Methods of Computerized Images for Medical Diagnosis Seminar: Medical Images Summer Semester 2005

Transcription

1 + Methods of Computerized Images for Medical Diagnosis Seminar: Medical Images Summer Semester 2005 Author: Tu-Binh Dang Matr.: For: Professor Domik University of Paderborn Tutor: Gitta Domik

2 Inhaltsverzeichnis Introduction Magnetic Resonance Tomography Basic physic of MRT Spatial encoding of MRT Computer Tomography The functionality of X-ray tube Absorption of x-rays Using of X-ray principle in CT Positron emission tomography (PET) Physic of PET Single Photon Emission Computed Tomography (SPECT) Comparision of the four methods Conclusion Literature Abbildungsverzeichnis Figure 1: MRT image of human scale... 1 Figure 2: Precession of the photon axis along the magnetic field B Figure 3: Differentiated Phases along the Y-axis... 3 Figure 4: Relation of a point in K-Space to the phases... 4 Figure 5: Relation of K-images to MRT image quality... 4 Figure 6: Structure of an X-ray tube... 6 Figure 7: Example of CT's basic principle... 7 Figure 8: Schematic build-up of a CT device... 8 Figure 9: Positron emission and annihilation... 9 Figure 10: γ-ray pairs building a line... 9 Figure 11: Fourier Slice Theorem... 10

3 Introduction In the area of medicine medical imaging has become one of the most important tools in the diagnosis and examination of diseases. Therefore it is crucial to understand at least the basic principals of the technique. This work will present and evaluate the four dominant approaches of this special field in medicine. These are MRT (Magnetic Resonance Tomography), CT (Computer Tomography), PET (Positron Emission Tomography) and SPECT (Single Photon Emission Computer Tomography). Generally these are different methods of creating images of the inside of opaque organs. Due to the underlying technique each method is specialized towards a certain application. For instance CT is best applied in the area of bone and lung while PET focuses on metabolism. 1 Magnetic Resonance Tomography Figure 1: MRT image of human scale Magnetic Resonance Tomography (MRT), also called Magnetic Resonance Images, is a medical diagnostic technique that creates images of the body using the principles of nuclear magnetic resonance. MRT is based on physical discoveries, which at first were not associated with the area of medicine. These basics were developed over a time frame lasting from the 1940s to In 1972 Paul C. Lauterbur had found an easy approach to spatially measure core resonance through the use of magnetic gradients. While his findings were not regarded as a major breakthrough, the following years brought forth a variety of pictures, including the first image of a thorax in Radiologists remained sceptical, since the production of the images was more complex than traditional X-ray pictures while the results were of lesser quality. The breakthrough happened in 1983 because of the now much higher quality of head scans which allowed for a significantly better tumour recognition. Due to the fact that MRT 1

4 is good at differentiating soft tissues it is mainly applied in the field of brain scans [Konecny et al. 2003]. 1.1 Basic physics of MRT The method uses the principle of the nuclide spin. If exposed to a magnetic field B 0 an atomic core changes its spin axis, now rotating around the magnetic field's direction until it reaches a new equilibrium. At equilibrium, the net magnetization vector m lies along the direction of the applied magnetic field B 0. This movement is called precession. During the precession the core will emit a set amount of frequency (the Larmor-frequency) in the form of radio waves which can be measured externally. Putting up a second magnetic field vertical to the first causes the core s pole to start another precession movement until the next equilibrium is reached. Switching it off again causes another precession movement [wikipedia.de 2005]. The time for a core to reach equilibrium is called the spin lattice relaxation time (T 1 ). The interaction with another core's spin is called transverse magnetization and dephasing. The time constant which describes the return to equilibrium of the transverse magnetization is called spin-spin-relaxation time (T 2). These relaxation times are essential components for measurement [Hornak 2004]. In 1971 R. Damadian detected the significantly different relaxation times of the pathologic tissue (such as a brain tumor) and normal tissue. Figure 2: Precession of the photon axis along the magnetic field B Spatial encoding of MRT This principal dynamic of proton spin is used in the image building process of MRT. Three magnetic gradients are set up along one of the three-dimensional axis (x,y and z). The first selects a cut along the z-axis of the body, missing however information about the spatial x and 2

