be written as 12

14 Figure 14: Schematic diagram of the two-dimensional image reconstruction problem [2]. α p(t, θ) = c f(x, y)ds, (7) α where (s, t) represents a coordinate system with s along the direction of the ray sum and c is the gain factor of detection system. The angle between x and s is θ, then the relationship between position (x,y), the projection angle θ and the position of detector is given by t = y cos(θ) x sin(θ). (8) The integral 7 which transform object distribution to its projections is also called Radon transform. Our goal of image reconstruction is to solve the inverse Radon transform [1]. In SPECT we measure distribution of radioactivity, so the equation 7 can be written as α p(t, θ) = c ρ(x, y)ds, (9) α where ρ is the radioactivity concentration distribution of the object. This equation is true if we ignore the effect of attenuation, scatter and collimator detector response. If attenuation is taken into consideration Radon transformation can be written as α +α p(t, θ 0 ) = c ρ(x, y)[ µ(u, v)ds ]ds, (10) α (x,y) where µ(u, v) is the 2D attenuation coefficient distribution and +α µ(u, v)ds (x,y) is the attenuation factor for photons that originate from (x,y), travel along 13

15 the direction perpendicular to the detector array and are detected. A major difficulty in reconstruction lies in attenuation factor, which makes the inverse problem difficult to solve analytically. But small differences in attenuation coefficient (different as in x-ray CT) are not as important in SPEC and then the attenuation coefficient in the body is aconstant and attenuated Radon transform can be written as α p(t, θ 0 ) = c ρ(x, y)[ µl(u, v)]ds, (11) α where µ is constant attenuation coefficient and l(x, y) is the path length between the point (x,y) and the edge of attenuator (patient s body). The solution of the inverse problem with constant attenuator has been a subject of several investigations. As already mentioned reconstruction method called simple backprojection where the reconstructed image is formed simply by spreading the values of the measured projection data uniformly along the projection ray into the reconstructed image array. By backprojecting the measured projection data from all projection views, an estimate of the object distribution can be obtained. Simple backprojection is given by ρ(x, y) = m p(y cos(θ j ) x sin(θ j ), θ j ) θ (12) j=1 where θ j is the j-th projection angle, m is the number of projection views and θ is the angular spacing between projections. The simple backprojection image 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 and not gamma ray. Positron then combines with an electron and these two particles undergo the process of annihilation (eq. 13). β + + e 2γ (E γ = 511keV ) (13) The energy associated with the masses of positron and electron is MeV, this energy is divided equally between two photons that fly away from one another at 180 angle. Each photon has an energy of 511 kev. These high energy gamma rays emerge from the body in opposite directions, which are detected by detectors around the patient. When two photons are recorded simultaneously by a pair of detectors (coincidence) (fig. 15), it is possible that annihilation event accures somewhere along the line connecting the detectors. When enough detection from all sides is collected then the picture can be reconstructed[1]. 14

16 Figure 15: Types of coincidences detected in a PET imaging system. A) True coincidence. B)Accidental coincidences, the two photons identified as arriving in coincidence have originated from different disintegratios. C) Scatter, ne of the photons has undergone Compton scattering before being detected. D) Multiple coincidences. More than two photons arrive in coincidence. Apart from the true coincidences, all other will result in incorrect spatial information. [2]. 6.2 Detectors PET system also uses scintillators detectors with PMTs but because of higher energy of gamma rays the detector needs higher density crystals. Instead of NaI(Tl) crystals BGO (Bismuth germanate) or LSO (lutetium orhosilicate) crystal 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 the disadvantages of this type of design are the requirement for many expensive PMTs. Second design is called a block detector design and here are five PMTs coupled to eight scintillator crystals. When one of outside four PMTs detect an photon interaction, that means that interaction accured in one of attached detectors. Center PMT is used to determine whether it was the inner or outer crystal. This is known as a digital coding scheme. We receive just signal 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 resolution and if block design is used, there is a degradation in resolution for a 2.2 mm. Also the angle between the paths of annihilation photons can deviated from 180 as a result of some residual kinetic motion at the time of annihilation. The resolution of this effect increases with detector ring diameter. Also the distance the positrons travels before annihilation, decrease spatial resolution[1]. These factors influence on resolution result for the center or axis of the to- 15

17 Figure 16: The individually coupled design is capable of very high resolution and because the design is very parallel it is capable of very high data throughput. A block detector couples several PMT to a bank of scintillator crystals and uses a coding sheme to determine the crystal of interaction. [1]. Figure 17: Factors contributing o the resolution of PET tomograph. [1]. 16

18 mograph. The path of the photon from an off-center annihilation event typically traverses more than one detector crystal, as shown on fig. 18. This result that resolution spread function along the radius of the transaxial plane. The loss of resolution depends on the crystal density and the diameter of the tomograph detector ring [1]. Figure 18: Because annihilation photons can penetrate crystals to different depth, the resolution is not equal in all directions [1]. 7 Conclusion In described methods we must pay attention also on energy that is absorbed from gamma or x-ray, because if too much energy is absorbed it could come to damage of cells, tissues or organs. It is necessary to achieve that patient receive as low absorbed dose as reasonably possible. Because of this, it is necessary to decide whether the imaging is necessary or not. Doses for different methods are shown in a table 1. For simple image is the most common method x-ray, but if more precise picture is needed, CT or MRI is used. There are also some other methods which have their own pros and cons. On figure 19 are shown different pictures for different methods of imaging. While some imaging scans such as CT and MRI isolate organic anatomic changes in the body, PET and SPECT are capable of detecting areas of molecular biology detail. These do this using radiolabeled molecular probes that have different rates of uptake depending on the type and function of tissue involved. Pictures made with MRI and CT are very similar, but there are some differences. First difference is that technology of MRI imaging is expensive method. Also time for image takes more than for CT. Images made with CT and MRI are not the same because MRI operates in a different way. MRI method of imaging uses a powerful magnetic field to align the nuclear magnetization of atoms (usually) hydrogen atoms in water in the body. Radio frequency (RF) fields are used to systematically alter the alignment of this magnetization, causing the hydrogen nuclei to produce a rotating magnetic field detectable by the scanner. This signal can be manipulated by additional magnetic fields to build up enough information to construct an image of the body. 17

19 CT, however, exploits absorption of gamma or x-rays in tissues. Absorption depend on the atomic composition of the tissue and not just on one nucleus. Method Absorbed dose [msv] Dental radiography Chest radiography 0.02 Mammography 2 Head CT 2-4 Chest CT 5-7 Abdomen CT 8-11 Background (/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 with SPECT and PET method [4]. 18

20 References [1] K. M. Mudry, R. Plonseyand and J. D. Bronzino, Biomedical Imaging. CRC, Boca Raton, 1st Edition, [2] P. F. Sharp, H. G. Gemmell and A. D. Murray, Practical Nuclear Medicine. Springer, London, 3rd Edition, [3] J. K. T. Lee,S. S. Sagel, R. J. Stanley and J. P. Heiken Computed body tomography with MRI correlation. Lippincott Williams and Wilkins, Philadelphia, 4th Edition, [4] 19