5 y arrangement. Therefore the second magnetic field adjusts the different phases of the spin movement, which vary from line to line. The third field is set up along the x-axis setting the spin speed which again varies from column to column. The three individual results can now be put together into a voxel map of the examined body slice. It first sounds quite easy to get each pixel of the voxel map with this procedure. In fact however it is not possible to measure the image point by point because the measuring signal received is the sum of emitted signals of all reacting protons. That means it is not possible to get an isolated signal from a specific area. The 'Lamor' or resonance frequency depends on the strength of the magnetic field [Settles 2005]. Therefore one can differentiate the resonance frequencies along the x-axis after setting up the first magnetic gradient. To get a specific slice it is necessary to stimulate the corresponding resonance frequency of this specific layer. Echo signals of only this layer will be received. This signal represents a measurement of all pixels of the image. To obtain the spatial encoding within a slice it is necessary to insert the phase encoding gradient along the y-axis and the frequency encoding gradient along the x-axis. Every combination of these two gradients yields one diphase pattern. Figure 3 shows an example of a diphase pattern where every position of the same row has the same phase. Figure 3: Differentiated Phases along the Y-axis The received signal corresponding to a specific diphase pattern is recorded as a point in K- space. The K-space is the areal (complex) frequency weighing in two (or three) dimensions of a real space object [wikipedia.de 2005]. The diphase pattern in the figure 4 belongs to a point in the coordination system in K-space. 3

6 Figure 4: Relation of a point in K-Space to the phases The image in real space is a product subsequently transformed via the inverse Fourier Theorem by the computer. According to Fourier Transformation points in k-space are needed to create a MRT image of pixels. The more diphase steps are taken and the more diphase patterns are considered, the larger the k-image and the higher resolution of resulting image. Figure 5 shows an example of the relation of the k-image to the real MR-image. Figure 5: Relation of K-images to MRT image quality 4

7 2 Computer Tomography Computer Tomography is a medical imaging method relying on x-rays. While the principal mathematical basis behind this technology was already published in 1917 by J. Radon, the real inventors did not know his formulae. The wish behind CT was always to have the ability of getting three dimensional images of the inside of human bodies. While first tries had been made with X-ray technology, it was too restricted for a three dimensional, spatial projection, since it only delivered 2 dimensional images. The basic idea for computer tomography was published by A.M. Cormack in 1963 on the basis of back projection. The technology itself however was introduced over the course of the seventies. A prototype came into existence in 1971 and first measurements on patients were conducted in Since these first measurements were very time and cost consuming the following years brought forth a development to reach maximum efficiency of these two factors and a third: image resolution. In 1979 the scan-time had been reduced from many minutes to only 2.5 seconds and the resolution had improved to 0,8mm. From then on a correct mathematical back projection has been used. Even shots of the moving heart became possible in the eighties. The spiral CT that is stilled used nowadays was developed in 1989, featuring a constantly rotating tube through which a body is slowly moved. Further developments up to the year 2000 led to a multi-layer CT that can take images of 3-5 layers at once. At the same time the resolution has improved to the point that one can get crystal clear images of coronary arteries pumping blood [Konecny et al. 2003]. 2.1 The functionality of X-ray tube An X-ray is an instance of electromagnetic radiation with a wavelength in the range of 10 nanometres to 100 pico-metres [wikipedia.de 2005]. Figure 6 represents the structure of an X- ray tube. Electrons are emitted from the heated cathode and are accelerated by high voltage towards the anode. The emitted electrons intruding into the material of the anode are slowed down by the electric field of the positive charged atomic nuclei. The deceleration of the electrons is a negative acceleration of the charging that according to electrodynamics leads to a radiation of electromagnetic rays. This is called decelerating radiation [Hering et al. 1999]. 5

8 Figure 6: Structure of an X-ray tube 2.2 Absorption of x-rays The x-rays sent through the object of the investigation will be recorded by different sensors. The comparison between measured and radiated ray intensities hints at the attenuation µ due to the investigated tissues. Ionisation and diffusion cause the attenuation of x-rays when passing the object of density x, therefore µ can be calculated via the following equation: I = I 0 e μx I represents the ray intensity after passing the object and I 0 is the intensity at the source. If the object is composed of different materials the equation will take this form: I = I 0 e (µ 1 x 1 +µ 2 x 2 +µ 3 x ) [Hering et al. 1999] 2.3 Using of X-ray principle in CT A cross-section image of a CT consists of X-ray images from different angles. The basic principle behind CT will be explained referring to a simple example: 6

9 Measurement sequence Figure 7: Example of CT's basic principle Figure 7 shows an example object of an area which is split into 9 equally sized squares. Three measuring sequences are applied to the sample and the identity I is determined. In CT the density d of different materials should be regarded as equal. Therefore the equation takes this form I = I 0 e d(µ 1 +µ 2 +µ 3 ) and is translated into a linear equation: 1 I ln. = µ 1 + µ 2 + µ 3 d I0 These linear equations gained from the measurement sequences build a linear equation system from which µ 11 -µ 33 can be calculated [Hering et al. 1999]. When grey or colour values are assigned to the absorption-coefficients one gets a representation of the sample s inner structure. In CTs the attenuation is displayed in grey values and projected on the Hounsfield scale ranging from to While water scores a zero on this scale, bones have a value of about 400 [wikipedia.de 2005]. To obtain an image with a high quality (resolution) the 3x3 matrix of our example would have to be expanded to a 256x256 matrix. This would then require solving an equation with unknown µ-coefficients. With nowadays technology this is indeed an easy task (Fourier Slice Application PET). Figure 8 shows the schematically structure of a CT. In this case the x-ray tubes rotate around the patient while the sensors are arranged in a circle. 7

10 Figure 8: Schematic build-up of a CT device 3 Positron emission tomography (PET) After the discovery of the proton in 1932 not too much time passed till F.R. Wrem, M.L. Good and P. Handler proposed to use positron emitters in medicine. In 1953 the first brain tumour was located using this method; however the procedure was extremely inefficient and costly. It took 20 years until the technology could be used commercially. The first of these newer devices was produced in In 1979 F-desoxyglucose [grape sugar - glucose] was first used as a tracer. The PET devices were upgraded mostly by enhancing the number of detectors and thereby increasing resolution. Also multi-layer PETs were introduced. In 1990 with the so called time-of-flight assisted PET the first layering of PET and MR images became possible. In 1998 the first combined PET and CT device was introduced. The high cost of the tracers still keeps this method from being used more frequently despite its high value in the area of oncology, cardiology and brain research [Konecny et al. 2003]. 3.1 Physic of PET Pet is a nuclear medicine medical imaging technique which produces three dimensional images of living organisms. In contrast to CT and MRT, PET deals with the method of emission measurement. That means the emission source is located in the investigated object. 8

11 Figure 9: Positron emission and annihilation During the PET procedure the patient is injected with a glucose solution which is combined with a short-lived radioactive isotope-substance called tracer. The latter emits positrons during the decay process. After travelling up to a few millimetres the positron annihilates meeting an electron, which produces a pair of photon gamma rays that are moving in opposite directions 180 degrees apart (Figure 9) [wikipedia.de 2005]. This photon gamma ray pair reaches two positions in the sensor ring equipped with about 600 detectors (figure 10). Two gamma quanta which are detected in the opposite degree positions within an interval of about 10 nanoseconds are registered as a pair. Connecting the arrival points of these two photons forms a line. Somewhere on this line an annihilation process has occurred but the information of the exact location is not encoded directly. Therefore the events on the line need to be stored for the further processing. ~ 600 detectors Figure 10: γ-ray pairs building a line 9

12 For every possible line a counter exists that registers the frequency of the annihilation events on the line. Then the Fourier Slice Theorem is used as shown in the figure 11 to reconstruct the probability function of all annihilation events. At first a projection of all the lines pointing to the same direction is performed. This projection has the form of a histogram and shows the frequency of events on the corresponding line. Fourier transformation of the projection returns the values of a line in the frequency-domain (k-domain) with the same angle as the original projection line. As with CT information of different projections from different angles is needed to complete the frequency-domain. After Fourier transformation of the whole object along the radial line the values in the frequency domain can be used to perform a 2D-inverse Fourier Transformation to get the values at x and y of the PET-image [Kak et al. 1988]. Figure 11: Fourier Slice Theorem The distribution of the radio nuclides enables the conclusion of metabolism procedures in the relative tissue. The stronger the occurred radioactivity the more active the corresponding area is. A result of recent research in PET technology has shown that this technology is capable of pre-diagnosing Alzheimer s disease years before its outbreak. This is accomplished by checking the metabolism activity in the hippocampus. Years before the actual disease broke out in test persons, researchers noticed a moderately lower activity (15-40% less) than in those patients that were not befallen by the disease later on. The current prognostic process can identify possible later Alzheimer patients about 9 years before the first symptoms begin to show [spiegel.de]. 10

13 3.2 Single Photon Emission Computed Tomography (SPECT) SPECT is very similar to PET also being a nuclear medicine medical imaging technique via gamma-rays. However due to the composition of the tracer substance (radiopharmaceutical) used in SPECT there is only one emitted γ-ray photon from every annihilation event. Another detection technique is used to measure and identify the line on which the annihilation events occurred. Otherwise a similar back projection to the one used in PET is performed to reconstruct the image [Lehnertz_4]. 4 Comparision of the four methods Table 1 displays the presented methods with their technical basis as well as their advantages and disadvantages. For example it is evident on the table that CT is good at identifying bone structure but possesses a high risk of ray exposition while PET has next to no risk but a low resolution. Another important point is that SPECT is much less costly than PET because SPECT uses long-lived radio nuclides. Thus the cyclotron (device for the production of radio nuclides) does not have to be in direct proximity of the scanner device. This however also bears a significant disadvantage namely an even lower local resolution than PET. Images taken with PET and SPECT inform about metabolism processes of the examined body. However it is hard to study morphology with these approaches, because the image resolution tends to decrease. In contrast CT and MRT deliver images that have a much higher resolution for morphologies. 11

14 Table 1: Technical principles Advantages Disadvantages MRT Nuclear magnetic resonance; Gradients; Fourier transformation CT X-rays; Hounsfield scale; Back projection PET Nuclear medicine; Positron emission; 2 Photons; Back projection SPECT Nuclear medicine; Positron emission; Single Photon; Back projection Better presentation of organs (soft tissues); less harmful Bone structure; quick process Biological active substance; no toxic effect; measurement of metabolism activity In comparison to PET: cheaper process Expensive; timeconsuming(10-45min); Bad image of bone structure High risks of ray exposition Low local resolution (5mm) In comparison to PET: Inferior quality of images 5 Conclusion While every single approach to medical imaging is important in its own right, there seems to be a more recent interest in combining them. A hardware fusion of multiple devices to maximize image quality was the first choice but has proven to be quite expensive. Another idea has been to take the medical images on their proprietary devices and then combine them via software. This is a natural conclusion since the different approaches' strengths can be combined (e.g. good image resolution of CT with metabolic data from PET) at a much lower price. Thus a medical diagnosis on the basis of multiple device images gets more and more accurate. While in fusion with software it is easy to combine any of the presented approaches, in hardware fusion combined CT and PET or SPECT devices seem most likely. This is partly due to the principle of back projection that is used in these three approaches. 12

15 Literature [Hering et al. 1999] Hering, Martin, Stohrer, Physik für Ingenieure 7.Auflage Springer Verlag, Berlin Heidelberg 1999 [Kak et al. 1988] [Konecny et al. 2003] [wikipedia.de 2005] A.C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging, USA 1988 E.Konecny et al., Medizintechnik im 20. Jahrhundert, VDE Verlag, Berlin Offenbach 2003 Wikipedia Die frei Enzyklopedie, (last accessed: ) [Hornak 2004] Joseph P. Hornak, Ph.D. The basic of NMR, (last accessed: ) [Settles 2005] [Lehnertz_3] [Lehnertz_4] M. Settles, Ortskodierung (last accessed: ) Lehnertz, staff/lehnertz/nukmed3.pdf Lehnertz, staff/lehnertz/nukmed4.pdf [spiegel.de] Spiegel Online, 13